Political Affiliation and Scientific Knowledge Levels

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

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

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

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

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"

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

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.