Archive for: May, 2010

Big Number Bogosity from a Christian College Kid

May 04 2010 Published by under Bad Probability, Big Numbers

I know that I just posted a link to a stupid religious argument, but I was sent a link to
another one, which I can't resist mocking.

As I've written about quite often, we humans really stink at
understanding big numbers, and how things scale. This
is an example of that. We've got a jerk who's about to graduate from a dinky
christian college, who believes that there must be something special
about the moral atmosphere at his college, because in his four years at the
school, there hasn't been a single murder.

Yeah, seriously. He really believes that his school is special, because it's gone four whole
years without a murder:

Considering that the USA Today calculated 857 college student deaths from 2000
to 2005, how does one school manage to escape unscathed? It's certainly not
chance or luck. For Patrick Henry College, it's in our Christian culture.

Critics mock us for our strict rules - like no dancing or drinking on campus,
no members of the opposite sex permitted in your dorm room, nightly curfew
hours - and the lack of a social atmosphere it creates. We have been the
subject of books (God's Harvard), television shows, op-eds, and countless
blogs who rant against our brand of overbearing right-wing Christianity that
poisons society's freedom.

Yet, what is the cost of students being able to "express" themselves? Is that
freedom worth the cost of drunk driving deaths, drug related violence, and
love affairs turned fatal?

There were 857 college student deaths in the five-year period from 2000 to 2005! Therefore,
any college where there weren't any murders in that period must be something really
special. That christian culture must be making a really big difference, right?

Well, no.

According
to Google Answers
, the US Census Department reports that there are 2363
four year colleges in the US. So, assuming the widest possible distribution of
student deaths, there were 1506 colleges with no student deaths in a five-year
period. Or, put another way, more than 60% of colleges in the US went that five-year period
without any violent student deaths.

Or, let's try looking at it another way. According to the census, there are 15.9 million
people currently enrolled in college. The school that, according to the author, is so
remarkable for going without any murders in the last four years? It has 325 students. Not
325 per class - 325 total.

In other words, among a group making up less than 2/1000ths of one percent of the college
population, there were no murders. Assuming that the distribution of violent deaths is perfectly
uniform (which it obviously isn't; but let's just keep things simple), given that there were
857 violent deaths in the student population as a whole, how many violent deaths
would you expect among the student body at his dinky christian college?

That would be a big, fat zero.

The fact that there were no violent deaths at his school isn't remarkable,
not at all. But to a twit who's incapable of actually understanding what
numbers mean, that's not the conclusion to be drawn. It's also not that the
violent death among college students is actually remarkably rare. Nor is it
that most college students will go through college without any
violent deaths on campus. No - according to a twit, with 857 violent
campus deaths over five years, the only reasonable conclusion is that
there must be something special about the ridiculous religious rules at his college
that prevented the great rampaging plague of violence from touching the students
at his school.

I actually spent five years as an undergraduate at Rutgers University in NJ. During that
time, there were no violent student deaths. (There was one death by alchohol poisoning; and there
was one drunk driving accident that killed four students.) But zero violent deaths.
Gosh, Rutgers must have been an absolutely amazingly moral university! And gosh, we had
all of those horrible sinful things, like dancing, and co-ed dorms!
How did we manage to go all that time with no violence?

It must have been the prayers of the very nice Rabbi at the Chabad house
on campus. Yeah, that must be it! Couldn't just be random chance, right?

Ok, now let me stop being quite so pettily snide for a moment.

What's going on here is really simple. We hear a whole lot about violence
on campus. And when you hear about eight-hundred and some-odd violent deaths on campus,
it sounds like a lot. So, intuitively, it sure seems like there must be a whole
lot of violence on campus, and it must be really common. So if you can go through your
whole time in college without having any violence occur on campus, it seems
like it must be unusual.

That's because, as usual, we really suck at understanding big numbers and scale. 800 sounds
like a lot. The idea that there are nearly sixteen million college students is just
not something that we understand on an intuitive level. The idea that nearly a thousand
deaths could be a tiny drop in the bucket - that it really amounts to just one death
per 100,000 students per year - it just doesn't make sense to us. A number like 800 is,
just barely, intuitively meaningful to us. One million isn't. Fifteen million isn't. And a ratio with a
number that we can't really grasp intuitively on the bottom? That's not going to be meaningful
either.

Bozo-boy is making an extremely common mistake. He's just simply failing
to comprehend how numbers scale; he's not understanding what big numbers really mean.

67 responses so far

The Danger When You Don't Know What You Don't Know

May 03 2010 Published by under Bad Logic

A little bit of knowledge is a dangerous thing.

There's no shortage of stupidity in the world. And, alas, it comes in many, many different kinds. Among the ones that bug me, pretty much the worst is the stupidity that comes from believing that you know something that you don't.

This is particularly dangerous for people like me, who write blogs like this one where we try to explain math and science to non-mathemicians/non-scientists. Part of what we do, when we're writing our blogs, is try to take complicated ideas, and explain them in ways that make them at least somewhat comprehensible to non-experts.

There are, arising from this, two dangers that face a math or science blogger.

  1. There is the danger of screwing up ourselves. I've demonstrated this plenty of times. I'm not an expert in all of the things that I've tried to write about, and I've made some pretty glaring errors. I do my best to acknowledge and correct those errors, but it's all too easy to deceive myself into thinking that I understand something better than I actually do. I'm embarrassed every time that I do that.
  2. There is the danger of doing a good enough job that our readers believe that they really understand something on the basis of our incomplete explanation. When you're writing for a popular audience, you don't generally get into every detail of the subject. You do your best to just find a way of explaining it in a way that gives people some intuitive handle on the idea. It's not perfect, but that's life. I've read a couple of books on relativity, and I don't pretend to really fully understand it. I can't quite wrap my head around all of the math. That's after reading several entire books aimed at a popular audience. Even at that length, you can't explain all of the details if you're writing for non-experts. And if you can't do it in a three-hundred page book, then you certainly can't do it in a single blog post! But sometimes, a reader will see a simplified popular explanation, and believe that because they understand that, that they've gotten the whole thing. In my experience, relativity is one of the most common examples of this phenomenon.

Todays post is an example of how terribly wrong you can go by taking an intuitive explanation of something, believing that you understand the whole thing from that intuitive explanation, and running with it, headfirst, right into a brick wall.

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54 responses so far