Damien Broderick wrote:
>
> At 11:39 AM 25/02/01 -0800, Max More wrote:
>
> >I'm something of a Singularity skeptic, though it does depend
> >on how the term Singularity is defined. I expect a powerful swell,
> >rather than a sudden spike.
>
> ...I sketched several technological curves starting and remaining fairly flat
> thousands of years ago and beginning their extraordinary bound upward only a few
> hundred years back, or even a few decades ago. On that scale, what we
> experience here and now as a powerful swell *is* a dramatic spike.
>
> It's true that in Vernor Vinge's fictional anticipation in MAROONED IN
> REALTIME, the exponential rate of technical advance self-bootstraps at such
> a dizzying rate that at last, within days, hours or perhaps seconds... the
> intelligences of the solar system... vanish overnight, leaving only their enigmatic
> detritus behind like an abandoned snake skin.
>
> Is that the sort of shape a Singularity must have? ...
> I'm agnostic on the matter...
I forwarded the full text of the above to a friend, who replied
with the following quote from a physics textbook:
A solution of a differential equation is more smoothly continuous
over most of space and time than is the corresponding physical
situation, but it is usually provided with a finite number of
mathematical discontinuities that are considerably more "sharp" than
the "actual" conditions exhibit. ...[D]iscrepancies between
calculated and measured values will turn up, due either to the
"oversmooth" behavior of the field over most of its extent or to the
presence of mathematical discontinuities and infinities in the
computed field, which are not present in "real life." ...An
important task of the theoretical physicist lies in distinguishing
between trivial and nontrivial discrepancies between theory and
experiment.
-- Morse & Feshbach, Ch. 1
--- Joe Fineman jcf@world.std.com
||: If it moves, fondle it, except porcupines, ball lightning, :||
||: and policemen. :||
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