Re: Re[2]: accept no limits

Anders Sandberg (
Fri, 8 Nov 1996 12:36:33 +0100 (MET)

On Thu, 7 Nov 1996 wrote:

> Anders Sandberg wrote:
> >Even if Malthus was an entropic bastard, his argument is valid. We cannot
> >expand faster than light, and inside a bounded volume (like spacelike
> >slices of our future lightcone) the Bekenstein Bound seems to hold. This
> >implies that exponential growth of *anything* only is possible in the
> >"short" term (which could be *very* long), then it has to grow as t^3 or
> >slower (assuming a Minkovsky spacetime).
> 'gene, my apologies to you. Until I understand what the "Bekenstein
> Bound" and the "Minkovosky spacetime" are, I will concede that perhaps
> you and Malthus are correct.

NO! You just fell into a common psychological trap: if something is said
with confidence and in scientese, it is probably true. That is not a good
heuristic, and quite often used by less than scientific environmentalists
(like Rifkin, who talks about his completely erroneous "fourth law of
thermodynamics"). You should instead demand clarification: "What the ****
is the Bekenstein Bound?!"

A quick answer: if you accept the uncertainty relations of quantum
mechanics, it follows that you cannot distinguish systems that are similar
enough (Delta x * Delta p >= hbar) using any means. This in turn implies
that you cannot store information as different states if they are too
similar. Now, if you try to store information in a spherical volume with a
finite amount of matter/energy inside, the uncertainty relations tell you
that there is a limit of how many distinguishable states there can be
inside, ergo the amount of information you can store there. This is the
Bekenstein Bound, which says that the amount of information that can be
stored is proportional to the radius and the energy inside the volume (it
is a very loose bound, you can cram several megabytes into a hydrogen atom
and around 10^80 or so bits into the solar system).

The Minkowsky space part was mostly a hedge to avoid having to deal with
curved space and all that. It is just plain, flat spacetime according to
special relativity.

(Fun problem: think of how to circumvent the Bekenstein Bound and get
infinite information. It is possible in theory)

Anders Sandberg Towards Ascension!
GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y