From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Mon Oct 13 1997 - 19:02:24 MDT
Anders Sandberg wrote:
>
> "Eliezer S. Yudkowsky" <sentience@pobox.com> 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.
My point is not necessarily that a given technology is feasible, and
particularly not that it is feasible to us. The Unbreakable-Limits position
says: "Such-and-such is theoretically and mathematically impossible under the
laws of physics, in the same sense that you cannot add two even numbers and
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 think
otherwise. You are no longer arguing that a given end is impossible under the
Laws Of Physics (which change all the time, anyway). You are arguing that 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 burden
of proof is definitely on the Constraintarian. One must demonstrate that a
given limit is mathematically unbreakable, and even then one may have left
something out. If there exists under known physical law one possibility in
which the constraint does not hold, the constraint is practical rather than
theoretical. Thus Tipler cylinders, which postulate no additional laws of
physics, are sufficient to demonstrate that time travel is not prohibited by
the known laws of physics.
My Continuing Challenge can be phrased as follows: "Name one practical limit
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 cylinders
demonstrate that CTCs are explicitly permitted by General Relativity, and
therefore physics explicitly permits computers that operate at infinite speeds."
> 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 the
Casimir (charged-plates) effect, well, then so what? So do your computing
between two charged plates! Saying that a "law" can be broken "only" under
some condition is like saying that a "secure" system can "only" be broken into
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 are
"unreasonable" in the sense of having a discontinous second derivative, but
still physically permitted. I'm afraid I can't recall or find exact details, though.
Here's a question I don't know the answer to: Does there exist a series of
arithmetical operations that is "Turing-complete" in the sense of performing
arbitrary computations on the ones and zeros making up the numbers? Would
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 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.
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 like
a sieve. You can't tell me it's mathematically impossible to go faster than
light, only that all the known methods for doing so have practical difficulties.
--
sentience@pobox.com Eliezer S. Yudkowsky
http://tezcat.com/~eliezer/singularity.html
http://tezcat.com/~eliezer/algernon.html
Disclaimer: Unless otherwise specified, I'm not telling you
everything I think I know.
This archive was generated by hypermail 2.1.5 : Fri Nov 01 2002 - 14:45:02 MST