The problem is that any SI, after a few cycles of self-enhancement, is twenty
trillion lightyears into the cloud. The fog gradient is irrelevant at such
distances, although I personally happen to think it's rather sharp. If we
have so much trouble predicting the actions of different cultures, how can we
predict the actions of a transhuman? Intuitively, if not formally, it would
seem to be as mathematically impossible as an abacus simulating a PowerPC 604.
> Possibly you're right, and the superintelligences are incomprehensible.
> However it seems that we should be able to at least generate some
> quantitative boundaries on their capabilities given our deepest current
> understanding of the laws of physics and mathematics.
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.
> 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.
> 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. Perhaps a clever
Being could exploit a chaotic Mandelbrot-like boundary to perform calculations
of arbitrary complexity in constant time.
> 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.
> My understanding may be off here, but let me put forth the reason I see
> chaotic computability entering into the picture with nanotech:
[deleted]
One being's "chaos" is another's "order". The mechanical nanotech you mention
is simply an enormous waste of computing power...molecularly speaking. It
takes thousands or millions of atoms to compute the position of an atom. The
theoretical maximum, of course, is one atom per atom. (Unless, of course,
you're using quantum computing. See, even I start doing it! Theoretical
maximum? Whose theory?)
--
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.