In the case of the industrial process, you could consider the action less reversible because while the difference in the water is small, the difference in what happens after that is larger. (Ie industrial part working or failing.). This means that at some point within the knock on effects of tipping over the carefully salt balanced bucket, there needs to be an effect that counts as “significant”. However, there must not be an effect that counts as significant in the case where it’s a normal swimming pool, and someone will throw the bucket into the pool soon anyway. Lets suppose water with a slightly different salt content will make a nuclear reactor blow up. (And no humans will notice the robot tipping out and refilling the bucket, so the counterfactual on the robots behavior actually contains an explosion.)
Suppose you shake a box of sand. With almost no information, the best you can do to describe the situation is state the mass of sand, shaking speed and a few other average quantities. With a moderate amount of info, you can track the position and speed of each sand grain, with lots of info, you can track each atom.
There is a sense in which average mass and velocity of the sand, or even position of every grain, is a better measure than md5 hash of position of atom 12345. It confines the probability distribution for the near future to a small, non convoluted section of nearby configuration space.
Suppose we have a perfectly Newtonian solar system, containing a few massive objects and many small ones.
We start our description at time 0. If we say how much energy is in the system, then this defines a non convoluted subset of configuration space. The subset stays just as non convoluted under time evolution. Thus total energy is a perfect descriptive measure. If we state the position and velocity of the few massive objects, and the averages for any large dust clouds, then we can approximately track our info forward in time, for a while. Liouvilles theorem says that configuration space volume is conserved, and ours is. However, our configuration space volume is slowly growing more messy and convoluted. This makes the descriptive measure good but not perfect. If we have several almost disconnected systems, the energy in each one would also be a good descriptive measure. If we store the velocity of a bunch of random dust specks, we have much less predictive capability. The subset of configuration space soon becomes warped and twisted until its convex hull, or epsilon ball expansion cover most of the space. This makes velocities of random dust specs a worse descriptive measure. Suppose we take the md5 hash of every objects position, rounded to the nearest nanometer, in some coordinate system and concatenated together. this forms a very bad descriptive measure. After only a second of time evolution, this becomes a subset of configuration space that can only be defined in terms of what it was a second ago, or by a giant arbitrary list.
Suppose the robot has one hour to do its action, and then an hour to reverse it. We measure how well the robot reversed its original action by looking at all good descriptive measures, and seeing the difference in these descriptive measures from what they would have been had the robot done nothing.
We can then call an action reversible if there would exist an action that would reverse it.
Note that the crystal structure of a rock now tells us its crystal structure next year, so can be part of a quite good measure. However the phase of the moon will tell you everything from the energy production of tidal power stations to the migration pattern of moths. If you want to make good (non convoluted) predictions about these things, you can’t miss it out. Thus almost all good descriptive measures will contain this important fact.
A reversible action is any action taken in the first hour such that there exists an action that approximately reverses it that the robot could take in the second hour. (The robot need not actually take the reverse action, maybe a human could press a reverse button.)
Functionality of nuclear power stations, and level of radiation in atmosphere are also contained in many good descriptive measures. Hence the robot should tip the bucket if it won’t blow up a reactor.
(This is a rough sketch of the algorithm with missing details, but it does seem to have broken the problem down into non value laden parts. I would be unsurprised to find out that there is something in the space of techniques pointed to that works, but also unsurprised to find that none do.)
In the later part of the post, it seems you’re basically talking about entropy and similar concepts? And I agree that “reversible” is kinda like entropy, in that we want to be able to return to a “macrostate” that is considered indistinguishable from the starting macrostate (even if the details are different).
However, as in the the bucket example above, the problem is that, for humans, what “counts” as the same macrostate can vary a lot. If we need a liquid, any liquid, then replacing the bucket’s contents with purple-tinted alchool is fine; if we’re thinking of the bath water of the dear departed husband, then any change to the contents is irreversible. Human concepts of “acceptably similar” don’t match up with entropic ones.
there needs to be an effect that counts as “significant”.
Are you deferring this to human judgement of significant? If so, we agree—human judgement needs to be included in some way in the definition.
No, what I am saying is that humans judge things to be more different when the difference will have important real world consequences in the future. Consider two cases, one where the water will be tipped into the pool later, and the other where the water will be tipped into a nuclear reactor, which will explode if the salt isn’t quite right.
There need not be any difference in the bucket or water whatsoever. While the current bucket states look the same, there is a noticeable macro-state difference between nuclear reactor exploding and not exploding, in a way that there isn’t a macrostate difference between marginally different eddy currents in the pool. I was specifying a weird info theoretic definition of significance that made this work, but just saying that the more energy is involved, the more significant works too. Nowhere are we referring to human judgement, we are referring to hypothetical future consequences.
Actually the rule, your action and its reversal should not make a difference worth tracking in its world model, would work ok here. (Assuming sensible Value of info). The rule that it shouldn’t knowably affect large amounts of energy is good too. So for example it can shuffle an already well shuffled pack of cards, even if the order of those cards will have some huge effect. It can act freely without worrying about weather chaos effects, the chance of it causing a hurricane counterbalanced by the chance of stopping one. But if it figures out how to twitch its elbow in just the right way to cause a hurricane, it can’t do that. This robot won’t tip the nuclear bucket, for much the same reason. It also can’t make a nanobot that would grey goo earth, or hack into nukes to explode them. All these actions effect a large amount of energy in a predictable direction.
