Thursday, 30 October 2014

Critical thinking

I've been asked to give a talk at a school to age 15+ pupils, and I'm wondering if a talk on critical thinking would be a good one. I'm not sure that it gets taught. How could you teach critical thinking at a faith school?

Critical thinking is, of course, pretty much the opposite of faith. If you take things on  faith, you don't need to think about them at all, let alone critically. But how do you do critical thinking? There's probably several ways, and several theories. Here's mine.

I start off with Bayes theorem, and evidence.

That tells you how you should modify your beliefs in the light of new evidence. And, of course, it was the major subject of my PhD Thesis. So I'll  talk about my PhD a bit.

It started 30+ years ago. I had a discussion with a colleague, about the difference between my forecasts for the current year, and his. His view was that his forecast for the year had to be better than mine, because it was based on some months of actual data for the first few months of the year. My view was that the monthly statistics were much less accurate than the annual stats, because of how they were collected. And that meant that a forecast based on annual numbers, could be better.

But I thought about that, and wanted to quantify it, and that led me to Bayes theorem, and how Bayes could be used for the estimation of economic parameters. I devised a methodology called "Recursive Bayesian Estimation" (RBE), which I generalised to multiple variables, and it was a whole new thing.

Until I discovered that electrical engineers had something called the Kalman Filter, invented a few years previously, and which turned out to be mathematically equivalent to RBE. A big disappointment for me, but because I was the first to apply this method to economics, I still got my PhD.

Anyway. RBE is all about how you combine your previous belief about something (such as, the price elasticity of beer) with fresh information about it, to give a new best belief. And you do it by weighting how good your previous estimate was, and how good your fresh information is.


When you read in the newspaper "The tooth fairy left John Campbell a pound under his pillow", you take your previous belief about the tooth fairy and weight that, you take the new information and weight that with how accurate it's likely to be, and you wind up with a new belief. In this case, you probably end up continuing to disbelieve in the tooth fairy. However, if the new information were better than "read it in the newspaper", but instead "saw her flutter in and put the coin in place", then the weighting is different, and maybe you do start to believe in the tooth fairy. Or maybe your previous certainty was so strong that you disbelieve the evidence of your own eyes - maybe you had a brain fart? One of the things I've learned from geocaching, is that your eyes usually see what you expect to see, not what is actually there.

By the way, can you prove that the tooth fairy doesn't exist? I don't think you can. All you can do is ascribe a very low probability to her existence. Or his.

As a general rule, I always take what I read in the newspapers (or any other "news" source) with a large helping of scepticism, because when they cover an area I actually know about, they get things badly, sometimes hilariously, wrong.

So far, non controversial. But then we apply that to the real world.

Take, for example, the Mormon religion. This was discovered (invented? Revealed?) by Joseph Smith. The big problem here, is that he was convicted of fraud. So I take my prior belief that people can be visited by an angel and given a set of gold plates of revelation (which is pretty much equivalent to being visited by the tooth fairy and being left a pound), and my weighting of the word of a fraudster, and wind up with a very low probability that Mormons have got it right.

Take, for example, Scientology. It's a religion (some say it's a cult) invented by L Ron Hubbard. I won't explain the full set of beliefs, but ... 75 million years ago Xenu brought billions of people to Earth in spacecraft resembling Douglas DC-8 airliners, stacked them around volcanoes and detonated hydrogen bombs in the volcanoes. The thetans then clustered together, stuck to the bodies of the living, and continue to do this today. I find it hard to take this seriously.

Discussing Mormonism and Scientology probably won't get me lynched. But what about the more mainstream religions? Jehovahs Witnesses have repeatedly forecast the end of the world, giving specific dates. So far, wrongly. Good evidence that they don't have it right. And hewre's a quote from the October 2014 edition of "Awake!", given to me free by a nice lady in Victoria. "Did the structure of the horse's legs come about by evolution? Or was it designed?" That's an easy one - evolution.

I probably don't need to cover Jupiter, Jove, Zeus, Athena, Odin, Thor, Mithras and all the other zillions of obsolete gods - I wonder what happens to a god that becomes obsolete?

Many American Christians believe that the world was created only 6000-odd years ago, and evolution is rubbish. It's hard to keep a straight face.

But then we come to mainstream Christianity. There's lots I could say without offending the audience. For example, what's more likely, a miracle whereby a woman gets pregnant by God, or a pregnant jewish girl told a lie? I once went caching with an ex-vicar. He told me that he'd lost his faith a long time ago, and he felt that he was making a living out of telling lies to people. It was a major effort for him to leave the church, though, because he lost his job, his home and his friends. He's a driving instructor now.

The reason that discussing mainstream Christianity probably won't offend the audience, is that this is a faith school, and the faith is Judaism. So what can I say about that? I think all I can say is, for everything in your life you should apply critical thinking, but in the matter of the jewish faith, just think what you're told to think.

And I'll try to keep a straight face.

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