The Beauty of E8

Here is another beautiful image of the E8 structure. This one shows depth and grid-like structures are more clearly emphasized. It's from an interview with Garrett Lisi here: http://backreaction.blogspot.com/2007/08/garrett-lisis-inspiration.html

The Star of David is the E8 Root

As I was reviewing Garrett Lisi's paper, An Exceptionally Simple Theory of Everything (6 Nov 2007), I noticed with some astonishment that the root of E8 -- the fundamental core of this pattern - is the symbol used to represent the Star of David.

Garrett Lisi's paper is available here: http://www.arxiv.org/pdf/0711.0770

E8 - Mother of All Patterns

An interesting story in the Ottawa Citizen this morning describes the theory of Garrett Lisi who has a PhD in physics from the University of California, San Diego. He has proposed "An Exceptionally Simple Theory of Everything" that is intended to act as the Grand Unifying Theory of physics It is based on a complex, eight-dimensional mathematical pattern called E8.

I'm affectionately calling it the Mother of All Patterns.

Within this larger 'mother' pattern, I think we will quite likely find sub-structures or smaller patterns -- classic data patterns. I also think that if this model is sound, it may also act as a pattern for how we organize and store data, both in our minds and externally.

I'd like to see someone write a search algorithm for E8. Perhaps this already exists. Perhaps this is Google's 'secret algorithm'.

Taxonomy of Patterns

There are many different ways to organize or map information. Here is a very good shortlist of some classic relational data patterns.

http://projects.edtech.sandi.net/staffdev/tpss98/patterns-taxonomy.html

Cluster - presents related aspects of a central idea/element

Hierarchy - Categories and subcategories; organization by relationship, ownership, levels of granularity, top-down, deductive, movement from top to bottom

Venn Diagram - Membership in overlapping categories, shared commonality

Timeline - temporal map or sequence/change over time

Flowchart - Steps in a procedure or process

Concept map - Labeled relationships

Causal Loop Diagram - Systems of cause and effect

Comparison Matrix - Table of comparisons

Inductive Tower - Building inferences and generalizations from data (reverse hierarchy; bottom up, rather than top-down movement

Quasiperiodic Crystal Pattern

http://tilings.math.uni-bielefeld.de/tilings/substitution_rules/square_triangle

Quasicrystals are aperiodic structures that produce Bragg diffraction, i.e. they show pure point spectra. Thus they share a defining property with crystals, but differ from them by lacking a regular repeating structure. They were considered to be mathematical artefacts, known as aperiodic tiling, but physical experiments gave evidence of their material existence. Within the field of crystallography and solid state physics the discovery has produced a paradigm shift which is indeed a minor scientific revolution. - from Wikipedia

Gestalt Principles

It might very well be that the Gestalt Principles of Perception act as the Geometry of Cognition. Geometry is a way to abstractly represent and describe the relationships between points, lines, planes, areas, surfaces and volumes in physical space -- a way to represent and understand physical matter -- the arrangement of objects in space and their relationship to other objects.

What if the Gestalt Principles of Perceptions are to mental space what Geometric Principles are to physical space? What if the Gestalt Principles provide the rules that give rise to the shape of cognition, rather than merely just applying to the principles of visual perception? What if the Gestalt Principles extend further - and are more widely applicable - than we thought? While this may seem a very obvious question to ask, it isn't really, if you imagine these principles as quite literally determining parameters for how information is perceived, processed and eventually filed in human memory.

Lists of the Gestalt Principles seem highly variable in their content but here is a list that seems quite complete:

- Proximity (objects close together in space are thought to belong together; are grouped together)
- Similarity (similar objects are grouped together)
- Continuity (we strive for good continuity; a break or disruption can be overlooked and perceived as continuous)
- Closure (we strive to close or complete an open shape)
- Smallness (smaller things are perceived to be foreground objects first, rather than objects that are farther away)

http://www.artinarch.com/vp12.html


From Wikipedia:
A notable weakness with the Gestalt laws of Prägnanz is that they are descriptive not explanatory.

