Mark on Science

Science is a special kind of magic, practiced by people called 'nerds'. No body knows how it works for sure, but it probably has something to do with computer machines.

Be careful, science is dangerous. Nerds get so lazy from all their science making that they only have enough strength to stare into space, talk to the internet, or drive their electric wheelchairs.

Sometimes nerds get angry. If too many nerds are angry at one time, electricity stops working and nuclear bombs go off. Damn you nerds! (but don't tell them i said that)

Luckily, normal people can reap the rewards of science without having to risk their own sanity, because nerds are happy to do science for you. They will accept monetary compensation, but are also happy to work for social approval.

One final note. Logic tells us that all nerds wear glasses, but that not all people who wear glasses are nerds. You may not agree with this opinion, but you'll have a hard time convincing me otherwise, as there are two sides to every fact.

Mysteries of the Bell Curve Revealed

Behold the famous Bell Curve (aka 'the normal distribution'), loved by some, loathed by many, but indispensable to social sciences like psychology. The Bell Curve is what you get when you graph the distribution of things like people's height, weight, mood, IQ, extroversion, exam scores, affinity for chocolate, willingness to vote Labor, or indeed almost anything in which people vary. Again and again the same pattern appears: some people are on one extreme (e.g., extremely tall), some people are on the other extreme (e.g., extremely short), but most people are relatively average.

Why should this be? Why should such a disparate range of variables all distribute in this way? Is this some sort of divine signal? Or perhaps a government conspiracy? How bizarre that exactly the same shape should come up again and again!

Well, there's actually a good reason for the ubiquity of the Bell Curve. I only realised this a couple of years ago when I saw a nifty little exhibit at the Questacon National Science and Technology Center in Canberra. The exhibit was quite simple. Mounted on a wall, inside a glass case, were a series of pegs arranged vertically in a triangle. Visitors to Questacon were asked to drop a ball into a small shoot at the top of the case, just above the top most peg. The ball would hit the peg and bounce either left or right, then fall and hit another peg and bounce either left or right, and so on, ricocheting all the way to the bottom.

The pegs were carefully arranged so that at each level the ball had a 50/50 chance of falling either to the left or to the right. And so, each time a ball was dropped, it would take a different path through the pyramid of pegs. When the ball reached the bottom, it would fall into one of several slots lined up along the bottom; sensors in these slots, wired up to a computer, recorded the end point of each ball's journey.

The computer kept track of the outcomes. A running tally of the number of balls that had fallen into each slot was presented on a little screen in the form of a bar graph: the greater the tally for a given slot, the higher its bar.

What kind of shape do you think this graph showed after tens of thousands of ball drops? That's right, a bell curve!


Slots 1 and 9 had the smallest tallies, slots 2 and 8 had slightly more, 3 and 7 more again, 4 and 6 had even more, but slot 5 had he largest tally of all. And from this exhibit it's not dificult to see why.

For the ball to make it to slot 9 everything has to go right...literally! (On each peg the ball has to fall to the right). Thus, there's only one path to slot 9. And similarly, for the ball to reach slot 1 everything has to go left, so there's only one path to slot 1. But for slots closer to the center there are multiple routes that the ball can take. In fact, the closer a slot is to the center, the greater the number of possible routes, and the more frequently the ball reaches it. The consequence of this is a lovely bell curve.

So how does this relate to other variables?

Consider the case of an exam. How well a given student does on the exam depends on many different factors. For example:

- How much effort was put into studying
- How intelligent the student is
- How confident the student is on the day
- How much sleep the student got the night before
- Whether the student gets to the exam on time
- Whether the student is sitting next to someone who will distract them in the exam

(etc.)

For a student to get the highest possible score on the exam everything has to go right. That is, all of the factors that influence exam score have to go favorably: the student has studied hard, is intelligent, is confident, arrived on time, etc. And conversely, for a given student to get the worst possible score everything has to go wrong. For most students, however, some things will go right and some things will go wrong (in various combinations). Thus, most students will obtain a relatively average score.

So with exams, as with the pegs, we can see that there are more paths to being average than to being extreme, resulting in a bell curve. The same is true for other variables. For example, there are many different things that influence height (genes, nutrition, etc.) and so there are many more paths to being of average height than there are to being either extremely tall or short. Similarly, there are many different influences on people's love of chocolate (past experiences, advertising etc.) and so ratings of chocolate admiration should also distribute as a bell curve.

In other words, the bell curve is the distribution you get when there are multiple independent influences. And so the ubiquity of the Bell Curve in social science is not really that mysterious after all. The bell curve, my friends, is simply the signature of complexity. No wonder it pops up everywhere.

Homework

Here's a wee experiment you can do at home. Take 5 coins and toss them all together. Count up the number of heads and write it down. Repeat this 30 or more times, each time writing down the number of heads that come up.

When you're done, count up the number of times you got 5 out of 5, 4 out of 5, 3 out of 5, 2 out of 5, and 1 out of 5. Now draw a bar graph. What does the shape of the graph look like?

If you're brave, try doing this with 10, 20, or 30, coins at a time. If you're smart, just do it in Excel.

