Monday, December 15, 2008

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.

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.

Thursday, September 18, 2008

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?

Tuesday, September 16, 2008

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).

Friday, June 27, 2008

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

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:

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).

Monday, June 16, 2008

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.,


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)



Distribution Statement : APPROVED FOR PUBLIC RELEASE

Hexagonal Columns, Giants Causeway - Ireland

Natural hexagonal volcanic columns in Ireland. They look similar to the dinosaur scales.


Hexagonal Pattern of Dinosaur Skin

A rare mummified dinosaur has been discovered in North Dakota. Notice the beautiful hexagonal pattern of scales. This mummy is thought to be 67 million years old.

From National Geographic:

A newly found "dino mummy" has exquisitely preserved bones, skin, and possibly muscle and internal organs, scientists have announced.

The duck-billed dinosaur, named Dakota, is already changing theories of how the extinct creatures looked and moved—and may contain preserved ancient proteins that could better reveal the dino family tree.

Photograph by Tyler Lyson © 2007 National Geographic

Thursday, May 8, 2008

Relationships - The Space in the Middle

I've been watching the progress of Jeff Hawkins' research on Numenta and was playing with a demo that has learned some simple shapes. The user can draw the shape and ask the application to recognize it. It returns an array of images to match the drawn input and a probability indicator bar beside each of the learned object shapes. Unfortunately, it didn't guess very well. I shared this demo with a colleague and neither of us were too impressed.

I started playing around with a simple drawing of a hat. I drew two extremes of a hat, one with a very tall top and short brim, and one with a very short top and a wide brim. I also drew the average between these two extremes, to show a prototypical line drawing of a hat. Then I thought there must be some understanding of the relationship between the brim and the top, because both can be varied so much and yet a hat can still be identified as a hat.

There has to be something more to recognizing simple shapes - some understanding of object relationships that is missing from the Numenta demo, which I think needs to be included if it is going to work properly.

This line of thinking lead me on a search to find a list of mathematical relationships. I have never had a natural aptitude for mathematical equations (I quit after a course in Calculus at university), although I do find it interesting if I can apply it to something in the real world.

Here is a formal definition:

"When two objects, qualities, classes, or attributes, viewed together by the mind, are seen under some connexion, that connexion is called a relation." - Augustus De Morgan

I found a list of mathematical relationships on another site that I want to explore further:
Java Programming Archive

- Linear Function
- Quadratic Function
- General Polynomial Function
- Arithmetic Function
- Transcendental Function
- Parameterized Equations
- Any relationship: y is related to x in some way
- Sequences?

It seems that people need, not only a memorized bank of images to draw upon, but some rules to represent relationships between the parts of an object/image, to make recall of the images possible from fuzzy data.

Wednesday, April 23, 2008

Establishing Criteria to Support my Hypothesis

The Protoglyphic Hypothesis

1. There is a common set of fundamental patterns shared by all humans that is used as a basis for thinking and understanding our world.

2. The patterns represent primary concepts about our world, and also act as structures to organize information.

3. The patterns are simple, abstract and geometric.

4. Each pattern has both a general meaning and a range of specific meanings - just like a word has a common popular meaning as well as a range of different meanings, based on context or juxtaposition.

What criteria would support this hypothesis?

1. Geographically Pervasive
The patterns are found throughout the word, in many different locations, on many different surfaces and artifacts.

2. Culturally Universal
The same patterns are found in many different cultures.

3. Temporally Persistent
The patterns are persistent in human culture, over time. From prehistoric to modern times, we see evidence of these fundamental patterns.

4. General, yet also Specific
We would not expect to see exactly the same specific meanings assigned to the same patterns found in different cultures. We would expect to find common general meanings assigned to the same pattern in different cultures.

5. Macro and Micro
The patterns are scalable. They exist at the micro level and at the macro level to represent movement and physical organization of matter and space.

6. Common across Disciplines
The patterns exist as primary structures in all disciplines: science, art, mathematics, physics, language...

Tuesday, March 25, 2008

Metatron's Cube

From Wikipedia

The Fruit of Life (a component of the Flower of Life) has thirteen circles. If each circle's center is considered a "node", and each node is connected to each other node with a single line, a total of seventy-eight lines are created. Within this cube, many other shapes can be found, including two-dimensionally flattened versions of the five Platonic solids. The true Metatron's Cube will include all five Platonic solids in such a way that the solids, existing in volumetric 3D space, have had their z-coordinates set to zero but their x- and y-coordinates retained, such that they are orthogonally flattened.