My thoughts on this: Of course they are descriptive. They rely on external input from the world around us. Our perceptions are judgements that we make on the world around us based on fuzzy information that involve thresholds and contextual information. We perceive things based on what's around, based on the context. It's an assessment of the figure/ground relationship that is cited as a fundamental component of the Gestalt Principles.

On another topic: Someone should take a look at the Reiser file system and see how this could represent information in human memory. The Reiser file system is a very interesting model.

Geometry is the Glue

Geometry is the way we describe the glue that binds together our world. Geometry is the language of physical structure. Geometry encompasses the principles that define relationships between points in space (or objects in space, or locations in space).

The image above is a Pennsylvania Dutch hex sign.
From Wikipedia:

Hex signs are a form of folk art, thought by some to be of a talismanic nature^{[citation needed]}, found in the Fancy Dutch tradition in Pennsylvania Dutch Country.

Artfully painted hexagonal star-like patterns are a well-known sight on Pennsylvania Dutch barns in and around central Pennsylvania, especially Berks County. However, the decoration of barns is a late development in Pennsylvania Dutch folk art. Prior to the 1830s, the cost of paint meant that most barns were unpainted. As paint became affordable, the Pennsylvania Dutch began to decorate their barns much like they decorated items in their homes. Barn decorating reached its peak in the early 20th century, at which time there were many artists who specialized in barn decorating. Drawn from a large repertoire of folk designs, barn painters combined many elements in their decorations. The geometric patterns of quilts can easily be seen in the patterns of many hex signs. Hearts and tulips seen on barns are commonly found on elaborately lettered and decorated birth, baptism and marriage certificates known as Fraktur. In recent years, they have been increasingly used by non-Pennsylvania Dutch persons as talismans for folk magic rather than as items of decoration. Some scholars argue that they have never had any connection with superstition or magic^{[citation needed]}. They are viewed as decorative symbols of ethnic identification, possibly originating in reaction to 19th Century attempts made by the government to suppress the Pennsylvania German language. In the 20th Century, mobile signs were produced as commodities. These signs could be bought and then mounted onto barns.

Paul Klee - in Search of Primitives

"The monument of Klee's obsession with this metaphysics was a singular book, The Thinking Eye, written during his teaching years at the Bauhaus - one of the most detailed manuals on the "science" of design ever written, conceived in terms of an all embracing theory of visual "equivalents" for spiritual states which, in its knotty elaboration, rivalled Kandinsky's. Klee tended to see the world as a model, a kind of orrery run up by the cosmic clockmaker - a Swiss God - to demonstrate spiritual truth. This helps account for the toylike character of his fantasies; if the world had no final reality, it could be represented with the freest, most schematic wit, and this Klee set out to do. Hence his reputation as a petit-maître.

"Like Kandinsky, Klee valued the "primitive," and especially the art of children. He envied their polymorphous freedom to create signs, and respected their innocence and directness. 'Do not laugh, reader! Children also have artistic ability, and there is wisdom in their having it! The more helpless they are, the more instructive are the examples they furnish us ....' In his desire to paint 'as though newborn, knowing absolutely nothing about Europe,' Klee was a complete European. His work ferreted around in innumerable crannies of culture, bringing back small trophies and emblems from botany, astronomy, physics, and psychology. Music had a special influence on him. He believed that eighteenth-century counterpoint (his favourite form) could be translated quite directly into gradations of colour and value, repetitions and changes of motif; his compositions of stacked forms, fanned out like decks of cards or colour swatches, are attempts to freeze time in a static composition, to give visual motifs the "unfolding" quality of aural ones - and this sense of rhythmic disclosure, repetition, and blossoming transferred itself, quite naturally, to Klee's images of plants and flowers. He was the compleat Romantic, hearing the Weltgeist in every puff of wind, reverent before nature but careful to stylize it. Klee's assumptions were unabashedly transcendentalist. 'Formerly we used to represent things visible on earth,' he wrote in 1920, 'things we either liked to look at or would have liked to see. Today we reveal the reality that is behind visible things, thus expressing the belief that the visible world is merely an isolated case in relation to the universe and that there are many more other, latent realities ...'
"Klee's career was a search for the symbols and metaphors that would make this belief visible. More than any other painter outside the Surrealist movement (with which his work had many affinities - its interest in dreams, in primitive art, in myth, and cultural incongruity), he refused to draw hard distinctions between art and writing.

