Game of Life could be modified with an additional rule that deleted all cells in a structure that forms the word “Hello world.” This would be faster-than-light interaction because the state of the grid at one point would influence the state of the grid at a distant point, in one time step.
Not quite. In the toy universe in which the Game of Life exists there is no light, no speed of light, and no limits on faster-than-light interactions.
To make this obvious, you say “in one time step”. What’s the speed of light in Game of Life time steps?
The speed of light in our universe is 1 Planck distance in 1 Planck time. Hence the connection between the speed of light and the idea that all interaction is local.
The closely analogous speed in Game of Life would be 1 grid square in 1 time step.
If Game of Life can be modified as described to allow FTL, nonlocal interactions, then so can the rules of our universe. At least, the burden of proof is on you to show why such modifications aren’t legitimate somehow.
Not quite. In the toy universe in which the Game of Life exists there is no light, no speed of light, and no limits on faster-than-light interactions.
So you agree that it is possible for a truly deterministic universe to have nonlocal interaction. I think it is a short step from there to my conclusion, namely that it is possible for a truly deterministic universe to have faster-than-light interaction.
If Game of Life can be modified as described to allow FTL, nonlocal interactions, then so can the rules of our universe.
Huh? The fact that you can make up whatever rules you want for a toy mathematical abstraction does NOT imply that you can do the same for our physical universe.
Do you think you understand what I am trying to do here? Because it seems to me that you are just being difficult. I honestly don’t understand what the problem is. It might be my fault, not yours. EDIT: So, I’ll do what I can to understand you also. Right now I’m thinking that you must have a different understanding of what the space of possible universes looks like.
Huh? The fact that you can make up whatever rules you want for a toy mathematical abstraction does NOT imply that you can do the same for our physical universe.
Watch me do the same for our physical universe:
Take the laws of physics, whatever they turn out to be, and add this new law:
—Fix a simultenaity plane if necessary
—Pick two distant particles
—Decree that every second, all the matter in a 1meter radius around each particle will be swapped with the matter in a 1meter radius around each other particle. As if someone paused the universe, cut out the relevant sections, and switched them.
These are silly rules, but they are consistent, computable, etc. The modified Laws of Physics that would result would be no less possible than our current Laws of Physics, though they would be much less probable.
Not just any old Laws are possible. Even consistent, computable Laws can be impossible. (I’m afraid I don’t know why you think this though. Perhaps you think there is only one possible world and it is not a Level IV multiverse or perhaps you think that all possible worlds conform to the laws of physics as some of us currently understand them.)
I’m thinking that universes which are consistent & computable are possible. After all, it seems to me that Solomonoff Induction says this.
Note that I am distinguishing between possibility and probability. I’m not claiming that my modified laws are probable, merely that they are metaphysically possible
If you have problems with the term “metaphysical possibility” then I can instead speak in multiverse terms: I am claiming that all computable, consistent worlds exist somewhere in the multiverse. If you don’t like that either, then I’d like to know how you think about possibility.
Note: I intend to edit this later to add links. I won’t change the text. EDIT: I added the links.
Not just any old Laws are possible. Even consistent, computable Laws can be impossible.
No, I’m not thinking that. The thing is, I don’t quite understand in which sense do you use the word “possible” here. It seems to me you say “X is possible” to mean “I can imagine X”.
I’m thinking that universes which are consistent & computable are possible.
See above. And saying “metaphysically possible” doesn’t help—are we still talking purely about your imagination?
If you have problems with the term “metaphysical possibility” then I can instead speak in multiverse terms: I am claiming that all computable, consistent worlds exist somewhere in the multiverse.
Ah. Well, do you happen to have any evidence for your claim?
then I’d like to know how you think about possibility.
You’ll have to be a bit more specific. Possibility of what? Possibility of universes with different laws of physics? I don’t know. Again, I am not sure what does the word “possibility” mean here.
It would help if you gave me a positive account of what you think, instead of just pointing out where you disagree with me.
True, the notion of metaphysical possibility is one that might be mysterious. I don’t think it is, but come to think of it, I don’t need to bother with it here—there are other notions of possibility that serve my purposes even better. So we need not discuss it further.
It seems to me you say “X is possible” to mean “I can imagine X”.
