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.
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.
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?
it won’t be easy to stop that average from converging sooner or later.
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.
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.
a pattern different from determinism with the addition of some randomness
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’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.
I’m mystified by this discussion. entirelyuseless seems to be saying that if you look at the history of choices someone has made in similar situations, they will show some kind of convergence, which I see no reason at all to believe. And CCC seems to be saying that every sequence of numbers shows this pattern, which I not only see no reason to believe but can refute. (E.g., consider the sequence consisting of one +1, two −1s, four +1s, eight −1s, etc. The average after 2^n-1 steps oscillates between about −1/3 and about +1/3.) And none of this seems to have anything much to do with free will; in so far as the “libertarian” notion of free will makes sense at all, it seems perfectly consistent with making choices that average out in the long run, at least with probability → 1 or something of the kind, and determinism is perfectly consistent with not doing so, since e.g. the sequence of numbers I just described can be produced by a very simple computer program (at least if it either has infinite memory or has at least a few hundred bits and isn’t observed for longer than the lifetime of the universe).
Well, that isn’t what “converges” means in mathematics (it means there’s a particular value towards which one gets and stays arbitrarily close), but with that definition it is indeed tautologously true that wandering around within a bounded region yields “converging” averaged values. (But not if the region can be unbounded. Easy counterexample: One +1, two −2, four +4, eight −8, etc.)
Well, that isn’t what “converges” means in mathematics (it means there’s a particular value towards which one gets and stays arbitrarily close), but with that definition it is indeed tautologously true that wandering around within a bounded region yields “converging” averaged values.
If the steps get smaller sufficiently slowly, there are counterexamples similar to yours with +1s and −1s. It’s difficult to get convergence short of explicitly imposing convergence.
Confinement to a bounded region implies accumulation points (points to which some subsequence converges), but there can be any number of those. They can even be dense in the space.
There are counterexamples to convergence-in-the-usual-sense, and my example was one of them.
If one takes CCC’s statement of what s/he meant by “convergence” absolutely at face value, then there are not only counterexamples but trivial counterexamples; e.g., begin 0,0,1; the first step moves the rolling average by 0 and the second doesn’t.
What I took CCC as actually meaning was that the differences converge-in-the-usual-sense to zero, or equivalently that one can make them small enough by waiting long enough. That’s straightforwardly true because if the diameter of your region is D then after n steps your average can’t move by more than D/n per step.
What I took CCC as actually meaning was that the differences converge-in-the-usual-sense to zero, or equivalently that one can make them small enough by waiting long enough. That’s straightforwardly true because if the diameter of your region is D then after n steps your average can’t move by more than D/n per step.
Just to confirm—yes, that’s what I’d meant. Which it trivially true, yes; that is why I couldn’t understand why entirelyuseless was attaching any special significance to it.
What I took CCC as actually meaning was that the differences converge-in-the-usual-sense to zero, or equivalently that one can make them small enough by waiting long enough.
That’s what CCC said in his last post, but it’s not a useful property for showing what was originally claimed by entirelyuseless, who said:
I meant that the changing average of the choices will converge, in the way I expect to happen in the beer case.
This doesn’t follow from shrinking steps, because:
That’s straightforwardly true because if the diameter of your region is D then after n steps your average can’t move by more than D/n per step.
The sum of that over all n is divergent, so the average can move around anywhere if you wait long enough. In fact, for any number of passes of averaging, that will still be true: if the underlying sequence goes somewhere and sticks there long enough, the average will eventually get there. Then the underlying sequence can go somewhere else, and so on.
To put this in more concrete terms, with an example of a property that for many people shows no long-term stability in their lifetime, consider physical location (relative to the geocentric frame). A person may live for years in one place, then years in another town or another continent, and make such moves at various times in their life. For such a person, there is no useful concept of their average location. In the case of the original example, a person’s taste in beer can make just as drastic changes, on top of which, the world changes and new beers are created, the space of the random walk changes as the walk is being made.
entirelyuseless’s original claim:
The random walk doesn’t converge. But the average position does.
I agree. (Did something I said give a contrary impression? I thought I’d said right at the outset that the original claims of both entirelyuseless and CCC are wrong.)
