4 ms·

> To give a preview of why doing this might devolve into an “engineering problem”, let’s consider a loose (but, in the end, not quite so loose) analogy. Imagine

> To give a preview of why doing this might devolve into an “engineering problem”, let’s consider a loose (but, in the end, not quite so loose) analogy. Imagine you’ve got molecules of gas in a room, all bouncing around and colliding with each other. Now imagine there’s a special molecule—or even a tiny speck of dust or a virus particle—somewhere in the room. Normally the special molecule will be buffeted by the molecules in the air, and will move in some kind of random walk, gradually diffusing across the room. But imagine that the special molecule somehow knows enough about the motion of the air molecules that it can compute exactly where to go to avoid being buffeted. Then that special molecule can travel much faster than diffusion—and effectively make a beeline from one side of the room to the other. Of course this requires more knowledge and more computation than we currently imagine something like a molecule can muster (though it’s not clear this is true when we start thinking about explicitly constructing molecule-scale computers). But the point is that the limit on the speed of the molecule is less a question of what’s physically possible, and more a question of what’s “engineerable”. This is posed as a computational resource problem, but it strikes me as an information problem. How do you know where the aggressor molecules are and what their paths (i.e. future states) are? Perhaps it’s possible to know the very local conditions and dodge an imminent collision, but does that generalize to arbitrarily long paths? Can I make it to the other end of the room, dodging only the molecules right in front of me? Or can I set out on a path from the beginning that has no solution in the end because it results in an unsolvable state? And if the only way to know is to know the full state of the molecules that may affect my journey, beginning to end, doesn’t their state have to be known at the outset of the journey? If the information about their state itself has a speed limit, and if their state is not fully observable or fully deterministic, what sort of computation can defeat that?

AnimalMuppet 6y ago
More, it betrays a very simplistic view of physics. How does the special molecule move? By magic? By willpower? By an internal combustion engine? It needs some way of changing its course. Molecules don't have such a mechanism, except for bouncing off of other molecules. And, how does the molecule know where the other molecules are? It's psychic? Lidar? Radar? How? What's it's energy source for emitting whatever it has to emit to be able to gather the information that it needs? The analogy is, if we take a superficial knowledge of physics, and don't actually think about the details, we can construct a wonderful-sounding-but-not-actually-possible scenario. That's perhaps an accurate analogy for what Wolfram is really proposing.
bee_rider 6y ago
It is actually computationally quite simple -- just follow Maxwell's Demon, it was already on it's way across the room to do the whole door closing thing, so it should be able to figure the path for you.
mnl 6y ago
This special molecule of Stephen's is essentially a Maxwell's demon (it could use that information to open or close the door by choosing appropriate collisions, or simply act as the gate itself). There's a lot of literature about that. Actually Stephen's special molecule is more powerful because it's omniscient. Ordinary Maxwell's demons just see fast or slow molecules coming at the gate and act accordingly. This one knows the momentum and position of every other particle it needs to know something about, which can be peculiar if you don't think about uncertainty.
jlokier 6y ago
> This is posed as a computational resource problem, but it strikes me as an information problem. I thought the point of the gas illustration was to show how the assumption there's an information problem (i.e. heat, second law) is actually not correct. That it only looks like an information problem and it's really a computation problem. The theory being that if you can compute were the molecules are going to be, from the initial state or from interactions you have already learned from, then the motions don't appear random any more. There are no surprises; you have "decrypted" the apparently random movements. It's just to illustrate the idea, and an immediate objection would be "but we can't know everything to that much detail". That is addressed by a more subtle version of the argument, which says: Although you don't know all the motions precisely, your ability to compute motions from the information you obtained so far gives you progressively increasing knowledge about motions locally or which you recognise as related, and causes "regions of effective coherence" to expand. It's effective coherence not actual coherence, because the molecule motions don't change, only the precision with which you can anticipate some of them as well as relationships between them. What would have appeared random, now with the benefit of some prior information and computation resolves gradually into local clusters of more predictable related motions, even if you don't know every motion accurately. With the result that the effective fluid properties change, so your ability to "swim" through the gas changes. In the 2d closed box model, with perfect balls and perfect interactions (i.e. a mathematically perfect simulation) it's plausible that this may work perfectly. That is, if you have your own "special" ball and it undergoes a number of collisions and you get perfect measurement of those collisions, eventually you end up with enough information to model the contents of the rest of the box. If in that model you can dynamically adjust something about the collisions of your "special" ball, for example changing the ball's shape, mass or radius, it's plausible that can be used to travel anywhere in the box much faster than diffusion, but only if you have the information up to that point and excellent computation - which might be irreducibly hard computation for a reasonably sized box.
- a1369209993 6y ago
  > an immediate objection would be "but we can't know everything to that much detail". No, the immediate objection would be "but it's physically impossible to know everything to that much detail, because you don't have enough bits of storage[0], and also because of Heisenberg's uncertainty principle". (Both objections are suffient on their own to make this not work except possibly for a homogenous spherical molecule-shaped unphysically-light and -compact hypercomputer in a frictionless vacuum.) 0: That is, it's physically impossible to pack enough bits to describe a cloud of gas onto a storage medium massing significantly less than the entire cloud of gas.

