Wednesday, November 19, 2008
But Metroblog noticed something in the article that really stands out and makes one wonder what the Queen's University administration was thinking. Included in the list of behavior which will receive "censure" is "If a student avoids a classmate's birthday party for faith-based reasons." I'm having trouble seeing how that is similar to calling someone "gay" as a slur or calling someone a "retard" (the second does not strike me as a big deal anyways. Sometimes you need a word to describe that someone is just not an intelligent person).
I, as well as everyone I've talked to about this, is puzzled about what this hypothetical has to do with the other situation. I had some difficulty thinking about what sort of situation they were talking about. Do they mean say an Orthodox Jew who would not go to a party on Friday night? Or maybe a Catholic not going to a party during Lent? Or a Muslim not going due to the presence of alcohol? How are any of these offensive? The closest I've been able to come to a minimally sensible interpretation in this context is a student who would not go to a party because there were gays dancing at the party (which actually is less halachicly problematic than mixed dancing).
The most coherent interpretation I have is that to someone birthdays are so important that it is unacceptably offensive to not attend them over silly religious obligations. If anyone has an interpretation that is more charitable or simply makes more, sense please post it.
I'm reminded of a conversation I had with a friend a few years ago when I could not go to an event because it was the same time as Shabbat dinner. She remarked "That's so `gay', where by gay I mean Jewish." I wonder how the Queen's University facilitators would respond to that.
Monday, November 17, 2008
The second development is that Catholic philosopher Francis Beckwith, a former Fellow of the Discovery Institute and a professor at Baylor University, has forcefully come out against intelligent design. In the past, Beckwith has spoken sympathetically about ID so this comes as a surprise. Unfortunately, he now opposes intelligent design for the wrong reasons:
Despite my interest in this subject and my sympathy for the ID movement’s goal to dismantle materialism and its deleterious implications on our understanding of what is real and what counts as knowledge, I am not, and have never been, a proponent of ID. My reasons have to do with my philosophical opposition to the ID movement’s acquiescence to the modern idea that an Enlightenment view of science is the paradigm of knowledge. By seeming to agree with their materialist foes that the mind or intellect cannot have direct knowledge of real immaterial universals, such as natures, essences, and moral properties, many in the ID movement seem to commit the same mistake as the one committed by the late medieval nominalists such as William of Ockham, who gave us what is often called “Ockham’s razor,”...I imagine some readers are sputtering a bit as they read that. The complete context of Beckwith's remarks does not cast Beckwith in a better light. Beckwith's remarks are disturbing for a great many reasons, but I will only focus briefly on two of them.
First, as one friend cogently asked what is an "Enlightenment view of science? Newton's? Bacon's? Hume's? Paley's? Whewell's?" One would like to think that a tenured philosophy professor such as Beckwith would be more precise with language.
Second, many if not most scientists would agree that science has no essential monopoly on on all knowledge. Moreover, many proponents of intelligent design would also agree even as proponents of ID frequently attempt to push the bounds of what science can reasonably talk about. Thus, Beckwith's objection is either to some sort of extreme strawman or Beckwith's objection is to the entire notion of science as a separate epistomological method. Indeed, Beckwith goes on to claim that "According to many scholars, the practical consequence of “Ockham’s razor”[sic] is that claims about a thing’s nature, purpose, or intrinsic dignity—universal properties it shares with other things of the same sort—are “unnecessary” for our scientific investigation of the world because they don’t add anything of explanatory importance to our direct empirical observations." It appears thus that Beckwith does object to the entire scientific method. This is the opposite of something like non-overlapping magisteria. This is aside from the fact that archaeologists engage in trying to find artifacts' "purpose" all the time. I have no idea how science would incorporate the "intrinsic dignity" of objects.
I've paid some attention to Beckwith in the past and knew he had reservations about intelligent design. For a long-time I suspected that his stated reservations were for rhetorical effect while he argued for the constitutionality of teaching ID in public schools. In my naivete I never would have thought that Beckwith's objection was to science as a whole.
Beckwith appears to be objecting to ID, not because it drags us back a few centuries, but because it does not drag us back far enough. As William Dembski takes a step to join the 19th century, Beckwith is trying his hardest to join the 10th.
Friday, November 14, 2008
Great Britain recently extradited Gerald Toben, an Australian national, to Germany to face charges of Holocaust denial after Toben landed at Heathrow airport. Toben is no doubt an odious human being. However, laws such as Germany’s laws on H holocaust denial are infringement of free speech rights. More disturbingly, Toben did not commit his crime in Germany. However, since his blog was visible in Germany, Germany asserts that he has violated their laws. And Great Britain is going along with it.
