Slashdot Mirror
The Mathletes and the Miley Photoshop
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:
- About two-thirds of all respondents (85 out of 127) said that the man did violate the law.
- 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.
- 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.
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Reminds me of when I worked front line hardware breakfix back in 1994 or so. A guy brought his machine in for service, and we transferred his files to a new hard drive. He had a hidden directory, and in it were pictures that had been clearly spliced. There were about fifty different shots of the same woman's face on various bodies engaged in porn acts.
He called to let us know his friend, Angie, would pick up the computer. Naturally I was somewhat surprised when I recognized Angie.
I agree child porn is immoral and should be illegal, but the main reason I think it should be illegal is so the girl isn't subjected to the photo shoot. A Photoshop job like this, despite being offensive, seems to be a protected right of Americans. South Park, for example, is composed of many offensive collages but I couldn't imagine condoning censorship of the show. I'd have to take the defendant's side on this issue, even though it seems wrong to side with someone who whacks off to that type of shit. It's America, you take the good with the bad.
"From the depths of my skeptical and rationalist soul, I ask the Lord to protect me from California touchie-feeliedom."
would people who are good at math, answer the question differently from everyone else? [...] 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.
You might be good at maths but you seem to be terrible at science. You can't demonstrate you collected results from anybody who was actually any good at maths, you just got a bunch of responses from people who thought they were good at maths. Maybe people with such a self perception are also more likely to pick views that are opposed to what they think most people will think in order to further demonstrate their superiority?
I think your study is quite interesting but it doesn't mean what you think it means. It also has an awfully small sample size.
Nick
Here in the UK I think you're allowed to have pictures of breasts at 16, have to be 18 for fully naked pics though. Then again in some other countries it probably wouldn't be illegal no matter what the ages were, but I consider this a very borderline case since she's 17 at the moment, so it doesn't seem too perverted from my cultural perspective - in the UK you can legally marry or have sex as long as you're both 16 or over (think it's 18 for homosexuals). You can also start drinking here at 18. I'm glad I don't live in the US :P
which is totally what she said
If the results are significant at the 1% level (you mean .01, not .99 - low p values indicate higher significance), then this does NOT mean that there is less than a 1% change that the results are due to chance. It means that IF THERE WERE TRULY NO DIFFERENCE, we'd expect to see an effect this large or larger only 1% of the time. This is Statistics 101 stuff. A p value conditions on the null hypothesis being true; it is not a statement about the probability of the null hypothesis. For that you need a Bayesian inferential technique.
Surveys are inherently difficult to present in a neutral fashion, especially when attempting to determine correlation. Take the following (simplified) survey for example:
I like Cheerios:
[Yes] [No] [Sometimes]
Rate your proficiency at math:
[Excellent] [Good] [Average] [Poor]
Now, let's say you found a statistically significant correlation between people who like Cheerios and people who are excellent at math. Congratulations! You just did not find a correlation related to math proficiency at all.
What you did just find is a correlation between people who selected the first option in your survey.
Now, randomizing your answers is a good start and will resolve the above issue. However, there are hundreds of other things which can affect your results and there is an entire survey industry formed around these problems. The immediate problems that spring to mind about the survey in TFA is:
-Respondents must have internet access
-Respondents must have signed up to Amazon's mechanical turk
-Respondents were paid for the survey
-Respondent proficiency at math/language was self-assessed
-Respondents must be able to comprehend English
Anyway, I could go on but my point here is this: despite the fact that a statistically-significant correlation that was found, that correlation may not stem from the questions themselves.
Karma: SELECT `karma` FROM `users` WHERE `userid`=138474;
"A Tennessee man is arrested for possessing a picture of Miley Cyrus's face superimposed on a nude woman's body. In a survey that I posted on the Web, a majority of respondents said the man violated the law -- except for respondents who say they were good at math in school, who as a group answered the survey differently from everyone else."
Therefore: Mathematicians like child porn.
Talk about flamebait summaries. Can we have something that roughly represents the article?
I have a ton of problems with the methodology as well. Self-selected tiny sample set with self-reported aptitudes used to make blanket statements, with no attempt to get a rational cross-section (which he acknowledges and then says it's not a problem despite lack of any evidence supporting that conjecture), and all the problems/bias associated with internet-only research (we are a biased sample set, in that we're all here).
In short: wanking. You can't even begin to effectively correlate decision making to mathematical ability without actually testing that ability.
If you asked me to describe my own math ability, I'd say "average", because I routinely deal with people who are so much better than me at math that I can't in good conscience say I'm better than that...I mean, I never progressed beyond the simplest multi-variable calculus! But put me up against someone who is average across the entire population, and I'll rate much higher.
ad logicam Claiming a proposition is false because it was presented as the conclusion of a fallacious argument.
So, if someone was to take the prosecutor's face and photoshop it onto a picture of a dead body, that photoshop artist would be arrested for murder? Clearly, the way the prosecutor has re-worded the law in his favor, the victim is being charged with a thought-crime.
And if MERELY THINKING of a sexual act with a minor is punishable, then we are in a very sad state of affairs.
What is up with this country?
If telephones are outlawed, then only outlaws will have telephones.
They rationally look at the question and examine the facts, such as they are, to arrive at a conclusion. Some find for and some find against and the fact that some find the (alleged) perp not guilty isn't just because they can add up and/or spell, and it's actually not relevant which way they vote - the interesting thing is that they considered the evidence before voting whichever way they thought was the right way rather than following the herd!
Eclectic beats from Leeds, UK
handmadehands.co.uk
This statistical extrapolation is not valid (AT ALL, UNDER ANY CIRCUMSTANCES, NEVER EVER). For this kind of analysis to mean anything, you have to conclusively demonstrate that you collected a representative sample of the population. That means: A random sample, drawn in a non-biased (or bias-controlled) fashion, from the whole underlying population. Ask a real statistician, and (s)he'll tell you: Your extrapolations are only as good as your sampling methodology.
You seem to be under the mistaken impression that you're somehow, magically, exempt from this mathematical fact because you are making relative comparisons between two subsets of your sample. Where the hell did you get that idea?
To understand why, try considering this hypothetical: What if the subset of the population that is drawn to answer your MechTurk question is biased in more than one way? For instance, it could contain a larger-than-normal proportion of highly-intelligent social misfits who sympathize with outcasts, as well as a larger-than-normal proportion of under-educated Moral Orals. It could easily generate similar results to yours, as could an infinity of other hypothetically biased samples.
Statistically, then, how do you differentiate between your pet theory and the infinity of alternatives? YOU CAN'T. Methods of statistical extrapolation obtain their effectiveness from their relationship with the law of large numbers (probability, basically). Your poor sampling method has completely discarded that link, leaving zero support for your conclusions.
You cannot fix this problem with math: If your sample is not a truly random sample, drawn from the full underlying population in a non-biased (or bias-controlled) fashion, your numbers don't mean shit W.R.T. the population, and they never will. PERIOD.
(As an aside, there are methods that can control for sampling bias in certain LIMITED circumstances, when the nature of the bias can be quantified. But you aren't using this method, AND it doesn't apply to your situation, because you can't make reliable quantifying statements about how your sample is biased.)
You are officially part of the problem. Either learn more stats, or STOP MISLEADING YOURSELF AND OTHERS by mis-applying them.
Shopping Miley's head on to a naked woman doesn't make her naked, just as shopping her head onto an old photo of Arnold Schwarzenegger doesn't suddenly make her a male bodybuilder.