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On June 24, a Tennessee man was arrested for possessing photos that showed the faces of three underage girls, including Miley Cyrus, superimposed onto the nude bodies of adult women. Assistant District Attorney Dave Denny said of the arrest, "When you have the face of a small child affixed to a nude body of a mature woman, it's going to be the state's position that this is for sexual gratification and that this is simulated sexual activity." The phrase "simulated sexual activity" apparently refers to a Tennessee sex crimes law which states in part: "It is unlawful for any person to knowingly possess material that includes a minor engaged in simulated sexual activity that is patently offensive."

Assuming this is the crime that the D.A. plans to charge him with, to me it seems obvious that the defendant didn't violate the law as written. For one thing, if the nude women in the pictures were just standing there (and neither the article nor the D.A.'s statement suggests otherwise), then there was no "sexual activity" in the photos of any kind, real or simulated. But even if the nude adult women in the photos had been engaged in sexual activity (even just striking a mildly sexy pose), the law still would not apply, because the law requires an actual minor to actually be engaged in something, even if that "something" is simulated sexual activity. So if a video showed a real minor that appeared to be masturbating or having sex with someone in a manner that was "patently offensive", that could violate the law. (Hopefully the "patently offensive" clause would exclude artistic movies like The Tin Drum, although that defense has not always worked.) But if the girls' faces were simply cut and pasted onto the bodies of the women in the photos, then the minors in question were not "engaged in" anything. The D.A. appears to have confused "material that includes a minor engaged in simulated sexual activity" with "material that simulates a minor engaged in sexual activity". And the D.A.'s statement that "this is for sexual gratification and that this is simulated sexual activity" — clearly implying that the pictures are for sexual gratification and therefore this is "simulated sexual activity" — is ridiculous. The defendant probably used pictures of Miley with her clothes on for "sexual gratification" — does that make the photos "simulated sexual activity"? (Dave Denny's office did not respond to my request for comment.)

But I was more interested in a different question: What would people in a survey think about whether the defendant violated the law? And, would people who are good at math, answer the question differently from everyone else? And would those people answer the question differently from people who are good at, say, English composition?

That might seem like an odd twist to put on it. But if you can show that a certain answer correlates with mathematical ability, that indicates something special about that answer. And if you can show that that answer appeals to people with math skills, but not to people with English/writing/composition skills, then that indicates something interesting not just about that answer, but about mathematical ability as well, as opposed to writing ability. Whether that answer is "right" or "wrong" (or whether you think those terms are even meaningful for a legal opinion), it is a fact, not an opinion, that people with self-reported higher math skills are more likely to pick that as the correct choice.

By contrast, when the D.A. makes a public statement about the criminality of the defendant's actions, the implication is that we should give some weight to his statements because of his qualifications, such as being a member of the bar. But if we were to ask other bar members to decide independently of each other whether the defendant committed a crime, would they converge on the same answer? If not, then why should we listen to him, as opposed to someone else with the same credentials? When an expert cites their credentials in support of an opinion, if it's not true that other experts with the same credentials would back them up on that opinion, I don't think people realize the extent to which there is no there there.

So in the survey, I described the man's alleged actions and the Tennessee statute, and asked people if they thought he had violated the law. I also asked respondents to rate their math skills as "Excellent"/"Very good"/"Good"/"Fair"/"Poor" and to rate their English/composition skills as "Excellent"/"Very good"/"Good"/"Fair"/"Poor". The survey was posted on the Amazon Mechanical Turk site, where you can post "tasks" for people to complete in exchange for small payments of, say, 25 cents apiece. Some companies use this for grunt work (like hiring people to review user-submitted profile photos to make sure they don't contain nudity), but I use the site mainly to conduct surveys.

I think it's unlikely that the Mechanical Turk users are a representative cross-section of the population, but I use it more to find significant relative differences between demographic groups. If 60% of women on the site answer a question one way and 80% of men answer it the other way, that probably suggests that in a real cross-sectional survey of the population, men and women would largely disagree on the answer as well. (The alternative would be that the kind of men and women who use Mechanical Turk are predisposed to answer the question differently along gender lines in a way that average men and women are not, but that seems unlikely.)

For this survey, I offered users 25 cents apiece for completing this survey and collected 127 responses. The results in a nutshell:

1. About two-thirds of all respondents (85 out of 127) said that the man did violate the law.
2. However, among the respondents who rated their own math skills as "Excellent", only 44% (12 out of 27) said he violated the law, and 56% (15 out of 27) said that he did not. Out of all ten ability groupings (five different ability groupings for math, from "Excellent" to "Poor", and five for English), this was the only group where a majority said that the defendant didn't violate the statute.
3. Respondents who self-rated their English/composition skills as "Excellent", were also more likely than average to vote that the man did not violate the law, but a majority of them still voted that he did.

