extrapolate exponential growth backwards to origin

[Roger Critchlow-2]

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

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[Steve Smith]

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