Re: Hole in a box

From: Anders Sandberg (
Date: Tue Feb 19 2002 - 06:23:24 MST

On Tue, Feb 19, 2002 at 10:41:54AM +0100, Eugene Leitl wrote:
> 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?

Storing. Computation can be assumed to be reversible, with the exception
of the irreversible bit erasures costing energy. I used classical bits,
since I was thinking of long-term storage - qubits aren't known for
their persistence.

A more quantum approach would be to use the Bekenstein bound. Assume we
have a radius R, mass M system. That allows us to store kMR bits in
quantum states. So if we use the same analysis as before,
kMR(1-f)=fMc^2/kTln2, producing the optimal f= kR/(kR+c^2/kTln2). kR is
a huge number for macroscopic R, again producing a f~=1.

> > > 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?

I assumed "simply" lossless conversion into energy. Clearly a more
careful analysis has to take the entropy change of matter -> energy
conversion into account and could perhaps calculate limiting efficiency.

> 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?

Sounds like a fun optimization problem. Given a number of small spheres
with blackbody heat emissions, which distribution minimizes average
distance for a given temperature bound?

If then spheres have radius r and disspiation W, the heat balance
of sphere i becomes

W + sum_j 4 pi^2 sigma T_j^4 r^3 / R_ij^2 = 4 pi sigma r T_i^4

(essentially a radiosity equation; I think I have oversimplified it a
bit by assuming R >> r). R_ij is the distance between sphere i and j. So
we need to find the configuration that minimizes sum_ij R_ij and where
max T_i < T_max. I would probably solve this by a genetic algorithm or
hillclimbing, but I don't have the time.

> > > 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.

True. I think degenerate matter offers enough stability to store
information (C12/C13 nuclei in a lattice), but it is not obvious how to
do processing in it. Even worse for nuclear matter.

Hmm, just a realization: my above argument implies that if the supercivs
are using nuclear densities, they will be highly visible by their energy
dissipation. But if you can't use neutronium for storage, then they will
likely be in the quiet region. So this provides a prediction that
nuclear matter may not be suitable for storage if we assume the
existence of supercivs, since otherwise they would be visible.

Anders Sandberg                                      Towards Ascension!                  
GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y

This archive was generated by hypermail 2.1.5 : Fri Nov 01 2002 - 13:37:40 MST