**From:** Amara D. Angelica (*amara@kurzweilai.net*)

**Date:** Sun Apr 20 2003 - 02:25:39 MDT

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In "The limits of complexity & change," May-June 2003 The Futurist

(http://ourworld.compuserve.com/homepages/tmodis/Futurist.pdf), Theodore

Modis presents a logistic model of complexity that asserts that "the

rate of change may soon slow down." He sets the peak of complexity

growth (inflection point) at 1990, which is when, he believes,

"complexity grew at the highest rate ever," after which complexity's

rate of change (but not cumulative growth) began decreasing. He bases

this on:

1. An analysis of 28 important canonical milestones that represent peak

complexity increases over the past 15 billion years and the ensuing

stasis, where importance = change in complexity x duration of ensuing

stasis.

2. An overall historic "logistic" or S-curve model of complexity based

on punctuated equilibrium. This model is assumes Darwinian competition,

i.e., limited resources, so the rate of growth vs. time follows a bell

curve and the assumption that we are currently (circa 2000) just past

the inflection point (peak of the bell curve). He bases this on an a

priori philosophical principle of complexity ("the evolution of

complexity in the universe has been following a logistic growth pattern

from the very beginning"), rather than on a specific analysis of current

resource limitations and their possible effects. "The next world-shaking

milestone should be expected around 2038," he says, based on the above

formula.

This is of course contrary to Ray Kurzweil's "Law of Accelerating

Returns" model of exponential growth

(http://kurzweilai.net/law), which argues that "the resources underlying

the exponential growth of an evolutionary process are relatively

unbounded" and that several forces the impel this growth, such as

positive feedback loops, the increasing "order" of the information

embedded, etc.

3. A reductio ad absurdum argument that the current exponential pattern

is "so steep that around the year 2025 we would be witnessing the

equivalent of all of the twentieth-century milestones in less than a

week, and the rate of appearance of milestones would continue to

increase. Sometime later, humans will become incapable of perceiving

changes that take place in fractions of a second. Does it still make

sense to talk in terms of change when no one preceives it?" The notion

that human perception (the classic "tree in the forest" argument from

Bishop Berkeley's idealism) is a prerequisite to reality is questionable

and Modis offers no support for this argument.

These arguments raise several interesting questions:

1. Is his forecasted exponential growth rate accurate, based on an

extropolation of current growth rates? (This is independent of the

question of resource limitations.)

2. Are a priori principles of complexity and rate of growth based on

historical growth data across various domains (cosmological, geological,

biological, sociological, and technological) meaningful?

3. Exactly what are the future resource limitations we face that would

cause a stasis in technological growth until 2038, given the promises of

nanotechnology, quantum computing, AI, etc., and other radical possible

developments that could lead to accelerated exponential growth? This is

not explicitly addressed, so the pessimisitic 2038 figure for the next

complexity jump seems unsupported. It seems to be based on an a priori

philosophical principle of complexity ("the evolution of complexity in

the universe has been following a logistic growth pattern from the very

beginning"), rather than on an analysis of specific resource limitations

in the future and their possible effects.

Note: a more technical version of this article is available:

"Forecasting the Growth of Complexity and Change"

(http://ourworld.compuserve.com/homepages/tmodis/TedWEB.htm).

I would be very much interested in comments by SL4 list members.

Amara D. Angelica

Editor, KurzweilAI.net

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