Wednesday, September 08, 2004

How to change minds

A fascinating article from The New Humanist:

Changing our mind: a Bayesian approach
An interesting way of looking at how we change our mind, supported by recent neurobiological evidence, and in good agreement with my reflections on my own experiences, is provided by what is called the Bayesian framework (see RS n. 20, January 2002). Bayesians think of our understanding of truths about things in terms of probabilities based on evidence.


Blogger Greyshade said...

The interesting thing about the Bayesian process is its robustness. An ideal Bayesian engine uses theoretically exact conditional probabilities and either assumes statistical independence of successive experiments or combines them into a multivariate experiment with a known correlation matrix.

Obviously our brains do not work in precisely this fashion. Our estimates of conditional probabilities will be subjective (and possibly filtered so as to bias the outcome in favour of comfortable beliefs). Our brains probably don't literally apply Baye's Theorem but they obviously do something which produces
similar results. The robustness of the Bayesian process means that "raional" observers will still arrive at the same conclusion (abeit with differnt degrees of conviction) given sufficient evidence.

There is, however, an important limitation and that is our "horizons". If we look only at the behaviour of objects travelling much slower than the speed of light we will (by repeated Bayesian experimentation) learn that these objects obey Newton's Laws of Motion. Only when we examine objects moving at relativistic speeds do we learn that Newton's laws are only approximations and break down quite badly at relativistic speeds.

Our assessment of conditional probabilities may also be constrained by limited horizons. The pre-Darwinian success of the "Argument from Design" (not only in Christendom) arises from the incorrect conditional probability -
P(Ordered Universe | No Design) = 0
This matches the shared human experience that order does not arise in the absence of design (eg random stones tossed onto the ground). It was not till Darwin actually worked out a mechanism whereby the biological world could (given billions of years nd a mechanism for accumulating incremental changes) arise by chance that the fallacy was exposed.

Bayesian inference (or its mental equivalent) is a powerful tool of enlightenment but it doesn't do everything.

9 September 2004 at 11:38 AM  
Blogger Sock Thief said...

Have you read what Steven Pinker has to say about innate scientific reasoning tools? In The Blank Slate he outlines what aspects of science may actually be instinctive and of course may, as you say, suffer from limited horizons.

For example, we have an innate sense of physics, but it is the physics of the everyday - Aristolian, not even Newtonian, let alone Einsteinian.

Ands we have innate statistical reasoning faculties which can also be limited, as you suggest. The Monty Hall problem is a good example.

What struck me about the New Humanist article is the attempt to look at the devlopment of political opinion in these terms. Politics, when it comes down to it, is the way in which we attempt to orgainise ourslves to deal with the unpredictable.

9 September 2004 at 12:36 PM  
Blogger Greyshade said...

I'm not familiar with the work you mention but I'll see if I can get hold of it. As a long-standing Bayesian I'd like to make the point that Bayesian inference is as firmly part of orthodox statistics as the normal distribution, the Central Limits Theorem or the Chi Square test. If you were to toss a coin ten times and it came up heads every time than any statistician will tell you that the odds against this happening with an "unbiased" coin is about 1000 : 1. If you asked a statistician to assess the probability that the coin was double-headed a Bayesian would reply that it was 1000 time moe likely than it was before you made the tosses (this is a slight oversimplification), a conventional "Frequentist" would reply that the probability of observing 10 consecutive heads is 0.001 if the coin is not two-headed (Tukey described this as giving a precise answer to the wrong question).

Our brains contain both "hard-wired" (which reflect our evolutionary history) and "software" features which reflect our lifetime learning. Bayesian inference is an approximate model of the way we learn (mainly because it involves feedback) but our brains almost certainly don't include Bayesian calculators. We don't instinctively calculate actual probabilities much less use them. An innumerate gambler will not be able to calculate the mathematical probability of any poker hand but he will have a very good idea as to how likely a pair of Queens over Nines (for example) is to be beaten and how that likelihood is altered by the betting and drawing behaviour of the other players.

Our "instinctive" conditional probabilities represent induction from analogous situations in our experience (but what IS analogous). A professional cricketer learns to determine whether he needs to run forwards or backwards in order to catch a cricket ball by comparing its apparent flight with that of thousands of other cricket balls he has encountered in matches and practice sessions. Someone who has never played the game must rely on experience of much less perfect analogies - perhaps even the evolutionary memory (innate physics) of some arboreal primate ancestor judging whether it can catch a tree branch which is falling upwards (relative to the primate) - and will probably make a mess of the catch.

I didn't see the bit about politics in the Pigliucci article. Was there another article somewhere?

9 September 2004 at 5:25 PM  
Blogger Sock Thief said...

The politics of the Pigliucci article are more implied. I hunted down a few more examples of his writing and he often makes a link to political process.

I must admit to only a passing knowledge of probability theory. The rudimentary statistics I'm familiar with only cover experimental error and a little bit on Poisson distributions for radioactive decay. So it’s interesting to get your point of view.

I've read a few things about the problems associated with gambling. Along the lines of our ancestors not really dealing with truly random events - e.g. plant distribution. Finding plants and game was achieved by employing methods that built on accumulated knowledge. One argument goes that with gambling people are, wrongly, dong the same. They invent methods but the events are actually random.

And in another article there was discussion of how to present sampling information to people, such as HIV results, in terms of frequency instead of probability which seems to be more readily understandable.

10 September 2004 at 8:15 AM  

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