I have already said that I agree that it is mathematically possible to prevent the average from converging, just that this is not likely to happen in real life. In RichardKennaway’s comment, “goes somewhere and sticks there long enough” means progressively longer periods of time, and so is not realistic.
I’m not saying that people’s choices converge in the sense of getting closer to a particular value, but that the average converges. You are right to say that this is not a necessary property of every sequence of values (and CCC was mistaken.)
You say that there is no reason to think I am right about this, but your proposed sequence of numbers suggests that I am, namely by showing that the only way the average won’t converge is if you purposely choose a sequence to prevent that from happening. Suppose you offer someone chocolate or vanilla ice cream once a week. I think there are very good reasons to think that the moving average would begin to change slower and slower very quickly, and would basically converge after a while. This would happen unless the person used a sequence like the above: namely, unless he chose a sequence with the explicit intention of preventing convergence.
I agree that someone can have this intention, and that this would not refute determinism. In that sense you could say that the whole discussion is irrelevant. But the relevance, from my point of view, is that it makes the question more concrete. The basic point is that you can, if you want, define free will so that it is not consistent with determinism. But then it will be consistent with determinism plus randomness, unless you propose some prediction which is not consistent with the second. And no one had done that. So no one has even suggested a definition of free will which would be inconsistent with being produced by some form of physical laws.
So no one has even suggested a definition of free will which would be inconsistent with being produced by some form of physical laws.
Given that our universe clearly does operate on some form of physical laws, if anyone were to provide such a definition of free will, it should be trivial to show that it’s not how our universe works.
I think there are very good reasons to think that the moving average would begin to change slower and slower very quickly, and would basically converge after a while.
Not if the person’s preferences are changing gradually over time. That is a real thing that really happens.
(For the avoidance of doubt: I agree that any notion of free will it’s credible to think we have is consistent with physicalism.)
I agree that a person’s preferences can change over time but it will not have the effect of an average that goes back and forth without his preferences changing back and forth, but remaining stable at the extremes for longer and longer periods of time (much like your sequence). This is not a likely thing to happen in real life.
Anyway I also agree that the particulars of this are not that important to my point.
Basically I am saying that deterministic physics plus randomness can produce any possible pattern, as you’re noting. So it can also produce the pattern produced by free will. Or do you have some idea of what free will would do which is different from deterministic physics plus randomness? If so, I haven’t see it suggested yet.
Basically I am saying that deterministic physics plus randomness can produce any possible pattern, as you’re noting. So it can also produce the pattern produced by free will.
Yes, I agree. It can. Deterministic physics alone can, if you have a long enough list of rules.
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.)
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.
I’m mystified by this discussion. entirelyuseless seems to be saying that if you look at the history of choices someone has made in similar situations, they will show some kind of convergence, which I see no reason at all to believe. And CCC seems to be saying that every sequence of numbers shows this pattern, which I not only see no reason to believe but can refute. (E.g., consider the sequence consisting of one +1, two −1s, four +1s, eight −1s, etc. The average after 2^n-1 steps oscillates between about −1/3 and about +1/3.) And none of this seems to have anything much to do with free will; in so far as the “libertarian” notion of free will makes sense at all, it seems perfectly consistent with making choices that average out in the long run, at least with probability → 1 or something of the kind, and determinism is perfectly consistent with not doing so, since e.g. the sequence of numbers I just described can be produced by a very simple computer program (at least if it either has infinite memory or has at least a few hundred bits and isn’t observed for longer than the lifetime of the universe).
...I had understood “converges” to mean that each successive sample moves the rolling average by a smaller and smaller amount.
Well, that isn’t what “converges” means in mathematics (it means there’s a particular value towards which one gets and stays arbitrarily close), but with that definition it is indeed tautologously true that wandering around within a bounded region yields “converging” averaged values. (But not if the region can be unbounded. Easy counterexample: One +1, two −2, four +4, eight −8, etc.)
If the steps get smaller sufficiently slowly, there are counterexamples similar to yours with +1s and −1s. It’s difficult to get convergence short of explicitly imposing convergence.
