it’s okay if you don’t reply. my above comment was treating this post as a schelling point to add my thoughts to the historical archive about this idea.
about ‘living in the moment’ in your other comment: if we ignore influencing boltzmann brains/contexts, then applying ‘ultimate neartermism’ now actually looks more like being a longtermist to enable eventual acausal trades with superintelligence* in a younger universe-point. (* with ‘infinite time’ values, so the trade is preferred to them)
A very, very crucial point is that this argument is only trying to calculate what is best to do in expectation, and even if you have a strong preference for one or other of these theories, you probably don’t have a preference that is stronger than a few orders of magnitude, so in terms of orders of magnitude it actually doesn’t make much of a difference which you think is correct, as long as there is nonzero credence in the first method.
i’m not sure if by ‘these theories’ you meant different physics theories, or these different possible ways of valuing a neverending world (given the paragraphs before the quoted one). if you meant physics theories, then i agree that such quantitative differences matter (this is a weak statement as i’m too confused about infinite universes with different rates-of-increasing to have a stronger statement).
if you meant values:
that’s not how value functions have to be. in principle example: there could be a value function which contains both these and normalizes the scores on each to be within −1 to 1 before summing them.
i don’t think it’s the case that the former function, unnormalized, has a greater range than the latter function. intuitively, it would actually be the case that ‘infinite time’ has an infinitely larger range, but i suspect this is actually more of a different kind of paradox and both would regard this universe as infinite.
paradox between ‘reason over whole universe’ and ‘reason over each timestep in universe’. somehow these appear to not be the same here.
i don’t actually know how to define either of them. i can write a non-terminating number-doubling-program, and ig have that same program also track the sum so far, but i don’t know what it actually means to sum an (at least increasing) infinite series.
actually, a silly idea comes to mind: (if we’re allowed to say[1]) some infinite series like [1/2 + 1⁄4 + 1⁄8 + …] sum to a finite number (1 in that case), then we can also represent the universe going backwards with a decreasing infinite series. i.e., [1 + (1 ÷ 10^10^34) + (1 ÷ 10^10^34^2) + …], where the first term represents the size of the end rather than start of the universe. this way, the calculation at least doesn’t get stuck at infinity. this does end up more clearly implying longtermism, while maintaining the same ratio between size of universe at different times.
but it’s also technically wrong, if the universe has a start but no end, rather than an end but no start.
(though in my intuitive[2] math system, these statements are true: [1/inf > 0], [1/inf × inf = 1], [2/inf × inf = 2]. this could resolve this by letting the start of the universe be represented as 1/10^10^34^inf (so that the increasing infinite series starting from here has the same sum as the decreasing infinite series above).
(i’m not a mathematician). i don’t understand how an infinite series can be writable in existing formal languages—it seems like it would require a ‘...’ (‘and so on...‘) operation in the definition itself, but ‘...’ is not {one of the formally allowed operations}/defined.
meant as a warning that this is not formal or well-understood by me. not meant as legitimation.
that said, i think a formal system which allows these along with other desirable math is possible in principle (and this looks related), maybe in a trivial way
as a simpler intuition for why such x/inf statements can be useful: if there is a sequence of infinite 0s which also contains, somewhere in it, just one 1, the portion of 1s is not 0 but 1 in infinity or 1/inf. similar: an infinite sized universe with finite instances of something (which is also trivially possible, e.g a unique center with repeatingly infinite area outwards from it)
it’s okay if you don’t reply. my above comment was treating this post as a schelling point to add my thoughts to the historical archive about this idea.
about ‘living in the moment’ in your other comment: if we ignore influencing boltzmann brains/contexts, then applying ‘ultimate neartermism’ now actually looks more like being a longtermist to enable eventual acausal trades with superintelligence* in a younger universe-point. (* with ‘infinite time’ values, so the trade is preferred to them)
i’m not sure if by ‘these theories’ you meant different physics theories, or these different possible ways of valuing a neverending world (given the paragraphs before the quoted one). if you meant physics theories, then i agree that such quantitative differences matter (this is a weak statement as i’m too confused about infinite universes with different rates-of-increasing to have a stronger statement).
if you meant values:
that’s not how value functions have to be. in principle example: there could be a value function which contains both these and normalizes the scores on each to be within −1 to 1 before summing them.
i don’t think it’s the case that the former function, unnormalized, has a greater range than the latter function. intuitively, it would actually be the case that ‘infinite time’ has an infinitely larger range, but i suspect this is actually more of a different kind of paradox and both would regard this universe as infinite.
paradox between ‘reason over whole universe’ and ‘reason over each timestep in universe’. somehow these appear to not be the same here.
i don’t actually know how to define either of them. i can write a non-terminating number-doubling-program, and ig have that same program also track the sum so far, but i don’t know what it actually means to sum an (at least increasing) infinite series.
actually, a silly idea comes to mind: (if we’re allowed to say[1]) some infinite series like [1/2 + 1⁄4 + 1⁄8 + …] sum to a finite number (1 in that case), then we can also represent the universe going backwards with a decreasing infinite series. i.e., [1 + (1 ÷ 10^10^34) + (1 ÷ 10^10^34^2) + …], where the first term represents the size of the end rather than start of the universe. this way, the calculation at least doesn’t get stuck at infinity. this does end up more clearly implying longtermism, while maintaining the same ratio between size of universe at different times.
but it’s also technically wrong, if the universe has a start but no end, rather than an end but no start.
(though in my intuitive[2] math system, these statements are true: [1/inf > 0], [1/inf × inf = 1], [2/inf × inf = 2]. this could resolve this by letting the start of the universe be represented as 1/10^10^34^inf (so that the increasing infinite series starting from here has the same sum as the decreasing infinite series above).
(i’m not a mathematician). i don’t understand how an infinite series can be writable in existing formal languages—it seems like it would require a ‘...’ (‘and so on...‘) operation in the definition itself, but ‘...’ is not {one of the formally allowed operations}/defined.
meant as a warning that this is not formal or well-understood by me. not meant as legitimation.
that said, i think a formal system which allows these along with other desirable math is possible in principle (and this looks related), maybe in a trivial way
as a simpler intuition for why such x/inf statements can be useful: if there is a sequence of infinite
0s which also contains, somewhere in it, just one1, the portion of1s is not 0 but 1 in infinity or 1/inf. similar: an infinite sized universe with finite instances of something (which is also trivially possible, e.g a unique center with repeatingly infinite area outwards from it)