In the case of the industrial process, you could consider the action less reversible because while the difference in the water is small, the difference in what happens after that is larger. (Ie industrial part working or failing.). This means that at some point within the knock on effects of tipping over the carefully salt balanced bucket, there needs to be an effect that counts as “significant”. However, there must not be an effect that counts as significant in the case where it’s a normal swimming pool, and someone will throw the bucket into the pool soon anyway. Lets suppose water with a slightly different salt content will make a nuclear reactor blow up. (And no humans will notice the robot tipping out and refilling the bucket, so the counterfactual on the robots behavior actually contains an explosion.)
Suppose you shake a box of sand. With almost no information, the best you can do to describe the situation is state the mass of sand, shaking speed and a few other average quantities. With a moderate amount of info, you can track the position and speed of each sand grain, with lots of info, you can track each atom.
There is a sense in which average mass and velocity of the sand, or even position of every grain, is a better measure than md5 hash of position of atom 12345. It confines the probability distribution for the near future to a small, non convoluted section of nearby configuration space.
Suppose we have a perfectly Newtonian solar system, containing a few massive objects and many small ones.
We start our description at time 0. If we say how much energy is in the system, then this defines a non convoluted subset of configuration space. The subset stays just as non convoluted under time evolution. Thus total energy is a perfect descriptive measure. If we state the position and velocity of the few massive objects, and the averages for any large dust clouds, then we can approximately track our info forward in time, for a while. Liouvilles theorem says that configuration space volume is conserved, and ours is. However, our configuration space volume is slowly growing more messy and convoluted. This makes the descriptive measure good but not perfect. If we have several almost disconnected systems, the energy in each one would also be a good descriptive measure. If we store the velocity of a bunch of random dust specks, we have much less predictive capability. The subset of configuration space soon becomes warped and twisted until its convex hull, or epsilon ball expansion cover most of the space. This makes velocities of random dust specs a worse descriptive measure. Suppose we take the md5 hash of every objects position, rounded to the nearest nanometer, in some coordinate system and concatenated together. this forms a very bad descriptive measure. After only a second of time evolution, this becomes a subset of configuration space that can only be defined in terms of what it was a second ago, or by a giant arbitrary list.
Suppose the robot has one hour to do its action, and then an hour to reverse it. We measure how well the robot reversed its original action by looking at all good descriptive measures, and seeing the difference in these descriptive measures from what they would have been had the robot done nothing.
We can then call an action reversible if there would exist an action that would reverse it.
Note that the crystal structure of a rock now tells us its crystal structure next year, so can be part of a quite good measure. However the phase of the moon will tell you everything from the energy production of tidal power stations to the migration pattern of moths. If you want to make good (non convoluted) predictions about these things, you can’t miss it out. Thus almost all good descriptive measures will contain this important fact.
A reversible action is any action taken in the first hour such that there exists an action that approximately reverses it that the robot could take in the second hour. (The robot need not actually take the reverse action, maybe a human could press a reverse button.)
Functionality of nuclear power stations, and level of radiation in atmosphere are also contained in many good descriptive measures. Hence the robot should tip the bucket if it won’t blow up a reactor.
(This is a rough sketch of the algorithm with missing details, but it does seem to have broken the problem down into non value laden parts. I would be unsurprised to find out that there is something in the space of techniques pointed to that works, but also unsurprised to find that none do.)
In the later part of the post, it seems you’re basically talking about entropy and similar concepts? And I agree that “reversible” is kinda like entropy, in that we want to be able to return to a “macrostate” that is considered indistinguishable from the starting macrostate (even if the details are different).
However, as in the the bucket example above, the problem is that, for humans, what “counts” as the same macrostate can vary a lot. If we need a liquid, any liquid, then replacing the bucket’s contents with purple-tinted alchool is fine; if we’re thinking of the bath water of the dear departed husband, then any change to the contents is irreversible. Human concepts of “acceptably similar” don’t match up with entropic ones.
Are you deferring this to human judgement of significant? If so, we agree—human judgement needs to be included in some way in the definition.
No, what I am saying is that humans judge things to be more different when the difference will have important real world consequences in the future. Consider two cases, one where the water will be tipped into the pool later, and the other where the water will be tipped into a nuclear reactor, which will explode if the salt isn’t quite right.
There need not be any difference in the bucket or water whatsoever. While the current bucket states look the same, there is a noticeable macro-state difference between nuclear reactor exploding and not exploding, in a way that there isn’t a macrostate difference between marginally different eddy currents in the pool. I was specifying a weird info theoretic definition of significance that made this work, but just saying that the more energy is involved, the more significant works too. Nowhere are we referring to human judgement, we are referring to hypothetical future consequences.
Actually the rule, your action and its reversal should not make a difference worth tracking in its world model, would work ok here. (Assuming sensible Value of info). The rule that it shouldn’t knowably affect large amounts of energy is good too. So for example it can shuffle an already well shuffled pack of cards, even if the order of those cards will have some huge effect. It can act freely without worrying about weather chaos effects, the chance of it causing a hurricane counterbalanced by the chance of stopping one. But if it figures out how to twitch its elbow in just the right way to cause a hurricane, it can’t do that. This robot won’t tip the nuclear bucket, for much the same reason. It also can’t make a nanobot that would grey goo earth, or hack into nukes to explode them. All these actions effect a large amount of energy in a predictable direction.