That’s not fair. My use of the phrase “X is possible” thus far meets much more stringent conditions than that. Why did you jump to the lowest common denominator? Do you not know much about the use of the word “possible?”
Ah. Well, do you happen to have any evidence for your claim?
Yes, my claim is entailed by the Level IV multiverse hypothesis. Are you claiming that that hypothesis is nonsensical? If so, I’d like to hear your alternative metaphysical theory of everything, if you have one, as well as an explanation of why this one is nonsensical.
In a truly deterministic universe, the concept of “faster-than light interaction” is largely nonsensical.
This was your original claim. Rather than talk about possibility I can just talk about sensibility. Is there a coherent truly deterministic universe in which faster-than-light interaction happens?
Obviously we aren’t asking whether or not there actually exists such a universe, because then your statement would be either trivially true or trivially false, depending on whether or not our universe has faster-than-light interaction.
So we must be looking at some sort of space of non-existent universes, whatever that might be, and checking to see whether there are any that are (a) coherent and (b) contain FTL.
What is this space that we must look at? Well, your question leaves this ambiguous. But it highly suggests that we are looking for some sort of possibility space, e.g. the space of metaphysically possible worlds. I propose that it is at least the space that Solomonoff Induction looks at. In fact, I could get away with less than that if I had to.
Anyhow, since your question leaves it ambiguous which space we are looking at, it is on you to clarify it.
Anyone can make imaginary constructs. Sometimes they involve pixies riding unicorns, sometimes they involve different Planck lengths. Apriori I see no good reason to treat constructs involving Planck lengths any different from constructs involving pixies.
When you say “A universe with feature X is possible” I literally do not understand the meaning of the word “possible” here. It doesn’t exist, it didn’t happen. Could it have happened? I have no idea and neither do you. In you mind you can substitute a different Planck length or break the FTL limitation, then squint at the result and say “Hmm, still looks fine”—but all that is happening inside your mind and again, does not look qualitatively different from leering at a fine pixie. In your mind, most everything is possible—not to mention that your mind cannot determine whether a universe with a different Planck length actually would have been fine.
This was your original claim.
Actually, no, it wasn’t mine. I jumped in this thread mid-discussion with a comment about the Game of Life.
So we must be looking at some sort of space of non-existent universes, whatever that might be, and checking to see whether there are any that are (a) coherent and (b) contain FTL.
My point is that this activity is no different from checking the non-existent universes for pixies and unicorns. It might be an agreeable mental pastime, but it has no relationship to reality.
How embarrassing—I forgot who the OP for this argument was. :( Sorry. If you don’t support the claim that I was attacking, then perhaps we don’t even disagree after all.
OK, so you are anti-realist about possibility. Fair enough; so am I. But that doesn’t mean the word “possible” is meaningless in the contexts that I used it in. Here’s an attempt at cashing out one version of “possible” that surely you would agree makes sense:
X is possible iff X is true in some theory in the search space of theories that we ought to use when making predictions.
The claim I was disagreeing with is the claim that determinism does not make sense when combined with FTL interaction. Even if we agree that possibility is just a game we play in our heads, the game still has rules, and the claim I am disagreeing with seemed to be a claim about the implications of those rules—namely, that those rules prohibited the combination of determinism and FTL interaction. But they don’t.
Maybe different people play by different rules. We can have a conversation about what rules we ought to play by. But I’m pretty sure that if we polled people who know about determinism and FTL, most would agree that they are compatible.
As an aside, your analogy with pixies puzzles me. Why did you think I would try to draw a distinction between pixies and FTL travel? Both are computable. Both are possible, by the rules that I and most people I know (and SI) play by.
Well, it seems like the part of this conversation that had to do with the original claim and counterclaim has petered out. Do you agree with this claim:
In a truly deterministic universe, the concept of “faster-than light interaction” is largely nonsensical.
If so, then we can keep going. If not, then we can move on to discuss the nature of possibility and its use against claims like the above. If you are still interested enough in continuing, that is. I won’t detain you against your will.
...
Making testable predictions about empirical reality? That’s a pretty high bar. For example, counterfactuals do not fare well under such rules.
