Religion, Sets, and Politics

A quick note on log odds

2011-11-07T18:41:00.000-08:00

Probabilties are usually numbers that range from 0 to 1. However, the standard way of representing probabilities is not always optimal. However, there is another mapping of probability that goes from negative infinity to infinity. This system called "log odds" has a number of advantages. In the standard log odds approach, one maps the probability of an event x to the quantity log(x/(1-x)). Brian Lee and Jacob Sanders wrote a good summary (pdf) of this system which discusses its advantage and disadvantages. As they observe, use of log odds allows one to immediately see how something like the change in probability from 51% to 52% isn't that big whereas the change from 98% to 99% is a much larger change in the sense that the chance of the event not happening has now halved. Log odds helps makes this sort of intuition immediatelty obvious from the numbers. Brian and Jacob discuss the advantages and disadvantages of log odds in detail, and show how it is particularly useful for doing Bayesian updates. I strongly recommend reading their piece.

Occupy Wall Street, Boundaries, and Gratuitous Promotion of Family Members

2011-10-12T12:29:00.000-07:00

My sister has a piece up at the Huffington Post discussing exactly how Occupy Wall Street lost her sympathy. She correctly points out actual problems with the Wall Street protesters, but I don't agree with what to her was the final point. She objects to the protesters deciding to protest the homes of the major executives, saying that they have a right to keep their private and public lives separate. I find this argument to be deeply unconvincing. When you are a major enough individual to be running a major corporation you have less of a right to privacy than a random individual. There might be an argument if these protests were directed at the homes of mid-level or upper level management. That argument doesn't apply to the CEOs of billion dollar corporations.

This is not a defense of the Occupy protesters in general. They aren't very coherent and those who have tried to state specific goals have given goals include goals that are unconsitutional, the immoral, the unethical, hopelessly naive, or just bad ideas. In that regard, they are essentially the left-wing equivalent of the Tea Party. It is possible that they will turn into something which does deal with the serious problems this country has, especially in regard to the massive income inequality which has become worse in the last few years but right now I'm not optimistic. The main thing that I would think needs to be done right now is getting the generic lower-middle class voter to understand that people like Herman Cain really have conflicting economic interests. There seems to be a certain class of economically badly off voters who somehow identify with the economic interests of people with incomes that are often an order of magnitude or more higher than their own.

As long as I'm pontificating about Occupy Wall Street, there are a few other things to note. First, whether or not one agrees with the protesters, the treatment of the protests by the police in some examples has been unacceptable. The mass arrest of protesters in Boston is a good example of this. Moreover, mistreating protesters is an easy way for people to build sympathy with a movement and come to agree with it whether or not the movement has any coherence or validity to their points. Second, using protesters behavior as evidence about economic policies is bad epistemology. This has lead to inane pieces like this one where various economic policies (some good, some bad) are justified simply by the existence of protesters. Protesters in this context are evidence of people unhappy with their current economic situation. Assuming that these people have any idea what to do about economic policy or that their existence can be easily traced to specific policies is unjustified.

In any event, my sister's piece is worth reading. She's not in the one percent, but she's not in the low percentages either. If OWS is going to succeed at anything they are going to need the people with average or moderately high incomes like my sister. Right now, they aren't doing that.

A brief note on non-transitive dice

2011-09-12T14:19:00.000-07:00

I've talked before about non-transitive dice. We say that given a pair of dice X and Y, X beats Y if more than half the time when the pair is rolled X has a larger number face up than Y. It turns out one can construct dice A, B and C such that A beats B, B beats C, but C in fact beats A. This is a neat and weird property.

During a recent discussion I used non-transitive dice as an example of a counter-intuitive aspect of mathematics, I was pointed to an even weirder variant. Consider the following set of dice: A has sides (5,5,5,2,2,2), B has sides (4,4,4,4,4,1) and C has sides (6,3,3,3,3,3).

Here A beats B, B beats C and C beats A. But here's the really cool part: Let's say I roll two copies of A, two copies of B or two copies of C. Now things actually reverse! That is, a pair of Bs beats a pair of As and a pair of As beats a pair of Cs and a pair of Cs beats a pair of Bs.

This is a much more sensitive property than just non-transitive dice. Most sets of non-transitive dice will not have this property. We can also describe this sensitivity in a more rigorous fashion. Suppose we have a strictly increasing function f(x). That is, a function such that f(x) is greater than f(y) whenever x is greater than y. Now suppose we take a set of non-transitive dice and relable each value x with f(x). Then they will still be non-transitive. But, given a set of non-transitive, reversable dice, reversibility is not necessarily preserved by the f mapping. This reflects the much more sensitive nature of the reversible dice.

Here's a question I have so far been unable to answer: Is it possible to make a set of die which do an additional reversal? That is, is there a set of dices such rolling three copies the dice results in another reversal direction?

Voluntary Taxation and Gratuitous Promotion of Family Members

2011-09-01T19:03:00.000-07:00

It looks like the last of my siblings has no entered the blogosphere. My sister Jacoba has a piece up at the Huffington Post discussing the reaction to Warren Buffet's statements that the rich are not being taxed enough. She points out that if people think that they aren't being taxed enough then they can always just right a check to the US Treasury.

Her point is an interesting one but I think it is misguided: Very few rich people think like Buffet does. Almost everyone who is in favor of higher taxes thinks that the group who should be paying higher taxes are the people with income slightly above their own income. Moreover, even if a large number of rich people agreed with Buffet, if those people gave much more of their money to the federal government while others in their income bracket did not those volunteers would suffer a relative loss of income. There's a fair bit of evidence that people's sense of status and wealth is a function of the people around them. So if most of the rich aren't paying as much it is quite understandable that the other rich would not want to. It is thus reasonable for some high income people to call for higher taxes even as they don't make voluntarily payments. In any event, the idea is an interesting one and the piece is worth reading.

The Fermi Paradox, The Great Filter, and Existential Risk

2011-07-05T13:33:00.000-07:00

The Fermi Paradox is a classic puzzle proposed by Enrico Fermi. Fermi observed that if one made back of the envelope calculations of the sort for which Fermi was famous, then one would expect to see much intelligent life out in space. Moreover, it doesn't take a society much more advanced than our own before one is likely to see direct evidence of its existence. So where is everyone?

One proposal to explain this apparent paradox is Robin Hanson's explanation that there is some "Great Filter" which culls species before they can reach the degree of civilization necessary to spread out to the stars on a large scale. . Various roadblocks and events can act as filters. For example, severe asteroid impacts every few million years set life back. However, that seems to be a rare and weak filtration effect. One obvious roadblock is the arrival of life itself. Life arising may be much more difficult than we expect, and thus life may be comparatively rare. But, life arose fairly early in this planet's history, rendering this claim unlikely.

The most disturbing possibility, and the one on which both Robin Hanson and Nick Bostrom have focused, is the possibility that, for us, most of the filter lies not in our past, but in our future. This is scary. Events which result in the complete destruction of humanity are described as existential risk. If such events lie in our future, they are not likely due to natural causes such as asteroid impact and gamma ray bursts, since such events are rare. Existential risk to us is more likely the result of dangerous technologies. In a similar vein, during the Cold War, Carl Sagan worried that the apparent absence of life in the universe might be due to every advanced society having nuked itself. In a post Cold War world, that particular worry seems to be less severe. However, Hanson and others have focused on other technologies, especially those arising from nanotechnology and rogue AI.

I am not that worried by the Great Filter. I suspect that the vast majority of Great Filter is behind us. One of the most obvious filtration points are the steps from a species being smart to that species having civilization capable of making sustained technological progress. On Earth, there are many extremely smart species that are almost as smart as humans. Lots of people know that other primates are smart and will name dolphins and elephants as other very species. But there are many others as well, especially birds. Keas, African Grey Parrots, and ravens are only three of the many examples. Almost every species of corvid is extremely bright, and is capable of puzzle solving that rivals that of human children. However, the steps from there to sustained civilization are clearly large. Only a single species developed language, and even after that point, we stagnated for hundreds of thousands of years before developing writing, which is when things really started to take off. So, it seems to me that we can plausibly point to a large filtration step just before the development of civilization.

There are other points which have been proposed as filtration points in the development of life as well. One common argument is the Rare Earth Hypothesis which posits that the existence and success of life on Earth required a large variety of different conditions. For example, Earth has a large moon which helps protect the planet from asteroid strikes. For most of the features frequently cited as part of Earth's rare nature we don't seem to have enough data at this point to reasonably judge how common such features are or how necessary they are for complex life. However, even neglecting the Rare Earth filtration effects, the pre-civilization filtration still seems large.

Moreover, many of exotic anthropogenic events can be safely ruled out as major aspects of the Great Filter. The most plausible anthropogenic events are rogue AIs, false vacuum collapse, bad nanotech, and severe environmental damage with accompanying loss of natural resources.
Rogue AIs are an unlikely scenario because it is unlikely that any AI would be bad enough to wipe out the creating species and then not quickly take large scale control over much of their surrounding space.[1] Thus, if societies are being destroyed by rogue AIs we should be able to see this. Moreover, we should exect our own solar system to have long since come under sway of such AI. Thus, we can safely rule out rogue AI as a major part of the filter.

Similarly, some physicists have proposed that space as we know it is a "false vacuum". While the technical details are complicated, the essential worry is that a sufficiently advanced particle accelerator or similar device could cause space as we know it to be replaced by space that behaves fundamentally differently than what we are used to. The new space would expand at the speed of light.

We don't need to worry about civilizations probing the nature of space to cause a collapse of the false vacuum. If there were a lot of civilizations doing this, we wouldn't be here to notice. It is remotely plausible that the new vacuum would expand slower than the speed of light. If for example, the new type of vacuum expanded at a millionth of the speed of light, that would be enough to quickly destroy any single-planet civilization that triggered such an event, but would be slow enough to take a very long time to spread before it became noticed by another civilizations. However, our current understanding of the laws of physics make it hard to see how a vacuum collapse could occur at less than the speed of light. So we can rule this out as a major part of the Great Filter.

Nanotechnology is one of the most plausible options for a section of the Great Filter in front of us for the simple reason that severe nanotech events don't create results that will destroy or alter nearby stars or the like. While there are a variety of nanotech disaster scenarios, they essentially revolve around some form of out of control replicator consuming resources that humans need to survive or disrupting the ecosystem so much that we cannot survive. If a nearby solar system had a severe nanotech disaster, we wouldn't be able to tell. This situation is similar to Sagan's nuclear war scenario in that it allows civilizations to frequently wipe themselves out in a way that we can't easily observe.

Environmental damage and overconsumption of resources is another possible problem. It is possible that species exhaust their basic resources before they become technologically advanced. If, for example, humanity ran out of all fossil fuels without adequate replacements, this could prevent further expansion. However, this seems to be an unlikely explanation for Fermi's paradox. Even extreme resource consumption and environmental damage is unlikely to result in the complete destruction of an intelligent species. This possibility is the modern equivalent of the Sagan concern about nuclear war, a possibility which gets undue attention due to the current political climate.

So, it seems likely that most of the Great Filter is behind us. However, this is not a cause for complacency. First, the argument that the Great Filter is behind us is a weak one. As long as our sample of civilizations remains a single civilization, we cannot do more than make very rough estimates. Moreover, even if most of the Great Filter is behind us, that doesn't imply that we are necessarily paying enough attention to existential risk. Even back of the envelope calculations suggest that we aren't putting enough resources into dealing with existential risk threats, whether natural or caused by humans.

What needs to be done? First, we need to get a better idea where filtration steps actually exist. The most obvious way to do that is to look for life on other planets. If we don't find any life on other bodies in the solar system, then that increases the chance that a large part of the filtration is overcome by life arising and so we can breathe more easily. If however, we find life elsewhere, especially complex life, this gives us increased reason to think that the filter is ahead of us.
Second, we need to put more resources into dealing with existential risks. One excellent recent step was NASA's WISE mission which looked for asteroids likely to impact the Earth. We're now tracking a lot more of the near Earth asteroids and are probably tracking all of the asteroids that are both large and likely to intersect Earth orbit. At present, we're paying very little attention to human-caused catastrophic risk events. Catastrophic AI seems unlikely, but it is clear that little attention is being paid to the issue. Similar observations apply to nanotech and other concerns. More resources should be devoted to examining these dangers before the technologies become fully developed by which time it may be too late.

Unfortunately, there's a tendency to dismiss risks that appear in popular science fiction precisely because they appear in such works. This is just as bad as using fictional works as a reason to eschew a technology. Moreover, humans have a lot of trouble thinking about large scale problems, and the scale of a problem doesn't get much larger than the complete destruction of humanity.

So overall, the Great Filter doesn't worry me too much. But, even without the threat of the Great Filter, we still aren't doing enough to deal with the big risks to our existence. If most of the Great Filter is behind us, it would be all the more tragic if humanity were to be destroyed now, when we are but a few generations of spreading beyond our planet.

[1] I thought that this point might be original to me, but while writing this blog entry I found that it has been made before. See, e.g. Katja Grace's remarks here.

Why I am a feminist.

2011-06-29T17:46:00.000-07:00

I self-identify as a feminist.I think human males in general should self-identify as feminists. If we want to live in a society that is as technologically and scientifically advanced as can be, we must support feminism.

By "feminist," I don't mean that someone who believes that males and females are identical. Obviously they aren't. And I don't mean that that there aren't innate biological differences, some of which will result in statistically significant differences in the general population. Such differences indeed exist.

By feminist I mean someone who supports identical rights for people regardless of gender. I also believe that we should encourage females to pursue whatever professions, occupations and hobbies that they want and of which they are capable and that we should discourage negative stereotyping about lack of ability.

I don't self-identify as a feminist out of some deep ideological grounding. I don't have any strong ideological affinity with most of the feminist movement. Sure, equality in the abstract is nice. However, it is clear that stereotypes about females negatively impact on everyone. And so, I support feminism, not out of some deep belief, but out of simple self-interest.

How many women have become housewives or secretaries who might otherwise have been the next Barbara McClintock or Emmy Noether but for the fact that they were mistreated and told that math and science were for men? I don't know. But I do know that, for each of the women who were discouraged, there is at least one more interesting theorem, one more cool biological fact, one more interesting astronomical phenomenon that society missed out on. And some of those would have gone on, not just make interesting discoveries but to make practical, helpful discoveries. I have trouble keeping count how many friends and relatives I've lost due to cancer and other illnesses. How many of them would still be alive today if the right little girl hadn't been told that she couldn't do math or that science was for the boys? I don't know, but I can guess that it is probably more than one.

I'm a feminist not because I'm a good person who cares about equality, but because I'm a self-interested person who wants to learn and benefit from everyone I can. I want to live in the best, most technologically advanced society that I can. Therefore, I am a feminist.

What is P ?= NP and why should you care?

2011-06-28T13:12:00.000-07:00

After my last blog post, readers remarked that they had no idea what
"P ?= NP" was and that I had completely failed to explain what I was talking about. They are correct. This entry is to remedy that problem.

First an analogy: Suppose you have a jigsaw puzzle. Assembling the puzzle correctly is difficult. But, if someone has the puzzle completed, one can generally tell at a glance that the puzzle is correct. (This isn't strictly true if you are dealing with someone like me who as a little kid would sometimes shove the pieces to fit in where they didn't belong. If one does this to sections that depict sky and clouds, it can be quite hard to tell that it is wrong.) But it seems that it is very difficult to tell how to assemble a puzzle. Moreover, it isn't even clear if one has all the pieces of the puzzle until one is nearly done with the puzzle. It can be a very frustrating experience to be nearly done with a puzzle and then realize that pieces are missing. What if there were a way to tell just from looking at the jumbled pieces in the box if one had the all pieces? Whether P is equal to NP is essentially asking if this is possible. The general consensus among computer scientists is that P is not equal to NP which means that puzzle-solvers are out of luck.

Let's break this down further. P is the set of types of puzzles that can be essentially solved quickly. So for example, "Is a given integer even or odd?" is a problem that lies in P. Given an integer, one can just look at the leading digit and see if it is even or odd. (I'm assuming that our integers are written in base 10). Similarly, the problem "given integers a and b, does a divide b?" is in P,;all one needs to do is divide a into b and see if there is a remainder. But not everything is necessarily in P. For example, the question, "is a given integer composite?" is not obviously in P, since checking requires successive search for divisors.

But, there is a larger class of problems, NP, which are problems which, if they have an answer of "yes," one can quickly convince someone else of the answer if one has the right information. In this context, "is an integer composite?" is in NP, since if I know a non-trivial divisor of the integer, and I want to convince you that it is composite. I can just tell you that number and you can check yourself. To make this more concrete, if I gave you the number 1517 and asked you if it were prime or composite, you would have to do a lot of unpleasant arithmetic. But, if told you 1517 is 37 times 41, you'd be able to check this easily.

Now, it actually turns out that whether a number is prime composite can actually be checked quickly using something called the AKS algorithm . This result was a very big deal, proven by Manindra Agrawal and two other mathematicians in 2002 . I remember when this happened. When the result was announced, I was a high school student who was then at PROMYS, a summer math program at Boston University, and people were distributing and looking over copies of the preprint. The algorithm they used was straightforward, but proving that algorithm really did what was claimed required deeper mathematical results from the area known as sieve theory.

Let's try to make these notions of P and NP more mathematically rigorous. To do that, we need a rigorous notion of what it means to calculate quickly. We want the length of time it takes to run our algorithims to solve our problems to not grow very fast. When mathematicians want something that doesn't grow too quickly, they often look at polynomials (that is, functions like n^2, or n^3, or n^4 +10n +2, as opposed to say exponentials that look like 2^n or 3^n). So, we will define an algorithm to be quick if the amount of time it takes to run is bounded by a polynomial of the length of whatever we inputted. So ,for example, in our earlier case of looking at whether an integer is prime or composite, the length of the input would be the number of digits in the integer. Thus, Agrawal constructed an algorithm that ran would when given an integer always tell you if the integer was prime or composite. Agrawal showed that there is a constant K such that his algorithm terminates in at most at most Kn^12 steps, where n is the number of digits of of the number to be test.

Whether P = NP is one of the great unsolved problems of modern mathematics. P ?= NP is one the seven Clay Millenium Problems, each of which has a million dollar prize. Moreover, there are many practical applications. There are many practical problems which appear in some form to be in NP, but have no known quick algorithm to solve them. These include problems in protein folding, circuit design, and others areas.

Readers have likely also benefited more directly from practical issues related to this problem without even realizing it. I've discussed on this blog before the Diffie-Hellman algorithm. This is one example of many cryptographic systems that are used by modern computer networks, most often without users even realizing that they are being used. These all rest on certain problems being easy to solve if one has extra information, but very difficult otherwise. Thus, if P = NP, then all these algorithms will become insecure. This would be bad. Unfortunately, the converse does not follow: There is a common misconception that if P is not equal to NP, then modern encryption is actually safe. This doesn't follow. It turns out that claims that encryption works implies that P is not equal to NP, but the reverse doesn't follow. It is conceivable (although unlikely) that P and NP are distinct and encryption still collapses. But, figuring out whether P = NP would be a major step in understanding whether or not encryption is really safe.
Those worried about the encryption for their bank accounts can rest easy. Most experts in the field seem to think that P and NP are distinct. This means your encryption is secure. On the other hand, this also means that a lot of practical problems are genuinely tough. One can't have it both ways. Either one gets lots of helpful fast algorithms or one gets good encryption. Right now, it looks like one gets good encryption.

So, how close are we to actually answering if P = NP? This looks pretty far off right now. There are a few methods that look somewhat promising, but a lot of the best current results are results that essentially show that certain techniques cannot answer the question. So right now resolving the question looks pretty far off.

Gasarch P = NP Poll

2011-06-26T17:21:00.000-07:00

A decade ago, Bill Gasarch conducted an informal poll asking computer scientists and mathematicians various questions related to whether or not P was equal to NP. He asked when people thought the problem would be resolved, which was it would be resolved, and what techniques they thought would be used. One thing that is striking about Gasarch's data is that a surprisingly large fraction of serious computer scientists seem to think that P = NP. Moreover, while Gasarch notes that some of those individuals explicitly said they were saying it for the sake of being contrary, a large fraction also were simply unwilling to guess which way it would be resolved.

Now, Gasarch is again conducting such a poll. I am noting this here, because he is accepting emails from not just computer scientists but individuals in general, although he wants people to note their academic background. Also, please note that he wants replies by email. Apparently some people have already failed to note this and have added them as comments to his announcement post.

My own opinion (which I will submit via email shortly), is that P != NP, and I'm about 95% confident in this regard. I assign low probability to the weirder possible results involving undecidability in ZFC. I have no idea when the problem will be resolved, and I have no idea what techniques will be used to resolve it, although the techniques used by both Mulmuley and Ryan Williams look interesting. Obviously, I'm not a computer scientist, so my opinions on these matters should be taken with a large dose of salt.

Gasarch's poll also has an open-ended question allowing one to pontificate on related issues. Unfortunately, I really don't have any strong opinion on any related issues other than something like "derandomization is nice, yay?" The obvious related question of whether P = BPP seems tough. A lot of people are convinced that this is the case, and there's been a lot of success in the last few years with derandomizing algorithms, but my impression is that there's very little in the way of general techniques of how to do this systematically.

I'm also curious what readers of this blog thing, so feel free to leave your speculations in the comments.

Planar Divisibility Graphs and The Bible

2011-06-20T18:47:00.000-07:00

I've talked about graph theory here before in the context of Ramsey theory.

However, there are many other interesting graph theory problems.

A graph is said to be planar if one can draw it on a plane with none of the edges intersecting. So for example, K3, the graph formed by three vertices all of which connect to each other is planar, but the similar graph K5 formed by five vertices all of which connect is not planar.
We can also change our notion of graph by allowing our edges to have directions, and represent them with arrows rather than straight lines. Thus for example, if one wanted to use a graph to represent who knows the name of whom with a bunch of people, using a directed graph would be quite natural.

Over the last few days I have been thinking about divisibility graphs of sets. These graphs arise when one takes some set of positive integers and assigns each to a vertex then draws the corresponding arrows when one integer divides another. (So for example, if our set was was {1,2,4} then 1 would have arrows going to 2 and 4 and 2 would have an arrow going to 4). For convenience, I am ignoring the arrows that vertices would have going to themselves.
Now, assume one has a set of positive integers A and we know that corresponding divisibility graph is planar. What can we say about how large the set is. That is, if we let A(x) be the number of elements in A which are at most x, how fast does A(x) grow? It is not difficult to see that one can get A(x) to grow at least about as fast as x/log x. One does this by taking A to be the set of prime numbers. The resulting graph is certainly planar since it has no edges at all. Then the prime number theorem does the rest. With a small amount of tweaking, one can get this to grow at about 2x/log x since one can include all the numbers of the form 2p and still get a planar graph. I suspect that the actual best possible growth is on the order of x/log x but I'm not sure. One possible approach to making a large planar divisibility graph is to use the greedy algorithm. That is, throw 1 into the set and then go by induction on each integer, throwing in the next integer if it still allows a planar graph. If one call this set G, then the first number not in G is 18. It seems at first that G grows quickly, and G includes every prime number. But most large integers are in fact not in G, a result of the fact that most large integers have a lot of prime factors. For example, every multiple of 6 other than 6 and 12 is not in G.

Now, you may be thinking, "Josh, this is an interesting math problem, but the title mentioned the Bible. What does that have to do with anything?" The truth is that the connection is tenuous. The problem about planar divisibility graphs occurred to me when I was tutoring a professor's young kid in graph theory, and we discussed divisibility graphs. The professor's family is Orthodox, and so another graph we talked was to take different Biblical figures and make a graph representing who had met whom. The major graph had three large components, one corresponding to the patriarchal time period (with Abraham, Issac and Jacob as the most connected points), one to the time around the Exodus (with Moses at the center), and one at the early monarchy, with David, Samuel and Solomon as the main points. However, an issue came up. My young student wanted to add Eli, the high priest during most of the of Samuel to the graph. This raised an issue which neither he nor I knew the answer: Did Eli ever encounter David? The text does not mention such an event, but the chronology seems tentatively to allow such a meeting. I'm also unaware of any midrashim claiming that they met. I'm mentioning this here therefore for two reasons: One can any more knowledgeable readers point me to anything in the text itself which deals with this, or can any of my more midrashically inclined readers point me to any midrashim that address whether they met?

Abusing Statistics

2011-06-16T15:22:00.001-07:00

A friend writing under a pseudonym has a new blog about the use and abuse of statistics in the media. He's a good writer. Since he came to statistics (and the mathy end of everything) somewhat late compared to most math and science bloggers, I expect that his take will be quite interesting. He will likely also do a good job explaining some of the relevant ideas to less mathematical people. The latest entry is on how not to conduct surveys. The entry is worth reading.

Dungeons, Dragons and Halacha

2011-06-06T13:27:00.000-07:00

In an earlier entry I discussed whether under halachah (Orthodox Jewish law) it would be acceptable to make a horcrux or become a lich if either were possible in real life. That entry was largely an excuse for bad wordplay related to the word "phylactery" which has a variety of meanings. A phylactery is in the most general sense an object which contains someting of religious or ritual significance. In the most common context, the word is used in the plural- "phylacteries" as an English translation of tefilin, the small boxes worn by some Jews at morning prayers. Another use of term is in Dungeons and Dragons, where the term is used to describe the object that a lich, a type of undead wizard, uses to store their soul.

However, I recently came across yet another meaning of this term in a Dungeons and Dragons context. There is a spell, described in the D&D book "Player's Guide to Faerun" called "Spell Phylactery" which allows one to store a spell on a scroll which "must be bound to your arm or forehead (usually rolled tightly or placed in a small box for this purpose)". This form seems more directly inspired by the phylacteries of the Jewish tradition. Unfortunately, even if D&D magic were real, it would not be halachically acceptable to make a three-way phylactery since the Spell Phylactery spell can only be cast by a worshipper of the goddess Mystra, which would be not allowed under halacha. Too bad. I really wanted phylacteries that functioned as both a phylactery and as a spell phylactery.

Harry Potter and the Methods of Rationality

2011-05-29T12:26:00.000-07:00

I've mentioned Harry Potter and the Methods of Rationality before. It is a Harry Potter fanfiction written by Eliezer Yudkowsky. The central premise of the work is that Harry instead of having abusive step-parents has loving step-parents and his step-father is a scientist. Young Harry grows up learning all about the scientific method, critical thinking, and cognitive biases. HPMR does have its positives and negatives. Overall it is hilarious but there are times when Harry is didactic and Yudkowsky has clear difficulty in making his characters sound like eleven year olds. But overall, it is worth reading. I am recommending the fiction now for two reasons. The fiction has recently become the most reviewed fanfiction on fanfiction.net. Second, for the last Vericon masquerade a friend and I cosplayed as the versions of Harry and Hermione from HPMR. Pictures can be found at her blog. Note that the costumes were not made entierly by us. The badges were made by Ellen Dimiduk who does excellent costuming work. Now, Yudkowksy has a policy that people who make cool artwork about the story get cameos in the story. So the latest chapter of HPMR mentions two Hogwarts students, Katarina and Joshua, who helped make costumes for Hogwarts students. So of course people need to go read it now since I'm a character! So if you aren't reading it yet, go and read.

A brief note on the Rapture

2011-05-20T13:26:00.000-07:00

Michael Hartell of the Sentinel and Enterprise interviewed me in my capacity as a spokesentity for the Boston Skeptics talking about the Rapture. Hartell's article focuses on Harold Camping's prediction that the Rapture will take place tomorrow. His article is worth reading, although there are a few things that didn't get into the final article that I think are worth mentioning: First, the entire "Rapture" doctrine as it exists in modern times is only a few centuries old and only became at all popular due to the preaching of John Darby in the early part of the 19th century. Second, this is a good example of the sort of serious damage that erroneous beliefs can create. The New York Times article on the same subject focuses on the Haddad family where the parents believe the Rapture will occur tomorrow and the children do not. In that article, the Haddads have stopped saving up for college for their children because they believe that it will never happen. The children will suffer when the Rapture doesn't take place and they then can't afford to get good educations. These parents are not going to risk their childrens' lives in the same way that parents who refuse to vaccinate are actively endangering their lives, but the basic problem is the same: hideously inaccurate beliefs about reality are hurting bystanders.

Multiplicative functions and almost division

2011-05-17T19:19:00.001-07:00

A function f(n) with range in the integers is said to be multiplicative if f(ab)=f(a)f(b) whenever a and b are relatively prime. A function is said to be completely multiplicative if this applies for all a and b whether or not a and b are relatively prime. Some of my prior posts have discussed multiplicative functions (e.g. this post on Mersenne primes and perfect numbers). An important thing to note is that a multiplicative function is determined by its values at prime powers, while a completely multiplicative function is determined by its values at primes.

