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Lumifer comments on Rationality Quotes Thread September 2015 - Less Wrong
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Most of my point is that you can not. Among I things, I change over time.
As a practical example, I drink beer. Various kinds of. My beer preferences do not converge over time. Instead, they wander over different styles, different hoppiness/maltiness/etc., even different breweries. I have no idea what kind of beer I will like in, say, a year, but it probably will be different from what I like now.
Showing that something works in a toy model does not show that the same thing works in actual reality.
Sure, I totally agree with you - in real life, we can really put a person in exactly the same situation twice. If we could, this whole free will argument would be a lot easier to solve.
That said, I do think the toy models are useful. Pretending we can do this experiment gives an answer to the problem I've never managed to pick a hole in (and tbh getting other people's input on it is the hidden motivation for entering this discussion):
If we could let you choose a beer, then rewind the universe - including all particles, forces, and known and unknown elements of cognition anyone might postulate such as souls and deities back to their starting position - then let it go again, there are only really two things that could happen: *1) you choose the same beer because that's what the universe was leading up to or *2) you choose a different beer despite the fact that all parameters of the universe known and unknown are the same.
The first outcome would suggest determinism; the second randomness, or at least independence from all variables which we consider "self" such as personality, memory and perhaps souls and things, since they were all rewound with the universe. I'd be really interested to hear of any third option anyone can think of!
As you say, showing this in a toy model isn't the same as showing it in actual reality; but when the actual experiment is impossible, one is arguing about abstract concepts anyway, and one has a lot of difficulty imagining outcomes not encompassed in the model I'm not sure we can do much better.
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.)