http://www.artchive.com/artchive/K/klee.html

Here's my question: Why are Klee paintings celebrated as masterpieces in the Guggenheim museum, when they look like quilts? People have been generating pattern fields like the ones seen in Klee's paintings for thousands of years. If Klee was searching to represent ‘the reality behind visible things’, then why does so much of his work look like the "primitive" arts and crafts of women and men throughout history? Rugs, pottery, patchwork quilts, and paintings of the aboriginals from Australia...were cultures in the past also trying to represent the reality behind visible things? The cognitive reality that all humans share?

Perhaps Klee's work was found particularly novel, especially within a 20th century context -- when people had lost sight of fundamental patterns, and needed to be reminded of them.

image reference:

http://www.metmuseum.org/special/se_event.asp?OccurrenceId={D88B5218-2B74-46D0-B36A-4ADC7B4D6A3A}

Patternmakers as Mirrors of Nature

Today, I started searching for patterns in nature, thinking that pattern makers are trying to mirror nature. We see these remarkable patterns in the world around us, and we copy them and reproduce them as objects. Patterns of honeycombs, and Komodo dragon scales, and spirals found in cactus. And then I searched for the oldest life on earth and found a one-celled creature. But I thought this level was still too high, too ‘gross’, so I searched for molecular structures and saw some beautiful patterns. And then I searched for atomic structures, and found a beautiful hexagonal matrix pattern for silicon that is visible at the atomic scale in an article: The World According to Nanometers. Again, I have seen this pattern in quilts.

The image (above is) of a silicon surface, captured by Taisuke Ohta, Fumio Ohuchi, and Marjorie Olmstead using a scanning tunneling microscope, patterns are visible at the atomic scale. Bright spots are individual atoms.

http://images.google.ca/imgres?imgurl=http://www.artsci.washington.edu/news/WinterSpring04/Photos/nano_image.jpg&imgrefurl=http://www.artsci.washington.edu/news/WinterSpring04/Nanotech.htm&h=300&w=300&sz=182&hl=en&start=50&tbnid=WS3-ztUHH3tunM:&tbnh=116&tbnw=116&prev=/images%3Fq%3Datomic%2Bpatterns%26start%3D40%26ndsp%3D20%26svnum%3D10%26hl%3Den%26hs%3DOTK%26lr%3D%26client%3Dfirefox-a%26rls%3Dorg.mozilla:en-US:official%26sa%3DN

In the late 1920s, an American quilt revival brought in a new color palette of pastel prints. Quilts made from these fabrics are sometimes referred to as Depression Quilts, since the styles and fabrics continued through the Great Depression. Mamie ordered her fabrics from a catalog, either Montgomery Ward or Sears, Roebuck and Co.

http://images.google.ca/imgres?imgurl=http://www.sohe.wisc.edu/depts/hlatc/quiltsExhibit/images/Med_sized_pix/GrandmaFlower_D1_MED.jpg&imgrefurl=http://www.sohe.wisc.edu/depts/hlatc/quiltsExhibit/flowerGarden.html&h=216&w=288&sz=25&hl=en&start=2&tbnid=ezPzIjSvW6jkFM:&tbnh=86&tbnw=115&prev=/images%3Fq%3Dgrandma%2527s%2Bflower%2Bgarden%2Bquilt%26svnum%3D10%26hl%3Den%26lr%3D%26client%3Dfirefox-a%26rls%3Dorg.mozilla:en-US:official%26sa%3DN

Now, the chances are quite likely that ‘Grandma’ never used an atomic microscope. And yet how did she know to replicate the atomic structure of silicon in her quilt pattern? This is the mystery that I’m trying to solve. I want to know how these two things are connected.