Let f and g be two functions from the positive integers to the integers. Let K(f,g)(x) be the number of n less than x such that f(n) does not divide g(n). We say that f almost always divides g if f(n) divides g(n) for almost all n if K(f,g)(x) = o(x) (or to put it another way, the set of exceptions has density zero). Obviously, almost divisibility is weaker than divisibility. Almost divisibility shares many of the properties of divisibility; it is a transitive relation. One important difference between divisibility and almost divisibility is that among positive functions, divisibility is an anti-symmetric relation (that is, if fg, and gf then f=g). This is not true for almost divisibility, but is true for almost divisibility if we restrict our attention to multiplicative functions.

Are there interesting examples of non-trivial almost divisibility where one doesn't have divisibility? Yes. Let σ(n) be the sum of the positive divisors of n, and let τ(n) be the number of positive divisors of n. Erdos showed that τ almost divides σ and showed through similar logic that τ almost divides the Euler φ function.

Why am I thinking about these functions? I noticed that some multiplicative functions divide a positive completely multiplicative function. Thus, for example φ divides the completely multiplicative f such that for any prime p, f(p)=p(p-1). However, other cases don't have such examples. It isn't too hard to show that there's no such completely multiplicative function for τ or σ. But, the situation changes drastically in the case of almost divisibility. We in fact have that for any function f from the natural number to the natural numbers, there is a completely multiplicative function g such that f almost divides g. We shall call such a g, a "completely multiplicative almost multiple" (or CMAM) Moreover, we can construct such a function explicitly.

Proposition: Let f(n) be a function from N to N, and let g(n) be the completely multiplicative function defined by g(p) = is the least common multiple of f(1),f(2),f(3)...f(2^p). Then g is a completely multiplicative almost multiple of f.

In order to prove this result, we need another notion, that of normal order. Often, to describe the behavior of a poorly behaved function, number theorists like to show that it asymptotic to a well behaved function in the sense that the limit of their ratios is 1. Thus, for example, the prime number theorem says that the poorly behaved function

π(n) that counts the number of primes that are at most n is asymptotic to n/log n.

But for many functions we care about this sort of statement is much too strong. Let ω(n) be the number of distinct prime divisors of n, and let Ω(n) be the total number of prime factors. Then these functions hit 1 infinitely often and so clearly are not asymptotic to any nice functions. However, ω and Ω possess a normal order, in the sense that for any ε > 0, we have that excepting a set of density 0, (1-ε) log log n < ω(n) < (1+ε) log log n and the same holds for Ω(n). (More refined estimates exist but we don't need them for these remarks.) An important heuristic that stems from this result is that most numbers look very close to square free in the sense that they have a lot of prime factors and very few of the prime factors occur more than once.

Now, to prove our result, we observe that excepting a set of density zero, we have Ω(n) < 2 log log n . So ignoring a set of density zero, the largest prime factor of n, call it p, is at least n^(1/(2 log log n)), and so f(n) appears as a term in g(p).

Obviously, for any f, the constructed CMAM grows very fast. However, this doesn't need to be the case, and it might be that in specific contexts one can substantially reduce this growth rate. So, this leaves me with three questions, one broad and two specific:

1) How much can we improve on reducing the growth rate of the CMAM for a function f? There are obvious steps to take in the construction but they still make it grow very quickly.

2) Let g(n) be a CMAM for σ. Does it follow that g(n) is not O(n^k) for any k? I strongly suspect this is true but don't see how to prove it.

3) One can through more careful work show that there is a CMAM for τ that is 0(x). What is the best possible growth rate for such a function?

While I've seen individual papers that have discussed specific functions being almost divisible by each other, I'm not aware any substantial work on their general structure. I don't know if this is due to my ignorance of the literature, the fault of almost divisibility being too weak a property to be interesting, or some other cause.

Osama bin Laden's death, Barack Obama, and the Judeo-Christian heritage of the United States: A response to my brother

2011-05-02T16:53:00.000-07:00

In the last 24 hours, everyone has been talking about Osama bin Laden's death. Last night, after the President's speech, people around the country celebrated. Here in Boston, this apparently became another excuse for college students to get drunk. I heard well into the night screams of "USA! USA!" and at one point an attempt to sing "America, Fuck Yeah!" from Team America.

There were more measured responses including a piece in the Huffington Post by my brother Nathaniel. Unfortunately, many of the more measured responses, including this one, are misguided.

Nathaniel listed five aspects of the President's remarks which in his view stood out:

1) Obama emphasized that America and al Qaeda are "at war." This is an important shift from the president who wanted to try Khalid Shaikh Mohammed in a civilian court in New York, and who vowed to shut down Gitmo during the 2008 campaign. The tone here tonight was clear: The terrorists who plot against the United States are (illegal) combatants who deserve the full front of our military fury, not our legal rights.

2) The president gave a nod to his predecessor, in an acknowledgment that America has never been, nor ever will be, at war with Islam. This took class and grace, and Obama merits credit for it.

3) This speech was traditional. From the inclusion of "under God" in his closing remarks, to the references to retributive "justice," Obama channeled the Judeo-Christian values that still define our nation -- again, a welcome shift from the president who went out of his way to give a nod to "non-believers" in his inaugural address.

4) Somehow, Obama managed to take this moment to combat feelings of American declinism. The memo: We can do anything we set out to do. Compare this simple yet effective message to his recent flop of a State of the Union speech, in which the example of our greatness was the fact that "America is the nation that built the transcontinental railroad." This moment disproves those who sing the song of the "fall of American Empire," resolve, and spirit.

5) Most importantly, Obama tonight reaffirmed America's role as a force for good in the world, a force that extends beyond our borders. After U.S. troops took a backseat in NATO operations against Muammar Gaddafi, many (including me) worried that our will to "oppose any foe" in the defense of liberty played second fiddle to the whims of the UN, EU, and the Arab League. Thankfully and surprisingly, Obama reaffirmed our commitment to be a "shining beacon on a hill" to light the world.

I don't have any significant problems with the second or fifth points, but the other three are problematic.

In his first point, Nathaniel portrays as a positive that which isn't. He also confuses a variety of different issues. Targeting high ranking terrorists and killing them is distinct from whether or not people such as Khalid Shaikh Mohammed should get civilian trials once they are in our custody. But we can direct our military against targets at the same time that we use civllian trials for those who are captured. The first World Trade Center bombers and the Oklahoma City bombers were both tried successfully in civil courts. Being at war does not mean we need to ignore due process.

Nathaniel's third point is deeply wrong. The Judeo-Christian heritage of this country is deeply exaggerated. The US Constitution bears almost no signs of Judeo-Christian values. There are only three signs of such religious influence in the Constitution, and all are comparatively minor. First, laws presented to the President become law in 10 days after presentation to the President, excepting Sundays. Second, the treason clause requires two witnesses of an overt act to convict or a confession in court. This requirement echos the Old Testament rule for conviction of severe crimes which requires testimony of two witnesses. Third, the Constitution is dated "in the year of our Lord," a conventional phrase at the time.

Moreover, Nathaniel's statement portrays the Judeo-Christian heritage in the worst light possible. I'm proud of my Jewish heritage. But there's something deeply wrong when that heritage's primary lesson is an endorsement of retributive justice. It is noteworthy that the most substantial impact of the Bible on the text of the Constitution is to make conviction and punishment more difficult, not to endorse retribution. Indeed, it is a common theme in that heritage that we understand that even our enemies are people who can suffer. At the Passover Seder, even as the deliverance of the Israelites is celebrated, we remove a drop of wine from the cup for each of the Ten Plagues, remembering the Egyptian suffering.

Most troubling of all is the notion that mentioning God constitutes a " welcome shift from the president who went out of his way to give a nod to "non-believers" in his inaugural address." Approximately 10% of the people in United States self-identify as having no religion, and about 2% of the U.S. population identifies as either atheist or agnostic. Non-believers in the US have ranged from Carl Sagan to George Clooney, from Neil deGrasse Tyson to Bill Gates. Non-believers are an important part of the United States, intertwined with everything that makes America a great nation. All citizens deserve the same respect, whether they are differ by skin color, politics, or religious beliefs.

Nathaniel's fourth point is also misguided. The building of the transcontinental railroad was a triumph of the American spirit. And yes, America is really in a decline when our example of "we can do everything" is to kill our enemies. We are the only nation that has ever sent people to the moon. Yet, no one has walked on the moon in forty years. The shuttle will soon no longer be operational, and the US will need to rely on Russia for space flight. We are in a decline. No speech can hide that. And pretending otherwise is not a good thing. We must fight that decline. But we cannot fight it if we do not acknowledge the threat.

Nathaniel ended his piece by saying that he was proud of the troops and proud of the President. I can understand being proud of the troops. They risked their lives. We should be thankful to those soldiers who put their lives on the line to protect what we hold dear. This is not a good reason to be proud of the Ppresident. Nothing he did substantially impacted this result. It is possible that actual policy changes by Obama somehow lead to these events by making it easier to track down Osama. But I've seen no indication of that. Let's not give him credit that he isn't due. It is likely that in the 2012 election I will vote to reelect Obama, but that has almost nothing to do with these events, and it shouldn't. Instead of responding to these recent events, we should all vote for whichever candidate we think will be the most competent President with the policies that are best.

Political Affiliation and Scientific Knowledge Levels

2011-04-02T19:43:00.000-07:00

Previously on this blog, I've talked about differing intelligence levels and knowledge levels of different political groups. I've also decried the extreme anti-science and anti-intellectual views that have been articulated by conservative spokespersons in the United States. Thus, I was interested in some recent work which suggests that by some metrics the political right is more pro-science than the left. Audacious Epigone showed that GSS data demonstrated that, on average, Republicans are more pro-science and scientifically literate than Democrats. Epigone made no effort to control for variables, such as income, education and race.

Epigone's statement prompted Razib Kahn to do a similar, more detailed analysis focusing on science knowledge and attitudes. Kahn organized the data by political self-identification along the conservative-liberal continuum rather than by an individual's party affiliation. Razib's analysis suggests shows that conservatives and liberals are almost indistinguishable in overall knowledge level. However, when one removes the questions that discuss specific pet issues of the modern right-wing (i.e. those related to evolution and the age of the Earth), conservatives arguably pull ahead slightly in terms of scientific knowledge. At the same time, the data shows that moderates are less scientifically literate and less science-friendly than both conservatives and liberals. On all of the 19 variables that Razib examined, political moderates never come out on top. That is, for each question, sometimes conservatives perform best, and sometimes liberals, but never moderates. This is consistent with other results that show that in general moderates are less intelligent and less educated than other groups. For example, moderates have lower vocabulary scores than the general population. Razib performed additional analysis to try to control for other variables and his piece is worth reading.

This data suggests that there is a significant and underappreciated disconnect between right-wing leaders and self-identifying conservatives. If the individuals on the right right aren't statistically distinguishable from the left when it comes to science issues why do so many conservative politicans go out of their way to make anti-science remarks? There are a variety of possible explanations, but none of them are satisfactory.

First, many of these anti-science comments have been directed towards biology and matters related to biology (e.g. John McCain's remarks about bear DNA and Sarah Palin's remark about fruit fly research.) It is possible that the religious right's negative attitude towards evolution is carrying over to biology as a whole. However, this doesn't explain the remarks about other scientific areas (such as Bobby Jindal's remark about volcano monitoring). Moreover, although the human evolution question is by far the one with the most extreme difference between liberals and conservatives, (The percentages that accept human evolution according to the GSS are 69% for liberals, 52% for moderates and 39% for conservatives), the other questions suggest that conservative attitudes about evolution have not spread to other areas of biology. For example, when asked if the statement "Antibiotics kill viruses as well as bacteria" is true or false such as understanding that antibiotics cannot harm viruses 60% of liberals answered correctly while 63% of conservatives answered correctly. (The statement is false.)

Second, right-wing leaders may understand that most conservatives are not anti-science but think that the more active conservatve base is heavily anti-science. Without more data, it is hard to test if the active conservative base is substantially more anti-science than rank-and-file conservatives. Eeven if this is the case, it seems there are more effective ways of energizing the conservative base than anti-science rhetoric.

Third, right-wing politicians mayhave erroneously bought into the false stereotypes about their own constituents. Given the prevalence of such stereotypes, this seems most likely. This hypothesis is also difficult to test because politicians aren't going to admit that they've been pandering to rubes. Unfortunately, this belief among the right-wing leaders that conservatives are anti-science could easily act as a self-fulfilling prophecy if it causes pro-science conservatives to either stop being conservative, or causes some conservatives to become more anti-science to fit their tribal allegiance. However, this possibility does have a bright side: If this explanation is correct, then right-wing politicians are likely to be more pro-science in practice than they appear to be in public. Moreover, conservative politicians may act pro-science if they can be convinced that their constituents really aren't as anti-science as the politicians them to be.

Illinois and the Death Penalty

2011-03-09T14:22:00.000-08:00

Governor Pat Quinn of Illinois just signed a law which abolishes the death penalty in that state. This legislation is to some extent symbolic, in that Illinois has had a moratorium on the death penalty for almost a decade. With this legislation, Illinois joins New Mexico and New Jersey as states that have recently abolished the death penalty.

I have discussed here before my attitude towards the death penalty, especially in regards to specific cases such as the ongoing case of Hank Skinner . I'm not intrinsically against the death penalty: societies have the right in general to execute those who have violated the social contract in particularly heinous fashions if that will assist the public good. However, the death penalty as practiced in the United States is capricious and disorderly. Prosecutors push for death sentences when it is politically convenient, and their are huge racial disparities in who is executed.

It is also clear that innocent people have been wrongly convicted, and that in at least some cases, innocent people have been executed such as Cameron Todd Willinngham. Evidentiary standards that allow junk science and superficially persuasive eyewitness testimony are leaving blood on all our hands. For a long time, I have found striking a certain section in the Biblical book of my namesake, Joshua. the Israelites are called thieves when one man steals at Jericho. How much worse are we as a society that we as a democracy repeatedly elect and reelect officials who kill innocent people in our name?

In the particular case of the state of Illinois, I have additional personal reason to be interested in this legislation. My uncle Seymour Simon was a justice on the Illinois Supreme Court. He was a staunch opponent of the death penalty and argued forcefully and unceasingly that the death penalty as implemented in Illinois was unconsciousable and unconstitutionally capricious. He died in 2006, and so did not live to see this legislation. I suspect I know how he would have responded if he had seen this: Illinois is down. Only thirty-five more states to go.

Space Shuttle Discovery launch

2011-02-24T15:32:00.000-08:00

I'm currently in Florida with friends watching the launch of Discovery. This will be the second to last shuttle launch (there's a small chance that this will be the third to last launch if they get enough funding for a final launch). I and Tyrol5 wrote an article for Wikinews about the launch which includes a picture taken by me of the launch. There are additional photos on my Facebook page.

On rotations of spheres

2011-02-14T20:09:00.000-08:00

Consider a sphere living in some number of dimensions. The sphere we are used to is the 2-sphere, denoted by S². Mathematicians call it this because even though it lives in 3-dimensions, it is itself a 2-dimensional object (in the sense that small sections of it look like the 2-dimensional plane). One can similarly talk about the n-sphere, which lives in n+1 dimensions. Thus for example, the 1-sphere, S¹, can be thought of all all points on a plane that are of distance one from the origin.

When one has a geometric object one of the most obvious things to do is to ask what rigid movements of the object will take it to itself. Thus, for example, for a sphere, a rotation about some axis through the sphere's center rigidly moves the sphere to itself.

Rotations seem simple, but they can be surprisingly tricky. For the 1-sphere if one does a rotation and then another rotation one is left with a rotation. This is an important and helpful property. It says essentially that rotations form what mathematicians call a subgroup of the group of all rigid motions. It turns out that this is still true for the 2-sphere, S² even when one uses different axises for the two rotation Now, you might find surprising the fact that for S³, the sphere of three dimensions living in four dimensions, this breaks down. The composition of rotations is not necessarily a rotation. In some sense the not obvious fact is not why this breaks down for three dimensions, but why it still holds true in two dimensions.

The above is well known to mathematicians or to many people who have played around a bit with geometric objects. But, I recently learned a related fact that I found startling. Call a rotation "periodic" if we eventually get every point back to where we started. So for example, if one repeat a 90 degree rotation (π/2 for those using radians) four times we will have every point back where we started. Now, it turns out that for rotations of S² even though the composition of rotations is a rotation, the composition of periodic rotations is not necessarily periodic. Once one knows that this is true it is easy construct examples. Consider two rotations around perpendicular axises each of 30 degrees (π/6 in radians). It isn't difficult to show that their composition although still a rotation is not periodic. This is a good example of how even basic geometry can surprise us even when we think we understand it.

Obama's State of the Union Address: A Response to Nathaniel

2011-02-02T16:41:00.000-08:00

President Obama delivered his State of the Union address last week. My younger brother has a piece in the Yale Daily News which extensively criticizes the speech. Nathaniel complains that the speech started with an inspirational message but "soon fell into a quagmire of policy." Nathaniel criticizes the speech for focusing too much on policy minutia and argues that, while referencing Kennedy, Obama fails to understand that inspiration requires large goals, not policy details. Overall, Nathaniel is correct that this was a disappointing speech. However, it was not disappointing because it went into detail: it was disappointing because the details were unimpressive.

While Nathaniel is correct that the speech was not very inspirational, he misses a broader point: We need policy expertise, and a President who is willing to present a State of the Union that discusses real policy issues is a good thing. After 8 years of George W Bush's flag-wrapping jingoism, after 8 years of Bill Clinton's contentless addresses, the American people should be happy that a President is willing to discuss serious policy issues. And if the American people don't like that, that's a problem with the American people, not a problem with their President.

Nathaniel has two other criticisms of the speech: that Obama was unwilling to take a stand on anything remotely controversial, and that Obama called for largescale spending that the recent elections show is not desired by the American people. These criticisms seem contradictory. One cannot in one paragraph complain that Obama was a coward and then in the next paragraph complain that Obama is too willing to engage in spending that many people don't want.

Some parts of Nathaniel's column do have merit. Nathaniel correctly identifies that Obama's comments about school reform were close to toothless. And Nathaniel correctly points out that Obama did not emphasize the degree to which the proposed initiative will place heavy burdens on the American people. And it seems disingenuous for Obama to claim to be willing to fund the " Apollo Projects of our time" while calling for a freeze in domestic spending.

While I disagree with much of Nathaniel's criticism, I am far from happy with Obama's speech. It certainly had its good points, but it had many failings. Obama failed badly in his discussion of energy policy. He gets points for mentioning nuclear power, something he has in the past downplayed. However, when discussing biofuels, he made no mention of the fact that the most prominent attempt at biofuel, corn based ethanol, is inefficient, environmentally damaging, and raises food prices which hurts the poor here as well as people in the developing world.

Similarly, Obama's emphasis on electric cars was similarly unpersuasive. The President did not discuss that electric cars’ power has to come from the general grid. While electric cars do overall pollute less and use less energy, this stems from economies of scale more than anything else. And the impact is not high. While Obama did discuss the energy of the future, he proposed no funding for research into genuinely new energy sources, such as fusion power. (In the particular case of fusion power, the US is putting resources into ITER, the international tokamak reactor, but the US is putting no money into other forms of fusion such as stellarators.)

Obama's discussion of school systems used metrics which are less than ideal. In particular, the fraction of a population which is going to college is an awful metric for success of students. Students who go to college are often unprepared and often come out not much better prepared than they went in. Moreover, many jobs, even high-tech jobs, don't require college degrees. We have serious problems with people going to college on loans they are unable to repay.

Obama was correct to talk about policy proposals in his address. The problem is not the discussion but the content of those policies.

Review of Jason Rosenhouse's "The Monty Hall Problem"

2011-01-06T07:42:00.000-08:00

I've had the recent pleasure of reading Jason Rosenhouse's "The Monty Hall Problem." Rosenhouse's book is a comprehensive investigation into the eponymous Monty Hall problem, variations of the problem, and the larger implications of the problem.

The original Monty Hall problem named after a game played on an old television game show "Let's Make a Deal" with host Monty Hall. Rosenhouse describes the problem as:

You are shown three identical doors. Behind one of them is a car. The other two conceal goats. You are asked to choose, but not open one of the doors. After doing so, Monty, who knows where the car is, opens one of the two remaining doors. He always opens a door he knows to be incorrect, and randomly chooses which door to open when he has a more than one option (which happens on those occasions where your initial choice conceals the car). After opening an incorrect door, Monty gives you the option of either switching to the other unopened door or sticking with your original choice. You then receive whatever is behind the door you choose. What should you do?

(Presumably you are attempting to maximize your chance of winning one's chance of getting a car). Most people conclude that there's no benefit from switching. The general logic against switching is that after the elimination of a door there are two doors remaining, so each should now have a 1/2 chance of containing the door.

This logic is incorrect. One door has a 2/3rds chance of getting the car if one's general strategy is switching. Many people find this claim extremely counterintuitive. To see quickly the correctness of this claim, note that if one chooses a strategy of to always switching, then one will switch to the correct car-containing door exactly when your original door was not the car door. This will occur 2/3rd of the time.

Many people have great difficulty accepting the correct solution to the Monty Hall problem. This includes not just laypeople, but also professional mathematicians, including most famously Paul Erdos who initially did not accept the answer. The problem, and variants thereof, not only raise interesting questions of probability but also give insight into how humans think about probability.

Rosenhouse's book is very well done. He looks not just at the math, but also the history of the problem, and philosophical and psychological implications of the problem. For example, he discusses studies which show that cross-culturally the vast majority of people when given the problem will not switch. I was unaware until I read this book how much cross-disciplinary work there had been surrounding the Monty Hall problem. Not all of this work has been that impressive, and Rosenhouse correctly points out where much of the philosophical argumentation over the problem simply breaks downs. Along the way, Rosenhouse explains such important concepts as Bayes' Theorem (where he uses the simple discrete case), the different approaches to what probabilities mean (classical, frequentist, and Bayesian) and their philosophical implications. The book could easily be used for supplementary reading for an undergraduate course in probability or reading for an interested highschool student.

By far the most interesting parts of the book were the chapters focusing on the psychological aspects of the problem. Systematic investigation of the common failure of people to correctly analyze the Monty Hall problem has lead to much insight about how humans reason about probability. This analysis strongly suggests that humans use a variety of heuristics which generally work well for many circumstances humans run into but break down in extreme cases. In a short blog post I can’t do justice to the clever, sophisticated experimental set-ups used to test the nature and extent of these heuristics, so I'll simply recommend that people read the book.

For my own part, I'd like to use this as an opportunity to propose two continuous versions of the Monty Hall problem that to my knowledge have not been previously discussed. Consider a circle of circumference 1. A point is randomly picked as the target point on circle (and not revealed to you). You then pick a random interval of length 1/3rd on the circle. Monty knows where the target point is. If you picked an interval that contains the target point, Monty picks a random 1/3rd interval that doesn't overlap your interval and reveals that interval as not containing the target point. If your interval does not contain the target point, Monty instead picks uniformly a 1/3rd interval that doesn't include the target point and doesn't overlap with your interval. At the end of this process, you have with probability one, three possible intervals that might contain the target point, your original interval, or the intervals on either side of Monty's revealed interval. You are given the option to switch to one of these new intervals. Should you switch and if so to which interval?

I'm pretty sure that the answer in this modified form is also to switch, in this case switching to the larger of the two new intervals.

However, the situation becomes a bit trickier if we modify it a bit. Consider the following situation that is identical to the above, but instead of Monty cutting out an interval of length 1/3rd, he picks k intervals of each length 1/(3k) (thus the initial case above is k=1). Monty picks where to place these intervals by each picking one of the valid intervals uniformly and then going on to the other, then revealing the locations of all his intervals at the end. The remaining choices for an interval for you to pick are your original interval or any of the smaller intervals created in between Monty's choices. You get an option to stay or to switch to one of these intervals. It seems clear that even for k=2, sometiimes you should switch and sometimes you should not switch, depending on the locations of Monty's intervals. However, it isn't clear to me when to stay and when to switch. Thoughts are welcome.

New Haven Schools (again), The Death Penalty, and Gratuitous Promotion of Family Members

2010-12-08T18:48:00.000-08:00

Two quick notes:

Nathaniel has another piece criticizing the New Haven Promise program. This piece says much of what he has already said but includes a few more direct proposals about what else should be done. Unfortunately, this piece is on National Review Online. While that's an impressive accomplishment, that does make me feel conflicted about linking to it. In general, while NRO does have some worthwhile material, a disturbingly large fraction of it has over the last few years come to resemble a nutshell of what is wrong with the modern conservative movement in the US. For example, considering that NRO is the same place where writer Mike Potemra complained that Star Trek promoted "peace, tolerance, due process, progress" which are much too liberal values. Aside from this issue, as I've discussed before, I think that the problems in the public schools, including New Haven, are more complicated than Nathaniel portrays them.

There is a piece by another member of my family that I can link to with fewer reservations. My father has a deeply personal piece up at the Oxford University Press blog discussing why he has grown to oppose the death penalty. I suspect that his changing views are similar to the general decline in support for the death penalty over the last 20 years. The general support for the death penalty has dropped over time although about two thirds of the US still supports the death penalty (I've seen claims that the US did not have strong support for the death penalty in the 1960s and that the level of support grew for some time before beginning its current downwards trend, but I've never seen data backing this claim up.) There's also evidence that more religious people tend to be more likely to support the death penalty. If that is a causal rather than correlative link, the current drop in support for the death penalty may be due to the general drop in popularity of organized religion over the last few years.

Public Schools, Unions, New Haven Promise, and GPFM

2010-11-14T14:56:00.001-08:00

Last week, my alma mater Yale University announced that the university would work together with New Haven to fund "New Haven Promise," a program which would provide funding to New Haven public school students who attend colleges in Connecticut. The program promises scholarships for New Haven public school students with only a few weak restrictions. For example, students with less than 90% attendance rates in highschool are not eligible.

There are a number of possible criticisms of this program. The most serious criticism to me seems to be the simple one that this program is not Yale's job. Alumni donate money to Yale with certain expectations. They might also donate money to other causes. But there is a basic expectation that money that goes to Yale will be used for Yale purposes such as going to scholarships for poor students at Yale, not to students at random other schools in Connecticut.

There are additional problems with this program. My little brother wrote an op-ed in the Yale Daily News arguing that this program would in fact cover up the real issues in the New Haven public school systems which need to be addressed. He argues that the teacher unions and the lazy and incompetent teaching which they allow are much more of a root cause of the problems. I'm not convinced of his claims. I'm especially unconvinced by his line that "Instead of staying after school to tutor or help run an extracurricular, unionized teachers typically leave as soon as the final bell rings" which seems to underestimate the great difficulty that even hard-working teachers need to put up with daily.

However, I do think that more broadly speaking there's a clear problem with unions in our public schools which prevent the removal of all but the most egregiously bad teachers. For example, consider the case of eighth grade science teacher John Freshwater in Mount Vernon, Ohio. Freshwater taught science so badly that other teachers in later years had to specifically reteach Freshwater's students. Freshwater told students that Catholics were not real Christians. Freshwater burned crosses into students' arms using a tesla coil. Despite all these issues, it has taken more than 2 years to have Freshwater removed. Thus, while I don't have enough detailed experience to personally evaluate whether the unions are a problem in New Haven (although my limited anecdotal evidence suggests that they are a problem), it does fit the general pattern of what is going wrong with American public schools.

Nathaniel's piece generated a variety of responses such this one by a New Haven public school teacher, this one by a New Haven alderman, and this one by another Yale student. Nathaniel has responded to the last piece here. All of these pieces are worth reading.

On Almost Commuting Matrices

2010-11-10T20:43:00.001-08:00

When mathematicians encounter a binary operation, one of the first things they ask is "when does the operation commute?" That is, given an operation * when does one have A*B=B*A? Some operations always commute. Addition and multiplication in the real numbers are examples of this. Sometimes they commute under certain restricted circumstances. For example, subtraction rarely commutes (1-2 is not the same as 2-1).

In high school, children are often taught about matrices and matrix multiplication. Matrix multiplication seems to be given in part simply to have an example of an operation which has complicated behavior regarding when it commutes. Of course, we can only meaningfully talk about this when the matrices in question are assumed to be square matrices since otherwise the multiplication won't even be defined. However, matrices have other operations which we can do on them other than just matrix addition and multiplication. In particular, we can also multiply a matrix by a scalar.

This raises the following question: When do matrices almost commute? By almost commute, we mean commute up to multiplication by a non-zero scalar. A general result seems difficult. But there is at least one pretty result which can be proven without too much trouble by looking at the eigenvalues and eigenvectors of a pair of matrices:

If cAB=BA for some constant c, and A is invertible, then c is a dth root of unity for some d such that d divides the number of distinct non-zero eigenvalues of B. It isn't that hard to generalize this result slightly with A not invertible. However, one then needs the slightly technical condition that A sends no non-zero eigenvector of B to zero. Note also that this result is most nicely stated in the slightly more restricted symmetric case when both A and B are invertible.

One pretty corollary of this result is that if A and B are invertible p x p matrices over the real numbers where p is an odd prime, with all distinct eigenvalues, then A and B are almost commuting if and only if they actually commute.

