RE: Hole in a box

From: Emlyn O'regan (
Date: Mon Feb 18 2002 - 19:48:35 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?

Anders wrote:
> 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
> macroscopic temperature burning matter to make more information will
> 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...

This stuff about "really advanced civilisations" (or individuals, or some
other concept), moving to an optimal limit of computation and staying there
has always gnawed at me as a flawed notion. I guess I can't accept that the
most advanced beings in the universe would just accept a physical limitation
like that.

I think of "optimal" energy/matter ratio refered to above as "cruising
speed". Does it seem unlikely that there might be higher entropy
alternatives that allow qualitative improvements in computational ability,
compared to cruising speed?

It seems to me that we must consider the motivation of these beings. Why do
they want to sit at cruising speed, cognitively, until the universe finally
dissembles into total entropy? These are beings who, it must be supposed,
have altered themselves *radically* to get to where they are; not
conservatives I think. Early adopters in a past life ? :-)

One must consider finally that the sole purpose of these entities is to
think. Really, deeply think. Unless they get to a point where there is no
more to think about, before they hit the limits of cruise speed, could these
entites possibly be satisfied stopping at what, to them, must seem an
entirely arbitrary point?

When the lifetime of the universe begins to loom as a large concern to you,
I think you would want to find a way out of the box. If burning the candle
at both ends could make a difference, if sacrificing quantity of computation
for quality "right now" was possible, it would have to be done. If nothing
else, just for the chance to be all that you could be.


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