Transient Equilibrium

Everything around us, and everything inside of us, is always moving, transitioning from one state to another. A steady-state is reached, and then another transition is underway, striving towards yet another steady-state, and yet another state of transient equilibrium. It continues. Life evolving.

My recent studies of sacred geometry (The Flower of Life) have me considering geometric structures as patterns of equilibrium that are never quite reached or held for long in a world that is always shimmering with movement. It's as if physical matter aspires to realize these configurations, perhaps because they are economical, and cost the least amount of energy.

There are certain arrangements, certain configurations that are more optimal for the form of physical structures. Why? Because they represent a state of equilibrium that is balanced amongst oppositional forces? This is beginning to sound very much like chemistry...

Flower of Life 6 shown above is by Peter W. Michel

http://www.petermichel.com/About.html

Rules: Paths Across Mountains of Data

This morning, I started thinking about Rules as Patterns of High Probability, like tributaries that stretch out across a vast landscape of information, as well-trodden paths across mountains of data.

How is a Rule formed? And how does one Rule become the rule of "best practice"?

In the beginning, there are no rules, just an information landscape to traverse. Over time, a path forms, based on trial and error. A Rule acts as an averaging principle that only evolves after repeatedly confronting similar situations, dynamics and consequences. A well-tested Rule could evolve into a Law, to embody a pattern with an extremely high level of persistent probability, within a broad range of contexts.

Mirror Writing - Natural Skill in a 3-D world

Mirror writing is a strange thing. I discovered I could mirror-write quite easily when I was 9 or 10 years old. It was fun to write backward messages on paper that could only be read in a mirror or flipped over and held up in front of a bright window. But why can some people do it, and others can't? Why do small children struggle to remember which way a lowercase b or d goes; or a g or p?

I did a search on mirror-writing and came across an interesting article written in 2002 called, Acquired mirror writing and reading: evidence for reflective graphemic representations by Gottfried, Sancar and Chatterjee.

http://www.scribd.com/doc/947583/Mirror-Write

They concluded:
"In summary, we suggest that mirror reading and writing, which at first glance appear to be a neuropsychological oddity, point to general principles underlying the processing and representation of visual forms. The adaptive advantage of mirror equivalency means that the nervous system harbors visual representations in their normal and reflected forms. The need for orientation specificity means that these different forms must also be distinguishable, and thus can be damaged selectively. These organizational principles that apply to objects int he world generalize to other visual objects, such as letters and words, even thought the adaptive advantage for these visual forms no longer applies. Finally, the functional modularity of visual representations themselves means that better access to one kind of mirrored visual form (lexical graphemes in this case) does not mean that access to all mirrored visual forms is privileged."

My thoughts:
In real life, we see an object and it can flip over and we know it is still the same object. What is unnatural is that something would remain forever rigid and fixed in one direction orientation. For example, a leaf on a tree doesn't remain fixed, forever pointing in the same direction for the duration of its lifetime. It can move around and flip over and we still see it as a leaf.

What is unnatural is than an object outline or shape would remain fixed in such a way as to always be pointing in the same direction. For example, in the case of lower case letters b and d, children have difficulty learning which way they go because they are the same reflected shape. The direction of the letter is learned, based on knowlege about the letter and its context in words that are also learned. This learning has to override our natural ability to see and know a shape and its mirror reflection as one and the same object. The child has to learn through repetition that the b and the d may look the same, but point in different directions, so they are not the same letter. This learning, applied to two-dimensional representations, runs counter to our natural categorization of visual images in a three-dimensional world. So the child learns that certain letters are directional, really that all writing is directional. But for those people with strong visual mirroring abilities, the learned process of writing letters with a particular direction can easily be inverted.

So, shape direction or orientation (reflection) is an attribute of shape form.

Association and Logic

Some thoughts: Visual and auditory systems came first in humans, much before language. The ability to gather information about the environment and to react to or act on it was something humans could do long before they could speak, just as animals do now. I started thinking about a multi-stage process with respect to the evolution of cognition and how information might be organized and accessed in the human mind.

If we imagine there are pools of information mapped in the mind of a human, gleaned from perceptual experience (perhaps based on Gestalt Principles of Perception) -- a collection of images and sounds, and then we introduce verbal language with syntactic structure, we can begin to imagine how structure and rules might be applied to enforce a layer of organization on top of (or virtually onto) all the pools or clusters of information recorded in the mind of a human.

The raw data 'objects' are the visual images and verbal components that are organized locally or by association, based on similarity, proximity, good continuity, etc. It's like a big clustered database, a cloud.

Manipulation of these information objects can be achieved in a more sophisticated fashion by applying syntactic rules. Language is linear and directional. I --> go --> there. I --> give --> you --> food. It identifies a subject (me), an action, and a place (in the first example). It identifies a subject (me), an action, another subject (you) and another object (food), in the second example.

I think human logic may have arrived with the dawn of verbal language ability. The principles of linguistics may act to order and structure associated information, if desired, into a logical form. By 'logic', I mean causal, or propositional. If -- > then. With logic, there is also a concept of cause and effect, and time.

