So... my first reaction to any "exponential" curve like this is to ask
(somewhat akin to Kennison's commentary) whether there is good reason to
assume exponential or geometric growth over an evolving system or set of
systems?
"S" curves are common in biological and other systems with both positive
and negative feedback... Early in the growth of a system, there is
roughly exponential or even geometric growth (depending on the
configuration/nature of the system) but at some point some form of
"saturation" sets in which ultimately adjusts the rate of growth
downward. At some point it goes through a roughly "linear" growth
period, then sub-linear usually asymptotic to some growth ceiling or
much lower linear growth... yielding a curve that looks roughly like a
script "S", or a linear curve with a concave up tail on the bottom and a
concave-down tail on the top.
Moore's law is only descriptive... while each phase in technology
(transistor, IC, LSI, VLSI, etc.) may have an exponential growth
"potential", that potential bumps up against some limit and goes linear,
then sublinear. The computer industry, being what it is, doesn't wait
for these curves to play out, they seek new innovations that will get
around the anticipated saturation/ceiling, putting the curve back on an
exponential track. The *net* rate of speed increases in the industry
is based on the superposition of multiple piecewise curves for each
phase in technology.
I would assume the same has happened in biological evolution. The
"innovation" involved is executed by Dawkin's Blind Watchmaker, perhaps,
but there is the same effect... by the time (or before) one strategy
plays out, another fresh one is invented/discovered and the complexity
curve changes horses midstream and catches a ride on the new one.
The result is a variation of the renowned "punctuated equilibrium" with
the "equilibrium" being in the growth *rate* rather than the growth.
Three phases: Burn Hot; Settle Down; Go Senescent !
I *think* this addresses Kennison's points at least partially... and a
finer grain (than we can probably measure) look at complexity over
geologic time might show the "punctuation marks" at the interfaces
between different "eras"... Prokaryotic/Eukaryotic,
single-cell/Colony/multicellular, introduction of organelles,
mitochondria, advent of oxygen metabolizers, Cambrian Explosion, etc.
I share Doug's fascination with processes spanning these time scales,
and especially for this kind of insight... that the more things change,
the more they stay the same. Or vice versa?
- Steve
I don't know if retrodicting an exponential growth curve back to it's
origin is technically an extrapolation, but aside from that quibble
this is very cute.
Plot Moore's Law, it hits the origin in the 1960's when there were
zero transistors on chips.
"A similar process works with scientific publications. Between 1990
and 1960, they doubled in number every 15 years or so. Extrapolating
this backwards gives the origin of scientific publication as 1710,
about the time of Isaac Newton."
Now make some assumptions about the time of origin of various genetic
complexities evident in the history of life on earth, and plot the
growth curve for that. When was its origin?
http://www.technologyreview.com/view/513781/moores-law-and-the-origin-of-life/
http://arxiv.org/abs/1304.3381
-- rec --
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