Norah Gaughan has written a new book ‘Knitting Nature’ April 2006 and she has based her patterns on natural patterns

http://www.berroco.com/knitbits/html/KB137_interview.html

Again, I’m thinking, ‘So what? People imitate nature? That is something we’ve all known about for a long time, right?” True, but what we haven’t discovered is how these patterns may be used in our own minds to organize information.

What type of information might be organized in a hexagonal pattern? We commonly organize and understand information that is organized in a graph, as a matrix. This is a pretty standard form of information organization that has been used for several centuries.

There is something quite circular with patterns, and our understanding of them.

We see pattern structures in nature at all levels of scale, from the atomic on up to plants and trees and shells and landscape. We ‘learn’ these patterns through living in our environment and we record these patterns in our memories. Then we attach information onto these structures at a low level, learn how to intellectually abstract from real, concrete (physical) instances into an abstract mental structure, and we see the same structure again in a virtual fashion… that we then describe using mathematics. This is considered ‘higher thinking’.

So, we internalize the patterned structures that we see in our environment, load these structures up with information until we can achieve a mental level of abstraction, so that we can create or replicate using our own minds and hands what we see out in the real world. Weird. We internalize and then we externalize. We are not just pattern recognizers, but we then also learn to become pattern generators. This is a uniquely human capability. This is what creativity is all about. Seeing patterns, internalizing patterns, abstracting patterns and making more patterns.

We are pattern recognizers, pattern recorders and pattern makers. Truly.

Patterns are an efficient way for physical matter to be organized. Patterns are rather social, when you think about them. Individual items are held together in relationship by an ‘agreed’ structure of organization, just like a society of humans. There are roles and rules.

As below, so above.

The Sound of Simple Shapes

A rather bizarre question popped into my head today. ...What does a spiral symbol sound like? If a spiral is a path, and the center of the spiral is the start point and the spiral is 'unwound' and transformed onto a line that represents time, then the sound would start out high-pitched (high frequency) and soft (low amplitude), and get lower in pitch (low frequency) and louder (higher amplitude) over time.

The sound of a circle? A short (brief) continuous tone of equal amplitude and frequency.

The sound of a square? A rising continuous tone, then held for a brief duration, then falling and held for a brief duration....remarkably similar to the prosodic structure for approval.

This is the general idea. If phosphene patterns are commonly found in prehistoric art (and carry on throughout the ages) in cultures with an assumed verbal language (but no written language), then is there a link between SOUND and these simple shapes/patterns? Perhaps the sounds of these shapes correspond with sounds heard in the natural environment, or perhaps the sounds correspond with chanting utterances of sacred rituals?

Keep in mind that the sounds I'm talking about here are not sounds arbitrarily assigned by humans to the phosphene symbol. The sounds here are achieved when the actual path of the symbol is 'unravelled' and transformed into a sound wave. Also rather strange is that the sound waves derived from these symbols look very much like the acoustic mappings of bird calls.

In prehistoric pottery, border patterns are prolific. If a border contains several discrete symbols, the resulting sound map would reflect simultaneity, achieving a harmonic set.

Phosphene Lexicon

Some qualified speculation about a Phosphene Lexicon....

"But what turned out to be truly amazing," said Cardenas-Arroyo, "was that many of the patterns made by the Tukanos were nearly identical to the phosphene patterns described 40 years earlier by Knoll." Moreover, he showed how phosphene-inspired patterns used in contemporary indigenous cultures are very similar to designs on ancient pottery.

"I believe that many of these design patterns were like an unspoken language that held symbolic meaning through their iconography, which transcended linguistic and cultural barriers," he said.

"Archaeologists should make a greater effort to decode the symbolism beyond the art."

