Monday, April 9, 2012

Why a degree in mathematics can leave you feeling like a mute...

O.J. Simpson and how America is seriously mathicapped.

What is "mathicapped" you ask?  Well, it's like handicapped.  But... with math.

We live in a society inundated with numbers.  Yet most people don't have a good grasp of basic mathematical concepts.

This is a serious problem for me personally because I have people in my daily life that will hand me a number and say something, well... stupid.

One example was a colleague in the sciences who posted an infographic on Walmart.  From the infographic it appeared that Walmart was an evil, nefarious organization who paid almost nothing in taxes.

Now, I'm not going to say that I agree with Walmart and its practices.  I don't.  I think Walmart is a symptom of many economic ills.

But the graph showed "revenue," not "profit," which is a totally different thing.  Walmart's revenues are huge - over $400 billion a year - but their profit margin is tiny.

Because taxes are on profit rather than revenue, of course their taxes were tiny next to their revenue.  Their profit margin is tiny.  Walmart pays a normal amount of taxes relative to its profit.

Another is when I talk about statistics in the death penalty.  For example, in the courtroom and on TV you learn that DNA evidence is just about 100% reliable.  If a guy did it by the DNA evidence, then he must have definitely done it.

But this is, once again, messing up the question.  The probability that the DNA of two people will genuinely match is really remote.  Depending on the number of markers used it can be on the order of billions-to-one.  (I discuss how DNA testing works here on David Kaczynski's blog at TU.)

But the probability of two people having a genuine DNA match not the right statistic to use to answer the question "How reliable is DNA evidence?"  The right question is "What is the chance of a false positive due to any cause?"

And the answer is "It's pretty high."  Depending on the lab, a false positive can be very likely, not because the DNA actually matches but because there's a huge chance of a match due to lab error.

OJ Simpson Trial

This goes back to my education in math.  At UIC, all science and math majors had to take "Reading in the Discipline."  In the sciences that was easy.  People just read research papers and popular articles.

But in math, our professor was a little at a loss.  For one thing, math is not something you can just pick up after reading a bit of Wikipedia and delve into a new article.  Each branch and subbranch of mathematics requires a great deal of study to really comprehend.  For another, there's very little actual math in popular articles.  Unlike everything from stars to fossils, people find math, well... boring.

But one marvelous article that he did find was on the misuse of conditional probability in the OJ Simpson murder case.  (I could not find the original article, but one that paraphrases the same argument is here.)

When confronted with the evidence that OJ Simpson beat his wife, OJ's defense team presented this statement:

"[A]n infinitesimal percentage—certainly fewer than 1 of 2,500—of men who slap or beat their domestic partners go on to murder them."

But that's the wrong question statistically.  The correct question is "Assuming that the wife has been murdered and the husband beat her, what is the probability that the husband is the murderer?"  And the correct answer is, according to the 2005 article cited above, about 8/9, or well over 80%, not less than 1% as the defense presented.

But people can't get that.  They aren't trained in math so they don't even know what questions to ask to get to the bottom of misleading graphs and numbers.

And that leaves me feeling like a mute - or, better yet, like the people around me cannot communicate in "real" language.  Because I want to talk to them and explain these ideas or even more advanced thoughts and ideas, but, sadly, they haven't been taught to speak in the same language as I have.

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