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Lumifer comments on Rationality Quotes Thread September 2015 - Less Wrong
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Within the toy model, yes. In actual reality, you still don't know.
The trivial third option is to drink wine :-P
On a bit more serious note, if you set up the problem so that the outcomes are X and not-X, there could be no third option.
I suspect that if we take the average of e.g. the bitterness of the beers that you have been drinking, it has already converged to an average, and future developments will probably not change that average much, even if there are some years when you drink sweet beers and some years when you drink bitter beers.
Empirically speaking, you are wrong.
Perhaps, although I don't see how you can know that unless you have been making measurements, or unless it has definitely been going in the direction of getting more and more sweet, or more and more bitter.
In any case, since beer does not differ an infinite amount in sweetness and bitterness, it won't be easy to stop that average from converging sooner or later.
Um, if I'm swinging from Lambics to Stouts with excursions into IPAs and Belgian Trappists, do you really think I converged on a particular bitterness?
Random walk, even if bounded, does not converge.
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.