- Felipe Cardenas-Arroyo
Columbian Archaeologist

http://www.iadb.org/idbamerica/Archive/stories/1998/eng/e998k.htm

Interpreting the Storyline of a Graphic

Going back a few weeks, I suggested that graphical depiction may be a compound form of language (or verbal expression). If this is so, then it is, indeed, linear. When a person looks at an image, their eyes start in a particular place, and travel to other interesting spots in the image. This eye travel creates a path over the image -- a linear path. Where the eyes start and stop and start and stop along the path depends on those things in the graphic that attract attention. In looking at a picture, or a graphic, people visually traverse it in a linear fashion. As to what a pair of eyes might find interesting enough to fixate on -- is another discussion entirely -- but I do think Gestalt Principles may play a part in this (at the most fundamental level). For example, the intersection of two lines, or a bump on a line, is much more interesting, than an uninterrrupted straight line. A vertical line is more active (dynamic) than a horizontal line. A diagonal line is supposed to be even more active than a vertical line. I need to find more information about how lines and simple shapes are interpreted, how people find meaning in these basic outlines. This will provide some insight as to how we might interpret phosphenes.

First Patterns

This is a search for first patterns, the fundamental patterns that underpin human thought. I want to discover the language - both the vocabulary and the rules - of pattern thinking.

Why is it we see the same phosphene shapes in arts and crafts -- and even in nature? Fundamental patterns must be the most resilient, most robust, most balanced types of patterns-- that rely on the physical properties of our natural world. The reason triangular shapes are so strong, the stability of the hexagon. A pattern is a field of structures bound together by certain principles, or rules.

Some patterns are stable and balanced. Others are, by nature, unstable and act as attractors (with receptive components). Some modules within patterns resist bonding with other parts of the patterns (funny how much this sounds like the bonds of chemistry). Some patterns are unstable and receptive to joining another pattern field. Some patterns are stable and resistant to joining another pattern field.

No evidence yet for Phosphene Maps

I haven't yet found any evidence in the drawing development of children for phosphene maps. Children draw scribbles, then straight lines, then curved lines, then closed shapes, the 'tadpole' figure, and then a stick figure with a body in a scene. There doesn't seem to be any mapmaking going on. I had hoped to find evidence of geometric patterns in early toddlers, but so far there doesn't seem to be any. This lack of evidence would support theories that geometric maps are actually more advanced than pictorial ones.

There are cultures where geometric patterns emerge as a dominant motif in art and decoration and for ceremonial purposes -- Native American cultures. It's also interesting to note that cultures such as these usually do not have a written language. They have an oral tradition, and then use geometric and curvilinear graphics to designate symbolic meanings.

I need to investigate more about cuneiform writing and the Mayan culture.

It may very well be that the geometric representations are a different branch of communication or expression that is unique to some cultures who (perhaps) are more oriented in right-brain (for lack of a better label at the moment) values.

I plan to read (again) Thinking in Pictures by Temple Grandin. This may offer some insight about visual representations and visual thinking.

Jennifer Bartlett - Painter

In the early 80s, while working on my arts degree, I became transfixed by the art of Jennifer Bartlett when her first series of paintings called "In the Garden" were featured in an arts magazine. The fact that I liked her work greatly surprised me, because I didn't really like contemporary art. My attitude towards contemporary art has always been, "I'm living it. Why do I need to look at it? Why remind me of what I already know?"

Anyway, I haven't even thought about Jennifer Bartlett for years, but with renewed interest discovered that one of her recent exhibits involves painting images of maps, and that she actually started out as a map maker. There is something in her work that represents some kind of 'first principles' of perception and cognition. Something fundamental about how humans represent and know about their world. Something timeless.

In the words of critic Maurice Berger, Bartlett’s art “juxtaposes the raw and the cooked, examining the way the world is filtered through the human mind and is encoded into cultural conventions or sign systems.”

The First Graphical Language

I am quite convinced that phosphene maps, or protoglyphs, are the First Graphical Language used in visual expression. I think there is a vocabulary, and there is a syntax. The rules that comprise the syntax have evolved through human experience and human perception of the natural environment.

