Tuesday, January 13, 2009

More tomorrow

Will you?

When I was little(r) I thought clouds were blue and the sky was white. I suppose this was on the assumption that 'nothing' (as I considered the sky to be at that time) would be white and 'something' (which is what the clouds seemed to be) would be blue. I thought this for a very long time. At a similar sort of time also developed the notion that, as I saw it, there was no reason to believe that since the sun (or sky, or clouds for that matter) were there today they would be there again tomorrow.

I realised that I had been wrong about clouds being blue when first in the window seat of an aeroplane. Since I was then above something white (which had to be the clouds) and the 'nothing' was still above, well then the sky must be blue. I did toy with the brief idea that there had to be something higher for it to be blue, but that didn't come til later still. It seemed pretty logical to me.

The idea that the sun would be coming up tomorrow, however, never really left.

Recently I was asked what the probability of the sun coming up tomorrow was. This was asked by someone who probably knows or else could easily work it out I'm sure. Since I couldn't reason a calculation to establish an actual estimation I said 0.5. This almost certainly arises from my failure to understand the concept of probabilty but also beceause of my lack of belief in empirical data. I may be wrong, but I don't see that the sun coming up today means it will come up tomorrow.

And so to Bayesian theory. This method is probably best summed up by saying that there are not only yes/no answers, there are part truths and part untruths. Karl Popper was of the view that science should aim to falsify untruths. This is, in essence, the null hypothesis, a concept which on a day-to-day basis I find quite depressing, and yet also true. We should, I suppose, always be trying to remove all the wrong ideas we have. Bayesian theory, on the other hand, suggests that the hypotheses we have should constantly be modified by the data that we acquire. So yes, it is ok to say that there are only white swans, until that little black signet arrives on the Queen's lawn. Hilborn and Mangel gave a nice discription of this (involving squirrels!) which is talked about here.

Taking Bayesian theory, however, it would seem that, you can never have a probability of 1, and you can never be sure.

I suppose its strange to not live by empirical rules, especially being a (part-time) scientist, and especially as it is the general basis of most human reasoning. What is certain, however, is that living this way means every today you go to bed terrified and every tomorrow you wake up astonished.

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