From: Larry (email@example.com)
Date: Thu Jan 04 2007 - 22:37:28 MST
On Thu, 4 Jan 2007, Philip Goetz wrote:
> On 1/4/07, Philip Goetz <firstname.lastname@example.org> wrote:
>> If it doesn't, that would imply that economic growth is limited by
>> energy supply.
> Of course, this must be the case. I was imagining that in an
> "information economy", people could continue to create wealth by
> learning or creating new things, and imagining that such activity
> takes little energy. But creating information does take energy.
> There is a precise relationship between bits and energy, though I
> don't understand it.
There is a really neat proof. Its actually the cost to erase unknown
bits, and replace them with known bits. Take a 1 particle gas, in a
volume X, slowly shove it into a volume X/2 while in contact with the
outside environment, you now know exactly one more bit of information
about the system:
"the particle is in the left side of the original volume"
The energy cost is the cost to erase/set a bit. Its interestingly the same
thing as a refrigerator, your fridge compressor, "erases" bits inside of
it by squeezing gas into a smaller volume, such that you know more about
the positions of particles in the gas. I suspect its roughly valid to call
a fridge a bit pump :) Deep space is /dev/null.
Like a fridge, erasing/setting a bit takes an amount of energy dependant
on the outside environments temperature. In deep space thats the
background radiation, the absolute limits of computing requiring
erasing/setting of bits is actually set by the background radiation.
So what happens if you have computations that don't require erasing bits?
You can have all the computation you want with no energy cost what so
ever. Thats seems to be how the universe gets away with the nasty tricks
it plays on us, like a single photon computing the "proper" path through
a huge hologram. Who knows maybe even protein folding?
Interestingly some useful problems can be stated in a fashion that doesn't
require discarding of bits, and theoritically can harness this should
we manage to build decent quantum computers.
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