energy of computation, mv^2 abuse?

Help, check my logic!

So I hang around Orion's Arm, a transhumanist SF project with ye olde
superfast AIs and big brains. And in the past I've thought "gosh,
neural signal speeds are meters/second, you could replace them with
wires and think a million times faster!"

But these says I try to be harder, and think about energy costs and
heat radiation needs. We'll ignore the heat for now.

My reasoning has been: a neural signal is big heavy ions moving around.
Actually they wiggle in place, while a potential moves down at meters
per second, but let that slide. Electricity is light (1/40,000 the mass
of a sodium ion) fast electrons moving around, a million times faster.

But kinetic energy is mv^/2, so if you plug in the values you get 2e7
times the energy to do the same amount of computation. Which is in the
ballpark of how I compare a brain (20 Watts, 1e18 "bits/second") and a
modern CPU (20-80 Watts, 1e10 bits/second (billions of ops/second,
tennish bits/op.)

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 -- switching v times
more signals -- so you end up needing v^3 the energy for v times the
computation. Though if you lower the mass of your signals, so that the
momentum remains the same (with the same ability to resist thermal
noise) then you can cut that down to v^2."

Which applied to the electric brain becomes "2e7 the energy to do the
same amount of computation, but you're doing a million times the
computation, so it becomes 2e13 times the energy." 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.

Plus it was just pointed out to me that electrons in wires actually move
at micrometers/second. OTOH the signal moves at near-lightspeed, which
is still much faster than neural signals, so I'm not sure that's actually
a problem. But I need other opinions/more knowledge.

I still feel that if you try to think/compute faster by using faster
signals, mv^2 should come bite you somewhere, and suffering v^3 because
you try to do v times more things with v^2 more energy does happen
sometimes (motion through a fluid) but I doubt my full application and
numbers right now.

-xx- Damien X-)
.

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