In early kabbalist scriptures, Metatron supposedly forms the cube from his soul. This cube can later be seen in Christian art, where it appears on his chest or floating behind him. Metatron's cube is also considered a holy glyph, and was often drawn around an object or person to ward off demons and satanic powers. This idea is also present in alchemy, in which the cube was favoured as a containment circle or creation circle.

Nature's First Pattern

From Charles Gilchrist's website on sacred geometry, above is an example image of what he calls Nature's First Pattern. Mr. Gilchrist encourages people to use this pattern to make a mandala.

Thursday, February 14, 2008

Migraines & Patterns

I've been playing around with the idea that geometry may be the way in which our minds average the fuzzy boundaries of probability fields out there, in the world around us, making us essentially quantum statisticians. Geometry is perhaps the method our minds employ to quantize our knowledge of a shifting, shimmering fluid world.

An excerpt from Patterns, by Oliver Sacks, recently published in the New York Times Blog.

"Much later still, when I first saw photographs of the Alhambra, with its intricate geometric mosaics, I started to wonder whether what I had taken to be a personal experience and resonance might in fact be part of a larger whole, whether certain basic forms of geometric art, going back for tens of thousands of years, might also reflect the external expression of universal experiences. Migraine-like patterns, so to speak, are seen not only in Islamic art, but in classical and medieval motifs, in Zapotec architecture, in the bark paintings of Aboriginal artists in Australia, in Acoma pottery, in Swazi basketry — in virtually every culture. There seems to have been, throughout human history, a need to externalize, to make art from, these internal experiences, from the decorative motifs of prehistoric cave paintings to the psychedelic art of the 1960s. Do the arabesques in our own minds, built into our own brain organization, provide us with our first intimations of geometry, of formal beauty?"

Thank you to Debi Parush for bringing this article to my attention. It's fascinating!

Note: I've had neurological migraines since I was a child, (complete with shimmering zigzags of light, pastel colours and a loss of the visual field), and always considered them normal, assuming everyone else had them as well.

Thursday, January 24, 2008

Phosphenes as Visual Categories

After reading some of Chomsky's work on innate transformative grammar, I must say I feel quite humbled in realizing how little I know about linguistics. Chomsky's work is remarkable in its depth and it appears almost scathingly flawless in its logic (politics aside). Yesterday I was considering the possibility that an innate grammar (or structural syntax) might also provide the framework for the way in which we organize visual imagery. But Chomsky's insistence on modularity makes me think that perhaps trying to use an innate grammar for visual processing is quite likely sheer folly.

Another line of thinking occured as I was driving into work this morning. What if phosphenes act as hard-wired visual categories that represent the prototypical movements observed in our natural, physical world? In other words, perhaps phosphenes represent the paths or trails, through physical space of animals, insects, clouds, water and everything else that a human might observe in nature. Imagine water going down the drain in a spiral shape, or rings emanating outward when a drop hits the surface of water, or a squirrel running across a tree limb, or a rock dropping off the edge of a cliff. We know that we share some instinctual fear reactions to certain silhouette shapes, such as a starburst spider shape, with animals. Could it be that the phosphenes are categories onto which we later map specific instances that are obtained from our interaction with the real world? That these categories become increasingly dense (or rich) with experience over time.

Wednesday, January 23, 2008

Parsing Geometric Patterns

Phosphene symbols may possibly be common to all mammals, since we share a similarly evolved visual cortex. But spoken language is without a doubt unique only to humans. No one knows why human brains got so big. Perhaps they grew to accommodate the demands of an evolving, and increasingly complex verbal language system. Having a syntax for language then allowed humans to develop rational brains that are both anticipatory and also reflective, or able to re-member and reassemble. Recognition may be an ability we share with mammals, but recall may be a uniquely human ability. Our rational brain structure, shaped by the demands of spoken language, perhaps made it possible for humans to not only associate sounds to meanings (spoken language) but also to organize and structure the language in our minds (syntax and memory). The demands of language could have been the impetus for human brain growth. Perhaps the evolved brain, suitable for sending and receiving spoken language, also primed humans in their early attempts at geometric graphical depiction, and quite soon after, written language. I think verbal language abilities in humans needed to be quite significantly evolved before attempts at graphical depiction was even cognitively possible.

