[ExI] SETI for Post Singularity Civ

[Anders Sandberg]

Some more thinking:


If we have a sphere with radius r with internal volume V(r) of computromium, the surface must have V(r)/X area devoted to cooling pipes to get rid of the heat. This can be formulated as the differential equation: V'(r)= 4pi r^2 - V(r)/X. The solution is V(r)=4 pi ( r^2/X^2 - 2 r/X - 2 exp(-r/X) + 2) X^3. This grows as r^2 for larger r, so the average computronium density falls as 1/r as the system becomes larger. 





Anders Sandberg, Future of Humanity Institute Philosophy Faculty of Oxford University
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