Palaeolithic humans lived directly in nature, as relatively small beings in a much larger world. It is difficult for contemporary humans to understand the relationship of early humans with nature, because for such a long time now we have lived in human-made environments. But just as contemporary humans quite voraciously 'want to know' what's happening 'out there' and watch the news or talk to neighbours or friends, I think early humans also had this curiousity and shared their knowledge of the greater world with their clan. Graphical depiction is a way to share information either as an aid to a verbal description or as a standalone communication when the subject is either unable to speak for some reason, either because they need to be quiet, perhaps aren't physically present, or may be incapacitated or even disceased.

Maps, Counting & Ownership

In trying to understand where to focus my research, it looks like it's going to be around the area of phosphenes, and what comes after phosphenes, some type of compound phosphenes, or phosphene maps.

I am convinced that somewhere along the developmental path of cognition in humans, there is an area that displays evidence of protoglyphs. I think it is after phosphene expression and before mandala expression. What I call protoglyphs may very well turn out to be phosphene maps.

Here's a proposed order for graphical cognitive development:

1. Phosphene expression (age 2)
2. Unintentional abstraction- phosphene maps (age 2-3)
3. Shape execution -- mandala first, then squares, triangles (age 3-4)
4. Shapes in settings
5. Cartoons in Settings (on the way to the figurative) (age 5-8)
6. Literal, figurative 'life-like' representations in a setting (age 8-?)
7. Deliberate abstraction in drawings and intellect (age 11+)

The idea here is that first, objects are learned, and then the objects are shown in a setting with relationships. First, phosphenes are expressed, and then phosphenes in settings with positions that represent relationships. This dynamic parallels the development of human children, even now, in that first the letters of the alphabet are learned, then words, then sentences. First, the components, and then rules to arrange the components.

The area I intend to focus on is the early paleolithic art of non-representational patterns. After reading an article published by Bednarik (R. G. Bednarik, The Earliest Evidence of Paleoart, Rock Art Research, 2003, Vol. 20, No. 2, pp 89-135), my first thought were that these patterns may represent:
1. Maps of Land/Areas - for shared discussion with others
2. Counting/Record-keeping - perhaps of large animals killed, or victories (notches in a belt)
3. Ownership - identification/clan symbols

Another assumption that I'm making is that learning must come before graphical expression is possible. In other words, something must be known and understood before it can be expressed. What this means cognitively, is that the knowledge, or knowing, was already in place for paleolithic humans, before it was expressed. The advantage of something written down or drawn is that it is unambiguous. How often do we hear, even today, "Put it in writing." Verbal knowledge can be easily misunderstood, and then mistranslated. The game of Chinese Whispers is a great example of how a simple phrase can unintentionally evolve and change as it is communicated from one human to the next.

Something else to think about when the meaning of phosphene maps is interpreted. Humans long ago had the same basic needs that we have today. Food, shelter, community...(a quick look at A. Maslow's hierarchy of needs can perhaps give us an indication of the 'first concerns' of paleolithic people). Issues of land occupation, record-keeping or counting of victories achieved, and ownership are all key parts of life today, just as I think they probably were 42,000 years ago.

Cognitive Archaeology

Cognitive archaeology is a theoretical underpinning of archaeological research that is interested in the material expression of human ways of thinking about things, such as gender, class, status, kinship. This is a relatively new movement in archaeology, probably started as a reaction to the dry positivism of processual archaeology, and related to the post-processual movement. Archaeologists associated with cognitive archaeology include James Deetz and Robert Bednarik; but there are lots of others.

http://archaeology.about.com/od/cterms/g/cognitive.htm

Language as a Front Runner

In some recent research, I was surprised to discover that language evolved before the depiction of graphic symbols. For some reason, I'd thought that graphical symbols came first, or at least -- alongside the development of spoken language. My husband asked, "How do the experts know that spoken language came first?" I had to reply that I didn't know yet why this was 'known' and that I'd have to find some proof, some verification of this assertion.

