Sunday, May 11, 2008

You are SO wrong

Of course, by "you" I mean everybody, and by "SO" I mean "very" or "really".

I know better than anybody how crap I am at maths, and don't think this is false modesty because I also know that I'm better at it than most people. Despite my crapness I also know enough about the subject and its history to get a sense of how demanding it is. It's not just about making sure that each step is mathematically correct, but that your problem is posed in a way that makes sense. Even given all the rigour that mathematicians bring and peer review, it isn't uncommon that a paper with errors in it will get published. Andrew Wiles is "famous" for proving Fermat's Last Theorem but it took a long time for people to discover that his initial attempt was incorrect, and it was probably only discovered at all because so many weirdoes were interested enough to check.

My point is that when it comes to actually knowing stuff for sure you can't do better than maths (or logic) but even here it's often less of a sure thing than you'd guess and it's really, really hard. And maths and logic is actually the easiest stuff that we can ever do. In real life we can't pose questions with similar precision and we can't move from one step to the next in the same deductive way, so why should we expect our chains of reasoning to lead to accurate conclusions? Well, we shouldn't. But we are often really confident about our beliefs when it comes to politics or economics or sociology, which are indescribably more difficult and complicated than maths.

If you have an argument that involves a chain of reasoning and on average you're 95% sure that each step is correct, the odds of your argument being right falls below 50% on the thirteenth step.

Or put another way, the odds of you being right declines exponentially with the length of your argument.

8 comments:

Tracy said...

I really like this post. It's a real mind-opener. I'll try to doubt my beliefs even more. But it starts to make everything feel like a mockery.

I wonder if the way our theories confirm or deny our experience of reality counts towards knowing whether they are right or wrong? Perhaps some theories are easier to factually determine as "correct" than mathematics and pure logic which is so abstract?

I guess the problem is that with most complex problems you can't isolate cause and effect, so it's too easy to attribute some thing to the incorrect causal processes to fit your mental theory.

Trevor Black said...

This helps make the argument for dispassionate debate. If what you think is probably wrong, and so is the argument you accept if shift to what someone who disagrees with you thinks... we shouldn't defend our arguments so passionately.

But we do.

It is also quite disorientating. We are brought up learning to debate. It is not a case of feeling no attachment to your argument.

So how do you get around your weasel hedging post. This post implies the ultimate hedge...

`Ja, I know I argued strongly... but I did say I was probably wrong.'

mutt said...

Tracy- I don't think everything should feel like a mockery. On the whole our beliefs are better justified than people in the past and there's no reason why we shouldn't keep doing better.

"I guess the problem is that with most complex problems you can't isolate cause and effect, so it's too easy to attribute some thing to the incorrect causal processes to fit your mental theory."

I think this is excellently put.

trevor- Way back when I suggested that we declare that (many of) our opinions are largely for entertainment purposes only. greg wasn't impressed, and you asked if it was a typo (I, to my shame, didn't reply); it wasn't.

If we argue some point very passionately, maybe we just like talking like that, or maybe we have super duper reasons for thinking it's true.

But I think it's important to make clear statements or claims, that make it easy to identify what kinds of arguments or evidence would show that it's wrong.

I'd love it if someone said, "here is my bold claim which I think has a 51% chance of being right"

sid said...

"on average you're 95% sure that each step is correct, the odds of your argument being right falls below 50% on the thirteenth step" I really don't like those odds.

Erika said...

What is the conclusive proof for what is right or wrong?
Aren't we all entitled to our own opinions whether others like them or not?

Stuart said...

There is no conclusive proof for anything.

Here's an essay I love arguing that none of us have the right to our opinion.

http://www.timesonline.co.uk/tol/comment/columnists/guest_contributors/article467194.ece

We do of course have the right to freedom of speech.

Erika said...

So what is the point of guarding our rights to free speech if we don't have the rights to our own opinions? We would then all only be free to say things that everyone agreed upon?

stuart said...

I don't think so. I guess the right to your opinion is pretty much the same thing as freedom of speech the way we normally use it.

People use the right to an opinion in different ways and having "rights" has a particular meaning.

Anyway, I can't do better than the essay, it's fun.