Confinement to a bounded region implies accumulation points (points to which some subsequence converges), but there can be any number of those. They can even be dense in the space.
There are counterexamples to convergence-in-the-usual-sense, and my example was one of them.
If one takes CCC’s statement of what s/he meant by “convergence” absolutely at face value, then there are not only counterexamples but trivial counterexamples; e.g., begin 0,0,1; the first step moves the rolling average by 0 and the second doesn’t.
What I took CCC as actually meaning was that the differences converge-in-the-usual-sense to zero, or equivalently that one can make them small enough by waiting long enough. That’s straightforwardly true because if the diameter of your region is D then after n steps your average can’t move by more than D/n per step.
Just to confirm—yes, that’s what I’d meant. Which it trivially true, yes; that is why I couldn’t understand why entirelyuseless was attaching any special significance to it.
That’s what CCC said in his last post, but it’s not a useful property for showing what was originally claimed by entirelyuseless, who said:
This doesn’t follow from shrinking steps, because:
The sum of that over all n is divergent, so the average can move around anywhere if you wait long enough. In fact, for any number of passes of averaging, that will still be true: if the underlying sequence goes somewhere and sticks there long enough, the average will eventually get there. Then the underlying sequence can go somewhere else, and so on.
To put this in more concrete terms, with an example of a property that for many people shows no long-term stability in their lifetime, consider physical location (relative to the geocentric frame). A person may live for years in one place, then years in another town or another continent, and make such moves at various times in their life. For such a person, there is no useful concept of their average location. In the case of the original example, a person’s taste in beer can make just as drastic changes, on top of which, the world changes and new beers are created, the space of the random walk changes as the walk is being made.
entirelyuseless’s original claim:
cannot be salvaged.
I agree. (Did something I said give a contrary impression? I thought I’d said right at the outset that the original claims of both entirelyuseless and CCC are wrong.)
I have already said that I agree that it is mathematically possible to prevent the average from converging, just that this is not likely to happen in real life. In RichardKennaway’s comment, “goes somewhere and sticks there long enough” means progressively longer periods of time, and so is not realistic.
I’m not saying that people’s choices converge in the sense of getting closer to a particular value, but that the average converges. You are right to say that this is not a necessary property of every sequence of values (and CCC was mistaken.)
You say that there is no reason to think I am right about this, but your proposed sequence of numbers suggests that I am, namely by showing that the only way the average won’t converge is if you purposely choose a sequence to prevent that from happening. Suppose you offer someone chocolate or vanilla ice cream once a week. I think there are very good reasons to think that the moving average would begin to change slower and slower very quickly, and would basically converge after a while. This would happen unless the person used a sequence like the above: namely, unless he chose a sequence with the explicit intention of preventing convergence.
I agree that someone can have this intention, and that this would not refute determinism. In that sense you could say that the whole discussion is irrelevant. But the relevance, from my point of view, is that it makes the question more concrete. The basic point is that you can, if you want, define free will so that it is not consistent with determinism. But then it will be consistent with determinism plus randomness, unless you propose some prediction which is not consistent with the second. And no one had done that. So no one has even suggested a definition of free will which would be inconsistent with being produced by some form of physical laws.
Given that our universe clearly does operate on some form of physical laws, if anyone were to provide such a definition of free will, it should be trivial to show that it’s not how our universe works.
Not if the person’s preferences are changing gradually over time. That is a real thing that really happens.
(For the avoidance of doubt: I agree that any notion of free will it’s credible to think we have is consistent with physicalism.)
I agree that a person’s preferences can change over time but it will not have the effect of an average that goes back and forth without his preferences changing back and forth, but remaining stable at the extremes for longer and longer periods of time (much like your sequence). This is not a likely thing to happen in real life.
Anyway I also agree that the particulars of this are not that important to my point.
Basically I am saying that deterministic physics plus randomness can produce any possible pattern, as you’re noting. So it can also produce the pattern produced by free will. Or do you have some idea of what free will would do which is different from deterministic physics plus randomness? If so, I haven’t see it suggested yet.
Yes, I agree. It can. Deterministic physics alone can, if you have a long enough list of rules.