These results are significant at the 99% level, which you can check using an online statistical significance calculator. In other words, despite the modest sample size, the answers given by the respondents with self-rated "excellent" math skills are so starkly different from everyone else's, that there's less than a 1 in 100 chance that the difference is due to coincidence. Almost certainly, something about mathematical ability is correlated with a person's likelihood of giving the "not guilty" answer. (At this point I'm going to give in to my bias and hereinafter refer to that as the "right answer.")

Furthermore, while respondents with "excellent" English/composition skills were also more likely than average to get the right answer (a difference that is also significant at the 99% level, given the collected data), they were considerably less likely to do so, than the users with self-reported "excellent" math skills (again, significant at the 99% level). I tabulated all the responses.

If I could afford to pay a larger sample, I would investigate whether the effect of "excellent" English/composition skills disappears entirely when you control for math skills. In other words, it's possible that the people with excellent English/composition skills were more likely than average to get the right answer, but only insofar as their English/composition skills were correlated with excellent math ability — and maybe people with "excellent" English/composition skills, but only average math ability, score no better than the average respondents.

One thing that jumps out at me: Even though 44% of the 27 people with "excellent" math skills said the man did violate the law, when you look at the 58 people who self-reported "very good" math skills, 74% of them said he violated the law. This would appear to confound my original hypothesis that good math skills lead people to converge on the correct answer. But I suspect that many people with self-reported "very good" math grades were probably just good students who studied hard and did the practice problems and got good grades in math, but without necessarily having the insight that makes someone an "excellent" math student. Without that insight, there was no reason to expect them to be better than average at answering a question that has no resemblance to their textbook's practice problems.

In fact, I suspect that many of the people who self-reported their math skills as "excellent", and who still answered "yes" to the question of whether the man violated the law, probably fell into that studious-but-not-insightful category as well. It would be interesting to test whether if you required respondents to actually answer a math question — not a standard textbook question, but a tricky question that required people to demonstrate an understanding of what is actually going on — if the correlation between correctly answering that question, and "correctly" answering the legal question, is even stronger.

But what I think is even more important than the correlation of the correct answer with "excellent" math ability, was the significantly lower correlation of the correct answer with "excellent" English skills. I've been saying for years that you can use excellent prose to defend an illogical idea, or you can use poorly crafted prose to defend a good idea, and so if you care about the quality of an idea and its impact on the real world, you have to look at the substance of an argument, not the style. Economics professor Steven Landsburg writes in his forthcoming philosophy book The Big Questions,

The bane of a college professor's existence is the student who has been taught in a writing course that there is such a thing as good writing, independent of having something to say. Students turn in well-organized grammatically correct prose, with the occasional stylistic flourish in lieu of any logical argument, and don't understand why they've earned grades of zero.

I call such people "vocabulemics", who seem to think the purpose of a discussion is to vomit up as many SAT vocab prep words as possible, rather than to form a coherent point. I've tried, and I can't think of any coherent point that could be made in order to argue that the Miley photoshopper really did violate the Tennessee law.

If you're still unconvinced by the results of a survey of mathletes, consider that they do match up well with the comments provided to me by Mark Rasch, a lawyer and computer security specialist with Secure IT Experts and the former head of the Department of Justice Computer Crimes Unit:

First, an image of a minor engaged in simulated sexual activity is not the same as a simulated minor engaged in sexual activity... In other words, if you posed actual minors, nude, and made it look like they were having sex, it would be a crime, even though there was no "actual" sexual activity. In most other contexts, when the legislature says "simulated sexual activity" they mean real people engaged in what appears to be sex. The government is trying to apply this theory to real sex but simulated minors. I don't think that passes statutory muster.. its not what the statute prohibits... Under that rationale, if you had, for example, a picture of two dogs mating, and glued pictures of kids on the dogs faces, this would be "simulated sexual activity" but would not be prosecutable. Where do you draw the line? Under federal law, you typically draw the line at the use and posing of real kids.

Depending on how you look at it, you may think that this opinion from credentialed expert Mr. Rasch, vindicates the opinion of the math aficionados who voted that the defendant did not violate the law. I think it's the other way around — the fact that this answer was correlated in the survey responses with mathematical ability, vindicates the opinion of Mr. Rasch.