Re: extrapolate exponential growth backwards to origin
Posted by
Steve Smith on
URL: http://friam.383.s1.nabble.com/extrapolate-exponential-growth-backwards-to-origin-tp7582746p7582840.html
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/
-- rec --
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