The first four columns (a to d) are four basins from the same dynamic system. The fifth column (e) is a basin from a different dynamic system.
a
b
c
d
e
&
Emergent, Self-Organized Form
Flash of Mind and Nature
Averaging versus Theory-based Pattern integration
Two Attractor Cycle Patterns (Parent 1 and Parent 2)
From same Dynamic System
AVERAGE THEM (Pixel by Pixel)
Compare averaging with a Genetic Procedure:
Take First Half of state vector from Parent 1
Take Second Half of state vector from Parent 2
Splice them
Start up system and examine the attractor cycle that results
Differences in Differences quote
"I have said that what gets from territory to map is transforms of differences and that these (somehow selected) differences are elementary ideas.
"But there are differences between differences. Every effective difference denotes a demarcation, a line of classification, and all classifications are hierarchic. In other words, differences are themselves to be differentiated and classified. In this context I will only touch lightly on the matter of classes of difference, because to carry the matter further would land us in the problems of Principia Mathematica.
"Let me invite you to a psychological experience, if only to demonstrate the frailty of the human computer. First note that differences in texture are different(a) from differences in color. Now note that differences in size are different(b) from differences in shape. Similarly ratios are different(c) from subtractive differences.
"Now let me invite you... to define the differences between "different (a)," "different (b)," and "different (c)" in the above paragraph.
"The mind boggles at the task."
Gregory Bateson, (1972) Steps to an Ecology of Mind, pp. 457-58 (Ballentine edition). The original lecture on which this essay was based was given January 9, 1970.
The linguist manipulates the syntactic, phonological, and semantic forms and judges and/or asks native speakers to judge whether the consequences are a well-formed sentence in the language, an ambiguous string or any one of an array of numerous other possibilities. The relevant reference point by the very nature of the research is internal to the bearer of the internal grammar – the native speaker himself.
They are sliding doors in the family room
Mary took John's shirt off
This pig is ready to eat
To put the matter in a somewhat different form, suppose that we succeeded in constructing an instrument that purportedly arrived at the same judgments for visual inputs as those possessed by normally sighted people.
How would we know whether the instrument worked?
The answer clearly is that we would accept the instrument as accurate if and only if the responses of the instrument matched those of normally sighted people. In other words, we would calibrate the instrument by using precisely the same set of judgments (intuitions) reported by the people involved that we presently use in the absence of such an instrument.
Thus in fields where the patterning under scrutiny is patterning of the behavior of human beings, the reference point and the source of the judgments will necessarily be the human being (p. 76).
Here the numbers are a translation of a pattern language and can have a meaningful relationship to Pattern
==> a series of quantities
==> numbers in terms of wavelengths OR conventions
CASE 1: AVERAGING numbers from Models
One Monet and Two Picasso's
Imagine Quantifying every pixel with a color number and averaging them
Imagine Beethoven's 7th and Shostakovich's 5th
In terms of their average pitch (a number based on a equation describing frequency) from moment to moment
Imagine averaging them
CASE 2: Assigning Quantities to relational patterns WITHOUT an intermediate pattern language (Math, pitch, color numbers, etc.) and then averaging them
Health
Aggressiveness
Prejudice
Intelligence
What can this mean?
What happens to any possible meaning when averaged (across different patterns, i.e., persons)?
My Opinion: An epistemological disaster results from assigning quantities to relational patterns and then averaging those numbers.
BUT, things do combine
I'd be astonished if it were by averaging very often in evolution and mind and process
==> a series of quantities
==> numbers in terms of wavelengths OR conventions 
