Re: Matrioshka Brain detail

Robert J. Bradbury (
Thu, 2 Dec 1999 02:54:29 -0800 (PST)

On Wed, 1 Dec 1999, Jeff Davis wrote:

> For Robert Bradbury and others,
> I've been following the discussion about ETCs--enjoying it thoroughly--and
> just finished reading your (RB's) paper on Matrioshka
> brains--delightful--and have a coupla of questions.

Well, I'm flattered, but bear in mind that the paper is more a collection of notes rather than a organized formal presentation.

> You (RB) have often mentioned the light speed limit on internode
> communication. The larger the MB gets the slower the entire brain thinks.

Yep, getting larger has diminishing returns on investment.

> 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?)

You probably have two interesting reference standards -- the thought rate for "survival" in your environment, and the thought rate for "survival" among your peers. I suspect the depth/complexity required for survival is lower than that required for inter-social interactions. However, there seems to be little *requirement* that intersocial interactions are required for survival (if solitary-SIs can resolve the problem of what to think about and/or how to keep themselves entertained).

> Even granting that different SI communities could have different "best"
> trade-off points, wouldn't any such point suggest a stabilization of
> consumption of local cosmic resources? (Of course, expansion and increased
> consumption would continue to the extent that SI communities "spawned" new
> SIs.)

Difficult to predict. The universe evolves at a very slow rate relative to SI thought capacity. SIs also have the ability, in contrast to bio-creatures, to put themselves into extended "suspend" mode (where energy is required only to repair damage from cosmic rays and similar hazards). One has to recontextualize "reproduction/spawning" in light of the fact that this is the natural way of creating variants on which natural selection can act. Once you have internal, virtual simulations, the external reproduction activities may be irrelevant.

> 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?

Yep, absolutely, though the regime below the cosmic microwave background temp. (as was discussed in the Drexler/Merkle paper on single electron computations) may be highly undesirable from an energy efficiency standpoint.

> 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.)

These are the Bremermann & Bekenstein bounds. (If you want access to the relevant papers, send me an off-list request.) The problem has relatively little to do with "resistanceless" computation and much more to do with the cost of erasing a bit. Interestingly enough, you can do "ultra-cheap" computing so long as you don't erase bits. This is what gives rise to the reversible computing methods (that multiple groups are working on).

Bottom line is that you pay the price somewhere. If you have really reversible computing, you have to have more circuits (and pay the price in state storage and propagation delays (as you unwind the calculations)). If you have non-reversible computing, you pay the price in up-front erasure of bits (in which the heat dissipation limits your power throughput).

> I suspect that you and Eric D. have already factored this into you
> thinking--I mean it IS obvious,...isn't it?)

Yep, Eric's computers are "reversible", meaning you don't pay the price of erasing bits, but you do pay the very low price of "friction".

> 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.

In a normal M-Brain, the SC levels are some of the very outermost levels with temps below LN2 coolants (unless very-high-temp SC are discovered). If you put "solar-power" into such a computer network, the radiators have to be out beyond the orbits of the outer planets (so you are much much bigger than a "planet"). Of course you can always reduce the input power to some much smaller level and have collections of SC planetoids orbiting a star that irradiate each other in their waste heat. This is not a sub-optimial structure, if the nature of your problem is one that requires a maximization of communication bandwidth (concurrent with a substantial reduction in aggregate processing power). Since the architecture of the human brain suggests that communication may have greater importance than actual computation, this model is not completely unrealistic.

> Hmmm. I guess you could have the
> full-star-surrounding collection of these, but the central brain must be
> kept superconducting cool.)

You have to keep all of them SC-cool, which will require fairly large orbital distances from the star (depending on individual power consumption)

> 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?)

H doesn't do superfluidity, He does. I've considered this architecture. It only works (for planetoid sized structures) when the power inputs are much less than sol power level outputs.

If you go through Nanosystems (and fluid dynamics) very carefully, you discover that circulating cooling fluid gets expensive. My indirect conversations with E.D. on this subject seem to indicate that even in a 1 cm^3 nanocomputer, consuming 10^5 watts, some large fraction (10's of %) of the power are going into circulating cooling fluid. In a planet sized computer, you would be putting 99.999+% of your power into cooling circulation. You would have to have a *big* benefit in reduction of communications costs to justify putting that much power into coolant circulation.

There is a small caveat here -- E.D. is not assuming superfluid coolants. He is however assuming *very* efficient phase change coolants. I know of no analysis that combines the interesting properties of superfluid He with solid->liquid H (phase-change). However, since H melts above the B.P. of liquid He, it is going to take a strange pressure environment for this, if it is even possible.

> As I was conjuring up this coldest of "dark matter" hydrogen(or helium)
> super-giant planets... [snip]
> 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.

This is an interesting idea and one which I will need to think more about (most of my M-Brain thinking has been confined to the transition stage when civilizations will start out trying to figure out how to fully utilize the energy their pre-existing star is generating).

My suspicion however is that you are still going to have a problem with the power costs of circulating cooling fluid. The densest computer nodes require external cooling, external cooling requires large radiators which dictates large inter-node distances (increasing propogation delays). You can compactify this somewhat, but you pay a price in the cost of circulating the coolant from the internal nodes to the external radiators.

> 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.

Not strictly true. Ander's original paper distinguished between cold-slow (error-free) and hot-fast (but error prone) architectures. The M-Brain architecture leaves the star intact but adds layers that range from very hot to very cold (limited by the matter available for radiator mass).

> 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.)

Yes, externally powered MBs have much more control over how much power to absorb and radiate. They can form denser communications nodes at their center (because there is no star there). The part I haven't looked at is the cost of absorbing external power and "pumping" it to the innermost nodes. There must be some cost to pumping power in and heat out, but these may be offset by reductions in internal communications delays.

Ultimately I think the best architecture depends a lot on the type of problem you are "thinking" about.

> Perhaps I'm missing something, but isn't the superconducting regime the way
> to go?

It is part of the equation. Since the real cost is the tradeoff between communications delays in reversing computations and the heat removal from irreversibly erasing bits, SC supercomputers don't buy you very much.
> How would this affect the crucial and fascinating question of the
> "visibility" of SI K1, 2, & 3 ETCs?
K1's are visible. K1's to K2s happen very quickly and get "colder" and less visible. How cold depends on how much matter is available & how old they are (older gets colder because cold outer layers get dedicated to long-term non-computational storage). Complete K3's that have converted galaxy masses into computers are relatively small (compared to galaxies), but are still relatively cold. Depending on their distance, they should look like very cold point sources.