So, if we want to decipher early geometric patterns, we might very well begin by applying a parsing method equivalent to natural language parsing. The rationale here is that the human mind evolved to accommodate spoken language, but that this also opened the door into the world of association and syntax for a different form of communication -- graphics. When parsing a natural language sentence, there is a start and an end, and an intermediary construction consisting of a subject and an object, possibly with an indication of a context of some kind. One attribute of natural language is its inherent ambiguity, not only in the words used, but also conveyed by sentence structure (ambiguous prepositional phrases) and also voice tonality and inflection. These additional 'channels' of information help to convey the meaning of the message.

It is possible I am simply restating what Chomsky has already proposed, so I must do a bit more research about his position.

Tuesday, January 22, 2008

Markings as Evidence of Ownership?

I showed my 5-year-old son the image of the oldest art object ever found and told him it belonged to a cave man and asked him why he thought there were lines drawn on it. He said, "The cave man made lines on his rock because it was important to him and he wanted to remember which one it was. And he wanted people to know that it was his rock."

Monday, January 21, 2008

The Meaning of Adinkra Symbols

This site of Adinkra symbols from Western Africa is really quite amazing. The meaning of each symbol is given on the site. The symbol shown above is the symbol of greatness, charisma and leadership. All of these symbols look very much like embellished phosphene symbols. I think these symbols may represent an intermediary step between abstract geometric representation and symbolic language.

Adinkra Symbols of West Africa

In looking at a global map and an associated timeline for prehistoric art, I wanted to review the evolution of symbols and pattern imagery found in Africa -- where the oldest art object (see previous post) has been found -- to see if I could identify a 'next step' or transitional phase. I was looking, in particular, for evidence of embellished phosphene symbols. And I think I've found them in the Adinkra symbols of West Africa.

Oldest art in the world - A System of Patterns

The world's oldest example of abstract art, dating back more than 70,000 years, has been found in a cave in South Africa.

Complex motif

Dr Christopher Henshilwood, from the State University of New York at Stony Brook, says: "They may have been constructed with symbolic intent, the meaning of which is now unknown.

"The engraving itself is quite a complex geometric pattern. There is a system to the patterns."

"We don't know what they mean, but they are symbols that I think could have been interpreted by those people as having meaning that would have been understood by others."

The engraved ochre pieces were recovered from Middle Stone Age layers at Blombos Cave, 290 kilometres (180 miles) east of Cape Town, and are at least 70,000 years old.

Dr Henshilwood says more than 8,000 other pieces of ochre were found in the cave, many of which had been rubbed smooth as if to make pigment powder.

Stone Age Map 10,000 B.C.

The oldest map in the world, discovered in Ukraine in 1966, is from about 11,000 - 12,000 B.C. Inscribed on a mammoth tusk it was found in Mezhirich, Ukraine. It has been interpreted to show a river with dwellings along a river.

I think this map may have been a battle/attack plan. The lines at the top indicate attacking from the top of the mountain. The shape of the buildings indicate what type of defenses they have. It looks like a catapult in several of the structures. I can imagine a general sending out a scout to make this drawing and then returning to the army with the map, so they could prepare for the battle.

Thursday, January 3, 2008

The 10 Sephirot - Patterns in Spirituality

This investigation into the world of patterns is leading to spirituality. This pattern represents the 'Sephirot'. It looks very similar to the central structure of E8.

The idea of the ten Sephirot (literally the "categories" or "symbols") is the most familiar and widespread of all Kabbalistic motifs. It first appears in the books of Sefer Yetzirah and Sefer Bahir, and probably dates from the first millennium. It is a very conscious attempt to offer an alternative to a rational, philosophical view of how God interacts with humans and vice versa.

In a nutshell, the Sephirot are like a transistor that enables us to receive messages and send them. If God, Ein Sof, is not physical in any way, then there is a problem as to how there can be any interaction between the purely spiritual and the material. By interposing the Sephirot they become the channels through which we receive and transmit the lines of communication with the Divine.

- from Jeremy Rosen's website: