<html><head></head><body><div><span data-mailaddress="hkeithhenson@gmail.com" data-contactname="Keith Henson" class="clickable"><span title="hkeithhenson@gmail.com">Keith Henson</span><span class="detail"> <hkeithhenson@gmail.com></span></span> , 18/1/2015 7:35 AM:<br><blockquote class="mori" style="margin:0 0 0 .8ex;border-left:2px blue solid;padding-left:1ex;"><br>Re the whole topic related to M brains, Jupiter brains and related,<br>nobody has ever answered my interrelated concerns of waste heat<br>dissipation and speed of light delays. The laws of the universe, as I<br>understand them, don’t allow for physically large objects to be fast<br>thinkers.</blockquote></div><div><br></div><div>Fast thinkers in what sense? A large object can have very fast local computations but long lags between parts. It doesn't have to be a computational unity.</div><div><br></div><div>Consider a spherical M brain of radius R and heat production P per volume. If it just cools by blackbody radiation the max radius for a given max temperature T is R = 3 sigma T^4 / P. If it does C computations per volume per second, the total computations are 4 pi R^3 C / 3. The delays will be of order R/c. If we demand that a computational module is roughly the size it takes to transmit a signal across it per computational cycle, and the relevant smallest components inside have linear size r and hence cycle time 1/(Cr^3), then modules need to be smaller than c/(Cr^3). So you get (Cr^3R/c)^3 modules inside the M brain. </div><div><br></div><div>If the figure of merit is just total computations then it scales as T^12 P^-3 C - it really pays off running it hot! If the figure of merit is the computations per unitary module then it scales as C^-2 r^-9 - running really tiny components is the key thing. If on the other hand you value modules, then they scale as C^3 r^9 T^12 P^-3 - back to the large hot brain. The overall ratio between M brain extent and cycle time is CRr^3; keeping it around unity makes the system about as integrated as a human brain.</div><div><br></div><div><br></div><div><br></div><div>Anders Sandberg, Future of Humanity Institute Philosophy Faculty of Oxford University</div></body></html>