Is it? I’m happy to lower the bar; I didn’t think this definition through very much. But thus far I see no reason to revise it. Why don’t counterfactuals fare well? Are you saying that under my definition of possibility, counterfactuals are impossible? That would mean that we shouldn’t consider theories that involve counterfactuals, which seems to me to be false, though it might depend on what theory of counterfactuals we are using.
I have no strong opinion. I suspect that this claim needs its assumptions fleshed out (e.g. that the speed of light is REALLY the limit of how fast information can propagate).
Why don’t counterfactuals fare well?
Because they are rarely useful for making predictions about reality. Not “never”, of course, just “rarely”.
Not quite. In the toy universe in which the Game of Life exists there is no light, no speed of light, and no limits on faster-than-light interactions.
To make this obvious, you say “in one time step”. What’s the speed of light in Game of Life time steps?
Yes, there is.
That’s a bit of terminological silliness that doesn’t have much to do with the original discussion.
The speed of light in our universe is 1 Planck distance in 1 Planck time. Hence the connection between the speed of light and the idea that all interaction is local.
The closely analogous speed in Game of Life would be 1 grid square in 1 time step.
If Game of Life can be modified as described to allow FTL, nonlocal interactions, then so can the rules of our universe. At least, the burden of proof is on you to show why such modifications aren’t legitimate somehow.
So you agree that it is possible for a truly deterministic universe to have nonlocal interaction. I think it is a short step from there to my conclusion, namely that it is possible for a truly deterministic universe to have faster-than-light interaction.
Huh? The fact that you can make up whatever rules you want for a toy mathematical abstraction does NOT imply that you can do the same for our physical universe.
Do you think you understand what I am trying to do here? Because it seems to me that you are just being difficult. I honestly don’t understand what the problem is. It might be my fault, not yours. EDIT: So, I’ll do what I can to understand you also. Right now I’m thinking that you must have a different understanding of what the space of possible universes looks like.
Watch me do the same for our physical universe:
Take the laws of physics, whatever they turn out to be, and add this new law: —Fix a simultenaity plane if necessary —Pick two distant particles —Decree that every second, all the matter in a 1meter radius around each particle will be swapped with the matter in a 1meter radius around each other particle. As if someone paused the universe, cut out the relevant sections, and switched them.
These are silly rules, but they are consistent, computable, etc. The modified Laws of Physics that would result would be no less possible than our current Laws of Physics, though they would be much less probable.
No.
On the basis of what are you making judgments about what kinds of physics laws are more possible or less possible?
Okay. So, this is what I think you are thinking:
Not just any old Laws are possible. Even consistent, computable Laws can be impossible. (I’m afraid I don’t know why you think this though. Perhaps you think there is only one possible world and it is not a Level IV multiverse or perhaps you think that all possible worlds conform to the laws of physics as some of us currently understand them.)
I’m thinking that universes which are consistent & computable are possible. After all, it seems to me that Solomonoff Induction says this.
Note that I am distinguishing between possibility and probability. I’m not claiming that my modified laws are probable, merely that they are metaphysically possible
If you have problems with the term “metaphysical possibility” then I can instead speak in multiverse terms: I am claiming that all computable, consistent worlds exist somewhere in the multiverse. If you don’t like that either, then I’d like to know how you think about possibility.
Note: I intend to edit this later to add links. I won’t change the text. EDIT: I added the links.
No, I’m not thinking that. The thing is, I don’t quite understand in which sense do you use the word “possible” here. It seems to me you say “X is possible” to mean “I can imagine X”.
See above. And saying “metaphysically possible” doesn’t help—are we still talking purely about your imagination?
Ah. Well, do you happen to have any evidence for your claim?
You’ll have to be a bit more specific. Possibility of what? Possibility of universes with different laws of physics? I don’t know. Again, I am not sure what does the word “possibility” mean here.
It would help if you gave me a positive account of what you think, instead of just pointing out where you disagree with me.
True, the notion of metaphysical possibility is one that might be mysterious. I don’t think it is, but come to think of it, I don’t need to bother with it here—there are other notions of possibility that serve my purposes even better. So we need not discuss it further.
That’s not fair. My use of the phrase “X is possible” thus far meets much more stringent conditions than that. Why did you jump to the lowest common denominator? Do you not know much about the use of the word “possible?”
