From: John Clark (jonkc@worldnet.att.net)
Date: Wed Oct 13 1999 - 11:37:59 MDT
O'Regan, Emlyn <Emlyn.ORegan@actew.com.au> Wrote:
>Reads a bit like nonsense I'm afraid. There is no flatter bit of an
>exponential curve; it looks the same forward and back (I'm taking some
>liberties), no matter where you stand on the curve. Multiplying by a
>constant amount per constant time period (like multiplying transistors per
>square inch on an IC by 2 every 18 months), says that the rate of change is
>constant.
That's a geometric curve not exponential, it can be described by a polynomial
like (X^n) where n is a constant and X a variable.
An exponential curve like (n^X) is not a polynomial. If n is only slightly greater
than 1 then at small values of X it does not even look like a curve, it looks
almost like a straight horizontal line, at medium values of X it looks almost like
a geometric curve, at large values of X it looks almost like a straight vertical line.
Moore's law looks geometric (but we can't be certain) not exponential so it's
spectacular but we can deal with it.
> So what we are concerned with re: singularity is not increasingly
> accelerated change; that's most likely not to happen.
The rate of change in a society of intelligent agents is proportional to the speed
of that intelligence. If our brain works faster we will learn ways to think even faster
in less time than it took us to do it before. That's exponential. X^n we can deal with,
n^X we may or may not be able to, anyway it'll be interesting.
John K Clark jonkc@att.net
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