Compression attained can be an exponential function of time. That’s not the same as saying that compression rate can grow exponentially. I mean, if it’s a “rate”, it already expresses how compression grows, so “the compression rate grows exponentially” means “the first derivative of compression grows exponentially”.
Anyway, compression can’t keep increasing indefinitely, due to the Planck constant. Mike Vassar once did some back-of-envelope-calculations showing that we have surprisingly few orders of magnitude to go before we hit it in terms of computational power—less than 20 orders of magnitude, IIRC. But two orders of magnitude is enough to kill us, in this scenario. Basically, it will take us something like 5 million years to reach another galaxy, at which point you might consider life safe. If we get just 2 orders of magnitude out of subjective time compression that’s like 500 million years, and our survival to that point seems dubious.
(I went back to clarify this because I realized people don’t usually think of 20 orders of magnitude as “surprisingly few”.)
By “compression rate” I meant “compression ratio”. Sorry for the confusion. But you know that if something grows exponentially, all of its nth derivatives do also, right?
I did know that the actual universe probably has some physical limits in how you can shrink a computation in space and/or time, thus my question. Actually, I thought you might have done the not-math “exponential” as a way of saying “A LOT!!!”
Okay, it is the same thing as saying that compression rate can grow exponentially.
I meant exponential. I don’t know if I believe it’s exponential, but almost all other futurists say that things are speeding up (time is compressing) exponentially.
Compression attained can be an exponential function of time. That’s not the same as saying that compression rate can grow exponentially. I mean, if it’s a “rate”, it already expresses how compression grows, so “the compression rate grows exponentially” means “the first derivative of compression grows exponentially”.
Anyway, compression can’t keep increasing indefinitely, due to the Planck constant. Mike Vassar once did some back-of-envelope-calculations showing that we have surprisingly few orders of magnitude to go before we hit it in terms of computational power—less than 20 orders of magnitude, IIRC. But two orders of magnitude is enough to kill us, in this scenario. Basically, it will take us something like 5 million years to reach another galaxy, at which point you might consider life safe. If we get just 2 orders of magnitude out of subjective time compression that’s like 500 million years, and our survival to that point seems dubious.
(I went back to clarify this because I realized people don’t usually think of 20 orders of magnitude as “surprisingly few”.)
By “compression rate” I meant “compression ratio”. Sorry for the confusion. But you know that if something grows exponentially, all of its nth derivatives do also, right?
I did know that the actual universe probably has some physical limits in how you can shrink a computation in space and/or time, thus my question. Actually, I thought you might have done the not-math “exponential” as a way of saying “A LOT!!!”
Okay, it is the same thing as saying that compression rate can grow exponentially.
I meant exponential. I don’t know if I believe it’s exponential, but almost all other futurists say that things are speeding up (time is compressing) exponentially.