3 ms·

If hardware next year is X times better (e.g. even 1.01 or 1% better) than this year, and you have a computation that takes T time today, then next year, it'll

If hardware next year is X times better (e.g. even 1.01 or 1% better) than this year, and you have a computation that takes T time today, then next year, it'll take T/X time. So waiting will take 1 + T/X years if time unit is years. So the condition you want is 1+T/X < T. This equation has solutions for given X where X is an improvement, so as long as there is any improvement, it's always true waiting to start large enough computations will be faster. Though even faster will be doing part of the computation now and then switching to new hardware later, so it's a false dichotomy.

MaulingMonkey 3y ago
> Though even faster will be doing part of the computation now and then switching to new hardware later Not necessairly. This still costs: • Programmer/development time to implement save/restore/transfer • Time on new hardware, bottlenecked by old hardware, restoring a partial computation from old disks or networks You're not going to waste time restoring partial calculations for anything from an Amiga cluster for time saving purpouses. Additionally, this scheme ties up hardware that then can't be used for "cost effective to finish on current hardware" calculations.
LegionMammal978 3y ago
> This equation has solutions for given X where X is an improvement, so as long as there is any improvement, it's always true waiting to start large enough computations will be faster. Though this does assume that X is a constant, or at least bounded below by a constant. If hardware performance improved up to an asymptote, then there would still be nonzero improvement, but it might not be enough for waiting to ever be worth it.
- seeknotfind 3y ago
  As "If hardware next year is X times better (e.g. even 1.01 or 1% better) than this year" highlights X is a constant as a simplifying assumption, I'd have expected you to say "As this assumes that X is a constant" not "Though this does assume that X is a constant". So, I'm not sure what your disagreement is. If your disagreement is that a constant is not appropriate here, consider the interpretation in this comparison of running a program on a slower computer A and then a faster computer B. There would be a constant difference in performance between these two computers, assuming they are in working order. So, taking the model with a single constant is appropriate for this example. If you are saying the performance improvement is bounded below by a constant, I would ask you, what is the domain of this function? Time? So we would be talking about continuously moving a computation between different computers? The only line here is a best fit line, emergent data, so I don't understand how this could be a preferred way to talk about the situation (the alternate to an assumption), because this is suggesting the emergent structure with nice continuity features is a preferred fundamental understanding of the situation, but it's not. Then, where you are talking about hardware performance improving up to a (assuming horizontal) asymptote. I guess this means "If hardware performance increase becomes marginal[1], there is a nonzero improvement." Or in other words, "If hardware performance increase is marginal, there is a marginal [performance] increase". Performance and improvement are both rates of change, so this is tautological. Finally, you state that waiting for such a marginal near-zero performance increase isn't worth it. I think most people would agree this is obvious if said in simpler terms. However, this is still not disagreeing with me, because I never suggested waiting was worth it. So, what's the disagreement? [1] which is well-established not to be the case, so I don't think this is a relevant case to the interesting factoid about waiting to start computation
  - LegionMammal978 3y ago
    My apologies, I misinterpreted you as talking about waiting for many years (given a sufficiently large task) for performance to continue increasing, since this thread started talking about Moore's Law. I have no disagreement in the single-year case you were actually talking about.

MaulingMonkey 3y ago

> Though even faster will be doing part of the computation now and then switching to new hardware later Not necessairly. This still costs: • Programmer/development time to implement save/restore/transfer • Time on new hardware, bottlenecked by old hardware, restoring a partial computation from old disks or networks You're not going to waste time restoring partial calculations for anything from an Amiga cluster for time saving purpouses. Additionally, this scheme ties up hardware that then can't be used for "cost effective to finish on current hardware" calculations.

LegionMammal978 3y ago

> This equation has solutions for given X where X is an improvement, so as long as there is any improvement, it's always true waiting to start large enough computations will be faster. Though this does assume that X is a constant, or at least bounded below by a constant. If hardware performance improved up to an asymptote, then there would still be nonzero improvement, but it might not be enough for waiting to ever be worth it.

seeknotfind 3y ago
As "If hardware next year is X times better (e.g. even 1.01 or 1% better) than this year" highlights X is a constant as a simplifying assumption, I'd have expected you to say "As this assumes that X is a constant" not "Though this does assume that X is a constant". So, I'm not sure what your disagreement is. If your disagreement is that a constant is not appropriate here, consider the interpretation in this comparison of running a program on a slower computer A and then a faster computer B. There would be a constant difference in performance between these two computers, assuming they are in working order. So, taking the model with a single constant is appropriate for this example. If you are saying the performance improvement is bounded below by a constant, I would ask you, what is the domain of this function? Time? So we would be talking about continuously moving a computation between different computers? The only line here is a best fit line, emergent data, so I don't understand how this could be a preferred way to talk about the situation (the alternate to an assumption), because this is suggesting the emergent structure with nice continuity features is a preferred fundamental understanding of the situation, but it's not. Then, where you are talking about hardware performance improving up to a (assuming horizontal) asymptote. I guess this means "If hardware performance increase becomes marginal[1], there is a nonzero improvement." Or in other words, "If hardware performance increase is marginal, there is a marginal [performance] increase". Performance and improvement are both rates of change, so this is tautological. Finally, you state that waiting for such a marginal near-zero performance increase isn't worth it. I think most people would agree this is obvious if said in simpler terms. However, this is still not disagreeing with me, because I never suggested waiting was worth it. So, what's the disagreement? [1] which is well-established not to be the case, so I don't think this is a relevant case to the interesting factoid about waiting to start computation
- LegionMammal978 3y ago
  My apologies, I misinterpreted you as talking about waiting for many years (given a sufficiently large task) for performance to continue increasing, since this thread started talking about Moore's Law. I have no disagreement in the single-year case you were actually talking about.