I’m not remotely a physicist, but I have a few comments, which I will do my best to confine to the limits imposed by my knowledge of my lack of knowledge.
Let us assume that you an all-powerful optimization process, and your goal is to finish an extremely long computation (say, a search for a very large Hamiltonian cycle) in the shortest possible amount of time. You have millions of galaxies to turn into computronium. What is the optimal expansion speed of your computer, considering our current understanding of particle physics, general relativity and thermodynamics?
By “optimal expansion speed”, do you mean “maximum possible expansion speed given particle physics, general relativity and thermodynamics (according to our current understanding thereof)”, or do you see some reason that a slower expansion would be beneficial to the ultimate goal (or is that the question)?
(Meanwhile, I’ll just say that I’d first want to either prove P≠NP or find a polynomial-time algorithm for the Hamiltonian cycle problem. P=NP may be unlikely, but if I were an all-powerful optimization process, I’d probably want to get that out of the way before brute-forcing an NP-complete problem. Might save a few million galaxies that way. Then again, an all-powerful optimization process would very likely have a better idea than this puny human.)
Of all the possible Universes in Tegmark’s level IV Multiverse, most don’t even have a concept of Time.
I’m not sure if something without a timelike dimension would really qualify as a universe. It’s really just a matter of definition, but since every mathematical structure has the same ontological status in Tegmark IV, including, say, the set {1, 2, 3}, a useful definition of “universe” will have to be more narrow than “every element of the Level IV Multiverse” and more broad than “every structure that can result from the laws of this universe”.
I’m not sure if we’d be able to rigorously define what structures count as “universes” (and it’s not terribly important, being that our definition of the word doesn’t impinge on reality anyway), but intuitively, what properties are necessary for a structure to seem like a universe to you in the first place? I’d be pretty flexible with it, but I think I’d require it to have something timelike, some way for conditions to dynamically evolve over at least one dimension.
By “optimal expansion speed”, do you mean “maximum possible expansion speed given particle physics, general relativity and thermodynamics (according to our current understanding thereof)”, or do you see some reason that a slower expansion would be beneficial to the ultimate goal (or is that the question)?
Avoiding heat death may be beneficial, for example. As I wrote to Mitchell Porter, to me, the most interesting special case of the question is: if you want to build the fastestest computer in the Universe, should it expand with the speed of light? I’m really not a physicist, so I don’t even know the answer to a very simple version of this question, a version that any particle physicist should be able to answer: Is it possible for some nontrivial information processing system to spread with exactly the speed of light? If not, what about expansion speed converging to c?
what properties are necessary for a structure to seem like a universe to you in the first place?
You (and Mitchell Porter) are completely right . At this point, I don’t have a convincing answer to your obvious question. In the meantime, Tegmark level IV is a good enough answer for me. (Note to Mitchell: it would be very hard to find someone less platonist than me. And I find Tegmark’s focus on computability totally misdirected, so in this sense I am not an intuitionist either.)
I’d be pretty flexible with it, but I think I’d require it to have something timelike, some way for conditions to dynamically evolve over at least one dimension.
I think we disagree here. Please see my answer to Mitchell about the emergence of time from the more basic concept of memory.
I’m not a physicist, but my understanding is that it is not possible for an information processing system to expand at or arbitrarily close to the speed of light; if we neglect the time taken for other activities such as mining and manufacturing, the most obvious limit is the speed to which you can accelerate colony ships (which have to be massive enough to not be fried by collision with interstellar hydrogen atoms). The studies I’ve seen suggest that a few percent of lightspeed is doable given moderate assumptions, a few tens of percent doable if we can get closer to ultimate physical limits, 90%+ doable under extreme assumptions, 99%+ not plausible and 99.9%+ flat-out impossible without some kind of unobtainium.
On the question of ontology, I’m a card-carrying neoplatonist, so you’ve probably heard my position from other people before :-)
I’m not remotely a physicist, but I have a few comments, which I will do my best to confine to the limits imposed by my knowledge of my lack of knowledge.
By “optimal expansion speed”, do you mean “maximum possible expansion speed given particle physics, general relativity and thermodynamics (according to our current understanding thereof)”, or do you see some reason that a slower expansion would be beneficial to the ultimate goal (or is that the question)?
(Meanwhile, I’ll just say that I’d first want to either prove P≠NP or find a polynomial-time algorithm for the Hamiltonian cycle problem. P=NP may be unlikely, but if I were an all-powerful optimization process, I’d probably want to get that out of the way before brute-forcing an NP-complete problem. Might save a few million galaxies that way. Then again, an all-powerful optimization process would very likely have a better idea than this puny human.)
I’m not sure if something without a timelike dimension would really qualify as a universe. It’s really just a matter of definition, but since every mathematical structure has the same ontological status in Tegmark IV, including, say, the set {1, 2, 3}, a useful definition of “universe” will have to be more narrow than “every element of the Level IV Multiverse” and more broad than “every structure that can result from the laws of this universe”.
I’m not sure if we’d be able to rigorously define what structures count as “universes” (and it’s not terribly important, being that our definition of the word doesn’t impinge on reality anyway), but intuitively, what properties are necessary for a structure to seem like a universe to you in the first place? I’d be pretty flexible with it, but I think I’d require it to have something timelike, some way for conditions to dynamically evolve over at least one dimension.
Avoiding heat death may be beneficial, for example. As I wrote to Mitchell Porter, to me, the most interesting special case of the question is: if you want to build the fastestest computer in the Universe, should it expand with the speed of light? I’m really not a physicist, so I don’t even know the answer to a very simple version of this question, a version that any particle physicist should be able to answer: Is it possible for some nontrivial information processing system to spread with exactly the speed of light? If not, what about expansion speed converging to c?
You (and Mitchell Porter) are completely right . At this point, I don’t have a convincing answer to your obvious question. In the meantime, Tegmark level IV is a good enough answer for me. (Note to Mitchell: it would be very hard to find someone less platonist than me. And I find Tegmark’s focus on computability totally misdirected, so in this sense I am not an intuitionist either.)
I think we disagree here. Please see my answer to Mitchell about the emergence of time from the more basic concept of memory.
I’m not a physicist, but my understanding is that it is not possible for an information processing system to expand at or arbitrarily close to the speed of light; if we neglect the time taken for other activities such as mining and manufacturing, the most obvious limit is the speed to which you can accelerate colony ships (which have to be massive enough to not be fried by collision with interstellar hydrogen atoms). The studies I’ve seen suggest that a few percent of lightspeed is doable given moderate assumptions, a few tens of percent doable if we can get closer to ultimate physical limits, 90%+ doable under extreme assumptions, 99%+ not plausible and 99.9%+ flat-out impossible without some kind of unobtainium.
On the question of ontology, I’m a card-carrying neoplatonist, so you’ve probably heard my position from other people before :-)