[ExI] Von Neumann Probes

[Jason Resch]

On Mon, Jan 26, 2026, 6:40 AM John Clark <johnkclark at gmail.com> wrote:

> On Sun, Jan 25, 2026 at 7:21 PM Jason Resch via extropy-chat <
> extropy-chat at lists.extropy.org> wrote:
>
> *>> If you try to go beyond Bremermann's Limit the energy/mass density
>>> would become so high that your computer would collapse into a Black Hole,
>>> and then information could go in but it couldn't get out so the machine
>>> wouldn't be of much use. *
>>
>>
>> *> I think here you are thinking of the Bekenstein bound.*
>
>
> *No. Bremermann’s Limit and Bekenstein’s Bound are talking about different
> things,*
>

I know.


> * although the end result of both is the same.*
>

The former defined a speed limit given the mass of a computer.

The latter gives a memory limit given the mass and volume of a computer.


> *Bremermann’s Limit tells you how many bits per second a given mass of
> matter can process information before it collapses into a Black Hole. The
> formula is:*
> C^2/h = 1.35*10^50 bits per second per kilogram.
>

I don't see what Bremmermann's limit has to do with black holes. More
massive black holes have proportionally more computing speed. The limit
does not end at black holes.

Black holes only serve to limit the maximum data density, which is why I
suggested you might thinking of Bekenstein's bound when you mentioned black
holes, as there black holes are relevant to preventing further progress in
data storage per unit of volume.

However black holes are not relevant to preventing growth in faster
computing speed as it relates to Bekenstein's bound.

Jason


>
> *Bekenstein’s Bound tells you how much Shannon information (a.k.a.
> entropy) you can fit into a sphere that has the surface area of 4πR^2** before
> it collapses into a Black Hole. The formula is: *
>
> *I= (2*π*R*E)/[(h/2π)*C*ln2]*
>
>
> *It's interesting that the maximum amount of information you can fit into
> a sphere is proportional to the sphere's area, not to it's volume as you
> might expect. *
>
> *John K Clark*
>
>
>>
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