[ExI] SETI for Post Singularity Civ
Anders Sandberg
anders at aleph.se
Mon Jan 19 01:50:04 UTC 2015
John Clark <johnkclark at gmail.com> , 18/1/2015 5:57 PM:
On Sun, Jan 18, 2015 at 5:50 AM, Anders Sandberg <anders at aleph.se> wrote:
> Consider a spherical M brain of radius R and heat production P per volume. If it just cools by blackbody radiation [...]
But why make that assumption? I think a large brain would have a active cooling system, and Helium-2 might be a good fluid to use to get the job done. Helium liquefies at 4.2 K but when it gets below 2.17 K it turns into a superfluid, Helium-2, that has zero viscosity, provided that the pipe the helium is flowing through does not have a diameter smaller than 10^-9 meters. Liquid Helium superfluid is also by far the best conductor of heat known, it conducts heat so fast (many times faster than the speed of sound) that there are no hot spots in it and thus no bubbles, all of the Helium superfluid is at the same temperature and so vaporization only takes place at the surface.
This is the second level of analysis. Superfluids are awesome, but they also carry no thermal energy - they can however transport heat by being converted into normal fluid and have a frictionless countercurrent bringing back superfluid from the cold end. The rate is limited by the viscosity of the normal fluid, and apparently there are critical velocities of the order of mm/s.
http://cds.cern.ch/record/808382/files/p363.pdf gives the formula Q=[A rho_n / rho_s^3 S^4 T^3 DeltaT ]^(1/3) for the heat transport rate per square meter, where A is 800 m s /kg at 1.8K, rho_n is the density of normal fluid, rho_s the superfluid, S is the entropy per unit mass. Looking at it as a technical coolant as in http://cds.cern.ch/record/330851/files/lhc-project-report-125.pdf gives a steady state heat flux along a pipe around 1.2 W/cm^2 in a 1 meter pipe for a 1.9-1.8K difference in temperature. There are various nonlinearities and limitations due to the need to keep things below the lambda point.
So if we use active cooling for a M-brain we can maintain it at a low temperature. However, the lowest cheap temperature would be 3K at present, and you would need to replace part of the volume with cooling pipes. So consider my spherical M-brain with active cooling. It has volume V=4 pi R^3 /3, and produces fVP Watts of heat where f is the fraction computronium. If pipes can remove X W/m^2, the total area of pipes leaving the sphere have to be fVP/X. At deeper levels they need to have area fVP(r/R)^3/X - f will actually be changing with depth, making analysis harder (at least for me, after midnight). But if we assume the pipes on average go down some fraction cR of the total radius we get cR*fVP/X = (1-f)V, or f/(1-f) = X/cRP.
If we set X=1.2e4 W/m^2, c=0.5, P=1e12 W/m^3 (rod logic at full power), then f/(1-f)=2.4e-8/R, which for a R=1 m brain gives a computronium fraction close to f=2.4e-8 and *way* less for planet-sized systems. Merkle's updates give just a few order of magnitude more density. If we instead assume near reversibility with dissipation at T=1.8 K and gates 16 nm^3 large, P=1553 W/m^3, giving f/(1-f)=15.45, or f just below 94% - way better, at least for small M-brains. If R=6000 km f immediately jumps back to uselessly small values.
Active cooling is better than passive cooling, but the payoff is lots of wasted volume. Which means longer signal delays.
Anders Sandberg, Future of Humanity Institute Philosophy Faculty of Oxford University
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