No Free Lunch, Budgetary Constraints, and Gratuitous Promotion of Family Members

2010-10-18T19:13:00.000-07:00

My father has a piece up at the Oxford University Press Blog arguing that both major political parties in the US are pretending to the public that there are painless solution to US budgetary problems. I'm not convinced that the current federal budget situation is as dire as he makes it out to be although I do agree that the state and local budgets in many areas are in very bad shape. However, the essential point seems spot on. Neither the Democrats nor the Republicans are willing to be honest with the voters. And this is clearly not a good situation. I don't see any quick resolution to these issues. I will however be slightly partisan in saying that it is clear that some groups are being more unhelpful than others and that the Tea Partiers are clearly one of the most unhelpful groups in question.

The AFA, Youtube, Christine O’Donnell, and Yale: A Rant About The Modern Right Wing

2010-10-08T18:37:00.000-07:00

For a long time, I've believed that the anti-intellectualism of the modern right-wing in the United States is a fringe phenomenon.

However, over the last few months, I have become increasingly convinced that anti-intellectualism is not just a fringe phenomenon but a general trend of the modern conservative movement. The leaders of the movement are either ignorant, anti-intellectual buffoons, or they believe that their base is composed of ignorant, anti-intellectual buffoons.

Prior to coming to this conclusion, I had seen much evidence for this claim that did not convince me. The GSS data show that people who self-identify as liberal on average have larger vocabularies than those who self-identify as conservative. However, this did not convince me. Among other problems, the overall trends in that data are complicated. Vocabulary is correlated not just with increased liberalism but with general political extremism. That is, people more likely to identify with extreme political views are more likely to have a large vocabulary. Moreover, having a small vocab does not mean that one is anti-intellectual. It just means one is less likely to be intellectual.

Moreover, as I've discussed before, by some metrics of political knowledge, Democrats perform on average more poorly than Republicans.

However, the evidence for widespread anti-intellectualism among the American right-wing has now reached proportions which are difficult to deny. It is easy to dismiss Sarah Palin's comments about fruit flies as simple ignorance. And it is easy to dismiss Bobby Jindal's remarks about volcano monitoring as an isolated incident. However, these are not isolated incidences and one can point to many similar instances. Two of the most glaring that I've seen recently are remarks by the American Family Association's head Tim Wildmon and remarks made by Delaware senate candidate Christine O'Donnell.

The American Family Association is a right-wing Christian political group most known for organizing the boycotts that the right-wing periodically directs against companies that they have decided are too gay-friendly. I happen to be on their mailing list and received an email recently which contained the following:

A few months ago, AFA commissioned Christian songwriter/singer Eric Horner to write a moving patriotic song to honor our national motto, "In God We Trust."
Without any fanfare, we posted it on YouTube. The response was so overwhelming that YouTube called us to find out what was going on!

The fact is, the video is patriotic and inspiring, and it shares the message of faith. People love it!

YouTube has told us that if we can get 20,000 people to watch the video, they will feature it on their front page. That means that the tens of millions of people who visit YouTube's website each day will be offered the opportunity to watch the video - a video with a Christian message!

(fonts and formatting as in in original)

So much about this claim is strange that it is difficult to figure out where to start. The text contains outright lies. Youtube does not in general contact people for making popular videos to “find out what was going on!” It is conceivable that there is some threshold where such contact would occur. But that threshold is surely far beyond 20,000 views. In comparison for example, this video of Christopher Hitchens has around 35,000 hits and it is not the most popular such interview with Hitchens. Or to use a more amusing comparison, this extremely NSFW tribute video to Ray Bradbury has around a million views. 20,000 views is not much on Youtube. And anyone who gave minimal thought would realize this. My conclusion must be that the AFA lied . This is nothing less than political conmen fleecing a mark.

The other example was Christine O’Donnell’s recent attack on my alma mater. The Senate candidate, fresh from her prior remarks about scientists engineering ultra-intelligent rats , has now decided that Yale is a bad thing. She tweeted:

My opponent wants to bring Yale values to US Senate. I want to bring liberty, limited government, fiscal sanity.

Now, in fairness, she included a link to an article in the American Spectator which seemed to prompt her remark. That article didn’t criticize her opponent Chris Coon for going to Yale or for Yale values, but for his statement that he wants to bring the values of the Yale Divinity School to the Senate. That article is an attack piece, but like many attack pieces, it does have some truth to it and points out correctly that the Yale Divinity School is more left-wing than the general American population. That’s not the same thing as complaining about Yale in general. But, apparently to Christine O’Donnell, the problem as a whole is “Yale” values. According to O’Donnell, the values of one of the best universities on the planet are inherently bad values. It is difficult to imagine a more anti-intellectual stance short of book-burning. And yet, O’Donnell won the GOP primary for the U.S. Senate against Mike Castle. Castle is reasonable, well-educated and experienced. He has a law degree from Georgetown. He has demonstrated competence for over 20 years in political offices. And yet, he lost in the primary.

Anti-intellectualism is not at all limited to the GOP. It is becoming increasingly clear that the Obama administration actively interfered with government scientists telling the public how bad the the BP spill really was. Moreover, the Huffington Post, a mainstay of the liberal blogosphere, is filled with proponents of pseudoscience. And they have recently branched out from making absurd medical claims to denying evolution. But even these problems are small compared to the scale and pervasiveness of anti-intellectualism among the current conservative movement.

I don’t know what has happened to the GOP. At this point, the party seems to be engaging in a spiral of anti-intellectualism. There may be a positive feedback loop in that the more intellectuals grow disgusted with the Republican Party, the less incentive Republican candidates have to care about intellectuals. But that cannot be the whole story. Many people who are not intellectuals are not anti-intellectuals. So, I don’t understand what is happening to the Republican Party. But it disturbs me greatly. I’d like to be able to reasonably vote for multiple candidates including moderate Republicans. But as long as these trends continue, I will be forced to keep giving my money, my time, and my vote to Democratic candidates. And when I need to mark down what my politics are in a little box, I’ll answer “liberal” or “progressive” because in the United States right now, putting down anything else is becoming perilously close to writing “I support willful stupidity.”

Jack Chick and Civil Rights

2010-09-02T12:36:00.000-07:00

There's a new Jack Chick tract up. This tract is entitled "Stinky" and is about an eponymous demon assigned to go up to the surface for Halloween. Stinky is supposed to find a gift for Satan so that a higher a ranking demon, #3, hopes to use to get a higher position in the diabolical hierarchy. Unfortunately, school has just resumed, so I don't have the time to go discuss the tract in detail. And honestly, as Chick tracts go, it is pretty mediocre. We don't even have the grand Catholic conspiracy appearing in this one. The plot-line is slightly less coherent than usual which also may lend to the mediocrity.

However, just when I thought that Jack Chick might be losing his did stand out. At one point, Stinky is trying to get past an angel so he can continue to tempt some humans. Stinky cries out "I demand my Civil Rights!" to which the angel responds "That doesn't work here, Stinky!" (eccentric formatting as in in the original). As far as I can tell, Jack Chick is attempting to make some sort of political argument here along the lines of "civil rights are a demonic concept." I don't know what to say to that.

Conservapedia, P=NP, and the Fields Medal

2010-08-17T13:34:00.000-07:00

Conservapedia, the right-wing, Christian alternative to Wikipedia has once again broken new ground. In previous entries we've discussed Conservapedia's founder Andrew Schlafly self-Godwining and Conservapedia's interesting take on Popperian falsifiability. Others have discussed Conservapedia's objections to special and general relativity. Now, Conservapedia is at it again.

Apparently, Conservapedia has taken a recent interest in mathematics. First, they added to their mainpage a take on the recent reports that Deolalikar had proven that P ≠ NP . Conservapedia announced:

University professors pile on against a non-professor's claim to have solved one of the millennium problems. MIT Assistant Professor Scott Aaronson declares, "Vinay Deolalikar still hasn’t retracted his P≠NP claim, but a clear consensus has emerged that the proof, as it stands, is fatally flawed." He absurdly adds, with a cite to Richard Dawkins, "the only miracle in life is that there are no miracles, neither in mathematics nor in anything else."

But the best of the public, aided by the internet, will inevitably solve more problems than liberal colleges will - just as Grigori Perelman solved another millennium problem. The future belongs to the conservative public.

(internal links and fonts suppressed)

Apparently, Aaronson's decision to quote Richard Dawkins meant that math must be evil. I'll leave it as an exercise to the reader to note some of the other more glaring errors. However, this was not the end of Conservapedia's attack on establishment math for being just too liberal. Shortly after this declaration, an addition about the Fields Medal went up. The Fields Medal, awarded every four years, is for mathematics roughly equivalent to a Noble Prize(there is no Nobel in math). Conservapedia announced a "Conservapedia exclusive":

[T]his Thursday liberals will likely give the coveted Fields Medal -- math's highest honor -- to an underachieving woman and to a communist-trained mathematician from Vietnam. Is the lamestream media holding back stories about this to create a bigger splash on Thursday?

(internal links and fonts suppressed)

It is not clear what "underachieving woman" Conservapedia is thinking of, but apparently the "communist-trained mathematician" is a reference to Ngo Bao Chau, who made headlines last year for proving the Fundamental Lemma of the Langlands program. Apparently Conservapedia believes that the general media cares so much about mathematics that a failure to speculate on who will win the Fields Medal is a sign of a media conspiracy. Why a "communist-trained" mathematician would be a big deal is not clear given thatabout half of the Fields Medal winners have been either from the USSR or trained in the USSR.

Also, apparently Conservapedia is unhappy that after Terence Tao got the Fields Medal four years ago he then endorsed Barack Obama for President, Finally, we come to the detail that forced me to write this blog entry. To deal with this apparent liberal bias and affirmative action in the Fields Medal, Conservapedia is starting its own award for mathematicians, the "ConservaMath Medal." According to the website this Medal is "the merit-based alternative to the Fields Medal, with winners announced at the same time so that real achievement is recognized." I'll let that speak for itself.

Integer Complexity: An Upper Bound Update

2010-08-06T15:09:00.000-07:00

It looks like I may have a final upper bound on the integer complexity problem. Recall we defined f(n) to be the minimum number of 1s needed to represent n as a product or sum of 1s. Thus, f(6)=5 because we can write 6=(1+1)(1+1+1). Harry Altman and I have been working on improving the lower and upper bounds on this function. Prior posts about this problem can be found under the label integer complexity. Harry has a large number of posts on the subject also, but they aren't all tagged so I'll just direct readers to the most recent one.

I'm writing this post to announce that we have a tight upper bound for f(n). Prior to our work, it was known that if n ≥ 2, we have 3log2 n ≥ f(n) ≥ 3log3 n. It is clear that the lower bound is hit infinitely often (whenever n is a power of 3). We (and by we I mean mostly Harry) have worked on understanding what n have close to the lowest possible value, and using this to understand other conjectures about f, such as the conjecture that if n=2^a*3^b then the most efficient representation for n is the obvious one. However, I've been also working on improving the upper bound, and whenever I've thought that I've been done improving the upper bound, I've then realized another way to tweak my proof to reduce the upper bound slightly. However, at this point, I'm confident that cannot happen anymore using the techniques in question, barring substantially new insight. Thus, I'm now announcing the new upper bound. We have for n ≥ 2, f(n) ≤ αlog2 n where α = 70/(log_2 102236160)= 2.630853... Note that this constant is just small enough for us to also state the weaker but prettier result that f(n) ≤ (19/5) log n. Unfortunately, the proof in question is very ugly, involving a large amount of case checking as well as nasty calculation of inequalities. I'm in the process of writing up the last bit. If readers are interested I can email people a draft of the proof when it is fully written.

Greece, Civil Unions in Hawaii and the Huffington Post:: Ethical Dilemmas about GPFM

2010-07-12T05:57:00.000-07:00

My twin has a piece up at the Huffington Post arguing that the veto of Hawaii's civil union bill by its Governor Lingle was not motivated by the reasons that Lingle gave. I'm having some qualms about linking to the Huffington Post. The website has had a long history of pushing anti-science and fringe medical beliefs, including homeopathy and claims that vaccines cause autism. Most recently, they've branched out into anti-evolution propaganda with a piece by David Klinghoffer of the Discovery Institute claiming that evolution was the root cause of Nazism. These issues with the Huffington Post are discussed in detail in this Salon piece and this statistical analysis. I'm concerned about driving traffic to a website which has such attitudes towards science and the scientific consensus. Moreover, it raises serious questions about their otherwise apparently good political coverage. In particular, if they cannot deal with empirical issues well, why should one think that they can deal with issues involving politics where far more cognitive biases come into play? I'm curious what readers think about this issue.

Meanwhile, I can without any concerns link to my father's recent piece at the Oxford University Press blog which discusses what lessons that the United States should take away from the Greek financial crisis. The piece gives a balanced view about the economic and demographic issues that face the United States today and how they compared to Greece.

Insane Clown Posse and Science: Deliberate Ignorance

2010-06-21T17:11:00.000-07:00

Insance Clown Posse is a rap group known for dressing up like clowns and demonstrating proficiency with using the word "fuck" as an adjective or adverb. Their fans, called Juggalos, often border on the fanatical. Recently the group released a song called "Miracles" in which they assert that all sorts of everyday things are miracles. This list includes eclipses, giraffes, magnets, rainbows, butterflies and how children look like their parents.

Warning: the following video is painful. The pain comes not just from the stupidity of the lyrics but the fact that the music just sucks. Watch at your own risk.

By itself, this song might be dismissed as silly. However, the song contains the lyrics "And I don't wanna talk to a scientist/Y'all motherfuckers lying, and getting me pissed." When this song came out, there was a fair bit of uproar. Although science is abused by people everywhere in the political spectrum, it is rare for such a direct attack to occur. Taken together with the fact that every single thing listed in the song was some bit of science that is normally explained before people are in 9th grade, the reaction was predictable and humorous. They included Learn Your Motherf#@kin’ Science: A Textbook for Juggalos(amusing but for the fact that they explain rainbows incorrectly) and Rebecca Watson's imagining of how the song lyrics were devised.

This could have ended there. But Insane Clown Posse managed to dig themselves in into an even deeper hole. In one interview, the interviewer asked them if they knew yet how magnets worked and they replied that they were proud that they did not. They also wrote an official response to criticism of the song in which they made it clear that not only don't like learning but "We feel like these haters are the big dumb, popular jocks ganging up on the little class clown scrub." It isn't clear to me in what universe Insane Clown Posse operates if they think that the people who like science were the "big dumb, popular jocks." I'm also a bit confused by the notion that the people who know things like how a rainbow works are "dumb" but it may just be that I'm too stupid to understand. Similarly, it may be due to my stupidity that I'm wondering how they would be sure to put a comma between "dumb" and "popular" but not between "big" and "dumb." Is big actually an adverb modifying dumb? Is "big dumb" some sort of compound adjective? If only scientists were popular; I suspect that such a world would be a much better place.

This could have ended there but then Insane Clown Posse made another mistake: They had a concert in San Francisco, a city full of nerds. Noisebridge, a volunteer group devoted to science education around San Francisco decided to use the Posse's visit to their fair city as an opportunity to educate the Juggalos. They made a series of posters explaining how various things work, with titles like "Fuckin' butterflies, how do they work?" They then dressed up with Juggalo-style clown facepaint as well as labcoats, and went to the concert. They videotaped the result:

As you can see in the video, the Insane Clown Posse roadcrew had seen the Noisebridge website in advance where they had planned the event. Apparently, the Insane Clown Posse was not happy with these scientists, forced them to leave, and tried to take away their video camera. Now, one might think that this was just the work of an overzealous roadcrew claiming to have authority from the people in charge, but there's the not so tiny detail that one of the Insane Clown Posse members bragged on his Twitter account that they "ran those scientist haters off." I wish I were making that up. If I had seen the phrase "scientist haters" in any other context I would have guessed that it meant people who hate scientists. What we have here are people who are so proud of their ignorance that they actually interfere with other people engaging in a humorous attempt to educate.

Now, what could possibly make this situation worse? If you guessed "Insane Clown Posse claims to be religious" then you win a gold star. The exact nature of the band's religious status is not clear. Although songs include lyrics about murder, cannibalism, and necrophilia, the individuals who commit these actions always suffer at the end. They have a series of songs centering around a Carnival which punishes people, and the last such song contains the lyrics "Truth is we follow GOD, we’ve always been behind Him. The carnival is God and may all juggalos find him! He’s out there!” And did I mention they hate gays? So the Insane Clown Posse apparently, hates science, hates gays, and believes in a deity whose chief job is to punish people. If you're wondering if they self-identify as Christian then you win another gold star.

Still, the level of anti-science attitudes here is shocking. It resembles nothing more than a caricature of what is wrong with contemporary Christianity. I don't think that band's Christianity has anything deeply to do with their anti-science attitude. For example, they haven't come out strongly against evolution. The correlation in this case is to some extent probably incidental. But there is a real lesson here and it is contained in their strange idea that scientists are the "big, dumb jocks." That idea is very divorced from reality. How can someone be so wrong about the world around them? Let me suggest that it is because science is the best method we have of finding out about the nature of reality. It isn't the only one, but it is the most reliable and the one that has given us the most fruit. So, when you take an attitude that is so anti-science and against the minimal knowledge of how basic genetics works, or any of a hundred other subjects, you are going to not have good methods for telling whether your beliefs about reality map accurately to reality. And the more effort you make to deny science, the further divorced from reality you will become, to the point where you believe the nerdy guys who work in the labs and like to understand how things work are actually "big dumb, popular jocks."

Israel and The Flotilla to Gaza: Another Excuse to Promote Family Members

2010-06-08T14:07:00.001-07:00

My father has a piece up at the Oxford University Press blog arguing that Israel was justified in its actions regarding the flotilla to Gaza. I'm not convinced by the argument. The situation seems complicated especially in that it is not clear that all the items that Israel is not letting are items that could be used to make weapons. The Israeli blockade has stopped hostilities, but it goes beyond that, effectively preventing the maintenance and rebuilding of Gaza's sewage treatment and power plants (See this summary). If the blockade was narrowly tailored to save Israeli lives it would be more morally defensible.

It seems that given the large amount of shouting about this issue, that this is not a bad opportunity to discuss some unambiguous facts about the current situation.

First, it is clear that the blockade has worked to protect Israeli lives. Rocket attacks from Gaza have become nearly non-existent after the blockade.

Second, it is clear that the motivation for the blockade is not primarily out of racial animosity for the Palestinians, although that may play some part. The evidence for this is that the West Bank, controlled by the moderate Fatah faction, is not under any similar restrictions.

Third, it is not clear, and likely will not become clear for the foreseeable future, who started the fighting on the Mavi Mamara. Eyewitness accounts are conflicting. Note that who started the fighting also has zero connection to whether or not the blockade is morally or legally justifiable.

Fourth, Hamas is refusing to accept the flotilla aid until demands are met. If one believes that this aid is vital, then this is a clear example of Hamas willing to let the people of Gaza suffer to suit its own political aims. However, it is important to keep in mind that this despicable behavior by Hamas is also not relevant to whether the blockade is morally or legally justifiable.

In any event, my father's piece makes a pretty strong argument, so go and read.

A Quick Note on the Mojave Cross

2010-05-12T14:33:00.001-07:00

Last entry, I talked about the Supreme Court of the United States ruling about the cross in the Mojave desert. The ruling was wrong-headed and I am highly worried about the broader implications of allowing the cross to stand. However, at the moment I'm more worried by recent news that the cross was just stolen. This is not a solution. There are situations where violations of rights are so severe as to merit breaking the law to preserve them. This is unambiguously not one of those situations. Whoever did this should be ashamed of themselves.

A Short Rant on Religious Freedom and the Courts

2010-04-28T19:32:00.000-07:00

Two recent events make it all the more clear that religious liberty for all is in jeopardy. Recent events show that even in civilized, Western countries, basic religious freedom, whether for believers, agnostics or atheists hangs by a series of thin threads. Great Britain and the United States provide the two most recent examples.

The United States Supreme Court ruled 5-4 that game playing with transfers of small plots of land allow the federal government to endorse specific religions. Readers are likely familiar with the ongoing case of the war memorial cross in the Mojave desert. The federal government attempted to transfer the land just surrounding the cross to a private veterans group to prevent any issues with the establishment clause. The court decided not just that this game playing was acceptable but that it probably wasn't even necessary. Justice Kennedy wrote:

A Latin cross is not merely a reaffirmation of Christian beliefs. Here, a Latin cross in the desert evokes far more than religion. It evokes thousands of small crosses in foreign fields marking the graves of Americans who fell in battles, battles whose tragedies are compounded if the fallen are forgotten.

Because of course, the fact that fallen soldiers of other religions are buried with other symbols is of course besides the point. And the fact that the commonality of the cross is solely because the US is a majority Christian nation is besides the point. And the fact that some (small) Christian groups are actually uncomfortable with the cross as a religious symbol is also besides the point.

But not to worry, since while the US Supreme Court is busy whittling away at basic separation and church and state, the British are busy destroying the rights of people to say things which offend religion. Apparently leaving anti-religious tracts around in the wrong places in England can get you convicted. After leaving anti-religious tracts in an airport prayer room, Harold Taylor received a six-month suspended sentence and is now not allowed to carry anti-religious leaflets in public. As far as I can tell, the tracts left by Taylor were deeply unfunny cartoons that wouldn't have convinced anyone of anything. Taylor probably needs a few lessons in how to be funny and not just annoying(Jennifer McCreight could likely teach him a thing or two). But that shouldn't be a criminal offense either. At least Taylor's situation would still be unambiguously unacceptable in the United States.

These events highlight how important it is that Obama's next Supreme Court nominee be a strong supporter of free speech. Unfortunately, his previous nominee, Sotomayor, has a mixed record on such issues. Let's hope the next one is better.

On the Coming Singularity

2010-04-19T18:07:00.000-07:00

Much has been said in the last few years about an approaching technological Singularity, beyond which humans or humans' descendants will be so far beyond anything we understand today that comparisons would be meaningless. I do not believe that the Singularity is imminent.

What do people mean when they speak of the Singularity? There are a variety of such notions, but most versions of the Singularity focus on self-improving artificial intelligences. The central idea is that humans will not only construct functioning artificial intelligences, but that such AIs will be smarter than humans. Given such entities, technological progress will increase rapidly as the AIs make discoveries and inventions that humans would not. This effect will be self-reinforcing as each successive improvement makes the AIs smarter. There are variations of this idea: Other Singularity proponents, generally described as Transhumanists emphasize genetic engineering of humans or emphasize direct interfaces between the human brain and computers. I am skeptical of a Singularity occurring in the near future.

Certainly Singularitarism is seductive. Variations of it make for great science fiction (Charlie Stross' Eschaton is an excellent example) and some version of the Singularity, especially those that involve humans being downloaded into immortal computers or the like, are appealing. Singularitarism may sometimes border on a religion, but it has the virtue of a minimally plausible eschatology, one that doesn't require the intervention of tribal deities, just optimistic estimates for technological and scientific progress. And to be sure, there are some very smart people such as Eliezer Yudkowsky who take the Singularity very seriously.

The most common criticism of Singularitarism is that we will not develop effective AIs. This argument is unpersuasive. There's no intrinsic physical law against developing AIs; we are making slow but steady progress; and we know that intelligences are already possible under the laws of the universe.We're an example.

While I reject most of the common criticisms of a coming Singularity, I am nevertheless skeptical of the idea for two reasons. First, while human understanding of science and technology has been improving over the last few hundred years, the level of resources it takes today to produce the same increase in understanding has increased dramatically. For example, in the mid 19th century a few scientists could work out major theories about nature, such as the basics of evolution and electromagnetism. Now, however, most major scientific fields have thousands of people working in them, and yet the progress is slow and incremental. There seems to be a meta-pattern that as we learn more we require correspondingly more resources to make corresponding levels of progress. Thus, even if we develop smart AIs, they may not lead to sudden technological progress.

Second, we may simply be close to optimizing our understanding of the laws of physics for technological purposes. Many of the technologies we hope to develop may be intrinsically impractical or outright impossible. There may be no room-temperature superconductors. There may be no way to make a practical fusion reactor. As Matt Springer suggested (here and here), we might activate our supersmart AI, and then it may say "You guys seem to have thought things through pretty well. I don't have much to add." This seems to be a common problem with Singularity proponents. It is a common argument by Singularitarians that essentially all challenges can be solved by sufficient intelligence. I've personally seen this argument made multiple times by Singularitarians discussing faster-than-light travel. But if it isn't allowed by the laws of physics than there's nothing we can do. If in a chess game white can force a checkmate in 3 moves, it doesn't matter how smart black is. They'll still lose. No matter how smart we are, if the laws of physics don’t allow something then we won’t be able to do that thing, any more than black will be able to prevent a checkmate by white.

There's a third problem with Singularitarism beyond issues of plausibility: It doesn't tell us what to do today. Even if no one had ever come with the Singularity, we'd still be investigating AI, brain-computer interfaces, and genetic engineering. They are all interesting technologies with potentially have major applications to help us answer fundamental questions about human nature. So in that regard, the Singularity as a concept is unhelpful: It might happen. It might not happen. But it tells us very little about what we should do now.

Newest Skeptics Circle

2010-03-25T08:54:00.000-07:00

Over at the Digital Cuttlefish there's a new Skeptics Circle up. It has a lot of good posts. You can tell that it is worth reading because it includes my recent post here on skepticism and the scientific method. So go check it out.

Hank Skinner: What You Can Do.

2010-03-17T13:22:00.000-07:00

In an earlier post I briefly discussed the case of Hank Skinner. Skinner is scheduled to be executed in Texas for a murder. It is very likely that Skinner is innocent. For a decade now, Texas has systematically blocked every attempt by Skinner to get DNA testing that could prove his innocence. But there is something you can do. The Innocence Project is trying to get permission for DNA testing. Right now, they need a stay on Skinner's imminent execution. So go send a note to Governor Rick Perry. It only takes a minute and every response helps. I know that I have some readers in Texas. It is important for everyone to contact the governor but if you are a Texas voter it is particularly important. Your voice matters. Don't be silent. We have enough innocent blood on our hands already.

Hat-tip to Katherine for pointing out this petition.

Edit: The Supreme Court has issued a stay on Skinner's execution. However, this may not lead anywhere so this petition could still be relevant.

The Skeptical Movement, Science and Naïve Popperism

2010-03-11T17:23:00.000-08:00

Members of the modern skeptical movement frequently emphasize their use of the scientific method. Moreover, when discussing the scientific method and whether a given claim is scientific, members of the skeptical movement frequently emphasize falsifiability and experimentation. Both of these tendencies are problematic.

The organized skeptical movement has done a very good job over the last 30 years promoting skepticism and critical thinking. The movement has helped people understand the deep problems with many superstitions and pseudosciences. However, the skeptical movement’s characterizations both of how the movement functions in regard to science and how science functions are inaccurate. Moreover, the movement tends to exaggerate the degree to which falsifiability matters in science.

Let us first examine the claim that the skeptical movement uses the scientific method. No matter how one characterizes science and the scientific method, a central part of the method is experimentation and observation. However, the vast majority of skeptics will not engage in direct experimentation or observation of data nor in fact should they. For example, in an earlier blog post, I discussed why claims of ghostly interference with electronics were extremely implausible. I didn’t need to engage in any experiments to reach that conclusion. I and the commentators in the thread discussed the matter based on what we reliably knew about the universe (especially how electronics work) and then made logical conclusions based on those results. No part of that process required any use of the scientific method.

If we wanted to investigate the claim in more detail, we might try to do actual experiments. But I can dismiss the claim of ghostly interference with electronics with a high degree of probability without experiments. Similarly, I can dismiss homeopathy without doing experiments or without such experiments having been done by anyone since the theory of homeopathy contradicts basic understanding of how the universe functions. The vast majority of skeptics will never actually use the scientific method, but rather rely on small bits of science and a lot of critical thinking. That’s fine. The movement is doing good work that way. But we need not pretend when talking to people that we’re engaging in science when we aren’t. This is all the more a concern because the emphasis on science distracts from the most important part of skepticism- careful critical thinking.

Skeptics often characterize science poorly. Skeptics frequently emphasize the need for claims to be falsifiable in order for them to be scientific. The philosopher Karl Popper first proposed that the demarcation between science and non-science is falsifiability- the ability to falsify a claim. Thus, in a classical Popperian framework, claiming that there is an invisible, intangible dragon living in my bathroom is not scientific because the claim is not falsifiable.

However, naïve Popperism is not a good description of science as a whole. While falsifiability is a useful approximation of what is often scientific, there are many problems with it as a description of all forms of science. For example, as pointed out by Quine, people can add defensive hypotheses to defend an underlying hypothesis; it is far from clear when such defensive hypotheses are acceptable and when they are not. In Quine’s formulation, a defensive hypothesis is a hypothesis that is added to prevent the falsification of another hypothesis. Thus, for example, to return to the case of an invisible dragon in my bathroom, you could try to test for its presence by searching on spectra other than visible light (such as looking at infrared light). When no evidence is found using that method, I might add the defensive hypothesis that the dragon also doesn’t interact with infrared light. As I add more and more hypotheses to counter each experiment, I prevent my claim from being falsified, but, at any given point, the claim that a dragon is in my bathroom remains falsifiable – in theory at least. In portraying a scientific method which relies completely on falsifiability the skeptical movement ignores issues such as those raised by defensive hypotheses.

