Re: [math-fun] Could change of base (binary ?> ternary) speed up computation?
Richard Howard <rich@richardehoward.com> wrote:
2) Low temperature sounds great, but energy tends to go down with temperature much slower than heat transfer. Low temperature computers are really hard to cool.
Right. That's why I said that running a computer in an air- conditioned room doesn't really gain you anything. The kT log(2) limit, i.e. that that's the minimum energy it takes to erase a bit, applies to the computer and air conditioner put together. That's why I suggested running the computer in the outer solar system instead. Or in nearby space behind a sun shield, like JWST. Tom Knight <tk@mit.edu> wrote:
I?ll let others worry about arbitrarily slow clocks. I like ones running at multiple GHz.
That's fine for next googol years or so, but when we approach the year googolplex, it's no longer realistic. For one thing, it takes a long time to radiate away waste heat at cryogenic temperatures. For another, the the components of the computer have to be widely separated so that they won't experience significant amounts of mutual gravitation, since an accelerated observer experiences a non-zero temperature (Unruh effect). For instance an observer experiencing 1 g (normal Earth surface gravity) will experience a temperature of at least 10^-20 K. Anyhow, there's not that much difference in speeds. A few gigahertz is one cycle every 10^33 Planck times or so. One cycle per eon (billion years) would be about one every 10^60 Planck times. Less than a factor of two difference (on a log scale).
It seems like going cold is the wrong way to go. Radiative cooling rate drops as T^4, while energy per erasure drops as T. Lose big trying to dump energy to the CMB at 3K. On the other hand, Robert Forward may have had it right in Dragon's Egg. A good computer would be built out of neutronium matter and run at the rate of nuclear reactions. It is easy to dump waste heat at 10^6 K or higher--t^4 becomes pretty big relative to kTln2/erasure. --R On Tue, Jan 8, 2019 at 11:59 PM Keith F. Lynch <kfl@keithlynch.net> wrote:
Richard Howard <rich@richardehoward.com> wrote:
2) Low temperature sounds great, but energy tends to go down with temperature much slower than heat transfer. Low temperature computers are really hard to cool.
Right. That's why I said that running a computer in an air- conditioned room doesn't really gain you anything. The kT log(2) limit, i.e. that that's the minimum energy it takes to erase a bit, applies to the computer and air conditioner put together. That's why I suggested running the computer in the outer solar system instead. Or in nearby space behind a sun shield, like JWST.
Tom Knight <tk@mit.edu> wrote:
I?ll let others worry about arbitrarily slow clocks. I like ones running at multiple GHz.
That's fine for next googol years or so, but when we approach the year googolplex, it's no longer realistic. For one thing, it takes a long time to radiate away waste heat at cryogenic temperatures. For another, the the components of the computer have to be widely separated so that they won't experience significant amounts of mutual gravitation, since an accelerated observer experiences a non-zero temperature (Unruh effect). For instance an observer experiencing 1 g (normal Earth surface gravity) will experience a temperature of at least 10^-20 K.
Anyhow, there's not that much difference in speeds. A few gigahertz is one cycle every 10^33 Planck times or so. One cycle per eon (billion years) would be about one every 10^60 Planck times. Less than a factor of two difference (on a log scale).
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Richard Howard