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entirelyuseless comments on Rationality Quotes Thread September 2015 - Less Wrong
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The random walk doesn't converge. But the average position does.
The concept of convergence does not apply to the "average position". It always exists.
You are probably thinking of statistical estimation with uncorrelated errors. That is not the case here, you are not estimating some unobserved parameter.
I mean your average position on any day taken as the average of all the values up to that day.
As days increase indefinitely, this changing average will converge (e.g. to the central value.)
But that doesn't mean my taste in beer will converge to some value. All it means is that the average of history of my beer wanderings will be somewhere around the middle of the range -- an observation which is quite useless for the free will debate.
The general point I was making is that there is nothing about free will, even if by definition it means you have more than one option in the same physical situation, which gives us a reason to expect a pattern different from determinism with the addition of some randomness. So unless someone can show how those patterns would be different, there isn't any special reason to suppose that our actions couldn't correspond entirely to the laws of physics, without that meaning we don't have free will.
That's heavily underspecified. Most everything can be fit into a pattern of "determinism with the addition of some randomness".
In any case, you started with a specific claim that the choices will converge. Outside of the toy-model setup I didn't think it was necessarily true and I still don't think so.
I meant that the changing average of the choices will converge, in the way I expect to happen in the beer case. I still think this will happen under all normal circumstances.
I, um...
I'm not seeing what that says about free will. If you pick out a selection of numbers from one to a hundred, and you keep going, then the more numbers you pick out the less effect each new number will have on the running average.
I just don't see how this leads to "free will can be explained by deterministic physics plus randomness".
I don't think it proves that. I think it suggests that it may be the case. We already know that deterministic physics plus randomness will result in statistical patterns like that. I am just saying that free will is going to result in statistical patterns as well.
As far as I know, those could be the same patterns, which would mean that free will would be consistent with deterministic physics plus randomness. That is not a proof. I am just saying I don't know of any specific reasons to think those patterns will be different. Do you have reasons like that?
The thing is, the "pattern" you've picked up is a pattern that every series of numbers follows - that every series of numbers must follow. Any hypothesis will result in the same pattern - if I think that free will is controlled by the number of cookies eaten in Western Australia every second Tuesday, and I try to see if it follows the pattern of the average converging to a value as more samples are added, I'll find the same pattern.
If "having the same pattern" is to have any sort of predictive power at all, then that pattern must be a pattern that the data can possibly not have under another hypothesis.