Unfortunately, the situation becomes even more complicated because sometimes one can add defensive hypotheses and still do good science. For example, consider the history of our understanding of the solar system. In the early 1600s, astronomers adopted Kepler’s model of the solar system in which planets orbit around the sun in ellipses. Subsequently this model was refined further by Newton whose mechanics gave orbits nearly identical to those of Kepler but slightly more accurate (essentially if there is a single planet around a star then Newtonian mechanics predicts an orbit that is a perfect ellipse. But in fact, gravitational attraction between planets makes the orbits slightly non-elliptical). However, with this very accurate, very precise model, new issues arose. The orbit of the planet Uranus seemed to be slightly off from what it should be. Thus, Alexis Bouvard posited the existence of an as yet unobserved planet, which later became discovered and named Neptune. Bouvard’s hypothetical planet was a defensive hypothesis built to defend the more cherished hypothesis of Newtonian mechanics against being falsified by experimental data. Bouvard’s defensive hypothesis was good science; the defensive hypotheses about my dragon are not. It is not clear how one can easily distinguish between the good defensive hypotheses and the bad ones.

So how do we determine when defensive hypotheses are acceptable and when they are not? Imre Lakatos suggested that we should look to whether a hypotheses is fruitful: hypotheses that lead to interesting predictions and new questions are fruitful; hypotheses that required unproductive defensive hypotheses should be rejected. While I am partial to Lakatos’s viewpoint, such an approach renders the line between science and non-science inherently subjective.

In addition to the problem of defensive hypotheses, there are many other problems with a falsifiability as the sole line between science and non-science. Naïve Popperism is insufficient to describe the borders of science. Skeptics need both a clearer understanding of the scientific method and a clearer understanding of how the skeptical approach relies on science

Jack Chick and Consistent Theology

2010-03-03T15:34:00.000-08:00

Two new Jack Chick tracts are up. They are both pretty mediocre. "The Royal Affair" tells the story of David and Bathsheba with a pretty standard threat of hellfire and brimstone at the end. There's nothing of note in the tract other than that Jack Chick apparently thinks that the word "literal" actually means "figurative." (Memo to Jack: David didn't go through a "literal hell." He went through a figurative hell. Figurative and literal have opposite meanings. They are not synonyms.)

The second tract, "Going Down?" is standard Chick tract but with a single interesting twist. It is not uncommon in Chick tracts for someone to have a near-death experience, briefly witness the horrors of hell, and then come back to life knowing about the terrible threat of hell. This tract is an example. However, whenever this happens in a Chick tract, the people who have experienced hell always then accept Jesus as their personal lord and savior. However, in this new tract, the person who experiences hell does not learn about Jesus but rather dies shortly thereafter being dragged back down to hell. Few tracts better illustrate the utterly random nature of the afterlife in Chick's universe: in this case, the return to this world appears to almost be a divine accounting error which doesn't even serve the minimal purpose of saving the individual's soul.

Contemplating this tract also leads to another issue: Chick's theology concerning the immediate afterlife is inconsistent. In most Chick tracts, when people die they stand before Jesus and are judged. In some tracts, such as the above, they are sent immediately to hell. I am aware of no tract in which someone dies and comes before Jesus only to come back to life. In a tiny minority of tracts (such as this one) people who die without Jesus instead go to a temporary realm to wait until they are judged on Doomsday.

Why is Chick's theology of the afterlife so varied? Does he realize how contradictory his various tracts are on this matter? The most obvious hypothesis is that Chick's theology has changed over time. However, there are no chronological trends in which of the three approaches to the afterlife he takes. I suspect that Chick simply does not care about the details of the afterlife that much since the primary issue is being saved or lost; all else is secondary. Thus, a combination of whim and plot-demands control the exact depiction of the afterlife. Given Chick's apparent lack of great intellectualism he may not even have given the matter enough thought to realize the inconsistent nature of his theology.

I do hope that the May tracts are better than this set. It is a big let down given that in January we had a tract about angels fighting werewolves.

Purim and Don't Ask Don't Tell

2010-02-28T16:09:00.000-08:00

Today is Purim, the Jewish holiday which celebrates the events recounted in the Book of Esther in which Esther and Mordechai stop Haman's plans to destroy the Jews. The story of the Book of Esther is one of hidden identity and palace intrigue.

My twin has a piece up at the Huffington Post that looks at the story of Purim in the context of the Don't Ask Don't Tell. Aaron argues that the story of Esther, in which she hides her Jewish identity from the king until she is forced to reveal it to save her people, bears a similarity to the military’s current policy regarding gays. In particular, Esther hid her ethnic/religious identity and the king did not inquire about that identity until events required Esther to disclose the truth. Aaron argues that this ancient tale reflects a basic truth about policies like Don't Ask Don't Tell: they are inherently unstable.

I am not impressed by the piece. The claim that DADT is inherently unstable is not novel: I don't think that anyone, whether they are for or against gays in the military, thought that DADT had any long-term stability. Policies in which an identity is acceptable only as long as it is not blatant are by nature unstable since such policies generally arise when certain groups are discriminated against, but the discrimination is not universally accepted and therefore must be discreet. To continue to use Jews as an example, the quotas on Jewish student admissions to Ivy League schools prior to the 1960s worked in a fashion similar to DADT. Applicants who were obviously Jewish were covered by the quotas. But little effort was made to actively determine the identity of general applicants. (This is to some extent an oversimplification. Dan Oren's excellent book "Joining the Club" discusses this in more detail). This ambivalence was in part due to the fact that Jews were accepted enough that a serious backlash was feared from excessive enforcement of the anti-Jewish quotas. Similarly, DADT in the military came as a compromise when both gay rights groups and anti-gay groups had political power. Such a compromise is inherently unstable.

Aaron also does not address the fact it is not clear from the text why Esther kept her Jewish identity secret from the king. Aaron cites the traditional commentaries which weave elaborate stories of Esther keeping the various classical prohibitions of Judaism such as kashrut and Sabbath observance. Some of the classical commentaries say that Esther kept her Jewish identity hidden because of Persian attitudes towards the Jews. Others invoke other explanations. For example, according to some commentators, Esther kept her identity hidden because of her relation to the line of Saul, the first king of Israel. If it became known that she was of royal blood, her political position would have become much more complicated. Given the ahistorical nature of the story of Esther, it seems to me that the likely reason for her keeping her Jewish identity hidden is primarily to make an interesting story.

My twin correctly notes that there are good reasons to abolish DADT and allow gays to serve openly in the military. However, those reasons exist without any analogies to Biblical texts. We can make the correct decisions without recourse to ancient texts whether we see those texts as religious or literary in nature. DADT is bad policy. We don’t need the story of Esther and Mordechai to tell us that.

Two Quick Notes on Civil Rights

2010-02-24T10:02:00.000-08:00

Unfortunately, I'm very busy this week and so haven't had much time to blog. Therefore I would like to quickly bring up two civil rights issues. First, Texas, the state known for executing people who were almost certainly innocent like Cameron Todd Willingham , is now set to execute another innocent man. Hank Skinner is set to be executed. The evidence against Skinner was based primarily on eye-witness testimony from a single witness who has since recanted. There are many other details about the case (such as the government's refusal to let Skinner have a DNA test) that make the situation appalling. Texas is going to execute an innocent man.

In the other news of appalling civil rights issues, we have an amazing act of censorship by Italy. An Italian judge has convicted three Google executives for violating Italian privacy laws. The crime apparently was running Youtube. in 2006, a group of youths uploaded to Youtube a video of them harassing and assaulting an autistic child. That's pretty despicable. And when Youtube received a legal complaint, they took the video down and cooperated with the Italian police in locating the children who made the video. Apparently, that is not enough. Any video which violates Italian privacy laws is now the fault of Google and Google employees can suffer both civil and criminal fines. Google has correctly outlined that this is a serious threat to free speech around the globe. This is all the more a problem because many civilized countries have extradition treaties with Italy. Considering the Italy is the same country which tried to require anyone in Italy uploading videos or writing blogs to register with the government, it seems pretty apparent that this is another example of Berlusconi and his corrupt media cronies trying to do their hardest to screw over media not under their control. Hopefully, either higher-level Italian courts will overrule this decision or the EU will step in.

Dick Cheney Undefeated

2010-02-21T11:54:00.000-08:00

My twin has a piece up at the Huffington Post arguing that Dick Cheney's recent outspokenness is due in part to Cheney's unique political position as an undefeated Vice-President. Cheney is the first VP in a long time who did not end his political path in an electoral defeat. Aaron argues that this, combined with other historical factors, puts Cheney in a unique position where it is socially acceptable for him to be loudly critical of the current President. The piece is interesting although I think he doesn't address one reason why there is attention given to Cheney: The Republicans have no natural leader at this point and Cheney is one of the few people who potentially could fit in that position. In any event, the piece is worth reading and provides some interesting historic tidbits about prior VPs.

Orthodox Jews, Vaccination, and Mumps

2010-02-16T18:44:00.000-08:00

I've discussed anti-science attitudes among Orthodox Jews in previous blog posts. I've also discussed how this has resulted in low vaccination rates among Orthodox, especially charedi, Jews. Now we are seeing the consequences. Over the last three weeks, a mini-epidemic of mumps has broken out in New York among the Orthodox population. The first cases started appearing this summer in Williamsburg, but there are now over 1500 cases and the epidemic has made inroads into the general non-Orthodox population. Apparently while a majority of the Orthodox Jews are vaccinated, the level of vaccination was reduced enough that herd immunity no longer applied. Quoting from the LA Times:

Mumps is marked by a swelling of the salivary glands, giving the victim a characteristic chipmunk-like appearance. Most victims have fever and headache, and a few suffer from hearing loss, meningitis and swollen testicles that can lead to infertility. It was once a common disease in the U.S., with an average of 186,000 cases per year before the mumps vaccine, now included in the mumps-measles-rubella, or MMR, vaccine was introduced in 1967. The mumps part of MMR is thought to be the least effective of the three vaccines, with 73% to 91% of those vaccinated obtaining proteciton after one dose and 79% to 95% after two doses.

Patient zero in the current outbreak was an 11-year-old boy who returned from England on June 17. Mumps has become more common in that country recently because of the substantial number of parents who refuse to let their children receive the MMR under the misguided belief that the vaccine can cause autism. About 7,400 cases of mumps were reported in Britain last year.
Orthodox Jews have accounted for more than 97% of cases, and the majority -- 61% - -are among 7- to 18-years-old. More than three-quarters of the patients are male. Among those for whom vaccination status is known, 88% had received one dose of MMR and 75% had received two doses.

The threat of sterility needs to be especially emphasized. In Orthodox Judaism, there are few things more important than having children. Mumps can induce infertility in both males and females. It is not at all unlikely that children who have gone through this epidemic will have trouble finding marriage prospects. Thus, the failure to vaccinate has produced what may become terrible, long-term problems for many children for the rest of their lives. The Orthodox unwillingness to vaccinate has become a self-inflicted wound. In this case, anti-science attitudes were far from harmless and the results may yet grow to more seriously threaten both the Orthodox population and other people as well. Failure to vaccinate children creates serious risk to your children and the people around your children. Vaccinate. For some of these children, it is already too late. They will bear the physical and social scars of their parents' decisions.

Math Anxiety, Math Education and Gender Expectations

2010-02-13T16:03:00.000-08:00

A recent study has shown that young girls in the United States who are taught by teachers with math anxiety are more likely themselves to develop anxiety of about math. The study is by psychologist Sian Beilock et al. at the University of Chicago. Her research looked at second graders’ anxiety levels in mathematics. She found that, with her sample, there was no correlation between gender and attitude towards math at the beginning of the school year. However, by the end of the school year, girls were much more likely to develop math anxiety. Moreover, girls were much more likely to develop such anxiety if their female teachers had math anxiety. Rather than summarize all of the more interesting details in the study, what follows first is a large quote from the study followed by my comments:

If it is simply the case that highly math-anxious teachers are worse math teachers, one would expect to see a relation between teacher anxiety and the math achievement of both boys and girls. Instead, teachers with high math anxiety seem to be specifically affecting girls’ math achievement—and doing so by influencing girls’ gender-related beliefs about who is good at math.

This study explores the relation between female teachers’ math anxieties and their students’ math achievement. Thus, it is an open question as to whether there would be a relation between teacher math anxiety and student math achievement if we had focused on male instead of female teachers. In one sense, the lack of male elementary school teachers in the United States makes this a hard question to answer. Yet, it is an important question, given research suggesting that girls are more socially sensitive than boys in early elementary school (16). Thus, it is possible that even with male teachers, a relation between teacher anxiety and female student achievement might occur. Nevertheless, the literature on math anxiety, gender modeling, and the impact of negative stereotypes on achievement lead us to speculate that any relation between male teacher anxiety and girls’ math achievement would be obtained through a different route than the one proposed here. Moreover, in the current work, the relation between female teachers’ math anxieties and girls’ math achievement was mediated (or accounted for) by girls’ beliefs that boys are better at math. Hence, it seems unlikely that a male teacher’s math anxiety would affect girls’ math achievement by pushing girls to confirm that boys are good at math.

In addition, children do not blindly imitate adults of the same gender. Instead, they model behaviors they believe to be gendertypical and appropriate (9). Thus, it may be that first- and secondgrade girls are more likely to be influenced by their teachers’ anxieties than their male classmates, because most early elementary school teachers are female and the high levels of math anxiety in this teacher population confirm a societal stereotype about girls’ math ability (2). This match between teacher math anxiety and societal norms would not hold for male teachers exhibiting math anxiety. However, if such a correspondence is important in influencing student achievement, we would expect that for school subjects for which girls are stereotyped to excel (e.g., language arts), male teachers’ anxieties would have an impact on male more than female students’ achievement.

It is important to note that the effects reported in the current work, although significant, are small. There are likely many influences on girls’ math achievement and gender ability beliefs overand above their current teachers’ anxieties. For instance, previous teachers, parents, peers, and siblings who either do or do notmodel traditional academic gender roles may play an important part in shaping girls’ gender ability beliefs and their math achievement more generally. Exploring these relationships—in addition to the influence of both male and female teachers—will help to elucidate the full range of social influences on student achievement.

In conclusion, we show that female teachers’ math anxiety has consequences for the math achievement of girls in early elementary school grades. Given that this relation is mediated by girls’ gender ability beliefs, we speculate that female teachers model commonly held gender stereotypes to their female students through their math anxieties. These findings open a window into gender differences in math achievement and attitudes that emerge over the course of schooling.

Interestingly, math anxiety can be reduced through math training and education (17 –19). This suggests that the minimal mathematics requirements for obtaining an elementary education degree at most US universities need to be rethought. If the next generation of teachers—especially elementary school teachers—is going to teach their students effectively, more care needs to be taken to develop both strong math skills and positive math attitudes in these educators.

How should we respond to this study? As with all initial scientific studies, the data is by its nature tentative, but in this case it looks very robust.Consequently I will for the remainder of this post assume that the phenomenon as described in Beilock et al. is accurate.

We currently focus most of our resources aimed at getting young women to be confident in math at the middle school and high school level. Moreover, prominent celebrities who have tried to deal with this problem have focused almost exclusively on this older age cohort. Danica McKellar for example has focused on encouraging mathematical confidence and learning in middle school girls. This new study suggests that much of the damage done to girls’ mathematical confidence occurs at a very young age. Thus, we may need to rethink where resources are being allocated. Unfortunately, this study does not as of yet include any long-term follow-up. So how much of this early math anxiety is correctable later is not clear. Aside from this sort of vague generality about resource allocation, here are four concrete proposals that need discussion.

First, let’s get the most controversial possibility out of the way: We may want to consider more direct encouragement of males to engage in elementary school teaching. Put less politely, we should consider affirmative action and other incentives to encourage males to go into elementary school teaching, at least for math. While this study showed that young girls picked up on the math anxiety of their female teachers, it is clear that young males did not gain math anxiety from female teachers. Moreover, math anxiety is simply less common among males. Thus, male students will be unlikely to pick up math anxiety, and female students will not pick it up from male teachers until they are older. This proposal has a number of problems. Foremost among them is that it assumes that male teachers will not act in an overly sexist fashion, either explicitly or implicitly denigrating female mathematical ability. Unfortunately, it is clear from anecdotal evidence that many teachers of both genders do explicitly disparage young girls’ mathematical ability. See for example this thread at SkepChick . Moreover, the exact impact of male teachers is far from clear: The study looked only at female teachers. Without more data about how students of both genders interact with male teachers both with and without math anxiety, this proposal must by nature be extremely tentative. The argument can be made that this will send a bad message to young children, i.e., that only males can teach or do math. However, that’s erroneous. Currently, around 90% of elementary school teachers are female. If we replace the females with math anxiety with males without math anxiety or even males with mild math anxiety, the fraction of teachers who are male will still be well below half. So this step also helps correct for a pre-existing gender disparity in elementary sc hool teaching.

Second, and almost as controversial as the first proposal, we can encourage teachers, especially females, to not go into elementary school teaching if they have math anxiety or simply aren’t very good at math. Unfortunately, we already suffer serious problems in the United States getting qualified people to teach elementary school. So directly altering who we encourage to become teachers is non-optimal. Similarly, increasing the required level of math background for elementary school teachers is not a good response. Moreover, as Beilock discusses, proper education can remove or reduce math anxiety. This leads directly to the third possible response.

Third, we must take more steps to directly reduce math anxiety in teachers and people planning on becoming teachers. This should likely focus on female teachers or teacher-candidates who have shown to have serious math anxiety issues. We can introduce them to additional areas of math, where the math is easy to understand and fun. Very elementary number theory and graph theory may be relevant areas. More broadly, we can also have them play mathematical games that get them more comfortable with the idea that math can be fun. Zendo for example would be an excellent potential confidence builder.

Fourth, we can take direct steps to expose young females to mathematically confident females. One method of doing so is to have the math sections of elementary education taught by separate teachers who are more mathematically confident. Even in schools with high percentages of teachers with math anxiety, some teachers will still likely be mathematically confident. Having those teachers handle the math teaching for other teachers (or possibly specializing to only teach math) is an option. Also, we can encourage young girls by having them directly interact with female mathematicians. Part of the problem is that mathematically confident females generally go into industry, sciences or upper tiers of academia, not elementary school teaching. So, mathematicians and scientists should visit local elementary schools. If schools can regularly sponsor visits by firefighters, police officers and members of other vocations and professions, there’s no reason that mathematicians and scientists can’t do the same thing. It doesn’t take much to show up and say “Hey! Look! I’m a lady who does math. And I enjoy it!”

Fortunately, resources which are spent encouraging the general public and children of all ages to be more mathematically confident can potentially work in general to help the situation with female students. Thus, work like Steven Strogatz’s new regular column in the New York Times to help make math more accessible to the general audience can be helpful.
No matter what happens we need to look at this data dispassionately at the same time as we try to gather more information about the transmittable nature of math anxiety. As a society we are short-changing many bright young females. Because those students then do not go into math-intensive areas of study,the society suffers. These problems need to be addressed. We are not doing enough now to address them.

Barack Obama, The US Senate, LBJ, and Gratuitous Promotion of Family Members

2010-02-13T15:54:00.000-08:00

My twin has a piece up at the Huffington Post arguing that Obama should take a lessons from Lyndon Johnson in how to work with the Senate. The central thesis is that Obama needs to take four lessons from Johnson. I'm not convinced that Aaron is completely correct here. I found his earlier piece arguing that the Democrats should force the Republicans to engage in genuine filibusters to be more persuasive. Both pieces are worth reading. At this point, it seems apparent that many Republican senators have zero interest in actually running a government and are genuinely trying to just be as obstructionist as possible. Richard Shelby's attempt to put a hold on every single Obama nominee seems to be the logical conclusion of the current Republican behavior. Both of Aaron's pieces are worth reading, but at this point, I suspect that Obama's best course of action at this point may be to try to get the public to understand how little cooperation he is getting from both House and Senate Republicans.

A Quick Note on a Silly, Pseudo-recursive Class of Functions

2010-01-30T17:32:00.000-08:00

Let f(n) be a function from the natural numbers from the natural numbers. Suppose further that f(1)=1, and assume that f(n) is equal to the number of positive integers k that are less than equal to n and satisfy f(k) | k. Then it is not hard to show that in fact f(n)=n. Now suppose we instead look at the exact same thing, but insist that f(n) count the number of k that are at most n and satisfy f(k)|P(k) where P is some fixed polynomial with integer coefficients.

For some choices of P, we do not have any function f which would satisfy the desired recursion. For example, if P(x)=x+1 we don't have any function f satisfying the recursion. To see this, note that we have either f(2)=1 or f(2)=2. If f(2)=1, then f(1)|1, and f(2)|2, so in fact f(2)=2. Consider the other case where f(2)=2. If so, since 2 does not divide 3, we must have f(2)=1. Contradiction and nd of p.

Here's my question which I have not been able to make substantial progress on: Are there any valid choices of P and f that satisfy the recursion and don't have f(n)=n for all n?

Thoughts and links after the recent Massachusetts election

2010-01-20T09:52:00.000-08:00

First, I have to say that a lot of liberals seem upset over Coakley's loss to Brown. Frankly, given Coakley's poor record on civil liberties (including her despicable behavior handling the Amirault situation) I can't find myself getting worked out over the matter. Two pieces I recommend on the matter: My twin has a piece at the Huffington Post talking about lessons the Democrats should take away from this election. Ed Brayton has a piece up talking about what this says about Coakley and the Democrats chances for their legislative agenda. Brayton makes the point that the Democrats still have strong majorities in both the House and Senate. So if they can't push through their agenda then it is hard to explain it as anything other than general incompetence.

A Different Take on Ireland's New Blasphemy Law

2010-01-16T15:50:00.001-08:00

Readers are likely aware that Ireland has a new anti-blasphemy law. The response to the law has been understandably negative. It is hard to reconcile outlawing of blasphemy and modern notions of free speech. The law has been met with mockery and derision. See for example here and here. However, Whiskey Fire has an interesting piece up arguing that the law makes much more sense in context. In particular, an anti-blasphemy law is required by the Irish Constitution. The new blasphemy law helps actually minimize the chance that blasphemy prosecutions will occur since the large fines mandated by the law force any blasphemy prosecutions have to occur under the Irish High Court rather than the circuit courts. This effectively prevents local yahoos from filing blasphemy charges. Whiskey Fire's entire piece is very worth reading and is a good example of how political situations can often be more complicated than they first appear.

Hat tip to Almost Diamonds.

Jack Chick, Native Americans and Henotheism

2010-01-12T13:25:00.001-08:00

Everyone's favorite Christian fundamentalist tract writer, Jack Chick, has a new tract, Crazy Wolf. This tract is apparently aimed at Native Americans and attempts to show how their traditional religious beliefs are really demon worship.

The tract starts with two stereotypical Native Americans talking about how one of their own, Mary, has accepted the "White God" and how they are unhappy with her. One of them, Margaret, is particularly unhappy because Mary tried to evangelize to Margaret's young daughter Sarah. I guess Jack Chick can't quite understand why someone might be justifiably upset if someone tried to interfere with one's kids’ religious upbringings.

Margaret then discusses how they tried to get a medicine man to put a curse on Mary, but "some strange power" prevented the medicine man's curse from working. So, they decided to ask the assistance of a powerful witch named Crazy Wolf.

Notice that every individual so far in this tract has an English name except for the old, evil witch. I guess it's just a sign of how baddass he is that he as stereotypic name, or something like that. At least his name isn't "Injun Joe."

Of course, Crazy Wolf tries to use his Devil-granted powers to shapechange into a massive wolf to eat Mary. He fails because of Mary and her pastor's prayers. An angel materializes which beats up Crazy Wolf. Mary then further prays that Crazy Wolf will accept Jesus as his personal lord and savior.

We all know this part of the routine: Injun Joe, sorry, Crazy Wolf, talks to Mary and accepts Jesus as his personal lord and savior. Crazy Wolf declares that "my real name is Billie Wolf." Apparently, he has a good name, but it only gets used once he's saved. Then, as happens in so many Jack Chick tracts, he dies a violent death, as Margaret shoots him with a shotgun in revenge for failing to kill Mary.

Crazy Wolf goes to heaven and is told that "You just made it by the skin of your teeth! You believed on(sic) Me and that saved you. Billie Wolf, enter thou into the joy of thy Lord." Margaret of course goes to hell to burn for eternity.

This tract raises some interesting issues about Chick's theology. For example, as with some prior tracts, demonic forces are not only real, but very powerful. There's an almost henotheistic aspect to the story. Henotheism is the belief that many deities exist while only worshipping one. Chick’s Jesus becomes relevant primarily after death or during the apocalypse. In Chick’s pantheon, there are many deities but Jesus, the deity of death and destruction, reigns supreme.

Implied in this narrative is the teaching that prayer for a soul can actively lead to salvation. This is confusing. The entire point of Chick’s theology is that all that matters is whether an individual has accepted Jesus or not. If God and prayer can alter that decision, then the even minimal theological explanation of why everyone is not saved breaks down. It becomes within God’s power to alter whether or not individuals are saved. This renders the primary evangelical apologetic of such a deity non-feasible. In particular, damnation is usually defended by arguing that God cannot force people to accept Jesus as their savior. Yet here we see God apparently doing exactly that.

The importance of names is also worth noting. Aside from the not so subtle racism associated with Chick’s name choices, this is part of a general pattern in Chick's theology. What one calls something matters. Thus, for example, in previous tracts aimed at Islam, Chick argues that Allah is not just another word for God. This brings up an issue: Consider the following hypothetical: Someone is explained the entire evangelical belief system but with the words "Satan" and "Jesus Christ" swapped throughout. Then that person accepts Satan as personal lord and savior, does Chick think that that person is saved or not? If names matter then presumably Chick would believe that such an individual is not saved.

The tract of course ends with the usual warning that only Jesus saves. But the wording is worth noting: "Trusting religion, idols, ceremonies, nature gods or the Virgin Mary to save you is only chasing the wind!" That last phrase is not normally in these tracts. I suspect that to Chick "chasing the wind" sounded like an Injun phrase. This fits Chick's Jesus using the phrase "skin of your teeth" which is much less formal than how Chick's faceless, glowing Jesus normally talks.

So what is the overall lesson of this tract? The take away message seems to be that Native Americans are primitive savages but they get cool magical powers. And as long as you accept Jesus eventually, you get to play with the powers for a long time.

Note: Between drafting and posting this review I ran across another review that is worth reading.

Unscientific America and Pluto: The problem isn't the scientists

2010-01-11T12:00:00.000-08:00

I recently read Chris Mooney and Sheril Kirshenbaum's Unscientific America. Their thesis is that anti-science attitudes and the general lack of scientific knowledge in the United States are not the fault of the public or the media, but largely of scientists failing to communicate effectively. My response to this thesis is not positive. This book has been extensively discussed elsewhere. (Of these discussions, I recommend PZ Myers take, Joshua Rosenua's, this balanced analysis by Scicurious, this positive review by Chad Orzel, and this review by Mike at Real Climate)

A major theme of the book is that scientists are out of touch with the general public and spend too much time mocking the public or denouncing journalists rather than trying to engage the public and journalists to understand science. This argument may have some merit. However, the authors offer little evidence for their claim. Simply put, Mooney and Kirshenbaum are wrong: bad science journalism is far more the fault of bad science journalists than it is the fault of disengaged scientists.

Mooney and Kirshenbaum’s primary example of scientists being out of touch with the general public is the 2006 decision to recharacterize Pluto. After the discovery of Eris in 2005 and discovery of other similar objects, it became apparent to astronomers that consistent classification standards required that either Pluto be classified as a non-planet or that many more objects would need to be labeled as planets. Thus, in 2006, the International Astronomical Union constructed a new definition of planets which reclassified Pluto to the status of “dwarf planet.” Readers will likely recall the media outcry that erupted in response to this “downgrading” which included internet petitions and resolutions by various state governments supporting Pluto’s right to continue to be a planet. Mooney and Kirshenbaum point to the popular reaction and astronomers’ failure to anticipate or understand the reaction as an example of how scientists are out of touch with the general public. (There has been some discussion over the validity of Mooney and Kirshenbaum’s point and see for example these two remarks).

However, while reading Unscientific America, serendipity struck and I had occasion to read an article in the December 26, Puerto Rico Daily Sun, from Scripps Howard News Service. This article discussed extrasolar planets and how astronomers have recently discovered smaller extrasolar planets which are closer to what life-sustaining planets would look like. From the article:

"The first extrasolar planets were discovered 15 years ago, and now more than 400 have been found and at an accelerating pace. The early discoveries were gas giants on the order of Jupiter and Pluto and they have orbited far too close to their stars. But as techniques have improved, astronomers are able to identify smaller, occasionally rocky, planets, orbiting far enough from their stars to be close to what is considered a habitable zone."

