First, there's the sometime implication that SIs will gobble up the universe--I've always wondered where that idea comes from, beyond the simple fact that given the capability of exponential growth and the availability of sufficient energy to carry it off, that they COULD. Beyond prudence, consideration, moderation, restraint, or some similar value-mediated reason for self-limitation, I wonder about one particular structural limiter on boundless cosmic consumption.
You (RB) have often mentioned the light speed limit on internode communication. The larger the MB gets the slower the entire brain thinks. Wouldn't that suggest a range of acceptable values centered around that point with the best (as judged by the SI community) trade-off between speed of thought--which I equate with rate of experience, how much living you accomplish per fixed unit of time--and complexity of thought-- which I think of as "depth" of experience (intelligence, sophistication?)
Second, (and here I think I'm probably gonna put my foot in it) isn't there going to be a type of "computronium" which will operate in a superconductive regime? Won't that "resistanceless" condition make it possible to function virtually without generation of entropy/waste heat (I have heard of a fundamental principle of computing/information theory that assigns a minimum entropy per op/(state change?), but I have also heard of some other theory of reversible or quantum computation which suggests a means to circumvent or drastically reduce this minimum entropic cost; though such theories are waaay over my head.)
I suspect that you and Eric D. have already factored this into you thinking--I mean it IS obvious,...isn't it?) With such a superconducting design I envision a spherically symmetric(for optimal density) array (I would call it a MB except that it's more like a solid planet than a rotating, concentric, orbiting array. Hmmm. I guess you could have the full-star-surrounding collection of these, but the central brain must be kept superconducting cool.) To whatever degree there was heat generation, I would see the array as porous and immersed in liquid hydrogen or helium--the former is more abundant, the latter the natural by-product of the energy source that runs the system. The coolant would naturally take advantage of superfluidity to carry away the waste heat frictionlessly. (Is hydrogen capable of superfluidity?)
As I was conjuring up this coldest of "dark matter" hydrogen(or helium) super-giant planets, it occurred to me that the ignition of a regular star occurs when the temperature at the center of gravitationally-compressed protostar/gas cloud rises by gravitational compression (the accumulation of the gravitational energy of the infalling hydrogen atoms) to the ignition point. If one calmly and deliberately "assembled" the coolant in already incompressible liquid form, then ignition could be forstalled right up to the point (which would define the limit on the size of the array) where the pressure alone would overwhelm the internuclear repulsive forces. Hydrogen and helium would have different ignition pressures. Additionally, if the architecture of the array was of closed self-supporting spherical shells, then the pressure of the coolant at each layer could be isolated and prevented from building up to critical at the center. This might permit a larger upper bound on the size.
I would not mention this at all, except that all previous discussions of J and M brains have settled upon heat dissipation as one of the prime controlling factors in architecture. All the designs I've heard of have envisioned operation of the brain at blistering heats, mostly in close proximity to the power source/star. This, with the single exception of your discussion of MBs in globular clusters, which envisions remote siting, and which would also be ideal for a superconducting-regime array (which would require its power absorption and waste heat emission be conducted entirely at its surface, whether in a GC or elsewhere.)
Perhaps I'm missing something, but isn't the superconducting regime the way
to go?
(Been there, done that, right?)
Best, Jeff Davis
"Everything's hard till you know how to do it." Ray Charles