In the past, Great Britain’s actions have been detrimental to free speech. Great Britain has been strongly criticized in the past for its libel laws under which the burden of proof to is placed automatically on the defendant. Together with a very low standard of what constitutes publication in Great Britain, Britain has become known for “libel tourism.” In one memorable case, an American author was successfully sued in Great Britain when 23 copies of her book were bought online by people in Great Britain. However, the British libel laws have at least one saving grace: they are civil penalties. The German law in question is criminal.
This is all the more disturbing because many countries are in the process of strengthening their laws restricting speech or are cracking down on offensive speech. Italy has recently attempted to prosecute an Italian comedian for insulting the Pope. The Netherlands recently decided to expand its anti-blasphemy laws to include speech offensive to any group. . If I insult the Pope and then land in Great Britain, would they send me to Italy or the Netherlands first?
Great Britain’s reaction to Toben is not productive. Great Britain should officially repudiate this stance and Germany should officially repudiate prosecution of people whose only crime is to have a website that can be accessed in Germany. These laws may be used now to imprison those whom we despise but the risk is too high.
Edit: The above contains some minor factual issues that don't detract from the central point. See the anonymous commentator's remark below for details.
Follow up edit: It looks like Toben will not be sent to Germany after all. See this article.
Wednesday, November 12, 2008
Sunday, November 9, 2008
This post is the third post of a series of three posts on why we care about prime numbers. The first entry gave an overview of primes. The second discussed the link between Mersenne primes and perfect numbers. This post will discuss practical applications of large prime numbers and provide a concrete example.
The main focus of this post is the Diffie-Hellman algorithm. Diffie-Hellman is a procedure whereby two people can have a conversation and at the end of the conversation they will share a secret number. The remarkable thing is that even if an eavesdropper hears the entire conversation, the eavesdropper will have no feasible way of figuring out the secret. . By repeating this procedure many times two people develop can have a list of secret numbers which they can use to encrypt messages to each other that only they can read. As is standard in cryptography, I will refer to three people, Alice and Bob who want to share a secret number and Eve the evil eavesdropper wishes to obtain their secret number.
There is a standard analogy in cryptographic circles to accomplish this sort of task. Suppose Alice and Bob want to exchange an object through a mail system that they don't trust. But they know the mail employees aren't going to be able to get into a locked box. How can Alice send an object to Bob? She cannot just send a locked box because Bob won't have a key. Nor can she send a box and a key because then the corrupt mailmen can use the key to open the box. Here is the solution: Alice puts her object into the box and locks it with her lock. She mails this to Bob. Bob puts a second lock on the box and mails it back to Alice. Alice now removes her lock and sends it back to Bob. Bob can now remove his own lock and gain access to the contents of the box.
Before we discuss this algorithm in detail we need a few small mathematical facts. We call doing arithmetic where we only care about the remainder when divided by k to be “arithmetic mod k”. So for example, 4+6= 3 mod 7 since 4+6 = 10 and the remainder of 10 when divided by 7 is 3. For a concrete analog, when we tell what time it will be on a clock some number of hours from now we are doing arithmetic mod 12.
Now, we need to define a primitive root: Suppose for a fixed prime p we have some u such that u1 u2 u3 u4… up-1 mod p cycle through 1,2,3,4… p-1 in some order then we say that u is a primitive root for p. For example, if p=5, then 2 is a primitive root for 5 since 21=2,22=4,23=3,24=1. But 4 is not a primitive root for 5 since 41=4, 42=1,43=4,44=1 so we only cycled through 1 and 4. Now, it happens that every prime p has some primitive root u. The proof will not be given here but this fact is the only piece of non-trivial number theory we will need for this procedure.
The last detail we need is to note how it is possible to quickly raises numbers to large powers. Naively, if I want to calculate xn for some fixed x and large integer n I need to multiply by x n times. And this applies if I am operating mod k also. But we have a nice trick called repeated squaring that allows us to get around this. Observe that if we know xy then we can calculate x2y by squaring xy. Thus, we can easily calculate x2, x4, x8, x16 all the way up to the largest power of 2 less than n. Then we can write n in base 2 and calculate xy in the obvious fashion by multiplying together the relevant powers of the form x2^t. Thus, calculating xn takes at most c log n multiplications for some fixed constant c.
We are now ready to outline the procedure.
