The Philosophy of Science

[fredrik]

the Bayesian update algorithm implicitly assumes that there is no such thing as a twenty+ sigma outlier.

...

Or the system just underwent an un-modeled state change and the twenty+ sigma outlier is in fact very close to representing the true state, in which case throwing out the twenty+ sigma outlier is exactly the wrong thing to do.

 

Yes exactly. To put this examlpe back in the context of my ramblings, I would phrase so so that the logic of correction here assigns infinite confidence in the prior _structure_. Now, that begs the question what the physical basis for such infinite confidence is. It really doesn't make sense. Instead this "infinite confidence" is rather a truncated guess, where you simply can further rate your own uncertainty, becaus constructing that measure will require more information capacity.

 

In the light of the present evidence, one can often see that perfectly rational decisions in the past was not optimal. But that doesn't mean there was somthing wrong with the decision. This is also part of the game. Sometimes you are right and sometime you are wrong. For example, the fact that people occasionaly do in fact get millionaires by playing on the lottery, does not make putting your money into lotteries a rational decision.

 

But also the opposite happens, apparently irrational decisions turn out to be keys to success.

 

When you try to analyse this, it seems impossible also to find a crystal clear and universal measures of rationality. IMHO, the measure of rationality itself, is evolving. This should result in a self-organising evolution.

 

I think if we can find a proper new mathematical and conceptual abstraction of this, this formalism can apply on a vast scale of phenomena. From the "evolution of physical law" that Lee Smolin and others are sniffing on, to the self-organisation in biology. No to mention the problem of understanding the intelligence of the brain.

 

This sort of information theoretic apporoach to the problem of induction, that takes into account the nature and representation of information from the inside view, to constrain what is possible (A clear example of what makes no sene is the very notion of an infinitely confident reference - this has IMHO no physical justificatin whatsoever), is the spirit in which I attack philosophy of science.

 

/Fredrik