Re: Constraints on the "singularity"

Anders Sandberg (
13 Oct 1997 20:02:56 +0200

"Eliezer S. Yudkowsky" <> writes:

> You are incorrect. I lay down this Continuing Challenge to all who listen:
> Before you place a physical constraint on the Powers, you must first place it
> on me. And now, watch as I shoot all your "constraints" down.

In order for this to be an useful challenge, you must shoot them down
using known laws of physics, or at least likely extrapolations (marked
as such) from known physics. Otherwise you can always win by using
(say) unobtainium, angels sent by the Omega Point or the pink unicorn
force. I think exercises like this are useful (yes, I do plan to
continue the nanotech thread from two months back when I get the spare
time), but they have to be stringent.

> > E.g.:
> >
> > Given Planck space, c, and the maximum density matter can achieve before
> > collapsing into a black hole, what is the maximum achievable
> > computational power per unit volume?
> What about negative matter? You can have an arbitary amount of computing
> material in a given volume, with net mass zero.

Negative matter implies negative energy (otherwise it would not work
in circumventing the Bekenstein Bound). So it would be energetically
favorable for vacuum to decay into negative energy states if they
existed; i.e. negative matter would cause vacuum decay. Besides,
outside the special conditions of the Casimir effect, negative
energy densities appear to be ruled out in general relativity by
the strong, medium and weak energy conditions.

> > Given the likely mass, age, and size of the universe, and the
> > constraints listed above, what is the maximum achievable computational
> > power of the universe?
> Infinite. There exist physical processes which are not
> simulable-to-arbitrary-accuracy by Turing machines. Even if all physical
> processes *are* simulable, they still use real numbers.

Could you name these processes? There has been some rather fierce
arguments about the "real number assertion" on this list in the past.
Basically, if you accept quantum mechanics it seems that you cannot
use arbitrary-precision numbers.

> > Given c, the age, size, and rate of expansion of the universe, how long
> > would it take an earth-spawned power to infest the galaxy? 1/10e6 of
> > the universe? 1% of the universe? 10% of the universe?
> General relativity makes the speed of light fundamentally arbitrary. They can
> infest the entire Universe in zero time, and finish before they started.

No. The speed of light is locally constant, that is a basic result from
the equations. You are right in that in some spacetimes there are timelike
paths that can get anywhere in space-time in a finite proper time (like the
Gödel universe, which is (I think) densely filled with CTCs), but there
doesn't seem to be any reason why we would be living in one of them. Most
tend to be pretty pathological, and if we are close to a Friedman universe
then we cannot get around it faster than a certain time.

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