Let's do a small example with Say p=17 and u=3. Bob says "My prime is 17, my primitive root is 3." Bob picks 6 as his random number. Bob calculates that 36 mod 17 which is 15. So he says "my B is 15."
Alice picks a random number, say 13 and calculates 313 mod 17 which is 12 so she says "My A is 12.".
Bob then calculates A^b mod 17, which is 126 mod 17 which is 2. Alice calculates B^a mod 17 which is 1513 mod 17 which is 2
So Alice and Bob now share the secret number S = 2. Obviously, for 17 it isn’t that hard for Eve to work out the answer. She just needs to write out a table of powers of 3 mod 17. But if instead of 17 she had to deal with a prime that was a few hundred digits long that strategy would never work; Eve's table would have more entries in it than the number of atoms in the universe. There are other strategies Eve could try to attack this but in general she doesn’t have many options.
An important caveat: No one knows a quick way of doing the discrete log but it has not yet been proven that there is no quick way to do so. Almost everyone who has studied the problem is very sure that there isn’t a quick way.
Diffie-Hellman turns out to have a variety of practical problems with implementation. So more often a related algorithm called RSA is used instead. In a later post, I will discuss RSA. RSA has even more counter-intuitive properties than Diffie-Hellman. While Diffie-Hellman required Alice and Bob to be work with each other, in RSA the intended recipient simply needs to publish a key which can then be used by anyone to encrypt messages such that only the recipient can read them. The standard analogy used by cryptographers to describe this procedure of a box that anyone is able to lock but only the person with a special key can unlock. The fact that this is mathematically doable turns out to be very useful. Readers have likely used RSA without even realizing it if they have engaged in almost any form of commerce over the internet. Modern web browsers and other software implement RSA in a way that is invisible to casual user. Even though one does not notice it RSA is responsible for keeping credit card numbers and similar data to safe and secure.
Both Diffie-Hellman and RSA rest heavily on the ability to find large primes. Moreover, the security of these algorithms is connected strongly to our understanding of prime numbers and their properties. Thus, the mathematics of large primes is vital to the functioning of the modern economy.
Edit: Added the locked box analogy.
 In fact we won’t really need that fact other than that we need in the procedure access to a prime that has a primitive root and we want to know that there are large primes with this property. Since all primes have this property, so do all large primes.
Wednesday, November 5, 2008
Here at Boston University students on the whole seemed to be very happy. They spent more time drunkenly screaming "Obama!" at the top of their lungs than actually sitting down and watching the ongoing returns in the House and Senate. And they kept screaming until about 2 AM when sane people were trying to sleep. I must wonder if they were plants sent by the Republican party to make people so annoyed with Obama that they won't vote for him in 2012.
Now as to specific elections: I'm disappointed at Chris Shays' defeat since he is a moderate Republican and it seems that people voted against him primarily for reasons that had little to do with his voting record. I'm appalled that Ted Stevens won despite his recent convictions. Really Alaska, haven't you been made fun of enough in the last year? Finally, as of right now, it looks like California's Proposition 8 passed which is unfortunate. My ideal is to have no legal recognition of any marriages but, if we are going to be recognizing some, we should recognize all of them.
Specific pieces I recommend reading: My twin has a piece up on the Huffington Post discussing McCain and Obama's respective final speeches. Mark Chu-Carroll has a piece up which discusses his personal views and raises interesting points about how statistics are reported during elections. Orac presents some worrying evidence that an Obama administration may not be as pro-science as many hoped. Razib Khan over at Gene Expression has as usual a variety of interesting posts with good analysis of data to back them up. There's a piece in Commentary's blogs by Abe Greenwald suggesting that the Republicans did not do anything wrong this election. Then people should immediately read Ramesh Ponnuru's response.
One final note: As I was writing this piece I noticed that this version of Firefox does not have "Obama" in the default list for the spellchecker. I presume that will not be the case for future versions.
Monday, November 3, 2008
When I see a comment in a blog or see a blog post that uses one of these terms, I know immediately to pay attention. I know that the comment will be the product of clear and careful thinking with a good attention to shades of gray. I know that the writer must be a great wordsmith and master of the English language, more skilled and knowledgeable than William Safire. The only thing that could make me pay more attention would be if the comment were written in all caps.
You have helped make dialogue in this country more nuanced, well-reasoned and calm. You have heightened political discourse to levels undreamed of by past generations. Without your repetition of these terms we would be a terribly divided nation with no appreciation that reasonable people can disagree. Thank you.