The author is apparently trying to talk about astronomy while discussing "gas giants on the order of Jupiter and Pluto." Of course, Pluto is not a gas giant. Pluto is a tiny ball of rock, so small it isn't able to keep orbital debris out of its path. That's the entire reason it got downgraded from being a planet. It is small and rocky, not a gas giant. Anyone paying any attention to the faux controversy over Pluto should remember this. Indeed, anyone who remembers anything from grade school would know that Pluto is small and rocky.

This foolish statement about Pluto shows what is really wrong. While scientists may not be the best communicators, putting a majority of the blame for the status quo on scientists is wrong. The problem isn't the scientists. The problem is not that the scientists mistreat journalists and the media. The problem is that the media is full of people so ignorant that we get an article from a major news service claiming that Pluto is a gas giant. Not all journalists are this clueless. But cloning Carl Zimmer simply isn't a viable option. If we're going to deal with this problem, we need to focus on the actual causes. And poor journalism is far more the fault of ignorant journalists than it is of unengaged scientists.

Orthodox Judaism, Science, and Natan Slifkin

2010-01-06T18:37:00.000-08:00

Both Orthodox and Ultra-Orthodox/Charedi Jews commonly reject many basic parts of the scientific understanding of the world. For example, many Orthodox Jews believe in a global Nocahian deluge some five thousand years ago and reject evolution. In the charedi world, this rejection of science is even broader. The charedi rejection of science is substantially different from that of other branches of Orthodoxy. Rather than simply reject specific theories based on their own theological predilections, charedim, including charedi leaders (called by their followers "Gedolim" which is Hebrew for "great ones") take an actively hostile view of science.

I was unaware of the depth of charedi fear of and disdain for science until I recently began examining the controversy surrounding Natan Slifkin. Slifkin is a charedi Rabbi who wrote a series of books looking at the interplay between Judaism and biology. Slifkin made three primary of arguments: First, he argued that the evidence for evolution was overwhelmimg. Second, he argued that belief in evolution was not incompatible with Judaism. Third, he argued that the Rabbis of the Talmud could be wrong about science. For the charedim, the second two points apparently caused far more concern than the first. In 2005, many of the Gedolim joined to issue a ruling in which Slifkin was labeled a heretic. Possession and reading of his books was banned.

The charedi rejection of science goes far beyond simple opposition to evolution. For example, I was recently disturbed to learn from a conversation with Slifkin that some major charedi Rabbis believe in spontaneous generation of small rodents. I had been aware that such beliefs had survived until the early 1900s, but I was shocked to find out that many prominent charedi rabbis still believe spontaneous generation of small creatures. The charedi attitude towards science is in many ways connected to a deep worry of persecution. Moshe Sternbuch, the current chief Rabbi of the Edah Charedis, a prominent organization of Israeli charedim, stated that scientists say the world is old because "they want to refute the words of our Sages and undermine the faith that exists amongst the Jewish people. Their main concern is to try to shake the faith in G-d — which has been accepted by us generation after generation."

For another example, see these videos of Rabbi Aharon Schechter in which Schechter gets actively angry at the thought of people trying to investigate evolution, the age of the earth and related questions:

This attitude, one of perceived persecution and anger, seems to stem from two sources: First the charedi worldview is very wrapped up in the history of persecution against Jews. Thus, the charedim see any modern event in that light. Second, the charedi worldview is profoundly self-centered. They assume that essentially everyone cares about what they are doing. Thus, if scientists come to a conclusion that clashes with standard charedi beliefs, the charedi infer that the scientists are trying to target them. In this regard, comparison between the charedi leaders and the leaders of fundamentalist Christianity today is not favorable to the charedim. While many evangelical Christians and fundamentalist Christians reject much science, it is rare for their leaders to claim that scientists are trying specifically to destroy their religion.

However, the anti-science beliefs discussed here are not held by just the charedim. The modern Orthodox also have serious problems with much of science. Alexander Nussbaum has examined modern Orthodox attitudes towards science (see his article in Skeptic as well as Nussbaum's article "Creationism and Geocentrism Among Orthodox Jewish Scientists." in the January-April set of Reports of the National Center for Science Education). Nussbaum found that even among orthodox Jews attending secular colleges, a large fraction reject much of biology, astronomy, geology and other branches of science. About three quarters of the respondents when asked about the age of the Earth, said that it was less than 7000 years old. The vast majority (around 90%) believed that all land animals descend from animals on Noah's ark. Possibly most disturbingly, around a quarter of the students believed that evolution was not only false, but that scientists were deliberately concealing this fact.

Nussbaum also found that undergraduates majoring in scientific areas were less likely to accept many aspects of basic science. Nussbaum proposed that:

It seems that the science majors and degree holders — precisely because they were more likely to be exposed to evolution — were subject to additional community influences not to be “taken in” by the “heresy” they would hear, and were even less accepting of evolution. And individuals with a science background from that community have the added responsibility to use their knowledge and standing to promote religious doctrine in scientific matters.

Presumably the science majors would respond that they are more involved in science and so are more able to see the terrible problems with vast swaths of modern science.

While I had seen Nussbaum's work many years ago, I had generally assumed that something was wrong with his work. While these anti-science viewpoints were not unknown among the Orthodox students when I was an undergraduate at Yale, these views were not as popular as they appeared to be in Nussbaum's study. However, I'm now a graduate student interacting with students at Boston University. Here it seems that the profile of the Orthodox beliefs fits Nussbaum's data much better. Indeed, I recently found myself in a situation with six Orthodox students in the room and five out of the six believed in a literal global flood. When a conversation ensued, one student was unwilling to say whether he believed or not some of the more interesting claims in the Talmud such as the aforementioned spontaneous generation or the existence of the phoenix. That may have been in part due to the student not wanting to discuss the matter, but the overall reaction still agrees strongly with Nussbaum.

Why are otherwise moderate theists so willing to disregard large sections of modern understanding of the world? There are a variety of factors at play. However, one factor that is worth considering is the Orthodox attitude towards Talmudic rabbis, Talmud, and associated midrashic texts. While in some respects Jewish willingness to look at associated commentary or to interpret verses using Oral Law allows for moderation and incorporation of new knowledge. That willingness can also backfire. In particular, for many Orthodox Jews, statements made by Talmudic rabbis are by nature intrinsically infallible. Thus, instead of using the Oral Law as a way of reconciling science and religion, it is used to add additional statements that must be taken as literally true. whether they are about mice arising from mud, or birds burning themselves to regenerate for another life.

So far, this anti-scientific attitude does have some limits. I'm not aware of any Orthodox Jews (regardless of type) who believe in a flat earth. But geocentrism does certainly exist among Orthodox Jews. Most disturbingly, however, is that these anti-science views seem to be becoming more common rather than less in the Orthodox world, especially in the charedi world. The charedi world is not disconnected from the rest of the Orthodox world. If the charedi world becomes more extreme, it will likely pull the rest of the Orthodox world in the same direction.

If Modern Orthodox Judaism is to be taken seriously as a reasonable religion, able to survive in the modern world, then these trends need to be countered by responsible Orthodox leadership.

Amazon, Internet Sales Tax, and Gratuitous Promotion of Family Members (again)

2010-01-06T09:29:00.001-08:00

My father has a piece up at the Oxford University Press blog. The piece discusses a serious discrepancy in how sales tax is administered in the United States. Sales tax is broken down by state. However, companies are not required to add on sales tax themselves unless they have a physical presence in given state. If a company does not have a physical presence in a given state, then customers in that state are expected to pay the sales tax themselves. In practice, almost no customer pays this sales tax. Thus, in practice companies such as Amazon which engage in sales primarily over the internet don't pay any any sales tax on their sales. This gives them a competitive advantage over physical stores. The piece is worth reading. The only issue that I have is that he does not address one issue which is also worth discussing: It may be that such sales tax practices are not only economically unfair but also regressive. If more well-off people are more likely to buy on the internet then they will not pay a sales tax where poorer individuals buying from brick-and-mortar stores will. At this point, internet access and internet use is so common that this may not be an actual problem. However, it is an additional concern with the current system. In any event, his piece is worth reading. Go and read.

Minyanim and Mathematics: A protocol for anonymous counting.

2010-01-04T10:29:00.001-08:00

In Judaism, many communal prayers require a minimum of ten people. This quorum is called a "minyan" which is often also used to mean a service in general. (In Orthodox Judaism, only Jewish adult males count for a minyam while in Conservative Judaism all Jewish adults count). However, certain liturgical elements on fast days (such as a Torah reading at the afternoon prayer) require not just ten present, but ten who are actually fasting.

However, people may not wish to advertise that they are not fasting even if they are willing to assist with the minyan. Moreover, even a very observant individual might have a reason not to fast and would not want people to know about it (such as a medical condition). This leads to the following problem: How do we determine how many people are fasting without requiring people to disclose whether or not they are fasting?

In a recent minyan I attended, this question was handled by the gabbai (the person in charge of running the minyan) asking everyone to close their eyes and hold up one hand if they were fasting. This is obviously unsatisfactory since the gabbai finds out who is fasting. One could suggest slips of paper or the like. but they could be easily connected to particular individuals. To make this problem interesting, it is helpful to assume that everyone knows the identity of the sender of any communication they receive. Is there a solution under which individuals' statuses remain private while the minyan is assured of 10 fasters?

Curiously the answer is yes albeit the solution is a bit cumbersome. Here's how: The gabbai picks a random integer (the distribution doesn't matter although in practice one might want a reasonable distribution that approximates a bell curve or an exponential distribution or something similar). The gabbai takes this integer and adds 1 to it if he is fasting. The gabbai whispers this number to another person. That person adds 1 to the total if he is fasting and similarly passes it on to another person. The last person gives his number to the gabbai. The gabbai now subtracts the random integer that they initially added. The total the gabbai has is the number of people fasting.

A few notes about this algorithm. First, it is important that, when the gabbai is picking a random integer, that every integer has some non-zero probability of being chosen. Consider, for example, what would happen if the gabbai was known to only pick positive integers. If the gabbai picks 1, the next person can tell if the gabbai is not fasting. Thus, the gabbai can never pick 1. But then, by the same logic, the gabbai won't be able to pick 2. Or 3. And so on. This problem is avoided if the gabbai can pick any integer whether or not it is positive.

There is also a degenerate case of if only the gabbia is fasting or only the gabbai is not fasting. In those cases, the exceptional individual can work out the status of everyone else.

The algorithm also assumes that people are not going out of their way to obtain information. If two people bracket a third and cooperate, they can figure out the middle person's status as a faster.

In fact, it turns out that it is possible to make a more sophisticated protocol that would prevent this and similar tricks. This would be a variation of an anonymous voting algorithm. However, these algorithms rely on clever cryptography with large prime numbers which is only believed to work rather than proven to work. Implementation also would require much more computation than can be done by hand.

Less intensive algorithms can be used to increase the number of people who must cooperate. It is, for example, an interesting exercise to construct a variation of the above such that finding out someone's status requires the cooperation of at least three people.

This algorithm in practice is cumbersome. Moreover, the goal it seeks to accomplish is minor since, if the fast day liturgy is used, those sections of the services actually need to be performed by people who are fasting. Thus, the gabbai will need to know the status of at least a few people. However, this algorithm has the slight advantage that, if there are not enough people to recite the fast day liturgy, then no one will know which people cause the deficiency.

Integer Complexity: Why Blogging is Fun

2009-12-30T12:37:00.000-08:00

A while back I wrote a blog entry about a generalization of the four fours problem. That entry focused on the function f(n) defined as the minimum number of 1s needed to represent n using just addition and multiplication. So for example, f(6)=5 since 6 = (1+1)(1+1+1) and there's no way to represent 6 with four or fewer 1s. Surprisingly little is known about the general behavior of f.

After that blog entry, two commentators, Etienne and Harry, took up examining f in more detail. Harry and I together produced new work on the behavior of f that will likely turn into a paper.

I will attempt here to briefly summarize what was known and how we've improved it. (Reading my original blog entry and my previous follow-up will probably help matters).

It was known that f(n) satisfied the inequalities 3log3 n ≤ f(n) ≤ 3log2 n for n greater than 1. We've improved the upper bound somewhat, replacing 3log2 n with 2.64log2 n. We've also shown that f(n) - 3log3 n is unbounded (that is one can make it as large as one wants if one chooses suitable n). We did this by defining what we call the "defect" of d(n)= f(n) - 3log3 n. We defined Ak to be the set of numbers with defect at most k. Then, we were able to show that each set Ak was way too small to contain every natural number. More technically, we showed that if one defines Ak(x) to be the number of elements in Ak that are at most x, then Ak(x) = O( (log x)^c) with c a function of k.

Also, it was conjectured that if one had a number of the form n=2^a3^b that f(2^a3^b)=2a+3b (aside from the trivial case when a=b=0). Essentially this conjecture stated that the most efficient representation for n arose from the obvious one, that is writing n = (1+1)(1+1)...(1+1) * (1+1+1)(1+1+1)...(1+1+1). Harry, was able to prove that this conjecture held for all such n as long as a was at most 10. Since then, we've been able to improve that bound to a at most 19.

It turns out that for much of the behavior of f, including both of the two problems discussed above, the sets of Ak and some closely related sets are natural objects to consider. Thus, we tried to work on making c as small as we could in the equation Ak(x) = O( (log x)^c). The initial proof gave a very poor bound on c (being able to take c=1024^k). After a series of improvements, primarily by Harry, he was able to take c=4^k and then using a combination
of ideas from the two of us, we got a linear bound. In particular, one can take c=3k/(5- 3log_3 5). Note how this bound grows much slower than the previous bounds. However, we do know that A1(x) is in fact of order log(x)^2 so there's some realm for improvement in that this proof gives an upper bound for c of about 4.96 for A1(x). One thing to note: While these results were proved using induction arguments (as one would expect), one cannot induct on Ak with k a positive integer. One actually needs to induct on Aαk for fixed α less than 1. A good choice of what alpha to use then becomes very important.

Harry has on his blog a long post that summarizes what we have accomplished and discusses them in more detail. See his posts here and here and the other posts he links to.

The moral to this story is that you don't know what interesting things will happen when you blog, especially when you have readers that are as smart or smarter than you.

Three Religions Meme

2009-12-27T08:51:00.000-08:00

James McGrath has recently tagged me (well. really a very large set of people) with the meme of naming three religions you find fascinating of which you are not or have not been a member.

I'm going to place a few additional restrictions on my choices:

First, I am not going to pick any purely fictitious religions. Thus, for example, I'm not going to pick any religions from Brandon Sanderson's Mistborn series (although there is a very large temptation to try to pick some of those). Similarly, I'm not going to pick any religion
that started as a fictional religion and then became real. Thus, Melkorism and Cthulhu worship are both out. Finally, I'm not going to pick any parody religions. Thus, Invisible Pink Unicornism and Flying Spaghetti Monsterism are both out although I will note that IPUism was around long before FSMism which is a sad little upstart in comparison (I mean, c’mon. It doesn't even have an oxymoron in its title.).

So of the real, non-parody religions, what will I choose are Cargo Cults, Roman Catholicism and Bahai in no particular order.

Cargo cultism is a religion with which some may not be familiar. It is also as far as I am aware the only example where nearly identical religions arose independently which already makes it very interesting. However, where and how cargo cults arose explains this feature. At the same time, it makes them all the more fascinating. During World War II, the United States used islands whose populations previously had had little or no contact with the outside world. Many people in Western and other civilizations believe in forms of sympathetic magic or the like, but small tribal groups often take this to an extreme. In these cases, the tribes saw the US soldiers doing apparently ritualistic activity that included marching in formation, talking to themselves on pieces of wire, and clearing out large fields. The tribes further saw the immediate responses to this activity: Airplanes came and dropped cargo to the soldiers, including food, medicine and clothing. The tribal members concluded that if they could engage in the same ritualistic behavior, they might get the same or even better results.
Thus, the cargo cults were born.

When the soldiers left, the tribes assigned priests who talked to spirits on the radio which would generally consist of a few pieces of wire. They cleared out or kept clear airplane landing fields. And they wore uniforms and conducted drills. These religions were derisively labeled "cargo cults." These remained strong through the mid 1970s. Members retained their beliefs and practices even when confronted with more features of modern civilization and explanations of what US soldiers had been actually doing. Cargo cults still exist in limited numbers today, seventy years after World War II.

The second religion is Roman Catholicism. The Church has been and remains a fascinating set of contradictions. On the one hand, it is hard to reconcile the gilded architecture and massive hierarchy with the ascetic messages preached by Jesus. The Church has a history of encouraging violence from the Crusades to the Inquisition. When the Church has not encouraged war and killing for its own ends, it has been silent when speaking up could save lives. The Church has also actively persecuted individuals such as Galileo who disagreed with the Church. On the other hand, the Church helped preserved learning that would otherwise be lost. The Church was a bastion of knowledge against the tides of ignorance (tides possibly encouraged by aspects of the Church. but still) The Church has provided shelter and relief to the poor for centuries. In the last fifty years, the Church has strived to modernize and reconcile its beliefs with science while many other religions have gone out of their way to attack science.

The Roman Catholic Church is the Church of Torquemada But it is also the Church of George Coyne and J. R. R. Tolkien. Whether the Church survives this next century and whether it embraces modernity or not will be some of the major questions impacting this century.

The third is the Bahai. The Bahai are the youngest of the major Abrahamic religions. They have consistently embraced reason over dogma and thus far have a history of being the least persecutory of the Abrahamic religions (although how much this is due to their still small numbers remains to be seen). If I had to name a single religion that I might be comfortable with drastically increasing in size over the next few centuries, I would likely name the Bahai.

Edit: It was pointed out to me by multiple people that I neglected to tag this meme for anyone. So I'll tag Kurt because he hasn't blogged much since he got married, Apikores because I'm just curious what he has to say, and Kat because she commented on this post already so hey, why not? And I suppose anyone else who has enough free time who reads this blog regularly and has a blog can consider themselves tagged.

Off-Topic Lovecraftian Horrors: Adventures of the Squamous and Rugose

2009-12-13T20:01:00.000-08:00

Here are two marginally related videos that I could not resist sharing:

First, we have the adventures of Lil' Cthulhu. It's a new day and the stars are right. It's time to play. Wake up Lil' Cthulhu!

This is an excellent video for those who want their children to be inducted into the ceremonies and blasphemous, mind-shattering secrets of the Great Old Ones from a young age. Starting early is important!

And following this, we have Heartache Over Innsmouth. This is a moving romantic song, about a man who has fallen in love with a girl who joins the cult of Dagon.

As far as I am aware, Dagon is the only deity in Lovecraft which actually appears in the Bible. Dagon was a common Semitic agricultural deity. For many centuries, commentators(such as Rashi) noted the similarity between Dagon and the Hebrew word for fish, dag. This lead them to believe that Dagon was some sort of oceanic or fish deity. Laboring under this belief, Lovecraft chose Dagon as the name of the horrific creature under the ocean which rules over the Deep Ones. Some later writers have attempted to retcon this discrepancy by suggesting that Dagon was not that horrific being's name but rather was a name given to it by the cultists as they needed a name. They thus chose that name due to their own mistaken belief that Dagon in the Bible was a fish deity.

Virgin Galactic, Star Trek and Retconning

2009-12-07T16:47:00.000-08:00

Virgin Galactic has unveiled their newest model of spaceship, SpaceShipTwo. Virgin Galactic, part of Richard Branson's Virgin Group, is trying to make affordable space tourism. Where by affordable, we mean affordable if you have $200,000 to burn. And all you get is a quick sub-orbital hop. We are at the dawn of private space travel, and one could easily spend much time discussing the long-term political, social and religious implications. I'm not going to do that.

Instead, I'm going to focus on the names of the ships. The first ship will be named the VSS Enterpise. VSS stands for "Virgin Space Ship." The second ship according to some reports will be the VSS Voyager. Yes. Enterprise and Voyager. As in from Star Trek.

Officially, the VSS Enterprise is named not just after the fictional ships but also the real ships that have been given that name, including the space shuttle Enterprise.

Now here's where things get complicated. The space shuttle Enterprise was named after the USS Enterprise (NCC-1701), commanded by James Tiberius Kirk; the real shuttle Enterprise is named after the fictional ship. But it gets better. The writers of Star Trek retconned in the existence of the Enterprise space shuttle into their universe. That is, in the Star Trek universe, the Enterprise shuttle is now one of the long line of ships that existed before the Federation ships. But the Enterprise shuttle in the Star Trek universe is not named after the starship USS Enterprise because in the Star Trek universe, Star Trek never occurred as a 20th century television show. There has even been a Star Trek novel which had a plot focusing on the space shuttle Enterprise finally getting a chance to fly (in both the Star Trek universe and in our own universe the Enterprise was used a test shuttle but never flew into space). I've been unable to track down this novel although I did read it many years ago. If anyone can track down the novel I'd be very grateful.

I suspect that in a few years we will see the same thing for Branson's ship. That is, there will be official Star Trek material which includes Branson's ship as a ship that existed in the Star Trek universe.

I'm hoping that the ships three and four are named Serenity and the Millennium Falcon. Star Wars at least has the advantage of having occurred a long, long time ago, in a galaxy, far far away. So they won't have to deal with the oddity of incorporating into the universe real ships that were named after ships from their universe.

Excessive Executive Compensation, Health Care and More Gratuitous Promotion of Family Members

2009-12-06T16:28:00.000-08:00

My twin has a piece up at the Huffington Post in which he examines the sections of the proposed health care reform that concern compensation for insurance executives. Under current regulations, corporations can easily deduct executive compensation. This legislation will substantially restrict such deduction by health insurance companies. Aaron argues that the proposed caps on such compensation do not go far enough. In particular, there is no good reason to have such restrictions for insurance companies and not other companies. He makes a good case and also explains in detail the relevant regulations that govern the status quo. My one nitpick is that in many locations a game of Ms. Pacman costs more than a quarter. Go and read.

Westboro Baptist Church at Boston University

2009-12-01T19:32:00.000-08:00

Readers are likely familiar with the Westboro Baptist Church as the strange cult run by Fred Phelps which is devoted to telling the world that God hates them. A lot. They are most known for the slogans "God Hates America" and "God Hates Fags." Pretty much there is no group they don't hate. They even have a song about called God Hates the World, to the tune of "We Are the World." They have a fascinating eschatology in which in the end time God will ask them what should be done with the rest of humanity and they'll gleefully tell God to send humanity to hell. Some people who don't know much about the Church have speculated that the Church exists really just to make the right-wing look bad.

Why am I thinking of the Westboro Baptist Church? Today they came to Boston University to protest. I think this time they were nominally protesting Jews. Or something like that. Apparently they had signs attacking a lot of different groups.

Unfortunately, I had office hours when they were protesting. This isn't fun. When Ray Comfort was distributing his version of Origin of Species to a hundred universities across the nation, he neglected to include Boston University and I was unable to get to Harvard or MIT where there was distribution.

I've concluded that there is a God. God is taunting me by dangling interesting groups just close enough that I'm aware of them but not so close as to actually get to talk to them. God probably sees me as sort of like a cat and sees the various crazies as akin to a laser pointer.

Just my luck, Neturei Karta will probably come to campus and I'll miss them also.

C.S. Lewis, the Trilemma, and Cultural Norms

2009-11-27T11:47:00.000-08:00

A common Christian apologetic argument is the Trilemma. First introduced by C.S. Lewis, this argument since Lewis has undergone modification. However, the basic argument has not changed. As the argument goes, Jesus, was either telling the truth when he said that he was God, Jesus was lying, or Jesus was insane. This is generally abbreviated as “Lord, Liar or Lunatic.”

Lewis used this argument primarily as a response to people who thought that Jesus was a good person. but not the Son of God. Lewis argued that this was not a possibility since, if Jesus was not telling the truth, then one of the other two possibilities must hold. In its more modern form, the argument is identical, but evidence is presented as well that the last two possibilities don’t hold.

The argument in either the original form of Lewis or in other variants, suffers from flaws. The most serious flaw is the reliability of the Gospels as record of what Jesus said. It is not at all implausible that Jesus didn’t claim to be the Son of God, but such claims were later asserted by followers. Or Jesus could have in fact said exactly what he is quoted as but have been genuinely mistaken. These are two are two good detailed discussions of these and other flaws. Rather than discuss the flaws, I’d like to examine why this argument is so effective apologetics.

The argument, especially in its post-Lewis form (such as that advanced by Joshua McDowell in his “Evidence that Demands A Verdict”) does not explicitly invoke the presupposition that the audience thinks that Jesus was a great man . However, in an unstated form, this approach is far more effective. We live in a society with few taboos stronger than saying negative statements about Jesus. Indeed, even if one asks most Jews who live in the United States what they think of Jesus, they will feel compelled to say something like “I think he was a great teacher” or something similar. Thus, to most people, the notion that Jesus was either a lunatic or a liar is so repulsive (or politically incorrect) that when faced with those alternatives, they have no choice but to rush to the third possibility. The Trilemma thus rests on implicit cultural norms that Lewis was willing to make explicit. His successors have been less forthcoming.

A Quick Note about Bill Sparkman

2009-11-24T22:08:00.000-08:00

Some readers may remember Bill Sparkman. Sparkman was a federal census worker who was found dead, hanging from a tree with the word "fed" scrawled across his body. At the time, the general consensus among progressive bloggers was that Sparkman's murder was evidence for the deep problems being created by right-wing rhetoric that stoked anger and paranoia. (See for example this note). The reply by the right-wing was interesting with all sorts of explanatory hypotheses proposed. Some of the responses on the right-wing were simply put, insane, such as incredibly baseless claim that Sparkman had been killed because he was pedophile. All of this looked like the standard behavior for the blogosphere and pundits but for one detail: It nows turns out that Sparkman wasn't murdered. According to police, he committed suicide and tried to make it look like murder to help get insurance money. I hope that all the bloggers who used this as evidence of the problems of the current right-wing rhetoric will post follow-ups but I'm not optimistic.

Note that this isn't intended to say that there aren't good reasons to be concerned with the increasing radicalization and paranoia of the American right. But Bill Sparkman's death should not be part of those concerns.

Spam and Commenting II

2009-11-22T12:02:00.000-08:00

Given the discussion in the comments for the thread below I am turning on CAPTCHA for commenting. I haven't been able to figure out how to ger reCAPTCHA working for blogger. If someone knows how to use that, I'll do that instead.

Spam and Commenting

2009-11-18T08:04:00.001-08:00

Over the last two weeks there has been a problem with spam bots. The problem has become annoying enough that it needs fixing. I am either going to turn on comment moderation or turn on a CAPTCHA system. Which do readers prefer?

Barack Obama, the Turing-Lovecraft Theorem and Horcruxes

2009-11-16T17:44:00.000-08:00

One nice thing about a blog is that you can see how people arrived at your blog. Many hits come from Google searches. Some of those Google searches are phrased explicitly as questions while in other cases what the individual is searching for is obvious. This blog entry will examine some of the more common search strings and questions which blog entries here do not already answer.

Search string: "Is Barack Obama a clone?" Number of searches: At least 15 counting all variations.

People searching for this question or some variation thereof normally find my entry on Barack Obama's position on cloning. So is Barack Obama a clone? No. Of course not. That's even stupider than thinking that Obama's parents deliberately faked a birth certificate so he could run for President 40 years later. That's even stupider than thinking that 9/11 was an inside job. That's even dumber than thinking that scientists invented evolution to undermine belief in God. Cloning is a really difficult technology. We've had trouble until recently even cloning mammals. The idea we could clone people 40 years ago is absurd. And there's no coherent aim to cloning Obama.

On second thought, maybe it isn't so unreasonable. It would explain a great deal such as why he's been so uncooperative about giving a long-form birth certificate for the birthers to examine. And it explains why he is so charismatic. Someone tell Orly Taitz! Obama wasn't born in Hawaii or Kenya or anywhere else! Maybe he was never born but cloned in a vat by the Illuminati! Sadly, this hypothesis contradicts the preexisting conspiracy theory that Obama is a reptilian infiltrator. Maybe he is a cloned reptilian hybrid?

Search strings: "Turing-Lovecraft Theorem" and "proof of Turing-Lovecraft theorem" and others. Number of searches: Around 10.

According to Charlie Stross's "The Atrocity Archives," (discussed in this blog entry) Alan Turing did not commit suicide but rather was killed by the British government because he discovered a very dangerous theorem. This theorem that disproves the Church-Turing thesis and if thought about the wrong way could summon Lovecraftian horrors. This theorem's exact statement and proof are not included in the book. The book is fiction. As in, not real. As in, no such theorem exists. Just as H.P. Lovecraft wrote fiction. As in, not real. As in, his monstrosities came from his imagination, not from horrific realms beyond the understanding of mortals.

Or maybe that's just what they want you to think. Don't you find it interesting that not only has Barack Obama never denied being a reptilian clone but he's also never denied that the Turing-Lovecraft theorem is real?

Search string: "How do I make a Horcrux in real life." Number of searches: Too many to count. I get this search or some variation almost every single day. The total number of searches is easily in the hundreds.

