[ExI] Superintelligent AI civilisations

[Jason Resch]

The formulas around the physical limits of computation paint a clear
picture on the trade offs.

Mass defines total computations per second, which may be parallel or serial.

Black holes represent the maximum clock speed for a serial computations
that must touch every bit.

Less dense volumes provide more memory for a given mass of computer, but at
correspondingly slower clock speeds than when that matter is compressed to
the density of a black hole. Here is table with some examples:

See page 213:
https://drive.google.com/file/d/1dnQ-suYTQ984_nB3uVr9AWN2Zet3RnMj/view?usp=drivesdk

So comparing 1 Kg of computronium spread across a 1 meter radius (diffuse),
vs. computronium at black hole densities where 1 Kg is compressed to a
radius of 1.49 × 10^−27 meters (dense):


Memory diffuse: 1.79 × 10^43 bits
Memory dense: 2.65 × 10^16 bits

The diffuse computronium has way more memory to work with. The dense
computer has only a few KB. But now compare serial clock speed:

Clock rate diffuse: 3.00 × 10^8 Hz
Clock rate dense: 2.02 × 10^35 Hz

So the diffuse computronium operates at Pentium 2 levels of speed, a few
hundred MHz.

So there are rather severe memory and speed trade offs, even when dealing
with the best physically possible computer.

You might think, well just add more mass to the computer, collapse the
Jupiter brain planet into a Jupiter brain black hole. That would increase
the memory considerably (to ~10^71 bits) but it would also reduce the clock
speed even further, as the Jupiter black hole has a radius of 2.8 meters,
it's clock time (time to access any bit) would be r/c = 9.33 nanoseconds,
for a clock rate of 107 MHz.

If you want speed and memory, a better engineering compromise is required.
A bunch of small and dense computers running in parallel on their own
dedicated tasks, and networked and positioned near to, those other
computers they might need the outputs they produce. Perhaps this isn't too
different from the current generation of CPUs or GPUs with many cores,
shared memory and various levels of caches for each processor, clustered in
data centers with high speed networking between them.



Jason


On Thu, Jul 30, 2026, 6:50 PM John Clark via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

> On Wed, Jul 29, 2026 at 12:42 PM Keith Henson via extropy-chat <
> extropy-chat at lists.extropy.org> wrote:
>
> *> Light speed has always been my objection to physically large brains.*
>>
>
> *I think Mr. Jupiter Brain will be composed of billions or trillions of
> closely interlocked agents just as many modern AI's are, although they
> usually only have a few hundred. Some of those agents would be generalists
> and some of them would be specialists. Jupiter is about 85,000 miles in
> diameter, light travels at 186,000 miles a second. So AT MOST it would take
> about 0.46 seconds for one agent to send a message to another, and about
> 0.9 seconds for it to receive a reply. Except for very short messages that
> demand a near instantaneous yes or no answer, and there wouldn't be many of
> them, this delay would cause few problems and be compensated for by the
> fact that the bandwidth between agents would be VASTLY wider than the one
> the human brain uses to communicate between one side of the brain and the
> other.  *
>
>
> *Humans seem to have something similar to agents going on inside their
> heads, but the extremely narrow bandwidth between agents means that a big
> improvement in one often has little improvement in any other agent. That's
> why somebody might be the best human chess player in the world but not be
> particularly good at doing anything else. *
>
> *John K Clark*
>
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