In summary, this would mean that information in the mind is initially grouped based on Gestalt Principles. It is associatively mapped and looks like a big cloud, or a collection of information molecules (where the nucleus is the concept and the atoms are attributes). The database of information is grouped based on shared attributes (colour, shape, size, behaviour, proximity in time). Then logical rules are applied across the associated categories, which can manipulate and change the shape of the information, to organize it in different ways.

But where do the patterns come in to play? This is the question. Are the pattern frameworks below the level of the logical rules? Do we average information into pattern structures?

Mind is Literally Life-like

I came across this great quote from Peter Godfrey-Smith, a professor of philosophy at Harvard:

"Life and mind have a common abstract pattern or set of basic organizational properties. The functional properties characteristic of mind are an enriched version of the functional properties that are fundamental to life in general. Mind is literally life-like."

Godfrey-Smith, P. (1996)
Complexity and the Function of Mind in Nature
Cambridge: Cambridge University Press


In other words, if we could ascertain the organization properties of nature, we could perhaps also apply these to cognition. While I want to investigate further 'environmental complexity theory', the issue for me is that of course the mind evolved in response to a complex environment, and that the environment has helped to shape it, but this doesn't really explain the unique qualities of the human mind. Animal minds, too, evolved in response to a complex environment, and yet animals don't (to our knowledge) share our language, memory and predictive abilities. So there must be more to this story. I suppose I'm more interested in determining HOW our minds are organized, their intrinsic structures, rather than finding out WHY they evolved at all. Asking WHY we have minds is something else entirely.

Another quote I've always loved is from Back to Methuselah, by George Bernard Shaw (which I first read in 1983):

"Imagination is the beginning of creation. You imagine what you desire, you will what you imagine and at last you create what you will. "

George Bernard Shaw Irish dramatist & socialist (1856 - 1950)

This quote eludes to Lamarckian theory
1. Evolution can occur as a consequence of the 'inheritance of acquired characteristics'
2. A property of life is that it generates increases in the complexity of organization

Searching on 'self-organizing complex systems in nature' returned something to the effect that such a system would be non-linear with a stochastic driver (fractal statistics, chaotic behavior, localized, bottom-up, additive, cumulative -- makes me think about ant-behaviour; communication only with your nearest neighbour).

Dandelions & Hyperbolic Browsers

I recently came across a paper that discusses how the cognitive styles of oral cultures are different from print cultures. Oral cultures represent an event like the spokes of a wheel with a central point and simultaneous branches extending out from the centre. Oral cultures value parallelism and wholism and the personification of nature. Print cultures are linear in the sense they focus on one path through time/space and cognitively represent an event as a process with a beginning, middle and an end, usually in detailed hierarchical trees.

Visual Metaphor, Cultural Knowledge, and the New Rhetoric

Robert N. St. Clair

http://jan.ucc.nau.edu/~jar/LIB/LIB8.html

I started wondering if these two very different cognitive styles might not just be part of a larger structure, and I remembered the structure of the hyperbolic browser that I saw more than 10 years ago. It looks like a 2-dimensional representation of a dandelion flower that's gone to seed (in all its fluffy glory).

The trees act as branches. They are primarily linear. And they grow from the centre radially.

And the hyperbolic browser image reminded me again of the E8 mathematical structure.

For more information on hyperbolic browsers:
http://www2.sapdesignguild.org/community/book_people/
visualization/controls/hypBrowser.htm

What a laugh to think that the structure of human thought may be echoed in the structure of the dandelion flower.

(Personally, I love dandelions and encourage them in lawn and garden. I've never thought of them as a weed).

Hexagon as a Spatial Average - Woldenberg

Accession Number : AD0722022

Title : Geography and the Properties of Surfaces. The Hexagon as a Spatial Average.

Descriptive Note : Interim rept.,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS LAB FOR COMPUTER GRAPHICS AND SPATIAL ANALYSIS

Personal Author(s) : Woldenberg,Michael J.

Report Date : 15 OCT 1970

Pagination or Media Count : 28

Abstract : The paper demonstrates that river basin areas and central place market areas tend to be hexagonal. River basins are bounded by ridge lines which meet three at a corner. Few ridge lines cannot define a corner, and more ridge lines are improbable. The nomenclature of river basins following Warntz (1968) and Schumm (1956) is extended. Market areas also must have three-edge corners. Graustein (1932) showed that large networks with three-edged corners must tend to have six sides per polygon, a relation that follows from Euler's law. The most if not all commonly occurring natural networks have three-edged corners, the polygons tend to be hexagons. (Author)

Descriptors : (*GEOGRAPHY, GRAPHICS), (*RIVERS, MATHEMATICAL MODELS), HYDRAULIC MODELS, NETWORKS, SURFACES

Subject Categories : HYDROLOGY, LIMNOLOGY AND POTAMOLOGY

Distribution Statement : APPROVED FOR PUBLIC RELEASE

http://stinet.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0722022