AnimalMuppet 6y ago

More, it betrays a very simplistic view of physics. How does the special molecule move? By magic? By willpower? By an internal combustion engine? It needs some way of changing its course. Molecules don't have such a mechanism, except for bouncing off of other molecules. And, how does the molecule know where the other molecules are? It's psychic? Lidar? Radar? How? What's it's energy source for emitting whatever it has to emit to be able to gather the information that it needs? The analogy is, if we take a superficial knowledge of physics, and don't actually think about the details, we can construct a wonderful-sounding-but-not-actually-possible scenario. That's perhaps an accurate analogy for what Wolfram is really proposing.

bee_rider 6y ago

It is actually computationally quite simple -- just follow Maxwell's Demon, it was already on it's way across the room to do the whole door closing thing, so it should be able to figure the path for you.

mnl 6y ago

This special molecule of Stephen's is essentially a Maxwell's demon (it could use that information to open or close the door by choosing appropriate collisions, or simply act as the gate itself). There's a lot of literature about that. Actually Stephen's special molecule is more powerful because it's omniscient. Ordinary Maxwell's demons just see fast or slow molecules coming at the gate and act accordingly. This one knows the momentum and position of every other particle it needs to know something about, which can be peculiar if you don't think about uncertainty.

jlokier 6y ago

> This is posed as a computational resource problem, but it strikes me as an information problem. I thought the point of the gas illustration was to show how the assumption there's an information problem (i.e. heat, second law) is actually not correct. That it only looks like an information problem and it's really a computation problem. The theory being that if you can compute were the molecules are going to be, from the initial state or from interactions you have already learned from, then the motions don't appear random any more. There are no surprises; you have "decrypted" the apparently random movements. It's just to illustrate the idea, and an immediate objection would be "but we can't know everything to that much detail". That is addressed by a more subtle version of the argument, which says: Although you don't know all the motions precisely, your ability to compute motions from the information you obtained so far gives you progressively increasing knowledge about motions locally or which you recognise as related, and causes "regions of effective coherence" to expand. It's effective coherence not actual coherence, because the molecule motions don't change, only the precision with which you can anticipate some of them as well as relationships between them. What would have appeared random, now with the benefit of some prior information and computation resolves gradually into local clusters of more predictable related motions, even if you don't know every motion accurately. With the result that the effective fluid properties change, so your ability to "swim" through the gas changes. In the 2d closed box model, with perfect balls and perfect interactions (i.e. a mathematically perfect simulation) it's plausible that this may work perfectly. That is, if you have your own "special" ball and it undergoes a number of collisions and you get perfect measurement of those collisions, eventually you end up with enough information to model the contents of the rest of the box. If in that model you can dynamically adjust something about the collisions of your "special" ball, for example changing the ball's shape, mass or radius, it's plausible that can be used to travel anywhere in the box much faster than diffusion, but only if you have the information up to that point and excellent computation - which might be irreducibly hard computation for a reasonably sized box.

a1369209993 6y ago
> an immediate objection would be "but we can't know everything to that much detail". No, the immediate objection would be "but it's physically impossible to know everything to that much detail, because you don't have enough bits of storage[0], and also because of Heisenberg's uncertainty principle". (Both objections are suffient on their own to make this not work except possibly for a homogenous spherical molecule-shaped unphysically-light and -compact hypercomputer in a frictionless vacuum.) 0: That is, it's physically impossible to pack enough bits to describe a cloud of gas onto a storage medium massing significantly less than the entire cloud of gas.