RE: Hole in a box

From: Eugene Leitl (
Date: Tue Feb 19 2002 - 02:41:54 MST

On Tue, 19 Feb 2002, Emlyn O'regan wrote:

> Anders wrote:
> > Assume we can store x bits / kg of matter. One stored bit is worth c^2/x

Just storing, or computing? Qubit, or conventional? Bits being beings, or
archives? Evolutionary/agoric scenario, or not?

> > J of energy if its substrate is transmuted. The entropy cost of

Are we talking fusion, or 100% efficiency singularity-catalyzed matter
conversion? Given that singularities are so hard to make, what is the
overall efficiency of the process? What is the growth kinetics?

> > 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.

Qubit based technology seems to require cryogenic environments, whereas
computronium will be obviously limited to the <1 kK temperature range
before you'll get into deterioration regime. Node cloud assemblies need to
be obviously small and sparse enough that you can get rid of that by
radiative transfer, which gives you a relativistic latency bound. What is
the optimal radial distribution of the node density, given above
constraints, anyone knows?

> > 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.

We don't know if degenerate matter (gravitation-stabilized, I presume?
That would make it essentially a flat spherical assembly around a core
otherwise useless but for energy generation) offers sufficient structural
variety to build computational machinery.

> > 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

I think agoric/evolutionary systems are not so rational as a whole, and
would tend to try to run as fast as possible (co-evolution does select for
faster reflexes, and an order of magnitude slower human is not employable
even if he uses less energy, as long as energy is cheap). If we look at
our solar system, and just at the Sun's output, we'll see that there is a
surplus of matter over energy. Iirc Robert said that Mercury alone is
sufficient to intercept the entire solar output if disassembled in a high
enough orbit to be still useful for photovoltaics and computation. Mercury
represents a very small fraction of mass in the system, even if we
consider heavier elements.

Once the Sun output is intercepted completely (would 2 MT of energy/s flux
be sufficient to fabricate and stabilize microsingularities?), and
utilized to the full, and we have surplus matter, pressure for lebensraum
would seem to create a demand for fusion outside. Speedup will be
1e5..1e6, but we might run out of energy sources but the Sun (assuming,
people won't start lifting matter from it) in a far shorter time period
than expected. Infrared luminosity of the system (lightdays to a
lightmonth) would seem to increase towards quite hight values.

> > 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.

Our physics is obviously impcomplete, and so far the universe has been
very favourable to us, but assuming that things will just get better and
better without further evidence is a bit too optimistic.

> 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?

I don't see what needs to be cruising, other than information. It might be
encoded in streams of relativistic pellets, but the carrier and transport
is negligable.

> 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 ? :-)

These beings are many and diverse, and so is their agenda. Assuming
anything else would see to require postulating a sustained diversity loss,
or supression of radiation after passage through a diversity bottleneck
(first autofeedback seed). Do you have a mechanism for that?

> 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

Nope. A lot of them might be nonsentient.

> 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?

Ecologies as a whole don't think an awful lot (even if containing
philosopher-king types), and do not like being controlled. They just are
homeostating there, more or less. (Never mind a few extinctions, it's
business as usual).

> 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.

We'll find out what to do shortly.

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