On hoaxes and creationism journals

Very recently, the Answers in Genesis (AiG) organisation has launched its own 'peer-reviewed' Young Earth creationism research journal -- the Answers Research Journal. AiG are the people behind the Creation Museum in Kentucky. They seek to rebut the standard theory of evolution and promote the biblical account of the creation of life on earth as literal scientific truth. Their new journal hopes to be a home for creationism friendly research that can't get published elsewhere.

My prediction: within the year, the Answers Research Journal will fall for a Sokal Affair style hoax.

The Sokal Affair was a hoax perpetrated on a postmodern cultural studies journal called Social Text by the physicist Alan Sokal. Sokal said that he wanted to see if the journal would "publish an article liberally salted with nonsense if (a) it sounded good and (b) it flattered the editors' ideological preconceptions." He wrote a hilariously silly paper called "Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity" full of the most amazing nonsense, submitted it, and they published it. (If you're familiar with postmodernist writing and understand just a couple of the basic ideas of Einsteinian physics, you'll find the article very funny.)

Surely someone else will have the same idea for hoaxing the Answers journal. A hoax of this type wouldn't be an immature game, it would serve to test the intellectual standards of a journal trying to sell itself as being a serious peer-reviewed science journal. It will be interesting to see whether there are any lines of argument in favour of creationism that the folks at Answers won't endorse.

And the academy award for best medicine in a leading role goes to...

They say that laughter is the best medicine. And don't get me wrong, I'm a big fan of laughter. But I still think that, even after all these years, the front runner for the category of 'best medicine in a leading role' has got to be the humble antibiotic.

I'm personally indebted to antibiotics this week for swiftly rescuing me from what felt like deaths door.

Three cheers for Flemming!

What else should be nominated for best medicine? and what should the selection criteria be?

P.S. More posts in the days to come, now that I'm on the mend.

The things you find when doing literature searches: study on the correlation between shoe size and penis length

I was simply poking around the internet for articles relevant to my PhD, and just a few wrong clicks landed me in the British Journal of Urology.

Those urologists sure do seem to have a lot of fun. If ever there was a scientific journal that could replace the in flight magazine on aeroplanes, the BJU would be it.

One article that caught my eye was titled "Can shoe size predict penile length?". I just had to find out the answer, because, let's face it, we've all wondered.

The abstract sums it up:

Objective

To establish if the ‘myth’ about whether the size of a man’s penis can be estimated from his shoe size has any basis, infact.

Subjects and methods

Two urologists measured the stretched penile length of 104 men in a prospective study and related this to their shoe size.

Results

The median stretched penile length for the sampled population was 13cm and the median UK shoe size was 9 (European 43). There was no statistically significant correlation between shoe size and stretched penile length.

Conclusion

The supposed association of penile length and shoe size has no scientific basis.

Myth busted!

(this blog post is so going to attract the wrong kind of google ads)

References

Shae, J. & Christopher, N., (2002). Can shoe size predict penile length? British Journal of Urology International, 90, 586-587

The logical fallacy in Paul Davies' article 'Taking Science on Faith'

The blogosphere is abuzz over the recent article in the NY Times by physicist Paul Davies. In the article Davies has a go at repackaging the old fallacy that science requires blind faith in the orderliness of nature.

Taking Science on Faith
By PAUL DAVIES

SCIENCE, we are repeatedly told, is the most reliable form of knowledge about the world because it is based on testable hypotheses. Religion, by contrast, is based on faith. The term “doubting Thomas” well illustrates the difference. In science, a healthy skepticism is a professional necessity, whereas in religion, having belief without evidence is regarded as a virtue.

The problem with this neat separation into “non-overlapping magisteria,” as Stephen Jay Gould described science and religion, is that science has its own faith-based belief system. All science proceeds on the assumption that nature is ordered in a rational and intelligible way. You couldn’t be a scientist if you thought the universe was a meaningless jumble of odds and ends haphazardly juxtaposed. When physicists probe to a deeper level of subatomic structure, or astronomers extend the reach of their instruments, they expect to encounter additional elegant mathematical order. And so far this faith has been justified. (continued here...)

But hang on, science doesn't presume orderliness, it just looks for it. Scientists examine various phenomena looking for reliable relationships between things -- rules that reality seems to hold to most of the time -- and sometimes they find them and sometimes they don't.

"Ah, but you wouldn't look for these reliable relationships and orderliness unless you believed (i.e., had faith) it was there" Davies might say.

Um, no! One looks for something because one entertains the possibility that it might be there.

For instance, let's say that I was playing a game of hide and seek with the readers of this blog. You all hide, and I begin to search for you. And the first place I choose to look is in a cupboard.

"Why are you looking in the cupboard?" Davies might ask.

"To see if anyone is in there," I reply.

"So you expect someone might be in there. You believe they might be in there. You have faith that they might be in there? You must, otherwise you wouldn't look."

"Well, I think someone might be in there, and I'm putting that hypothesis to the test. I certainly think it is possible that no one will be in there, Paul."

Scientists don't need to believe in an orderly lawful universe, they just look for it and very often find it. But scientists are quite open to the possibility that they won't. That's completely different from religious faith.

More analysis of the Davies article can be found over at Edge.