What we agree on is that the large random region will quickly settle down into a field of ‘ash’: small stable or oscillating patterns arranged at random. We wouldn’t expect any competitior AIs to form in this region since an area of 10^120 will only be likely to contain arbitrary patterns of sizes up to log(10^120), which almost certainly isn’t enough area to do anything smart.
So the question is whether our AI will be able to cut into this ash and clear it up, leaving a blank canvas for it to create the target pattern. Nobody knows a way to do this, but it’s also not known to be impossible.
Recently I tried an experiment where I slowly fired gliders at a field of ash, along twenty adjacent lanes. My hope had been that each collision of a glider with the ash would on average destroy more ash than it created, thus carving a diagonal path of width 20 into the ash. Instead I found that the collisions created more ash, and so a stalagmite of ash grew towards the source at which I was creating the gliders.
Could you just explain a bit “will only be likely to contain arbitrary patterns of sizes up to log(10^120)” please ? Or give some pointers with other usage of such calculation ?
This is very much a heuristic, but good enough in this case.
Suppose we want to know how many times we expect to see a pattern with n cells in a random field of area A. Ignoring edge effects, there are A different offsets at which the pattern could appear. Each of these has a 1/2^n chance of being the pattern. So we expect at least one copy of the pattern if n < log_2(A).
In this case the area is (10^60)^2, so we expect patterns of size up to 398.631. In other words, we expect the ash to contain any pattern you can fit in a 20 by 20 box.
So just to connect this back to your original point: if we knew that it were possible to construct some kind of intelligent entity in a region with area of, say, 1,000,000,000 cells, then if our overall grid had 21,000,000,000 total cells and we initialized it at random, then we would expect an intelligent entity to pop up by chance at least once in the whole grid.
Yeah, although probably you’d want to include a ‘buffer’ at the edge of the region to protect the entity from gliders thrown out from the surroundings. A 1,000,000 cell thick border filled randomly with blocks at 0.1% density would do the job.
I performed the same experiment with glider guns and got the same result “stalagmite of ash” result.
I didn’t use that name for it, but I instantly recognized my result under that description <3
When I performed that experiment, I was relatively naive about physics and turing machines and so on, and sort of didn’t have the “more dakka” gut feeling that you can always try crazier things once you have granted that you’re doing math, and so infinities are as nothing to your hypothetical planning limits. Applying that level of effort to Conway’s Life… something that might be interesting would be to play with 2^N glider guns in parallel, with variations in their offsets, periodicities, and glider types, for progressively larger values of N? Somewhere in all the variety it might be possible to generate a “cleaning ray”?
If fully general cleaning rays are impossible, that would also be an interesting result! (Also, it is the result I expect.)
My current hunch is that a “cleaning ray with a program” (that is allowed to be fed some kind of setup information full of cheat codes about the details of the finite ash that it is aimed at) might be possible.
Then I would expect there to be a lurking result where there was some kind of Maxwell’s Demon style argument about how many bits of cheatcode are necessary to clean up how much random ash… and then you’re back to another result confirming the second law of thermodynamics, but now with greater generality about a more abstract physics? I haven’t done any of this, but that’s what my hunch is.
If you can create a video of any of your constructions in Life, or put the constructions up in a format that I can load into a simulator at my end, I would be fascinated to take a look at what you’ve put together!
I can definitely see this intuition! But one of the biggest differences between our universe and Life is that Life’s rules aren’t reversible, which means entropy can go down universally. So I think that’s pretty good reason to believe that e.g. an ash-clearing machine is possible.
Most glider guns in random ash will immediately be destroyed by the chaos they cause. Those that don’t will eventually reach an eater which will neutralise them. But yes, such things could pose a nasty surprise for any AI trying to clean up the ash. When it removes the eater it will suddenly have a glider stream coming towards it! But this doesn’t prove it’s impossible to clear up the ash.
See here https://conwaylife.com/forums/viewtopic.php?f=7&t=1234&sid=90a05fcce0f1573af805ab90e7aebdf1 and here https://discord.com/channels/357922255553953794/370570978188591105/834767056883941406 for discussion of this topic by Life hobbyists who have a good knowledge of what’s possible and not in Life.
