[ExI] Chips The Size Of[interplanetary] Dust [and matrioshka brains]

[Russell Wallace]

On 9/3/07, Eugen Leitl <eugen at leitl.org> wrote:
> Whenever the heat production in the computation volume exceeds the
> rate of dissipation through the surface bounding such volume you have
> to fragment into computational volumes. How large the volume can become
> depends very much on the mode and speed of computation. We don't know
> yet, but km^3 would seem to be on a tall side, m^3 would seem quite
> doable, however, though perhaps requiring fractal cooling channels.
> Buckytronics does seem to like UHV and cold, though, since collisions
> degrade the operation by geometric distortions.

Yeah. Of course the nodes should probably be disks rather than
spheres. Thickness is perhaps the primary variable... which also
depends on the thickness of the whole shell. Let's look at some
numbers to get a feel for the sort of magnitudes involved.

Suppose there's 100 Earth masses of material to work with (if our
solar system is reasonably representative, that's likely to be typical
to an order of magnitude, assuming most of the hydrogen and helium
isn't useful, and omitting helium fusion and starlifting as potential
sources from the current analysis), and that the radius is 2 AU.

m = 6e26 kg
r = 3e11 m
a = 4 pi r^2 = 1.13e24 m^2
m/a = 530 kg/m^2

So we're looking at on the order of a meter total thickness. Of course
radius isn't a fixed constant, but this seems like at least a
plausible set of figures for a starting point.

Now I'll conjecture that there's no point making the thickness of the
shell more than a few times that of individual nodes, because inner
ones trying to cool will just be dumping waste heat into the outer
ones, which are a) starved of sunlight and b) reflecting some of the
heat back at the inner ones.

Of course it might be useful to have a hierarchy of nodes at
substantially different operating temperatures and radii, e.g. the
inner shell operates at room temperature and dumps IR as waste heat,
the outer shell operates at cryogenic temperature, uses IR as energy
source and dumps microwaves as waste heat, to get the most computation
out of every joule. How does that affect the analysis? I'll postulate
for the sake of argument that the total number of nodes in all layers
is no more than 100, so the thickness of an individual node will be 10
mm.

10 mm? Okay, now we are down to dime-sized nodes along the z-axis at
least. But this is in space, where structures can be pancake-flimsy.
I'll conjecture it would be feasible and desirable, even with that
thickness, to make nodes disc-shaped and at least 1 km across.