Yes, my claim is entailed by the Level IV multiverse hypothesis. Are you claiming that that hypothesis is nonsensical? If so, I’d like to hear your alternative metaphysical theory of everything, if you have one, as well as an explanation of why this one is nonsensical.
This was your original claim. Rather than talk about possibility I can just talk about sensibility. Is there a coherent truly deterministic universe in which faster-than-light interaction happens?
Obviously we aren’t asking whether or not there actually exists such a universe, because then your statement would be either trivially true or trivially false, depending on whether or not our universe has faster-than-light interaction.
So we must be looking at some sort of space of non-existent universes, whatever that might be, and checking to see whether there are any that are (a) coherent and (b) contain FTL.
What is this space that we must look at? Well, your question leaves this ambiguous. But it highly suggests that we are looking for some sort of possibility space, e.g. the space of metaphysically possible worlds. I propose that it is at least the space that Solomonoff Induction looks at. In fact, I could get away with less than that if I had to.
Anyhow, since your question leaves it ambiguous which space we are looking at, it is on you to clarify it.
My thinking is pretty simple. Crude, even.
Anyone can make imaginary constructs. Sometimes they involve pixies riding unicorns, sometimes they involve different Planck lengths. Apriori I see no good reason to treat constructs involving Planck lengths any different from constructs involving pixies.
When you say “A universe with feature X is possible” I literally do not understand the meaning of the word “possible” here. It doesn’t exist, it didn’t happen. Could it have happened? I have no idea and neither do you. In you mind you can substitute a different Planck length or break the FTL limitation, then squint at the result and say “Hmm, still looks fine”—but all that is happening inside your mind and again, does not look qualitatively different from leering at a fine pixie. In your mind, most everything is possible—not to mention that your mind cannot determine whether a universe with a different Planck length actually would have been fine.
Actually, no, it wasn’t mine. I jumped in this thread mid-discussion with a comment about the Game of Life.
My point is that this activity is no different from checking the non-existent universes for pixies and unicorns. It might be an agreeable mental pastime, but it has no relationship to reality.
How embarrassing—I forgot who the OP for this argument was. :( Sorry. If you don’t support the claim that I was attacking, then perhaps we don’t even disagree after all.
OK, so you are anti-realist about possibility. Fair enough; so am I. But that doesn’t mean the word “possible” is meaningless in the contexts that I used it in. Here’s an attempt at cashing out one version of “possible” that surely you would agree makes sense:
X is possible iff X is true in some theory in the search space of theories that we ought to use when making predictions.
The claim I was disagreeing with is the claim that determinism does not make sense when combined with FTL interaction. Even if we agree that possibility is just a game we play in our heads, the game still has rules, and the claim I am disagreeing with seemed to be a claim about the implications of those rules—namely, that those rules prohibited the combination of determinism and FTL interaction. But they don’t.
Maybe different people play by different rules. We can have a conversation about what rules we ought to play by. But I’m pretty sure that if we polled people who know about determinism and FTL, most would agree that they are compatible.
As an aside, your analogy with pixies puzzles me. Why did you think I would try to draw a distinction between pixies and FTL travel? Both are computable. Both are possible, by the rules that I and most people I know (and SI) play by.
Making testable predictions about empirical reality? That’s a pretty high bar. For example, counterfactuals do not fare well under such rules.
I did not know whether you would wish to draw such a distinction or not. Now I do :-)
Well, it seems like the part of this conversation that had to do with the original claim and counterclaim has petered out. Do you agree with this claim:
If so, then we can keep going. If not, then we can move on to discuss the nature of possibility and its use against claims like the above. If you are still interested enough in continuing, that is. I won’t detain you against your will.
...
Is it? I’m happy to lower the bar; I didn’t think this definition through very much. But thus far I see no reason to revise it. Why don’t counterfactuals fare well? Are you saying that under my definition of possibility, counterfactuals are impossible? That would mean that we shouldn’t consider theories that involve counterfactuals, which seems to me to be false, though it might depend on what theory of counterfactuals we are using.
I have no strong opinion. I suspect that this claim needs its assumptions fleshed out (e.g. that the speed of light is REALLY the limit of how fast information can propagate).
Because they are rarely useful for making predictions about reality. Not “never”, of course, just “rarely”.