[extropy-chat] mathimatical model for the singularity

[ps udoname]

Ray Kurzweil seems too simplistic to be again, and statements like ' the
singularity will happen in 2029' are FAR too accurate. Better to be like
Vinge and give intervals like 2005-2030.
Anyway, what I was thinking is you could start with a S=e^kt (S=scientific
progress), and then modify it so that k is a function of intelligence rather
then a constant, and intelligence is a function of S.
For simplicite's sake, dS/dt = kS becomes dS/dt=(cS+ N)S (c is a constant
denoting how quickly science incereaces intelligence, N is the natural
intelligence of a hunter gather)
 dS/dt=(cS+N)S

Which solves as :

S=N/((e^-Nt)-c)     (these are new values of N and c which have been
multiplied by another constant)

Which looks like S=Ne^Nt at first, and then has an asyptope at t=
-(ln(c))/N.

And the entire reason why the singularity is called the singularity is that
is has an asymtope, which is somthing s-curves lack.



On 21/11/06, Robert Bradbury <robert.bradbury at gmail.com> wrote:
>
>
> On 11/21/06, ps udoname <ps.udoname at gmail.com> wrote:
> >
> > I was just thinking that I see a lot of people who say things like "the
> > singularity WILL be exponential" and seem to think that the whole of human
> > progress can be described as p=e^kt.
> > This seems a little simplistic to say the least. I was going to say that
> > I could come up with a better model, but I'm sure someone must have already
> > done that somewhere....
> >
>
> Ray Kurzweil discusses it extensively in Chapter 2 of The Singularity is
> Near titled "A Theory of Technological Evolution"  which goes on for 75
> pages with lots of graphs (and a discussion of S-curves).
>
>
>
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