This search and very similar search turn people to the blog entry arguing that it is acceptable under halacha (Orthodox Jewish law) to make a Horcrux if one had the ability to do so. Fortunately, horcruxes are not real. They are fictional. They are from the Harry Potter books. The Harry Potter books are fictional. Again, fictional means not real. You cannot split your soul into pieces using a magic wand. Sorry. But no.

Again. This may just be what Barack Obama wants you to think. That way, if the public does ever find out about his reptilian clone heritage and tries to kill him, they won't realize that he'll be unstoppable unless his Horcrux is destroyed. What would his Horcrux be? Remember, that if he is a reptilian clone, he obviously enjoys laughing at us while he and his reptilian compatriots slowly take over the world. So he might leave clues about his intentions. Isn't it a bit suspicious that Harry Potter, who turns out to be an accidental Horcrux for Voldemort, sees the shape of an acorn in his tea leaves in "Harry Potter and the Prisoner of Azkaban" and yet Obama was elected with the help of an organization called... ACORN?! All the pieces are coming together!

Sadly, there were two common hits from Google that don't seem to fit this. Indeed, they seem to be questions from people who don't have a problem distinguishing fact from fiction. I'll try to put together serious blog entries about those topics when I have time.

And apologies to Glenn Beck.

Malcolm Gladwell, Memes and Intellectual Honesty

2009-11-10T19:00:00.000-08:00

I recently read Malcolm Gladwell’s “The Tipping Point.” As with Gladwell’s previous books, I found the book to be full of interesting tidbits, but lacking a coherent thesis. The book was sufficiently mediocre that I decided against reviewing the book. This is not a review. This is a discussion of Malcolm Gladwell’s lack of intellectual rigor.

Gladwell’s primary thesis is that ideas or behavior can, under the right circumstances, spread like an epidemic. What precisely this means is not clear. However, there is another, serious problem with this book, a glaring omission. People sometimes talk about something being “blindingly obvious.” In this case, the omission is so obvious that it is more akin to staring at the sun at high noon. This omission can be summarized by a single word that appears nowhere in the text: Meme.

In his 1976 book, “The Selfish Gene,” Richard Dawkins, coined the term “meme” to mean, in essence, a unit of cultural transmission that reproduces and is selected for, akin to how genes are selected for by natural selection. Since 1976, “meme” has been used more loosely to mean an idea or behavior that spreads in a viral fashion. The idea of a meme is similar, if not identical, to what Gladwell discusses. Despite that, the word “meme” never appears once in Gladwell’s book. Nor is Dawkins mentioned or referenced once in the text.

Gladwell’s book was first published in 2000, many years after Dawkins’s coinage. This is not a case of two minds independently and simultaneously arriving at the same idea, like Leibniz and Newton. This is one mind, presenting an idea and then another mind publishing a similar idea while failing to acknowledge prior work. By academic standards, this is completely unacceptable.

One might think that, possibly, Gladwell’s research was sloppy, and so he never learned about Dawkins’s term “meme.” However, I read Gladwell’s book on Kindle, which includes many updates since the original book was published. It is implausible that, in the last nine years, Gladwell has never heard the term “meme.” And yet, he felt no need to add even a footnote or a sentence about Dawkins’s important prior work.
Most damningly: Gladwell does mention the word “meme” in passing on his website in the FAQ about the book:

5. Are you talking about the idea of memes, that has become so popular in academic circles recently?
It's very similar. A meme is a idea that behaves like a virus--that moves through a population, taking hold in each person it infects. I must say, though, that I don't much like that term. The thing that bothers me about the discussion of memes is that no one ever tries to define exactly what they are, and what makes a meme so contagious. I mean, you can put a virus under a microscope and point to all the genes on its surface that are responsible for making it so dangerous. So what happens when you look at an infectious idea under a microscope? I have a chapter where I try to do that. I use the example of children's television shows like Sesame Street and the new Nickelodeon program called Blues Clues. Both those are examples of shows that started learning epidemics in preschoolers, that turned kids onto reading and "infected" them with literacy. We sometimes think of Sesame Street as purely the result of the creative genius of people like Jim Henson and Frank Oz. But the truth is that it is carefully and painstaking engineered, down to the smallest details.

So an idea “very similar” to his doesn’t deserve a single mention in the entire book. Furthermore, the claim that the idea of a meme isn’t well-defined is simply false, as one can see from actually reading “The Selfish Gene.” Gladwell’s claim that individual memes have not been examined in detail is also false. Indeed, there was a Journal of Memetics for almost a decade that examined memes in detail. And if one accepts Dawkins notion that religion is inherently memetic, then all of religious studies is essentially an examination of memes. Some modern scholars have specifically examined religion in that context. In fact, Gladwell himself examines the rise of Methodism in the United States as an example.

Gladwell comes across as a child trying to explain why his hand was in the cookie jar. He advances a series of unconvincing, somewhat contradictory explanations, hoping that we will ignore the larger problem. So far as I can tell from Google searching, this strategy has worked; people have noted that Gladwell is talking about memes but no one has called him out for his failure to acknowledge this prior work. This isn’t acceptable. Gladwell’s behavior is intellectually dishonest. His failure to credit Dawkins or others who have thought about these ideas before him does a disservice to those individuals and to honest intellectual discourse. I don’t think Gladwell’s behavior constitutes plagiarism, but it certainly would be punished if it occurred in an academic setting. Failure to cite prior work results in a paper being rejected from any legitimate journal. If a student hands in an assignment that fails to cite prior work, the student receives a bad grade, if not outright failure. Gladwell owes his readers and Richard Dawkins an apology for his failure to acknowledge that Gladwell’s idea recycles Dawkins’s earlier work.

Dan DeLong, Animal Sexuality and High School English

2009-10-31T16:56:00.000-07:00

Mike Dunford has drawn my attention to a situation in Piasa, Illinois where high school English teacher Dan DeLong assigned extra-credit reading about gay animals. The situation seems to be a bit complicated. The assigned article discusses how homosexuality is common in the animal kingdom. DeLong has been suspended from his job and faces a disciplinary hearing.

If a teacher simply assigned reading from areas of study outside the teacher's area that would be a legitimate concern. However, it appears that the assignment was to read the essay and examine the essay's structure and argumentative form. Therefore, this is simply a normal high school assignment. Teachers assign all sorts of different reading about different subjects. That's part of the normal school curriculum. One might be able to describe a problem if one had evidence that DeLong had assigned the essay to make some sort of political, moral, theological or other point. However, I haven't seen any claim that that was the case. The objection simply seems to be that some parents were uncomfortable with the reading.

Unless the school had some sort of blanket policy about the teaching sexual material requiring parental permission I don't see anything that DeLong has done. While news reports are still sparse with details it seems like this is more about fear of gays and homosexuality extended to such a point that even discussing gay sex in animals triggers a backlash. That's stupid. There's simply no other way to describe it. DeLong should be restored to his position as soon as possible.

Update: DeLong has been reinstated.

Benford’s Law: Human Intuition, Randomness and Fraud

2009-10-29T13:53:00.000-07:00

Suppose we look at some set of fairly natural data, say the populations of various countries. Let’s look at the leading digits of their populations. For example, the United States has a population slightly over 300 million. So, for the United States, the leading digit would be 3. What fraction of countries would you expect to have a leading digit of 1? Most people would guess 1/9th since there are 9 possibilities (1,2,3,4,5,6,7,8,9) and no obvious reasons to prefer any digit over any other digit. However, you’d be wrong:The actual percentage is slightly over 25%. In fact, it turns out that we should expect about 30% of countries to have a leading digit of 1. This strangely large number of 1s shows up frequently in natural data and is known as Benford’s law. It turns out that for many natural data sets we expect about 30% to have a leading digit of 1, about 18% to have a leading digit of 2 and so on. Benford’s Law is an important statistical rule that has a variety of generalizations and has practical applications (such as in detecting fraudulent or manipulated data).

Where is this strange pattern coming from? I didn’t have a good understanding of this until it was explained to me by Steven Miller. Consider a finite list of numbers that is reasonably well-behaved. For each member of our list, we can write it in scientific notation. So, for example. if we had 236 on our list, we would write it as 2.36 * 10^2. Note that the lead digit is then determined by what the lead digit is in the part of the scientific notation that isn’t the exponent. (This part is sometimes called the mantissa when one wants to be fancy) Now, for each number on our list, instead of looking at the number x, we can look at log10 x. What does this do to the scientific notation? Well, scientific notation then corresponds to the log of the mantissa + an integer that is the power of the exponent. So, for example, log10 (2.36 * 10^2)= .3729...+ 2.

Let’s examine the non-integer part of log10 x (call this f(x)) What distribution do we expect for f(x)?, It is a fixed value between 0 and 1 with no clear cut offs or biases in any direction so the most obvious thing to do is to make it a uniform distribution. That means that there’s about a 5% chance that f(x) falls below .05, about a 20% chance that f(x) falls below .2, about a 50% chance that f(x) falls below .5 and so on.

So what does this tell us about the leading digit? If the mantissa is below 2, then we have lead digit 1. If the mantissa is between 2 and 3, then we have lead digit 2 and so on. The mantissa is below 2 if f(x) is less than log10 2 = .301. Accordingly, we should expect that the mantissa is below 2 about 30.1% of the time. Thus, a number should have a lead digit of 1 about 30.1% of the time. Similar logic works for how frequently we should expect the lead digit to be 2, or 3 or so on.

What is wrong with the intuition that every lead digit is just as common? When we calculate probabilities, we are used to using the simplest probability distribution we can imagine, something like picking a positive integer from 1 to 10^n for some fixed n. We are used to this approach primarily because it is easy to calculate. Consequently, most probability problems in high school and college assume that we have such a uniform distribution since that assumption makes the math much easier. But actual distributions in real life don’t often look like this. For example, we might have a Bell curve or some other distribution. For almost any distribution that arises in nature, Benford’s law will apply due to the logic we used earlier.

So what does this do for us? Perhaps most importantly, we can use this insight to detect fraud. When humans try to make up data, it often fails to fit Benford’s law. In general, humans are bad at constructing data that passes any minimal test for randomness. Failure to obey a generalized version of Benford’s law was one of the major pieces of evidence for election fraud in the last Iranian election. The recent questions regarding whether Strategic Visions Polling was falsifying poll data arose when Nate Silver noticed that its results diverged substantially from Benford’s law.

For more information on Benford’s Law and related patterns in data, as well as more mathematical discussions of that data, see Terry Tao’s blog post from which I shamelessly stole the hard data about populations of nations.

HPV, Cancer and Friends

2009-10-18T13:50:00.001-07:00

Stephanie Zvan who blogs at Almost Diamonds has cervical cancer. A recent Pap smear came back with abnormal results and follow-up work found the cancer. Stephanie has talked about her experience and given follow-up information about her prognosis. Pieces responding to Stephanie's situation are at ERV and PalMD that are both worth reading.

I'm going to use this as an opportunity to go over some very basic issues:

First, for many cancers, getting them caught early matters. This is the case for many cancers. If you are a woman make sure you get regular Pap smears. If you are a man make sure to get regular prostate exams. No matter who you are, if you are older, make sure to get a regular colonoscopy. Etc. Etc. These exams save lives. When cancer is found doesn't just impact what treatment options there are but can be the difference between life and death.

Second, get the HPV vaccine. Unfortunately, this vaccine is not yet available for men but is available for women. HPV is one of the leading causes of cervical cancer. HPV is also associated with penile cancer in males. Once one has a given strain of HPV, getting a vaccine later isn't going to help matters. Moreover, HPV transmission is not prevented by condom use. HPV is a nasty little bugger and is much more easily transmitted than most STDs.

Stephanie grew up before there was a vaccine. However, in another respect, she is lucky. Stephanie and her husband don't intend to have children. However, for others they aren't so lucky. If you are a woman, get vaccinated. Men, when the vaccine is finally approved for males, please get vaccinated. Not only will this protect you, it will prevent you from getting a nasty disease which could then be given to those you love.

Stay informed. Stay protected. Stay safe.

Edit: Apparently the vaccine has now been approved for males. Good timing.

Where Are All the Smart Apologists?

2009-10-15T14:11:00.000-07:00

Recently I read The Screw Tape Letters, a series of letters written by C.S. Lewis. The letters purport to be from an old demon giving advice to a young demon. Lewis is a smart, funny and talented writer. What the demon Screwtape says is as revealing and clever as what he does not say. This is not the only great work of apologetics by Lewis. Why are there no great Christian apologists like Lewis today?

Lewis is far from perfect. Lewis gave birth to one of the most annoying apologetic arguments, the Trilemma. However, even there his intelligence and originality shine through. I have not seen any contemporary apologist produce any argument that isn’t a tired repackaging of pre-existing arguments.

Who are the major apologists today? There really aren’t any in the influential way that Lewis was. But if one had to identify those who today continue the tradition of Christian apologetics, one would probably list Ray Comfort, William Demsbki, and Alister McGrath.

Do any of these people measure up to C. S. Lewis? No. Consider these writers individually:
Does Ray Comfort stack up to Lewis? No way. Ray Comfort is an idiot and an ignoramus. He’s the man who most famously tried to claim that the modern shape of the banana was evidence for a divine creator. Yes, the banana, a fruit that has been heavily modified by extensive breeding by humans, a fruit whose wild form is a nasty hard thing full of seeds.

Does William Dembski stack up to Lewis? Wililam Dembski isn’t an idiot like Comfort. He has a real PhD in mathematics. But this also is a man who, after intelligent design failed in the courts, was reduced to teaching apologetics at a second rate seminary while giving course credit to students for trolling pro-evolution websites. I can’t see C.S. Lewis doing that. Moreover, Dembski’s writing ability resembles that of a 7th grader trying to sound like he’s really bright and well read. I should know. I used to write like Dembski when I was in 7th grade. Demsbki also seems to spend most of his time fighting with other Christians. (He really, really doesn’t like theistic evolution.)

Does Alister McGrath stack up to C. S. Lewis? Now we are getting closer. McGrath is a respected theologian who also has a degree in biophysics. He’s bright. He’s willing to accept both science and religion. He has on occasion made cogent arguments. But there are two problems: First, he’s a dreadfully boring writer. I have trouble staying awake when I read anything he writes. Someone needs to get Ben Stein to do a book on tape of one of McGrath’s books. It would be the ultimate sleep aid. Or maybe it would be a weapon of mass destruction as just playing it nearby would cause individuals within a hundred mile radius to fall into irreversible comas. This brings us to the other issue with McGrath: The subjects and titles of his books are equally dreadful. His two most well known books are "The Dawkins Delusion?" and "Dawkins' God." Ok, Alister. We get the point. You don’t like Richard Dawkins.

So why are there no great apologists for Christianity today? Here are four possible explanations:
First, perhaps great apologists are simply rare and C.S. Lewis is a great outlier. This isn’t a satisfactory explanation. I could compare the modern stock of apologists with G. K. Chesterton and they would still not match up.

A second argument is that Christianity is not the common belief among intellectuals that it was fifty or sixty years ago. Since a smaller fraction of intellectuals today are deeply Christian and since apologetics is valued less today as it has been in the past, intellectuals are much less likely to go into apologetics.

Third, the state of the evidence has changed over time to make belief in Christianity less probable. This argument is almost certainly wrong. The major modern controversies implicating Christianity and Judeo-Christian religions in general have existed for a very long time. The Documentary Hypothesis and similar theories about other Biblical texts have been around for more than a century. So has evolution. Thus, the need to address these issues (either by reconciling Christianity with them, or by refuting them) has existed for a long time.

Fourth, the modern focus of apologetics has been the watchmaker analogy and variations thereof. The watchmaker analogy is an argument for the existence of God based on an analogy to a watch found in the desert which one would immediately realize had a designer. It is no coincidence that the three apologists listed above, all have arguments that revolve around the watchmaker. Ray Comfort uses a particularly stupid form of the watchmaker argument. William Dembski uses a particularly obfuscated form of the watchmaker argument. And Alister McGrath doesn’t really use the argument itself but rather spends most of his time arguing that Richard Dawkins hasn’t sufficiently refuted the watchmaker argument and that if Dawkins is fallible God must then exist.

This focus is understandable: The watchmaker argument and other teleological arguments for the existence of God are some of the hardest to refute. However, the focus of all contemporary apologetics on a single argument has left the industry stagnant and uncreative. In such circumstances, it isn’t surprising that apologetics fails to attract many intellectuals. Moreover, the focus on the watchmaker argument has caused much of modern apologetics (and thus many of modern apologists) to go head to head with much well-established science. C. S. Lewis in contrast was open to the possibility that evolution was correct. If the entire apologetic system revolves around attacking basic science, one shouldn't be surprised that not many bright, educated people are willing to lead it.

I’m not completely satisfied with any of these explanations. However, the decline of contemporary Christian apologetics needs explanation.

New Largest Prime Number Found

2009-10-15T10:38:00.000-07:00

The largest known prime has now been bumped up. The recently discovered prime is 2^43112609 − 1 which in base 10 has around twelve million digits. As with all the largest primes discovered for most of the last hundred years, the prime is a Mersenne prime, that is it is one less than a power of 2. As with the last few Mersenne primes discovered, this was discovered by the Great Internet Mersenne Prime Search which uses distributed computing to search for Mersenne primes. I've blogged before about Mersenne primes. For more details on why we care about Mersenne primes and their history dating back to the ancient Greeks see this post and this post.

There are reasons to suspect that if 2^n-1 is prime that n-1 should be likely to have a lot of small prime factors. In this case, 43112609 -1= 2^5 * 7 * 11 * 17497. So while some of the prime divisors look very small, it has at least one prime very large prime divisor and so doesn't seem to fit this pattern well. This is in contrast to the last discovered Mersenne prime 2^42643801 - 1. In that case one has 42643800 = 2^3 * 3^3 * 5^2 * 53 * 149. It remains to be seen if this new example is simply an outlier or if we need to reevaluate what we expect the exponents of Mersenne primes to look like.

Glenn Beck, International Law, and Hypocrisy

2009-10-05T08:15:00.000-07:00

The last time I discussed Glenn Beck on this blog, we discussed Beck's general ignorance and contempt regarding basic legal history. Most astounding of Beck's claims was the claim that the notion that laws change over time was an idea that arose in the 1920s as a response to "Darwinian evolution."

After remarks like that one might think that Beck isn't a bad person but just incredibly ignorant. However, Ed Brayton has drawn attention to Beck's latest interaction with international law demonstrates his true hypocrisy.

Beck frequently use the "I'm just asking questions" gambit to insinuate hurtful and borderline libelous claims. In response, One enterprising individual started a satirical website "Did Glenn Beck Rape and Murder a Young Girl in 1990?"Frankly, this seems to me to be over the line of reasonable civil discourse (even if it is amusing).

How has Beck responded to this website? Beck has petitioned World Intellectual Property Organization to remove control of the domain from the satirist. Beck's argument is that the domain creates confusion with his brand name and therefore is a violation of international conventions on trademarks. That claim is so profoundly stupid that I'm not going to bother addressing it.

The lawyers for the website responded by explaining in detail what was wrong with Beck's claim and noting that his appeal to WIPO seemed to be an attempted run-around of the First Amendment of the Constitution of the United States. What makes Beck's behavior noteworthy is that, as one of the commentators to Brayton's blog observed, Beck has a history not just of complaining about transnationalism but of any intervention of international law into U.S. affairs. Indeed, Beck wrote in a March 30, 2009 column:

"Once we sign our rights over to international law, the Constitution is officially dead. When you say things like, 'We are not going to put the Constitution behind international law,' you say that in the international court, if you say that on the floor of the United Nations, you are a freak show."

In the same column Beck also wrote this gem:

"Let me tell you something. When you can't win with the people, you bump it up to the courts. When you can't win with the courts, you bump it up to the international level."

I'll let those comments speak for themselves.

Lockhart’s Lament: A Cogent Criticism of Math Education

2009-09-30T19:23:00.000-07:00

I’ve received multiple requests to blog about Paul Lockhart’s “A Mathematician’s Lament.” Lockhart is a math teacher who is fed up with elementary and high school math education. I haven’t blogged about Lockhart's piece primarily because I agree with most of what he has to say and also a lot of people have already talked about it. (See for example, Scott Aaronson’s insightful commentary.)

Lockhart’s thesis is that much of mathematics education is simply wrong. According to Lockhart, the vast majority of our math education before college is rote learning that does not convey what mathematics is about. Lockhart argues that much of what children do in high school would be the equivalent of painting by numbers if we translated it into art. Mathematics is far more about exploration and understanding than it is about rote memorization. Lockhart argues that, by failing to let children understand and explore, we are not even teaching them mathematics. Lockhart further argues against rote math education based on practicality i.e. that these are techniques children will need when they are older.

Lockhart makes many good points and I recommend that people read his piece. As someone who has worked for many summers with the PROMYS program which uses a method similar to that outlined by Lockhart, I have much sympathy for his viewpoint. However, there are three problems with his thesis.

First, Lockhart overemphasizes the willingness of students to do exploratory mathematics. Exploration is intrinsically difficult. Moreover, it is difficult to get people to do math exploration if they don’t want to. If one tries to get youngsters to explore and they can’t do it effectively , the result is that parents will do the “exploration” for them. I’m sure there are readers of this blog who remember their parents “helping” with art projects back in elementary school.
Second, Lockhart underemphasizes the actual importance of rote learning and drills in picking up basic mathematics. Students need to be able to add, subtract, divide and multiply. They need to be able to do these things quickly in real life. Moreover, they need to do them enough times that they develop an intuition for orders of magnitude and when answers look right or wrong. That requires drilling in arithmetic from a young age. Lockhart addresses this issue briefly, but his response is unsatisfactory.

Third, Lockhart’s choice of focus on specific aspects of the high school and elementary curriculum is poor. He is correct in his criticism of the large amounts of trig memorization that occur. But he is incorrect in his example of the quadratic formula. In order to have an intuitive understanding of parabolas and other curves of degree 2, you need to know the quadratic formula. Moreover, the formula comes up frequently enough in later math classes that not knowing it would be a serious barrier. Finally, there are some items that educated people just need to know. Understanding the quadratic formula is one of those things that educated people just need to know in the same way that you can’t be an educated citizen of the United States and not know who Abraham Lincoln was.

Despite these criticisms, Lockhart is essentially correct. There are many serious problems with how we teach math and Lockhart correctly identifies many of them. While the massive overhaul that he outlines may not be necessary, it would substantially help matters if children were exposed at a much earlier age to what mathematics actually is, a subtle and beautiful art.

Alan Turing, Apologies, and Cthulhu

2009-09-10T17:19:00.001-07:00

The British Government has finally apologized for its treatment of Alan Turing. Turing was one of the greatest mathematicians of the twentieth century. He was responsible for founding computer science and he lead the effort to crack the Enigma encryption used by the Germans during World War II. This work saved many Allied lives and according to some historians proved crucial to the victory over the Axis forces. Without Turing's work, our world would look very different. However, Turing was gay. In 1952, Turing was convicted for engaging in homosexual acts. He was forced to undergo hormone therapy which lead to weight gain and other problems. Turing's security clearance was revoked. At the time, homosexuals were considered a security risk because of the potential of blackmail. The fact that the entire risk of blackmail was because they were considered a security risk apparently did not matter. Nor did it matter that since Turing was publicly gay, there was no possible risk of blackmail. Turing's ongoing consulting work with the government was terminated. Turing's life took a steady downhill side. In 1954, he committed suicide.

I am ambivalent about this apology. On the one hand, it is good to acknowledge how horribly Britain treated one of the saviors of civilization. On the other hand, apologies to the long dead always strike me as hollow. The living always face more than enough issues that are of far more practical importance than assuaging the feelings of the long-deceased.

Rather than discuss the pros and cons of such apologies, I am instead going to suggest three pieces of further reading.

First, Wikipedia has an excellent biography of Turing which explains his accomplishments and his mistreatment in far more detail than one can easily do in a short blog entry.

Second, Greg Egan, an excellent science fiction writer, has written a short story imagining a world in which Turing's life went slightly differently. In this case, "slightly differently" means had the assistance of a time-traveling robot. The story is more serious than one might think from that summary. The story looks at Turing's interactions with C.S. Lewis. I'm not sure the story is completely fair to Lewis overall, but it is very well-written and is an amusing what-if. Like most of Egan's writing, there's just enough plausibly correct mathematics to make it interesting.

Third, Charles Stross has written an amusing novel The Atrocity Archives in which Turing figures in the background. The essential premise is that Turing did not commit suicide but was assassinated by the British government to cover up far scarier discoveries he made (so presumably the Brits still owe Turing an apology in that universe). In that novel, mathematics is deeply connected to magic and thinking about certain theorems can accidentally lead to summonings of Cthulhu and other eldritch horrors. Turing was killed for discovering a series of powerful theorems including a proof that P=NP which if invoked improperly could destroy our universe. Unlike the Egan story, this is not a story I can claim has much in the way of serious merit. But it is very fun. By most accounts, Turing was a man with a sense of humor about things. I'd like to think that he'd smile to know that fifty years after he was dead, Great Britain would be apologizing to him at the same time that people were reading novels which linked him to Lovecraftian horrors.

Health Care, Death Panels and GPFM

2009-09-08T19:33:00.000-07:00

Recently, Sarah Palin and other prominent Republicans have repeated claims that the proposed health care legislation would result in the creation of so called "death panels."This claim was quickly determined to be an egregious falsehood. However, the damage was already done and all elements of the proposed legislation that dealt with end-of-life issues were removed. My father has a piece up at the Oxford University Press Blog arguing that in fact death panels aren't such a bad idea. Essentially, the point is that one of the major reasons our health care costs are so high in the United States is because we go through tremendous effort to extend life during the last few months of life for many elderly. It is an issue very much worth discussing.

However, there are two related matters I'd like to mention. First, we should not lose track of how incredibly mendacious Palin and her compatriots have been about this matter. The fact that Bush's earlier proposed health care legislation had nearly identical end-of-life provisions is just one of the many ways in which Palin has simply become divorced from anything resembling reality. At this point, one must wonder if reality has taken out a restraining order on Palin.

Second, as someone who grew up with a very Jewish ethic about end-of-life issues it is emotionally very hard to agree to actively deciding that we will no longer provide health care to certain people. In classical Jewish thought, every effort must be made to continue to sustain life, regardless of cost. However, this view was constructed when medical technology was very different. Two-thousand years ago we didn't have the option to add a few painful months of life to someone at the cost of millions of dollars. We do now. This different situation may require serious reexamining of this sort of belief. This probably isn't an issue for most people in the US or at least the form it will take will be very different. Catholicism for example has for a long time tried to make a distinction between ordinary and extraordinary standards of medical care. In event, as medical technology becomes even more advanced, more and more value systems are going to need to serious think about these issues. Go read his piece here.

Jack Chick’s New Tract

2009-09-03T17:40:00.000-07:00

Jack Chick has a new tract, “Some Like it Hot.” I’ve discussed Chick’s tracts before. This one, however, takes us to a new perspective: The entire theological system as explained by the Devil. Like all good Jack Chick tracts, even the title of the tract provides amusement. The title is an apparent attempt at something resembling wordplay referring to the 1959 movie of that title starring Marylin Monroe and Jack Lemmon. Apparently, Chick’s idea of a clever pop cultural reference is to a film that came out fifty years ago. It seems that Chick’s understanding of pop culture stopped sometime in the 1960s. This is consistent with other data, such as his continuing bashing of rock music as satanic while not addressing more modern forms of devil music such as rap.

The premise of this new tract is that a grandfather and his grandson find themselves both in Hell. While wandering around the landscape, they wonder why Henry, the intervening parent, is not there and then realize that he accepted Jesus as his personal lord and savior. The Devil then decides that he wants to talk to the two of them. The Devil gives a long rambling speech, outlining the basic theology. Jack Chick’s Devil seems to be not only incompetent, but doesn’t understand basic time management. As with any Jack Chick tract, we need some bashing of other religions. Thus, the Devil declares:

I alone control every major religion in the world! Isn’t that a pleasant surprise. We’re overrun with religious leaders down here… and all their followers! We’re “blessed” with popes galore and “holy men” like Buddha and Muhammad… all of them got here by trusting their “good works.”

This paragraph is vintage Chick. We’ve got the required Catholic bashing and we’ve got the deep misunderstanding of other religions. Memo to Jack: There’s nothing in Buddhism remotely resembling a notion of “good works.” We understand that you can only think in terms of your religion and its own theological disputes, but that doesn’t mean that everyone else thinks in the same way as you.

The Devil’s rant is accompanied by pictures of various people burning in Hell. One of them appears to be dressed as a Pope, another has peyos and a black hat, while another is wearing a turban. Apparently good Christians never wear turbans.

The Devil continues his rant, explaining that he really hates Henry because Henry saved so many souls. Since the Devil cannot take out his wrath on Henry who is in Heaven, he decides to take it out on these two and thus throws them into a bottomless pit.

