Re: Constraints on the "singularity"

Eliezer S. Yudkowsky (
Mon, 13 Oct 1997 20:02:24 -0500

Anders Sandberg wrote:
> =

> "Eliezer S. Yudkowsky" <> writes:
> =

> > You are incorrect. I lay down this Continuing Challenge to all who l=
> > 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.

My point is not necessarily that a given technology is feasible, and
particularly not that it is feasible to us. The Unbreakable-Limits posit=
says: "Such-and-such is theoretically and mathematically impossible unde=
r the
laws of physics, in the same sense that you cannot add two even numbers a=
get an odd number". I simply point out that the current, known laws of
physics make the limit a practical, rather than a theoretical, one. The
Constraintarians are reduced to saying: "Well, sure, it's theoretically
possible, but I don't think it's practical." Well, but then the SIs may =
otherwise. You are no longer arguing that a given end is impossible unde=
r the
Laws Of Physics (which change all the time, anyway). You are arguing tha=
t a
possible end is not achieveable - because *we* can't think of any way to =
do it.

Considering the pace of technology and the past history of failure, the b=
of proof is definitely on the Constraintarian. One must demonstrate that=
given limit is mathematically unbreakable, and even then one may have lef=
something out. If there exists under known physical law one possibility =
which the constraint does not hold, the constraint is practical rather th=
theoretical. Thus Tipler cylinders, which postulate no additional laws o=
physics, are sufficient to demonstrate that time travel is not prohibited=
the known laws of physics.

My Continuing Challenge can be phrased as follows: "Name one practical l=
which is mathematically unbreakable under the currently known laws of
physics." Under these rules, I can't say: "Maybe general relativity is
wrong" - although it certainly could be. But I can say: "Tipler cylinde=
demonstrate that CTCs are explicitly permitted by General Relativity, and=

therefore physics explicitly permits computers that operate at infinite s=

> 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.

One flaw, no law. If I (or the SIs) can only have negative energy under =
Casimir (charged-plates) effect, well, then so what? So do your computin=
between two charged plates! Saying that a "law" can be broken "only" und=
some condition is like saying that a "secure" system can "only" be broken=
using a backdoor.

> 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.

There was something in my Penrose about Turing-unsolvable processes that =
"unreasonable" in the sense of having a discontinous second derivative, b=
still physically permitted. I'm afraid I can't recall or find exact deta=
ils, though.

Here's a question I don't know the answer to: Does there exist a series =
arithmetical operations that is "Turing-complete" in the sense of perform=
arbitrary computations on the ones and zeros making up the numbers? Woul=
analogous analog operations on real numbers permit an infinite number of
Turing computations?

> No. The speed of light is locally constant, that is a basic result from=

> the equations.

He wasn't asking about "local" constants.
He asked how long it would take to fill up the galaxy.

> 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=
> G=F6del universe, which is (I think) densely filled with CTCs), but the=
> doesn't seem to be any reason why we would be living in one of them. Mo=
> tend to be pretty pathological, and if we are close to a Friedman unive=
> then we cannot get around it faster than a certain time.

Black holes. Tipler cylinders. Naked singularities. Quantum gravity. =

Instantaneous (?) propagation of state-vector reduction. Tachyons. =

Wormholes. As far as I can tell, relativistic constraints on speed leak =
a sieve. You can't tell me it's mathematically impossible to go faster t=
light, only that all the known methods for doing so have practical diffic=
-- = Eliezer S. Yudkowsky
Disclaimer: Unless otherwise specified, I'm not telling you
everything I think I know.