On 2008-03-27, Damien Sullivan <phoenix@[EMAIL PROTECTED]
> wrote:
> But when I thought about all this abstractly, my model went "you
> speed up the computer by driving signals v times faster, which takes
> v^2 more energy, plus you're doing v times more computation
Computational power requirements really don't work like that.
Electronic computers don't have electrons moving at near light speed.
From one point of view, what they have is electromagnetic waves moving
along wires acting as waveguides. The electrons in the wires are just
the means by which the waves are guided, and hardly move at all.
> Thermodynamic limits -- kTln2 joules to erase one bit -- seem to
> keep a 20 Watt 300 K system like the brain from doing more than 1e22
> bits/second. So something feels wrong.
A brain doesn't process nearly that much, so it doesn't seem too wrong
to me.
Another factor is that reversible computation can surpass that
particular limit anyway. Such a process involves keeping most of the
intermediate state information during a computation, and rolling it
back afterward. Only the input state information need be erased.
If a particular type of computation requires too much intermediate
state to retain, then it can be broken up into segments. This would
increase the entropy generation, but much less than erasing
intermediate states at every logic element in every step.
Furthermore in a high-tech setting where computational efficiency is
of very high importance, it should be possible to run the actual logic
much colder than the environmental temperature. I'm sure operating
temperatures in the range of millikelvin would be theoretically
achievable, adding orders of magnitude to the computational power.
I have no idea what entropy savings reversible computation would bring
for typical problems. A factor of 10? 10^9? It would probably
depend upon what task was required, and some measure of inherent
computational entropy. If this limit became important in the future,
I suspect that algorithm design would at least in part be based around
minimising it, and so estimating the entropy of our current best
algorithms would almost certainly be misguided.
- Tim
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