This raises a number of issues. First, even Jack Chick seems to think that there’s some element of justice regarding people who go to Hell. So what theological justification allows the Devil to torture people who happen to be related to people he doesn’t like? Second, is this tract really a great argument for accepting Jesus if the most likely result is that one’s family is stuck in a burning hot wasteland where one can actually find and talk to people you know? It may be that Chick is just getting soft in his old age and so we don’t have the default setting of eternal all consuming flame while surrounded in darkness. However, if I had accepted Jesus as my personal lord and savior and had relatives who had not, I’d be tempted not to witness to people. Maybe, I’m just a horrible human being, but I’d have a lot of trouble trying to save strangers if it meant my friends and loved ones would suffer more in Hell. I don’t think that’s what Jack Chick is trying to accomplish.

Lockerbie and Guantanamo: YMGPFM

2009-08-23T09:52:00.000-07:00

My twin has a piece up at the Huffington Post arguing that Abdel Basset Ali al-Megrahi return to Libya is an argument for keeping the Guantanamo prisoners in the United States. The argument in essence is that if we keep them in the US we will have better control over what happens to them in the long run. I am however, somewhat jealous: His piece has already gotten him called all sorts of nasty names. Nothing I blog about seems to ever do that.

The International Community Should Recognize Somaliland

2009-08-19T19:27:00.000-07:00

Somalia is the perfect example of the failed state and has been so for almost twenty years. Since the fall of Siad Barre’s dictatorship in 1991, the country has been in a perpetual state of civil war. Most of the country is ruled by various warlords, and the country is in a state of perpetual war, with so many different clans and different Islamic extremist groups that it is hard to even keep count. In large parts of the country, it isn’t even clear who is in charge. All attempts by other countries to alleviate the situation have failed. Yet the international community continues to pour billions of dollars of aid into Somalia.

However, there is an exception. After Barre’s fall, the north of Somalia declared independence and named itself Somaliland. Like the rest of Somalia, Somaliland is composed of rival clans. Unlike the rest of Somalia, clan members have been willing to embrace the rule of law over the short-term dominance of their clans. Somaliland has not been perfect. It has had on and off conflicts with the neighboring Puntland, which is another autonomous entity created after the collapse of the Somali government. However, Somaliland has been relatively stable and, moreover, has attempted to comply with international law. Unlike Puntland and the various warlords controlling the remaining areas, Somaliland has moved to prevent piratical behavior by its residents. It has gone so far as to convict people simply for plotting piracy.

Despite the strides Somaliland has made as a nation, its situation is precarious. Its independence is not recognized by any country. The economic situation is much better than in the rest of Somalia, but Somaliland is by no means prosperous. Most importantly, Islamic extremists have recognized the success of Somaliland and have deliberately tried to destabilize it with terrorist attacks.

The Islamic extremists and the clan warlords recognize that, as Somaliland continues as an example of peace and stability, the example of a successful state threatens them and their respective domains. The United States and the rest of the international community need to recognize this as well. There are two simple steps to help this fledgling state: First, we must give formal recognition of Somaliland as a separate country. Second, some of the international aid directed to Somalia must instead go directly to Somaliland. Much of this aid is wasted as food supplies and other forms of aid are often seized by warlords and other groups. The people of Somaliland will actually benefit from this aid.

Somaliland has stood on its own feet for almost twenty years in a land of bloodshed and violence. During that time, the country has embraced the rule of law and helped the international community address piracy. No one else in the area is either willing or able to confront piracy. It’s time the international community had the wisdom and courage to recognize Somialand as an independent state in the community of nations.

Revisiting the Four Fours

2009-08-17T20:35:00.000-07:00

In an earlier blog entry, I discussed a generalization of the four fours problem. In that entry, we discussed the function f(n) defined to be the least number of 1s needed to represent n as a product or sum of 1s using any number of parentheses. (Thus, for example, f(6)=5 since we may write 6=(1+1)(1+1+1)). That entry inspired some discussion both in the comments thread and later by email on the general behavior of f. Harry Altman and I made some progress on the general behavior of f, that may lead to a paper.

One open problem is whether f(2^a*3^b)=2a+3b in general (ignoring a=b=0). This conjecture essentially says that the most efficient way to represent such a number is in the obvious fashion of writing (1+1) a times and writing (1+1+1) b times. Harry has shown that for any value of b if a is at most 15, this holds. Harry's proof involves a large amount of case checking but may be able to be pushed up to larger values of a. He thinks he may be able to construct a computer program that can examine the relevant case types in a systematic fashion.

My own work (with some input from Harry) has focused primarily on the global behavior of f. In the blog entry, I commented that the best known bounds on f were 3log3 n ≤ f(n) 3 ≤ log2 n for n>1 . I have reduced the upper bound to 2.65 log2 n. The remainder of this blog entry will attempt to give the general idea of the proof by sketching out the simpler result that we may take
f(n) ≤ 2.95 log2 n.

The strategy of our proof is similar to the proof that f(n) ≤ 3log2 n but more involved. We will prove this inductively on. For general n ≥ 2, let S(n) be the statement "If for 2≤ k ≤n-1, we have f(k) ≤ 2.95 log2 k, then we have f(n) ≤ 2.95 log2 n." We will show that S(n) holds for all n ≥ 1, and thus the induction holds.

First, observe, that if 2|n then S(n) since we may write n = (1+1)(n/2) and so f(n) ≤ f(n/2) + 2 ≤ 2.95log2 (n/2) +2 ≤ 2.95log2 n + 2 -2.95log2 2 ≤ 2.95log2 n. We thus may assume that n is odd. A similar remark then applies if 3|n. Now, we have either n ≡ 1 or 2 (mod 3). If n ≡ 1 (mod 3), we may write
n = (1+1)(1+1+1)((n-1)/6)+1 and so we get f(n) ≤ f((n-1)/6) + 6 and similar logic applies.

By nearly identical logic we can through arduous case checking obtain that we have S(n) unless n ≡ 7 (mod 8), n ≡ 8 (mod 9), and n ≡ 4 (mod 5). Note that the difficult cases for any modulus always occurs at n ≡ m-1 (mod m). This is not a coincidence, but discussing why that occurs would take us farther afield.

Before proceeding further, let us introduce a helpful notation. We will write [x,y](n) to mean (n-x)/y. Thus, our above results can be phrased in terms of this notation. For example, n the case that n ≡ 1 (mod 6) above, we could write f(n) ≤ f([1,6](n))+ 6. We will also use the notation [x,y]^i(n) to mean repeating the [x,y] function i times. Thus for example, [1,2]^2(11)=2. This notation makes things nicely compact. Now, let a be the largest integer such that 2^a|n+1 and let b be the largest integer such that 3^b|n+1. By the above remarks, we may assume that a ≥ 3 and b ≥ 2 and c ≥1. It does not take much work to see that we then have f(n) ≤ f([1,3]^b[0,2][1,2]^a (n)) + 3a + 4b + 2.

Now, assume that S(n) is false. We thus have 2.95 log2 n ≤ 2.95 log2 (f([1,3]^b[0,2][1,2]^a (n)) + 3a + 4b + 2 ≤ 2.95 log2 n/(2^(a+1)3^b) + 3a + 4b + 2. Canceling the 2.95log2 n on both sides and bringing the log terms over to the right hand side we obtain 2.95(a+1) + (2.95log2 3)b ≤ 3a + 4b + 2 which implies 13.5b + 19 ≤ a. Note that we did implicitly use that 5|n+1 since otherwise we would not be assured [1,3]^b[0,2][1,2]^a (n) is not negative or 0 since otherwise we would be unable to take its logarithm.

Using similar logic but reducing first by 3s before reducing by 2s we can get a similar lower bound for b in terms of a: 1.387a +2.391 ≤ b. The pair of equations has no solutions with a ≤ 3. Thus, our assumption that S(n) fails for some n is false.

The essential idea of this proof is that just as the proof for 3log2 n used the base 2 expansion, of n, we can be assured that we can in some sense reach a number with a good expansion in either 2 or 3 without expending much.

This, is of course, a toy example. With not much more effort, we can reduce the constant to 2.8, using slightly stronger inequalities and using bases 2,3 and 5. The full proof for 2.65 is more detailed but uses the same basic idea with 2,3,5,7,13 and 17. It also turns out that it helps to not think of the bases so much as the p-adic expansions, something which I hope to discuss in a later blog entry.

Skepticism Is Not an Excuse for Sloppiness

2009-08-09T13:17:00.000-07:00

While browsing a local bookstore a few days ago, I ran across a copy of James Randi's "The Supernatural A-Z: The Truth and The Lies." Randi is a professional magician and has been at the forefront of the skeptical movement for some time. The book is an encyclopedia of supernatural and fringe claims described from a skeptical perspective. Randi is a witty and clever writer. I therefore bought the book and looked forward to an entertaining learning experience.

Unfortunately, this was not to be. Browsing through the book, I found that it contains many errors and misleading statements. And these were only those detected by me from the (small) set of entries of which I had some prior knowledge.

One of the most glaring series of errors occurs in the entry Tetragrammatron. The entry reads (with internal formatting suppressed):

In the kabalah, this is the term for the four-letter name of God. In effect, it is the name of a Name. It varies from text to text. Some versions are JHVH, IHVH, JHWH, YHVH and YHWH. Since these are too sacred to be spoken outloud, the word `Adoni' is used when the name is spoken. This has led to a serious misunderstanding, since in Hebrew texts only the vowels of Adoni (or of `Elohim' - this makes it more confusing) are printed. Thus are produced the reconstructions Yahweh, Jehova, etc.

There's so much wrong with this entry that I'm not sure where to start. I'm going to refrain from pointing out the many minor errors, such as that the term "tetragrammatron" isn't actually connected to kabalah. There's no circumstance where only the vowels are printed. I'm not completely sure where Randi got this idea or what statement that this was based on. The most obvious is that in Hebrew generally only consonants are printed. It is possible that somewhere Randi got vowels confused with consonants and then thought it was something which applied only to the four letter name. The other likely possibility is that Randi was confused by the practice that, on the occasions when something is printed with vowels (such as prayer books and certain religious texts), sometimes the four letter name is printed with the correct consonants but using the vowels from Adoni. However, this practice is not the root of the vowelization in either "Yahweh" or "Jehovah."

This is not the only severe error. The entry for the Necronomicon reads:

Several additions of this grimoire have appeared. Said to have been first published in about AD 730, in Arabic, as Al Azif, by Abdul Alhazred, an English translation is attributed to John Dee. It relates powerful formulas for calling up dangerous demigods and demons who are dedicated to destroying mankind.

It is a bit surprising that a nominally skeptical work would discuss the Necronomicon without mentioning that it is a completely fictional work. The Necronomicon was originally written about by H.P. Lovecraft in his horror writing in the 1920s and 30s. It is in his explicitly fictional universe that all the details above are correct. Since Lovecraft, various hoax Necronomicons have been written, but those are all very much modern creations. While this is an error primarily of omission rather than commission it is a massive mistake which makes one wonder how much attention Randi has paid to the subject.

These are not the only entries with errors. There are misleading statements about the doctrines of Christian Science, and there are claims that are so wrong that two-minutes of fact checking would find them. For example, Randi claims that Cotton Mather presided over the Salem Witch Trials.

All these errors I found from browsing through the book for about an hour. There are many entries about which I know little or nothing and I have made no effort to check the accuracy of these entries.

There are serious pragmatic and ethical concerns with this sort of sloppiness. Pragmatically, there are three major issues: First, a moderately credulous individual might pick up this book, read through it and react against skepticism as a result of seeing such a major spokesperson of skepticism engaging in such intellectual laziness. Second, a skeptic might read the book, and rely on the incorrect information for later use and thus be caught out in a debate or discussion. Third, it is common for members of fringe groups to accuse skeptics of not taking the time to understand what they are analyzing. This gives unfortunate weight to that charge.

There are three ethical problems: Most seriously, readers expect when they buy a book by James Randi to buy a book that is accurate and has been subject to minimal fact-checking. It does a disservice to readers to sell them such poorly researched material. Second, Randi and the skeptical movement as a whole have repeatedly and correctly criticized various fringe groups for engaging in poor research and outright sloppiness. It is thus the height of hypocrisy to engage in the same behavior. Third, it is in general unethical to promote falsehoods and misunderstandings.

I'm also disturbed that I can find little discussion on the internet about the flaws in this book. The skeptical movement cannot be skeptical of others and then turn a blind eye to the flaws of their own. That's not skepticism. That's tribalism.

Are We in the Middle of a Technological Revolution?

2009-07-13T14:57:00.000-07:00

It is a common meme that we are in the midst of a technological revolution. When I made an off-hand remark in an earlier post that I did not think we were in such a state, Etienne disagreed. This post explains why it is inaccurate to state that we are in the middle of a technological revolution.

What do we mean by a technological revolution? The term is difficult to define. Here are four possible definitions: First, a technological revolution can be defined as a period during which new technologies result in rapid alterations to societal and cultural behavior. This is a vague concept but it has more precision than that of a generic technological revolution. We shall call this the social definition of a technological revolution. This definition has the advantage that it places little emphasis on when a given technology was actually invented and instead emphasizes the impact of technology.

Second, a technological revolution can be defined as the development and improvement of technologies at a pace more rapid than has been the historic norm. We shall call this definition the historical definition of a technological revolution.

Third, a technological revolution can be defined as the rapid development of new technologies faster than has been the historic norm. We shall call this the inventor's definition of a technological revolution. This inventor’s definition differs from the historical definition in that it focuses only on technologies which are new, not improvements upon existing technologies. Unfortunately, the distinction between significant improvement of an existing technology and fundamentally new technology is not that clear.

Fourth, a technological revolution can be defined as the accelerated construction of new technologies such that much of the population are unable to cope with the rapid changes in daily life. We shall call this the old-geezer definition of a technological revolution. Given that, whenever new technologies are developed older individuals have trouble adapting to them, the fourth definition seems to be less useful than the other definitions. We shall therefore focus on the first three definitions.

We are arguably in the middle of a technological revolution by the social definition, but the argument is not as strong as one might think at first glance. When most people point to a technology today which has altered social behavior, they point to the internet. The internet has allowed people to communicate conveniently when they are continents apart. It has also produced a series of media where the barrier to entry for the common citizen is almost non-existent. This has led to the free flow of all sorts of content, whether blogs, videos or collaborative projects such as Wikipedia.

TIME Magazine went so far as to declare the Time Man of The Year last year to be "You." However, this should raise alarm bells. Any bandwagon on which TIME has jumped is almost certainly overhyped. This is no exception.

The actual social impact of the internet has been small. Even the major social-networking sites such as Myspace and Facebook have relatively few people on them. Myspace has about 100 million registered accounts, but many are simple spam or are bands and small corporations using Myspace as webhosts. This is not fundamentally different from what people were doing fifteen or twenty years ago with personal webpages on sites like geocities. The total number is simply larger.

The barrier to entry to the internet may be small, but the barrier to being substantially noticed on the internet is higher, arguable as high as it was in the age of conventional publication. Moreover, much of the content (such as silly videos on Youtube) is content that would have likely been created without the internet and the only change is that the content is publically available.

Thus, the argument that we are in the midst of a technological revolution is weak under the social definition of such a revolution.

What about by the historical definition? Here again the argument for a contemporary technological revolution is weak. Moore's Law (that computer power doubles approximately every 2 years ) is valid , but it has been valid for almost sixty years. Similar observations apply to other technologies.

Most of the time when people speak of a current technological revolution they speak of technologies related to computers. However, for this particular definition, others might point to advances in the biological sciences. However, here also they would be wrong to assert that something unique is occurring now. We have in the last few years made major strides in our understanding of genetics and related areas of biology. PCR in particular has opened new frontiers. Yet even here, there are clear limits to what has been accomplished. Our improved understanding of genetics has produced not much in the way of direct medical breakthroughs but, rather, has increased our understanding of how very complicated and non-Mendelian many diseases are (see for example this discussion by Carl Zimmer). Meanwhile, genetic tests for some simple Mendelian diseases such as Tay-Sachs have existed for about forty years. Thus, the pace we are advancing in biology is not so rapid as to justify the label “revolutionary”.

What about the inventor's definition? This is by far the one with the clearest answer. And the answer is “no”. All of the major modern technologies are old. The electronic computer itself is almost 70 years old. The internet (even if one doesn't count ARPAnet but rather the internet as a large scale network) is 30 years old. The World Wide Web is 20 years old. The cellphone is about 30 years old. The primary improvements in the contemporary world have made existing technologies faster, smaller and cheaper. But little has changed with the underlying technologies.

By the most reasonable definitions of a technological revolution, we are not living in one today. Technologies continue to improve at a rapid, but not revolutionary, pace.

Sonia Sotomayor and More Gratuitous Promotion of Family Members

2009-07-06T14:37:00.000-07:00

My father has a piece up at the Oxford University Press blog arguing for the confirmation of Sonia Sotomayor. He was earlier in favor of the confirmation of Samuel Alito. He argues that the most important condition is once again satisfied: Sotomayor is a qualified legal professional.

I'm not sure I agree with his argument. Frankly. there seem to be many qualified candidates who have a great deal of experience. I personally am also deeply concerned about Sotomayor's attitude towards both free speech and civil liberties issues ( Doninger v. Niehoff being the most serious example). I worry that with her on the Court many close decisions that would otherwise support civil liberties will otherwise go in the other direction.

In any event, the piece is worth reading and raises a number of interesting points. Go read it.

Perez Hilton is a Sexist Bigot: A Rant on Misogyny and Math

2009-06-21T16:06:00.000-07:00

While researching for my last post on Fox News and informed blog readers, I read too much Perez Hilton. Perez Hilton traffics in negative stereotypes damaging to young girls. He thinks stereotyping himself gives him license to stereotype others.

In a recent post on Jessica Alba playing a mathematician in an upcoming movie , Hilton wrote:

They want us to buy into her as a math genius?

Ha ha ha ha!

To help things along, we bet she's going to do the 'ugly' thing, a la Charlize Theron in Monster, right?

What a joke.

The formatting is the original with internal links suppressed. Perez Hilton thinks that hot chicks can't do math. I have taught math to children of a variety of ages. It is difficult to convince young women in our society that they can do math. Young women often lack self-confidence about mathematics. Many of them think that "only the ugly, unpopular girls" do math. One high school student once told me that she didn't want to go to a summer math program because if she did "everyone will think I'm uncool."

Perez Hilton reinforces this perception. Hilton is gay, an oppressed, frequently stereotyped minority- and he fits the stereotype. He does after all work as a "reporter" on celebrity gossip. He thinks stereotyping himself allows him to do the same to others.

One might say: "well, maybe Perez is correct." He's not. Danica McKellar, who played Winnie on The Wonder Years, is an accomplished actress, a published mathematician, and is smoking hot. There are many examples of female accomplished scientists and engineers who are very good looking. Julie Payette is Canada's most accomplished astronaut and was described by one teenage acquaintance as an "AILF," an acronym I will not spell out so I can keep this blog's PG-13 rating.

Perez, sir, you are an ass. You are actively harming young children's education. You are perpetuating damaging prejudices. Think before you speak. Or even better, just do the mathematicians and math teachers of the world a favor and shut up.

Bloggers, Fox News, and an Informed Audience

2009-06-20T11:35:00.000-07:00

In April of 2007, the Pew Research Center released a study about the knowledge levels of individuals in the United States. Many self-identifying liberals and liberal bloggers have pointed out that the study showed that regular viewers of Fox News have one of the lowest levels of political knowledge compared to many other groups. Only 35% of Fox News viewers were classified as being in the high knowledge group. This was low compared to many other samples. For example, 41% of CNN viewers, 54% of Daily Show watchers, and 54% of users of major newspaper websites were classified as being in the high knowledge group.

However, these bloggers have ignored other data in the study. In particular, the study found that people who use blogs as a news source are almost as ignorant as Fox News viewers. Only 37% of people who use blogs as a news source are in the high knowledge group. The difference between the Fox News viewers and the blog readers is statistically indistinguishable. Moreover, although Fox News viewers performed poorly, by some metrics conservatives performed better than liberals.

How were people determined to be in the high knowledge group? A series of 26 questions was asked of which 23 (decided in advance) were used to judge the examinees' knowledge level. An example of the questions asked is what party is currently in control of the House. People who correctly answered 15 questions or more were placed in the high knowledge group; people who correctly answered 10 to 14 questions were classified in the middle knowledge group; people who answered fewer than 10 were classified in the low knowledge group. The study had a total sample size of 1,502 and a percent error of 3.5%.

One interesting question to ask is if a breakdown of the mid -and low level knowledge groups allows us to distinguish the knowledge levels of the blog readers and the Fox News viewers. Here again, Fox News viewers perform poorly. 35% of Fox News viewers fall into the low knowledge group. Fox News has the second highest percentage of people in the low knowledge group (excepting people who do not get news regularly). However, the real poor performers are the blog readers of whom 37% fall into the low knowledge category. What is happening with these blog readers? I propose five possible explanations.

First, it is likely that part of this result stems from the aggregation of all blogs compared to just a single news network. Thus, the group of blog readers includes those who are reading Perez Hilton or TMZ and not much else. Thus, they only know about what celebrity is cheating on whom or what celebrity threw a tantrum. These celebrity gossip mongers could be reducing the apparent knowledge base of blog readers. One way to test this hypothesis is to examine the breakdown of what blogs people are reading. However, the study does not do so. It is likely that the inclusion of Perez Hilton readers and the like is bringing down the knowledge numbers for the blog readers. However, I doubt that this explains entirely the extremely poor performance of blog readers.

Second, a liberal can point to the low knowledge level of Fox News viewers and suggest that conservatives as a whole have poorer knowledge levels. From this premise, the argument would continue, what is bringing down the knowledge level of the blog readers is the presence of conservative blog readers who have abysmal levels of knowledge. However, this argument doesn’t fit with the other data from the Pew survey: viewers of the O’Reilly Show and listeners to Rush Limbaugh both score relatively high for news awareness (51% and 50% in the high knowledge group respectively). Furthermore, Democrats were substantially more likely to fall into the low knowledge group than Republicans, with 26% of Republicans in the low knowledge group and 31% of Democrats. This may be due in part to the slightly lower average income of Democrats .The study confirmed a strong correlation between income level and knowledge level, but did not investigate whether Democrats and Republicans have closer knowledge levels when income is a fixed variable.

In short, the Pew data refute the standard liberal perception that viewers and listeners of conservative shows are uninformed. Presumably, O’Reilly and Limbaugh’s audiences are at least as conservative as the generic Fox News viewer. Consequently, there is no reason to think (given this data) that readers of conservative blogs are less informed than readers of moderate or liberal blogs or that conservatives are in general less informed than liberals.

Third, the apparently low knowledge numbers for blog readers could be due to the highly specialized nature of many blogs. If a person only cares about a small number of issues, he may only read blogs focusing on those issues. If those issues have little to do with general political concerns, he may not have reason to learn or recall data such as who controls Congress. This is again a hypothesis that could be tested by looking in more detail at what blogs people are reading.

Fourth, many of the most successful news blogs are hosted on major news websites. A variety of New York Times reporters have blogs at nytimes.com where they report on stories, add their own commentary or add follow up notes to earlier articles they have published. This leads to the question of what one means by blog. The Pew study made no attempt to provide a coherent definition. Thus, people who read blogs by reporters may be classifying those blogs as part of major newspaper websites which could be leading to an artificially uninformed collection of people who identify themselves as reading blogs.

Fifth, blog readers could be genuinely unknowledgeable. This is, to me, the most distasteful explanation. However, it is the simplest explanation for the data and does bear serious consideration.

Note that the percentage of Fox News viewers who are in the high knowledge group is not low compared to the overall percentage of people in the United States who are in that group. That number is also 35%, and is brought down primarily by the large number of viewers of local TV news and viewers of network morning TV shows. So under this metric, blog readers and Fox News viewers look very much the same, with political knowledge levels close to those of the general population.

One implication of the Pew data is clear: Liberal bloggers need to stop using this study to attack Fox News and must stop attacking the knowledge base of conservatives as a whole. More studies need to be done. If this data continues to hold under further scrutiny and when Hilton-type blogs are removed from the picture, then bloggers as a whole need to ask why their readership is so dismally ignorant and what bloggers can do to alleviate the situation.

Iran and Gratuitous Promotion of the Other Brother

2009-06-19T09:42:00.001-07:00

Normally when I point to something a sibling has on the Huffington Post it is something by my twin. However, this time, there's a piece by my little brother. Nathaniel talks about the history of the V for Victory symbol and how it is now making its way into Middle-East politics. It is very worth reading. The history of the symbol and how it has evolved makes for fascinating reading. I think that he may be underestimating how diverse its symbolism is in the Middle-East and how fast the symbol's meaning is changing. Anyways, check it out.

Yeshiva World News creates Anti-Semites

2009-06-18T16:33:00.000-07:00

Many readers are likely aware of the controversy surrounding Rabbi Leib Glanz. Rabbi Glanz is a part-time chaplain for the New York City corrections department who came under scrutiny after reports emerged that he had used his influence to help a convicted criminal hold his son’s Bar Mitzvah at the prison. The event included about 60 guests. Prison employees were paid overtime to help with the event. This by itself showed an astonishing lack of judgment on the part of Glanz. However, further details emerged which showed a pattern of Glanz systematically performing favors for Orthodox criminals, especially Satmars, the chassidic sect of which Glanz is a member. A member of the clergy who is corrupt or has severely misplaced priorities is such a common event that it is usually not worth noting. What is worth remarking on is the reaction to these events in a part of the larger Orthodox community.

Yeshiva World News, a popular ultra-orthodox news publication, ran an editorial on Wednesday that argued that the real problem wasn’t anything that Rabbi Ganz had done. No, the real problem was that the matter came to the attention of the proper authorities in part because fellow Jews had told the government and the press about Ganz’s behavior. The article is misleading in that it implies that the criminal in question, Tuvia Stern, was merely awaiting charges . This is not accurate. Stern was convicted and is serving a sentence. Moreover, although Rabbi Ganz is a chaplain for The Tombs which is used primarily as a holding prison for not yet convicted criminals, most of the favoritism he is accused of providing benefited convicted prisoners.

From the article (comments in brackets are my translations of relevant Hebrew and Yiddish phrases):

The inmate had arranged to have his son’s Bar Mitzvah celebration in the jail where he was being held. This information was subsequently leaked to the press at which time they had to act on the information. And act on it they did. What a travesty!

This has caused an obvious chillul Hashem [disgrace to God’s name] of the highest magnitude and has put the orthodox community at large and all frum [orthodox] inmates, once again, under great and unwarranted scrutiny. It has had a tremendous ripple effect and has left in its wake the evisceration of years of mesiras nefesh [self-sacrifice] and infrastructure that has been built for inmates past, present, and future.

We all know how important the mitzvah of Pidyan Shvui’im [redeeming andcomforting captives] is and it is not our place to judge another Jew. That is a job for Hakodosh Baruch Hu [The Holy one Blessed be He] alone. Our job is to make sure that we do all we can to facilitate these individuals and their families in their time of need to the best of our ability. No one would condone any of their alleged behavior and some may agree or disagree with the considerations they may have received until this point, but no one would disagree that we must stand by our fellow Jews and help in any way we can. Unfortunately, that was all lost and a lesson that will come at a severe price. Who knows what will, Lo Aleinu [God forbid], await these prisoners as they get shipped off to Riker’s Island. Their potential mistreatment is beyond our comprehension as they will be in the company of the worst criminals in our state.

Does someone really believe a good thing was done here? Is this what our Torah teaches us? The anti-semitism this has caused will be on their head and only death can be m’chaper [atone] the chillul Hashem [disgrace to God’s name]. We, as Jews, must think long and hard of the far reaching ramifications of our actions.

So to be clear: An Orthodox Rabbi engaged in behavior that was at best ethically dubious, he got caught, and YWN is complaining that fellow Jews reported on him.Centuries ago, one of the worst things a Jew could be was a “mosser,” a term generally translated as “informer” but more accurately rendered as a “snitch.” A mosser was someone who reported the transgressions of other Jews to the non-Jewish government. In an era when pogroms could occur on the flimsiest pretext and where Jews handled most legal matters internally, this was a reasonable stance. However, this has not been the case for hundreds of years in most of the world, and has never been the case in the United States. Yet, here in the United States in 2009, we have an Orthodox Jewish publication criticizing Jews for reporting clearly inappropriate behavior out of concern that such reporting will lead to increased anti-Semitism. This position is both reprehensible and short-sighted. I know what will lead to increased anti-Semitism: Non-Jews learning that a substantial part of the Jewish community considers itself so divorced from the civic life of the United States that it thinks that people who report the failures of government employees are worthy of death.

I hope that the sane elements of the Orthodox community will condemn this outrageous editorial in the strongest possible language. Jews are American citizens with the same rights and the same obligations as all other American citizens. The United States has welcomed and extended civil rights to Jews in a historically unprecedented fashion. This editorial displays profound unawareness of and ungratefulness for that reality.

Hat tip to Onion Soup Mix.

