> This is an important point that seems to be often ignored in discussions
> of the "singularity". While a simple interpolation and future
> projection of (for example) available computing power may show a
> vertical asymptote, the underlying equations that govern the rise of
> computing power are subject to constraints that may result in a
> flattening of the curve.
This is true. So far I have never seen any argument for that it would
never flatten that was not based on "but maybe SI will circumvent it" -
invoking the abilities of unknown, unknowable future beings is not
a good way of doing projections (except by me, since I'm guided by
the Omega Point reaching back in time. See what I mean?).
> I'd be very interested in seeing (and would write myself, if time and
> knowledge allowed) an analysis of what a post-"singularity" plateau
> might look like, given the most stringent constraints we know of.
My ever-unfinished paper about jupiter brains contains some of the
potential contraints on very powerful computing systems. It can be
found at http://www.nada.kth.se/~asa/Hx/Brains2.ps in PostScript.
> Chaotic Computability Constraints: The most ambitious nanotech
> scenarios posit universal assemblers that can be programmed or designed
> to build specific structures. IMHO this is a clearly chaotic system.
Why? The designs of Drexler, Merkle et al look rather rigid and
non-chaotic to me.
> 1) Where a Spike subject to these constraints will begin to level off.
If Vinge is right, it will not level off until we suddenly run into
the limits set up by physics; had our rate of development been constant,
the curve would be a nice sigmoid and the levelling off would be
a mirror image of the development leading up to it (a few centuries
of fast development, followed by millennia of ever slower development
and then millions of years of ultimate-level stasis). But since the
rate is assumed to increase in a Vingean singularity, the curve would
be asymetric: we get a superexponential suddenly turning horisontal.
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> 2) Just how severe and insurmountable these constraints are. Will
> superstring-engineering allow us to bypass Planck's constant? Will some
> new, higher-level theory of complex systems provide more computationally
> efficient means of simulating chaotic systems? Will quantum computing
> have any benefit here? Can a sufficiently advanced entity construct a
> pocket universe where Planck's constant and c are different from our
> own? Is there any way to communicate between that universe and this
> one?
Sasha has sketched a near infinitely fast computer based on wormholes and
basement universes; Tipler has sketched infinite computations done
in finite time. Given a sufficiently ultra-advanced hypothetical technology
and a lot of handwaving, you can probably circumvent any law of nature.
But we cannot say much about it, since it by definition is outside our
knowledge.
-- ----------------------------------------------------------------------- Anders Sandberg Towards Ascension! asa@nada.kth.se http://www.nada.kth.se/~asa/ GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y