What we agree on is that the large random region will quickly settle down into a field of ‘ash’: small stable or oscillating patterns arranged at random. We wouldn’t expect any competitior AIs to form in this region since an area of 10^120 will only be likely to contain arbitrary patterns of sizes up to log(10^120), which almost certainly isn’t enough area to do anything smart.
So the question is whether our AI will be able to cut into this ash and clear it up, leaving a blank canvas for it to create the target pattern. Nobody knows a way to do this, but it’s also not known to be impossible.
Recently I tried an experiment where I slowly fired gliders at a field of ash, along twenty adjacent lanes. My hope had been that each collision of a glider with the ash would on average destroy more ash than it created, thus carving a diagonal path of width 20 into the ash. Instead I found that the collisions created more ash, and so a stalagmite of ash grew towards the source at which I was creating the gliders.
EDIT: There’s been a development of new GoL tech that might be able to clear ash: https://www.conwaylife.com/forums/viewtopic.php?p=135539#p135539
Could you just explain a bit “will only be likely to contain arbitrary patterns of sizes up to log(10^120)” please ? Or give some pointers with other usage of such calculation ?
This is very much a heuristic, but good enough in this case.
Suppose we want to know how many times we expect to see a pattern with n cells in a random field of area A. Ignoring edge effects, there are A different offsets at which the pattern could appear. Each of these has a 1/2^n chance of being the pattern. So we expect at least one copy of the pattern if n < log_2(A).
In this case the area is (10^60)^2, so we expect patterns of size up to 398.631. In other words, we expect the ash to contain any pattern you can fit in a 20 by 20 box.
So just to connect this back to your original point: if we knew that it were possible to construct some kind of intelligent entity in a region with area of, say, 1,000,000,000 cells, then if our overall grid had 21,000,000,000 total cells and we initialized it at random, then we would expect an intelligent entity to pop up by chance at least once in the whole grid.
Yeah, although probably you’d want to include a ‘buffer’ at the edge of the region to protect the entity from gliders thrown out from the surroundings. A 1,000,000 cell thick border filled randomly with blocks at 0.1% density would do the job.
I performed the same experiment with glider guns and got the same result “stalagmite of ash” result.
I didn’t use that name for it, but I instantly recognized my result under that description <3
When I performed that experiment, I was relatively naive about physics and turing machines and so on, and sort of didn’t have the “more dakka” gut feeling that you can always try crazier things once you have granted that you’re doing math, and so infinities are as nothing to your hypothetical planning limits. Applying that level of effort to Conway’s Life… something that might be interesting would be to play with 2^N glider guns in parallel, with variations in their offsets, periodicities, and glider types, for progressively larger values of N? Somewhere in all the variety it might be possible to generate a “cleaning ray”?
If fully general cleaning rays are impossible, that would also be an interesting result! (Also, it is the result I expect.)
My current hunch is that a “cleaning ray with a program” (that is allowed to be fed some kind of setup information full of cheat codes about the details of the finite ash that it is aimed at) might be possible.
Then I would expect there to be a lurking result where there was some kind of Maxwell’s Demon style argument about how many bits of cheatcode are necessary to clean up how much random ash… and then you’re back to another result confirming the second law of thermodynamics, but now with greater generality about a more abstract physics? I haven’t done any of this, but that’s what my hunch is.
If you can create a video of any of your constructions in Life, or put the constructions up in a format that I can load into a simulator at my end, I would be fascinated to take a look at what you’ve put together!
I can definitely see this intuition! But one of the biggest differences between our universe and Life is that Life’s rules aren’t reversible, which means entropy can go down universally. So I think that’s pretty good reason to believe that e.g. an ash-clearing machine is possible.
Interesting! Thank you for these links
Thanks for linking to my post! I checked the other link, on Discord, and for some reason it’s not working.
The link still works for me. Perhaps you must first become a member of that discord? Invite link: https://discord.gg/nZ9JV5Be (valid for 7 days)
Thanks. I also found an invite link in a recent reddit post about this discussion (was that by you?).
At a large enough scale the ash field would probably contain glider guns that would restart the chaos and expand the ash frontier.
Most glider guns in random ash will immediately be destroyed by the chaos they cause. Those that don’t will eventually reach an eater which will neutralise them. But yes, such things could pose a nasty surprise for any AI trying to clean up the ash. When it removes the eater it will suddenly have a glider stream coming towards it! But this doesn’t prove it’s impossible to clear up the ash.