Captain Kirk and Kashrut

2009-06-14T18:16:00.000-07:00

New technologies frequently raise new questions for systems of law. In this regard, halachah, the system of Judaic law as used by Orthodox Judaism, is no exception. However, since halachah concerns itself with many ritualistic issues that would not be of concern to most other legal systems, questions related to new technologies arise more often in halachah than in most other systems.

The rapid growth of modern technology has left Orthodox Rabbis almost overwhelmed in dealing with new issues. It is therefore not surprising that they have had little time to address questions of predicted technologies and discoveries which do not yet exist. This has not stopped the laity from speculating about such issues, especially when prospective technologies are connected to popular culture such as Star Trek and Star Wars. This post will discuss two of the major halachic questions raised by Star Trek and outline their possible resolutions. First, is replicated food kosher? Second, can aliens or androids convert to Judaism?

The first thing that many people think about when they think about Orthodox restrictions is kashrut, the traditional dietary restrictions on religious Jews. Star Trek: The Next Generation and later shows have a technology called “replicators” which allow users to materialize practically any food from pure energy. This technology raises a variety of issues. First, can an Orthodox Jew replicate non-kosher food such as pork and then consume it? The answer appears to be yes. Kashrut does not depend so much on the chemical composition of a food, but its history. For example, gelatin made from a ritually slaughtered animal is kosher while gelatin made from an improperly slaughtered kosher animal might be chemically identical and yet not be kosher.

However, there is an halachahic question whether food that looks non-kosher can be consumed. For example, many will not consume fake bacon made from beef or cheeseburgers which use soy meat. If one believes that such foods are unacceptable, then replicated pork would be likewise unacceptable.

There are however, other problems raised by replicators that only become obvious if one has spent far too much time with Star Trek. In particular, the Enterprise 1701-D has a hydroponics garden. Fans traditionally explain this garden by pointing out that in Star Trek canon certain molecules cannot be replicated and others are very difficult to replicate. Thus, when called to replicate food that contains those molecules, the replicators transport the molecules from stored material, in some cases, material harvested from the hydroponics garden. While for most purposes plant matter is always kosher, there are two circumstances where this is not the case: First, grape products have their own rules of kashrut for historical reasons. Second, during Passover, leavened products are not kosher. Thus, it is possible that material in the Enterprise’s garden could result in the replicators making unkosher food. This is a serious issue, since tools used to prepare non-kosher food can under many circumstances become not kosher themselves and transmit their kashrut status to any new food subsequently made with them. It is not clear from the description of how replicators function to decide whether or not replicators have this problem.

One general question that is raised by many science fiction shows is whether aliens can convert to Judaism. This question is difficult in that there’s no clear halachic definition of what constitutes a person. If one is a Young Earth Creationist, then this shouldn’t be a hard question to answer: people are those beings descended from Adam and Eve. However, Star Trek is explicitly not YEC, so that answer is out. Moreover, in the Star Trek universe it is possible for humans to interbreed with certain types of aliens (Spock of course is only half-Vulcan). Thus, an interfertility test as favored in the biological species definition may not work.

Moreover, it isn’t clear that a nonhuman being could not still be subject to halachah if that being was sufficiently sentient. This is connected to the more realistic question of whether an African Grey Parrot can convert. I have been told but not seen in any source that the test for whether someone is too mentally challenged to be able to understand enough to convert is whether they can recite and explain the Shemai. It isn’t clear to me that a Grey Parrot would not be able to do so (although whether you could convince an African Grey that this vaguely defined, amorphous, unobservable “God” entity existed is not at all obvious to me).

A question related to that of aliens converting is that of robots. In this case, there is a more direct precedent, in that this question has been asked previously about golems. A golem in Jewish folklore is a large creature made of clay which is animated by mystical rituals. (Under no circumstances should one confuse a golem with a small creature with a magical ring that it calls its Precious. That would be confusing fact with fiction) Golems cannot convert and cannot take part in any mitzvah since they have no souls. Presumably, the same result would apply to robots and androids. So if anyone of you wanted to see Data as a cantor, you are out of luck.

So the food on the Enterprise is kosher, but you can’t form a minyan with Data.

New Mersenne Prime Found

2009-06-13T16:35:00.000-07:00

Mersenne Primes are primes that are one less than a power of 2. Small examples are 7 (one less than 8) and 31 (one less than 32). I've blogged before about Mersenne primes here and here. To recap, each Mersenne primes corresponds to an even perfect number. It is unknown whether there are infinitely many Mersenne primes. However, we do understand them well enough that we have a very fast test for whether a Mersenne number (a number one less than a power of 2) is prime. Thus, the largest primes known are generally Mersenne prime.

The newest Mersenne Prime is 2^42643801 - 1. This is in fact not the largest prime discovered because it is actually smaller than the previously discovered Mersenne prime. This prime, like most of the other Mersenne primes recently discovered, was discovered by the Great Internet Mersenne Prime Search. This project uses a distributed computing system to search for Mersenne primes. Volunteerrs install the GIMPS software on their machines and the program runs in the background, quietly searching for Mersenne primes. The program is set up to only use processing power that the computer is not otherwise using. Thus, the program has no negative impact on performance. This is another example of the triumphs of modern technology and mathematics.

One other thing to note: There are technical reasons to suspect that 2^n-1 will be more likely to be prime when n-1 has a lot of small prime factors. In this case, 42643800 factors into 2^3 * 3^3 * 5^2 * 53 * 149 so n-1 does in fact have many small prime factors in this example.

Awkward Parties and Ramsey Theory

2009-06-11T17:23:00.001-07:00

Suppose you are throwing a party. Suppose further that you decide that you wish to make sure that, at the party, there is a minimum of awkwardness in the social interaction. To minimize awkwardness, you want to be sure either that there are at least three people at the party all of whom know each other or that there are at least three people who all don't know each other. Is there some number of people we can invite to guarantee that one of these two conditions will occur?

The answer is yes. In particular, if there are at least six people at your party, you will have three mutual strangers or three mutual acquaintances. Let's convince ourselves this is true: Assume there are at least six people at your party. Pick one of them, say Alice. (If you do have Alice, I incidentally recommend that you don't invite Eve since they don't get along well.) Now, of the at least five other people at the party, assume that Alice knows at least three (the argument is identical if she doesn't know at least three). Now, if any of those three people know each other, then that pair form a set with Alice of three people all of whom know each other. Then we are done. But if all three of those do not know each other, then they form a set of three which all don't know each other. So we either way, we must have our group of three people.

This problem, although it seems trivial, is an example of a problem from Ramsey Theory. Ramsey Theory is, roughly speaking, the study of inevitable structure, i.e., if we make certain types of objects large, what will we necessarily find in the objects? In this case, the objects in questions are examples of what are called graphs. By a graph, we mean a set of points (which we call vertices) and a set of edges connecting some of the points. In the situation above, we draw an edge between two points if and only if two people are friends.

Thus, the above result says that, given a graph with at least six vertices, there are either vertices forming a triangle or there are three vertices with no edges connecting them. There are two minor helpful pieces of notation: We say a graph is complete if, for any pair of vertices, there is an edge connecting those two vertices. We say a graph X is a subgraph of another graph Y if one can obtain X by cutting out some number of vertices from Y and then throwing out any edges in the remainder that do not connect on both ends to the remaining vertices.

With this notation, we have an easier way to visualize this problem: Is there some n such that a complete graph of n vertices with all edges colored red or blue must contain a red or blue triangle?

One might wonder about our original problem whether six is the minimum number of people? As it happens there is a pretty diagram we can draw to show that five is insufficient:

(Creative Commons 2.5 license. Original at http://en.wikipedia.org/wiki/File:RamseyTheory_K5_no_mono_K3.svg )

Given this framework, it is also natural to generalize to the following: Given some k, is there an n such that a party with at least n people must have a collection of either k mutual acquaintances or k mutual strangers? Or, framed in terms of red and blue edges, given some k, is there an n such that any complete graph of n vertices must contain a complete k subgraph with all blue edges or a complete k subgraph with all red edges?

Surprisingly, the answer turns out to be yes. However, to prove it we need to consider a slightly more general question. We define R(r,b) to be the minimal n (if it exists) such that a complete graph of n vertices with edges either red or blue must contain either a complete subgraph of r vertices with all red edges or a complete subgraph with b vertices with all blue edges. In our earlier party notation, R(r,b) counts the minimum number of people needed at a party such that no matter who is at the party there will be r people who are all mutual strangers or b people who are all mutual acquaintances.

We shall show that R(r,b) exists and is bounded for all r and b. Since our original problem is essentially R(k,k), this will answer that question. We first note that we easily have a few small values of R. For example, R(1,1)=2, R(1,n)=R(n,1)=1, and R(2,n)=R(n,2)=n. By our earlier remarks, R(3,3)=6. We need, however, a more general statement.

Lemma: For all positive integers r,b > 1, if R(r-1,b) and R(r, b-1) exist, then
R(r, b) ≤ R(r - 1, b) + R(r, b - 1) + 1.

Proof: Assume as given and consider a complete graph Z with R(r - 1, b) + R(r, b - 1) + 1 with all edges painted either red or blue. Pick a vertex v, and partition the remaining R(r - 1, b) + R(r, b - 1) -1 vertices into two sets X and Y. A vertex m goes into X if v has a blue edge to m and otherwise goes into Y. (For those still using the party analogy, we have picked a specific individual at the party, say Veronica, and now have split the entire party into people who either are friends or are not friends with Veronica).

Now, let us denote how many vertices are in X by |X| and how many vertices are in Y by |Y|. It is clear then that |X|+|Y| ≥ R(r - 1, b) + R(r, b - 1). Thus either |X| has at least R(r, b-1) elements or |Y| has at least R(r-1, b) elements. Assume we are in the first situation (the case in which |Y| is at least R(r,b-1) is essentially identical). Now, since X has at least R(r,b-1) vertices, we know that X either contains a complete subgraph of r vertices with all red edges or contains a complete subgraph of at least b-1 vertices with all blue edges. Now, if X contains a complete subgraph of all red vertices, then we are done (since X is a subgraph of our original graph Z). If X instead contains a complete subgraph of b-1 vertices with blue edges, then that subgraph with v thrown in now has all blue edges (since everything in X connects to v by blue edges) and has b elements. So in either situation we have a graph of the desired size.

From this bound it easily follows that R is always defined and bounded since we can always break R(r,b) into being bounded by values of R for smaller arguments. It isn't that hard to make this bound slightly stronger. It is more difficult to find lower bounds of R(r,b). The first such non-trivial lower bounds (i.e. bounds that were not just linear) were found by Erdos who used a then very clever method that is now a standard technique for these sorts of problems. Erdos constructed an estimate for how likely a random graph was to contain a complete subgraph of all red or all blue vertices. That is, Erdos estimated the probability that a given graph with n edges (with the edges randomly colored blue or red) contained a complete graph with k blue edges or k red edges. Erdos was able to show that if the graph was small, then the probability that a graph did not contain such an object was less than 1. If the probability was less than 1, there had to be some graph with that many edges which did not have the complete graph. Using this, he was able to show that R(k,k) > 2^(k/2).

Note that this procedure is completely non-constructive. It doesn't tell you how to even make such a graph for a given k. It simply says that if you keep randomly picking colors for a graph of that size then you will eventually hit a graph that shows that R(k,k) < n.

R(k,k) grows very quickly with respect to k. Moreover, R(k,k) is not at all easy to calculate. We know for example that R(4,4) =18. But even R(5,5) is unknown. (We know it lies somewhere between 43 and 49). The range is even worse for R(6,6) which we know must lie between 102 and 165. The problem looks at a naive glance like it can be brute forced. However, in order to show that R(k,k) = n, one needs to show that any graph with n vertices has the desired property. It is not hard to show that complete graph with n vertices has n(n-1)/2 edges. Thus, if any edge is colored either red or blue, we would have 2^(n(n-1)/2) different cases to check. Thus, to verify R(4,4)≤18 by brute force one would need to check 2^(14*(13)/2) = 2^91. That's about 10^27 cases. That just isn't doable. And the numbers get even more daunting for larger k.

There is a story that Erdos used to illustrate the comparative difficulty of this problem by constructing the hypothetical of an alien species landing on Earth and threatening to destroy us if we cannot give them the value of R(5,5). In that case, Erdos thought it would make sense to get all the world's mathematicians to drop what they are doing and work on the problem. However, if the aliens instead asked for R(6,6), we would be better served trying to fight the aliens. Calculating the exact values of R is really hard.

Now, one might not like the exact parameters of the problem. One might object that people don't simply know other people or not. They might have never met them before but have heard of them. Or they might recognize their faces but not have talked. Or they may have only talked briefly. Or they may be good friends. Or they may have known each other in the Biblical sense. So what happens if instead of just two possible colors between edges, we generalize to c colors? It turns out that the argument used above can be generalized to any finite number of colors. But the values get bad much faster. Generalizing the notation in the obvious sense, it is possible to show through not too difficult arguments that R(3,3,3) ≤17 and in fact it is known that R(3,3,3)=17. However, R(4,4,4) and R(3,3,3,3) are both unknown.

Some readers may also object to the party statement of the original problem. First, presumably for most parties the host knows everyone present. Does that simplify the problem? While one might guess that assuming that there is a vertex that has all blue edges would simplify things a lot, it turns out to be not substantially different than the original problem.

Another objection is that having a large number of people who don't know each other at a party doesn't make it less awkward, but rather more so. Consider a party with n people, n-1 of whom all know each other and the nth person who doesn't know anyone else. This could be very awkward for the nth person. Alternatively, the nth person could be some sketchy dude who is much older than everyone else and wandered in from the street (he probably has a mustache too). In that case, everything is much more awkward for the n-1.

There is however a practical solution: Every person knows at least one other person. And as long as you have at least one other person to talk to it substantially reduces awkwardness (even if it doesn't minimize it). So if we invite every single human being to the party everyone will have at least one friend to talk to. Therefore, I'm inviting the entire human race to a party next Saturday evening at 7 PM Eastern Standard Time. The venue is planet Earth. It is the third planet in the Sol system. If you have trouble finding it, just look for the big source of radio emissions that isn't the local star.

Please show up. If you don't, your absence might make it very awkward for someone who does come.

Haunted Locations

2009-06-10T10:18:00.000-07:00

Many years ago, I ran across a website devoted to chronicling haunted locations throughout the United States. The website was full of fascinating entries. By happenstance, I recently found the website again and it has not lost its amusement value.

The website, theshadowlands.net, has user-submitted entries for haunted locations. The entries have minimal punctuation and grammar, rendering some of them borderline incoherent. But entries that aren’t incoherent are often hilarious. I’ll avoid mocking the writing because that’s just too easy. Many of the entries report electric lights flickering and unexplained power failures. Apparently none of these people have heard of bad wiring or old buildings. It might be interesting to interview these people to see how much their reasoning resembled that discussed in my earlier post on electronics and the supernatural.

Let’s start with my home state of Connecticut. One highlight is Loomis Chaffee High School. We are told that “One can expect that such an old establishment would have a history.” Yes, because 140 years old is so old. I’m surprised that every city in Europe isn’t crawling with ghosts.

Albertus Magnus College in New Haven is listed as having no less than four haunted sites. One of them, Rosary Hall, has a no longer functioning elevator. The area must be haunted because “staff have reported an evil presence it, as well as freezing cold blasts of air and moaning sounds.” Yes, elevator shafts never make noise. Nor do they ever have wind come through cracks. Elevator shafts after all aren’t long columns that can easily funnel air.

In Illinois, we have a cursed graveyard. What is the main evidence that the graveyard is cursed? “Some murders took with place within a mile.” I used to be a skeptic, but now I’ve seen the definitive evidence to convince me that there is real supernatural evil in the world. After all, some murders took place within a mile of a location said to be haunted. One question: there have been murders about a block from my house. Should I be worried that I’m at the epicenter of a horrible curse?

In Pennsylvania we have a place where dowsing rods were used to verify the presence of ghosts. I guess dowsing rods don’t just find gold and water anymore. Now they also find ghosts. And this also explains why all controlled tests of dowsing rods have failed: obviously they were done in locations where ghosts were present and the dowsers’ readings were confused by the ghosts. No doubt the evil skeptics make sure to perform the tests over old Native American burial grounds.

Let’s jump over to Massachusetts. We have an abandoned train tunnel where “On some nights temperatures drop several degrees.” Right, getting colder at night is a sure sign of a haunting. In Haverhill, we have among other locations “Lizzie Bordens lawyers house” (ERV would be happy about the lack of apostrophes). Apparently if a murder is famous enough, the lawyers get to haunt places also. After the lawyer died, a family lived there but there were problems: “The family moved out that month of fright and fear.” I think I’ll go back on my promise of not mocking the writing style by noting that that sentence did not have a period at the end; I had to add that. But even with the bad grammar, I’m really scared now. I wouldn’t have believed if the family had only moved out of fear or out of fright. But they moved out due to both. The ghost must be real and very dangerous. And now we come to the entry that forced me to write this blog post.

In Marblehead there is a middle school that is severely haunted. According to the page:

In the girls’ locker room there is a ghost of a young man who died in a motorcycle and he haunts the girl room. Also there was a report of UFOs over the school and it was even in the local news paper there was a photo of the UFOs. The town of Marblehead was a built on a psychical portal a sort of window that lets in both negative and positive spiritual energy, a “hellmouth” as it was called in the 17th century.

I thought that the idea of a “hellmouth” as a magical portal was a late 20th century idea. By sheer coincidence, the only other one of which I’m aware also happens to be at the site of a school. That school is Sunnydale High in Sunnydale California. Apparently someone has been watching too much Buffy the Vampire Slayer.

Aside from notable individual entries, there are also larger patterns in the entries. None of the Ivy League schools are haunted. Harvard isn’t mentioned at all. Yale is only mentioned in passing when talking about a building bought by the earlier mentioned Albertus Magnus. Similar results apply to the rest of the Ivy League. What could explain this apparent lack of ghosts? Here are a few possible explanations for this apparent lack of otherworldly manifestations: One explanation is that the ancient Ivy League schools already have a secret society devoted to stamping out ghosts and so everyone else not involved do not get a chance to notice the ghosts. This society might not only be devoted to dealing with ghosts. They might also deal with other threats, especially when they work with their colleagues from Miskatonic University. Yale no doubt plays a critical role in all this since it has the Voynich Manuscript, which we all know is really the Necromonicon.

This hypothesis however isn’t satisfactory. Many other schools also aren’t mentioned. Stanford does not have any entries nor does the University of Chicago. It seems like the more prestigious the school, the fewer ghosts it has. Maybe there are ghosts at those institutions but the ghosts are scared that, if they manifest themselves, then the smart people at those schools will make proton packs and go all ghost busters on their asses.

Another possibility is that the people at these schools are just more closed-minded. They have their “books” and their “science” and their “critical thinking.” Consequently, even when they see clear evidence of ghosts, they rationalize it away by saying things like “Hey, a mile from a location is pretty far away” or “elevators shafts are long and generally leaky. Wind can go through them easily” and other stuff that is generally said by closed-minded, skeptical meanies.

Now, suppose for a second that we set aside the convincing evidence of ghosts that we’ve seen. Forget about the cursed graveyards with murders within a mile. Forget about the haunted elevator shaft. Definitely forget about the hellmouth which has nothing at all to do with a fictional television show starring Sarah Michelle Geller. What other explanations could exist for this apparent disparity in ghost reports? Two possible explanations then emerge: First, people at more prestigious schools are more skeptical and so say things like ““Hey, a mile from a location is pretty far away” or “elevators shafts are long and generally leaky. Wind can go through them easily” and other stuff that is generally said by people who bother to use their brains. However, my own experience with Yalies does not make me inclined to think of them as a terribly skeptical group. Second, people at such schools don’t feel a need to tell spooky stories to give their schools a unique reputation. If your school isn’t so well known, having a ghost might make you feel like you’ve got some unique flavor.

Full disclosure: Boston University, where I am a graduate student, has an entry: The room that Eugene O’Neill died in is said to be haunted by his ghost. So far, the ghost has bothered none of my classes.

Obama in Cairo

2009-06-05T13:58:00.000-07:00

I don't have time to blog on this topic but there are few pieces I'd like to recommend.

First, of course, is my twin's piece at the Huffington Post where he looks at some of the influences that went into the speech. He argues that the speech used a variety of lines that taken in historical and literary context are less unambiguously positive than one might think. I'm tempted to argue that what Obama did amounts massive quote mining, taking many religious quotes simply out of context. Read the piece and be the judge.

There is also been some complaints in the atheist end of the blogosphere that Obama implied in the speech that all Americans believe in God. This strikes me as an opinion worth reading but overall is naive and misguided. Given what he did in this speech and what Obama is setting out to accomplish, I don't think people should seriously have expected any form of inclusion of atheists and agnostics that would not have resulted in backlash from the Islamic world. Obama explicitly mentioned non-believers in his inauguration speech. Be happy with that.

Also, David Horowitz has an interesting piece praising Obama's speech from a neo-conservative perspective. If David Horowitz is praising something Obama did, we can safely assume it was the correct thing to do.

Finally, see also Ed Brayton's piece also taking a very positive stance on the speech.

Two New Jack Chick Tracts

2009-05-28T12:28:00.000-07:00

Jack Chick has recently added to his website, not one, but two new tracts: "Evil Eyes" and "It's a Deal."

Jack Chick is a best-selling evangelical tract writer and conspiracy theorist. His tracts encourage people to accept Jesus as their personal lord and savior. This by itself would not be cause for note. However, Chick is refreshingly explicit in articulating and endorsing the more ridiculous elements of extreme evangelical beliefs. Multiple tracts revolve around good individuals being damned because they died before they accepted Jesus as their personal lord and savior while bad individuals are saved at the last minute since they accepted Jesus before they died. Multiple tracts state explicitly "It isn't a question of good or bad. It is a question of saved or lost." If one tried to write a parody of the evangelical conception of God and tried to accent its wretched, cruel and capricious nature, one would have trouble constructing a deity that looked more cruel and evil than that in Jack Chick's mind.

Like many extremists, Chick feels a need to make his argument primarily by attacking groups he dislikes. Thus, he has tracts about how all sorts of people are going to hell: Jews, Catholics, atheists, Mormons, Muslims, Catholics, Dungeons and Dragons players, Wiccans, Catholics, Protestants who think that good works help for salvation, evolutionists, and Catholics. Did I mention he really doesn't like Catholics?

In the past, his anti-Catholicism has generally been highly conspiratorial, claiming among other things that the Catholic Church secretly founded Islam as a way to control the Arab world. Apparently all of the historical conflicts between Christendom and Islam were really just to prevent us from realizing the truth. Or something like that. He also thinks that the Catholic Church founded liberation theology to help control the communists. As with Islam, the fact that the Church has generally been unfriendly to liberation theology is obviously just more evidence for the conspiracy (although honestly in this case, I suspect that he simply heard the term "liberation theology" at one point and jumped from there).

However, one of the new tracts, Evil Eyes, takes a new angle on his anti-Catholicism. In the past, he has portrayed the low level personnel in the Church such as most priests as simple pawns in the larger conspiracy. In this tract however, the Catholic priest in it publicly doubles as a priest of Santeria. Now, one important thing about Jack Chick is that he believes that every deity of every other religion is really an actual demonic entity. Thus, in this tract, an individual uses a voodoo curse on a man to turn him into a zombie. The local Catholic priest, who is also a Santero, tries all he can but is powerless. However, the day is saved when the young born-again cousin uses the true word of God to expel the demon that is the cause of the curse. At the end, the priest gives up both Catholicism and Santeria to become a true born again Christian. One of the most fascinating details in this tract is that not only does Chick think that it is perfectly natural for a Catholic priest to also practice Santeria, but he considers it natural that the priest would do so as part of an accepted community practice. Chick sees everyone else's religions as part of one large blur and assume that the practitioners themselves also see them that way. This is not unique to Chick but is also true for other evangelicals such as the writers of the Left Behind series.

The second tract involves Satan making a deal with a basketball player to have his soul in exchange for letting the player play really well. This tract is part of a running series of tracts that Chick is producing now which are particularly aimed at African-Americans and hence have all African-American characters and stereotypical black plotlines. I'm not sure what Chick is thinking given that African-Americans have one of the highest percentages of evangelicals of any racial group. In any event, as with most Chick tracts involving contracts with the Devil, the protagonist realizes that he's in deep trouble and accepts Jesus as his lord and savior, thus nullifying the contract. The point is then made that the Devil doesn't need a contract to get your soul. This leads to a question: More often than not in Chick tracts, people end up in hell. Furthermore, even people who know about the Devil and God often wind up in hell; in at least some cases people wind up in hell even after seeing the Devil first hand. Therefore, why does the Devil bother to make contracts with people? Indeed, it seems in the Chickverse that making a contract with the devil is a sure sign that you'll eventually realize that you really need Jesus. So if the Devil is trying to collect as many souls as he wants, he shouldn't be trying to make contracts at all.

The only thing more striking than the cruelty of Chick's God is the incompetence of Chick's Devil.

There's a fascinating element to Chick tracts. Aside from the interesting view into a warped mind whose views are shared by a disturbingly large number of people, one learns all sorts of tidbits that one wouldn't learn otherwise. For example, according to the Dark Dungeons tract, not only is Dungeons and Dragons a way to lure children into the occult but if your character advances to at least eighth level , then you will start to learn real spells. Obviously, I was never patient enough. I'm am however curious. D&D 4.0 recently came out. The power level of magic in the game is substantially reduced from that of 3rd edition. Does this mean one has to get to a higher level before one learns real magic? If so, this seems like yet another reason to not play 4th edition.

Atheism and Nihilism

2009-05-24T13:19:00.000-07:00

The blogger Yeshivish Atheist recently posed the question whether atheism necessarily implies some form of nihilism. YA listed me as one of the people he would like to hear from in this matter. This entry is my attempt to respond to his inquiry. The question posed is far ranging and so this entry will be broadly focused.

YA ‘s inquiry asks whether atheism allows for the possibility of life having intrinsic “purpose, meaning or morality.” The short answers are “unlikely, no, and maybe.” First, it isn’t clear to me why these three issues are related. The primary reason for seeing them as related seems to be that religions, especially the Abrahamic religions, see these three issues as interrelated. This is similar to the common perception that abiogenesis and the evolution of life into diverse species must be related. This attitude towards evolution and abiogenesis arises primarily because, for thousands of years, the common answers to these questions not only gave a single explanation for both, but did not even distinguish between the two issues. The situation is similar in regards to meaning, purpose and morality. The three are not necessarily related though they have been historically.

First, does human life have intrinsic purpose? From an atheistic perspective, the answer is “no.” However, it isn’t at all clear to me why people find the existence of purpose to be important. It comforts humans that they are part of some master plan. However, cows have a purpose: they provide humans with milk, meat and leather. If I were an intelligent cow who found that cows had been bred by humans to serve as a food production device, I doubt that I would find this to be a purpose that filled me with contentment. Thus, the atheist must ask: Why does the theist or the deist feel so confident that the purpose of humanity or that individual’s life is so worthwhile?

Second, does human life have intrinsic meaning? This question is harder to answer, especially in so far as meaning is much harder to define. Many theists are fond of claiming that, if there is no afterlife, then life has no meaning. Thus, “meaning” is frequently a proxy for some way to stave off the overpowering feeling of the inevitable oblivion that awaits. We die. Even our accomplishments and memories will one day be forgotten. And human civilization will eventually collapse. All of this takes places in an uncaring void. In that sense, then life has no intrinsic meaning. Unless one buys into a Kurzweil–style Singularity (most sane people do not), there is no stopping this. We can all find things that we have find interesting, or personally worth doing. But there is no meaning in this life other than what we make for ourselves.

Third, is there intrinsic morality? Of the three issue posed by YA, this is the one that has the most chance of having some sort of “yes” as an answer. As with purpose, theism and deism do not do a much better job at providing morality than atheism. The Euthypro dilemma- Is what is moral commanded by God because it is moral, or is it moral because it is commanded by God?- makes claims of intrinsic moral authority as provided by theism to be problematic. However, there is some evidence to suggest that there may be something resembling intrinsic morality. In particular, there are clear trends in moral thought over the last few thousand years. In that time, humanity has embraced broader notions of what constitute basic rights and has extended further the set of individuals to whom those rights apply. A few hundred thousand years ago, one would have no moral duties to anyone outside one’s own small tribe. That has broadened so that many now feel moral obligations to everyone, everywhere. The fact that many different societies are embracing similar moral systems suggests that they may be doing so because they are approximating some external moral system. This argument is by no means airtight. The argument is couched in terms like “rights” which have only made much sense for a few hundred years. There are also other explanations for this trend. For example, it may be that humans have evolved to care more about those they can easily communicate and identify with. This broadening of moral attitudes then simply reflects the reality that communication and transportation are far easier now than they were in earlier ages.

To summarize: If one is an atheist, it is unlikely that life has any intrinsic meaning, purpose or morality and theism doesn’t do a substantially better job of answering these issues. The appropriate response seems as it often is to be that of Randall Munroe:

Original at http://xkcd.com/167/ , licensed under Creative Commons Attribution-NonCommercial 2.5 License.