# Re: Hole in a box

Date: Mon Feb 18 2002 - 08:37:13 MST

On Mon, Feb 18, 2002 at 01:28:50AM -0800, Robert J. Bradbury wrote:
>
> Of course we feel in the current era that producing and using the
> energy as rapidly as we can is the correct perspective. Perhaps
> this is because we are in the era where bits generated per unit
> energy consumed exceed bits consumed per unit energy generated.
> But will that always be true?

Assume we can store x bits / kg of matter. One stored bit is worth c^2/x
J of energy if its substrate is transmuted. The entropy cost of
erasing one bit is k T ln 2. So using one kilogram of matter to
calculate would give us c^2/ kT ln 2 bits of irreversible computation
(such as error correction). As long as c^2/x > c^2/kT ln 2 the matter
would be more valuable. This implies x < kT ln 2, i.e. at almost any
lead to an increase of information as long as there is any matter left
to store the results in.

If you have M kilograms of matter and use the fraction f to produce
information, then if you end up with just enough matter to hold the
result you get: x(1-f)M=fM c^2/kTln2. The "optimal" f is
x/(x+c^2/kTln2). If x is 10^24 bits/kg (molecular matter storage) and
T=3 K, I get f=3.2e-16. On the other hand, for x 10^50 (nuclear storage
close to the Bekenstein bound) f~=1. In the first case the matter
is so bad at storing information that you cannot use much of it for
energy, since you will run out of storage. In the second case you can
cram a lot of info into it, so you don't need much.

The breakpoint is at x=3.13e39 bit/kg, I guess around degenerate matter.

So it seems that we would expect that hot or high-density civilizations
would want to gather as much matter as possible for storage, while cool
civilizations with lower memory density would rather burn their matter
to power their computers. So given these assumptions the really advanced
civilisations using nuclear storage would likely want to imitate cosmic
dark matter...

```--
-----------------------------------------------------------------------
Anders Sandberg                                      Towards Ascension!