But, if language did come first, and graphical depictions came after this, this could imply one of two things: 1) graphical depictions were initially linear, because language is a linear form (OR) graphical depictions developed adjacent to or in parallel with the development of language. Because of the way in which the cortex has separated language and visual processing, this leads me to think that graphical depiction may very well have developed after speech, and can be understood as a compound form of speech. (A picture is worth a thousand words).

Apparently, not much research has been done so far in deciphering the meaning of the patterns of the Middle to Upper Paleolithic period. According to Bahn (1998), "Apparently non-figurative art-motifs which convey nothing to our eyes other than the patterning, has existed from the beginning. Indeed, it often dominated the art of the Paleolithic period and its study is one of the long-neglected challenges of archaeology."

What I came across today is fascinating, though, moving on the language first, linear depiction first theory. What does an old secret Celtic language comprised of lines, read right to left, called ogam (ogam: Ancient alphabet, in which letters are formed of parallel lines which meet or cross a base-line. Possibly of Irish origin), and a bird call and morse code (Amercode from the 1920s) all have in common? I'm not exactly sure yet. But they all have linear components that are remarkably similar. Take a look for yourself. It makes me wonder if perhaps bird calls were the initial inspiration for humans to attempt language. And it makes me think about the 'click' language and how and where it originated.

More on Protoglyphs

In thinking about how protoglyphs might form in the mind, here are some 'first thoughts' (recently resurrected from old memories). What follows below is a very rough draft as I work through this sequence.

1. In the earliest stages of development, the brain has a set of hard-wired patterns that are innate and common to all people (phosphenes may be examples of these patterns). Exactly what these patterns look like is still unknown. They need to be identified. The patterns are represented in the brain by neural receptors that are sensitized or physically receptivity to external stimuli for these patterns.

2. As development and learning continues, the brain is exposed to pattern instances experienced in the external environment. Samples of fuzzy data are pieced together, and the pattern becomes 'activated' and robust in the brain. Over time, the pattern becomes 'averaged' into a geometric prototype of the pattern. The brain has now learned the pattern and it can be reliably recalled when an instance is presented in the environment. The interesting thing here is that the presentation of the pattern (in the external environment) can stimulate recall for one or more instances, one or more instances can recall the pattern from memory, or a single instance can recall another instance. I think an advanced mind may lose its ability to recall these lower order patterns, and only be able to recall specific instances. I think protoglyphs may lie just at the border of consciousness or may even be subconscious for some people. For people who aren't 'visual thinkers', it is quite likely that their prototypes reside below the level of conscious thought.

3. More data is presented through multisensory 'enforcing instances'. Each instance that is encountered is mapped onto the geometric prototype. This is a protoglyph. A protoglyph is both the pattern itself, the 'sacred geometry' and all corrollated instances associated to it. Imagine a circle (to represent a pattern) and an array of fuzzier misshapen circles superimposed over the 'perfect' circle as messy data. Each instance now mapped in the mind now also has associated with it all other instances that share this particular pattern/structure.

4. The protoglyphs can combine in ways to create 'compound protoglyphs' or compound patterns.

The Alphabet vs. the Goddess

In 'The Alphabet vs. the Goddess', Leonard Shlain (1999) proposes that the process of learning alphabetic literacy rewired the human brain, with profound consequences for culture. Making remarkable connections across a wide range of subjects including brain function, anthropology, history, and religion, Shlain argues that literacy reinforced the brain's linear, abstract, predominantly masculine left hemisphere at the expense of the holistic, iconic feminine right one. This shift upset the balance between men and women initiating the disappearance of goddesses, the abhorrence of images, and, in literacy's early stages, the decline of women's political status. Patriarchy and misogyny followed.

Shlain contrasts the feminine right-brained oral teachings of Socrates, Buddha, and Jesus with the masculine creeds that evolved when their spoken words were committed to writing. The first book written in an alphabet was the Old Testament and its most important passage was the Ten Commandments. The first two reject any goddess influence and ban any form of representative art.

(http://www.johnniemoore.com/blog/archives/001619.php)

Oldest Celtic Symbol - Phosphene Composite

This ancient Celtic Design is taken from the Celtic Burial Mound at New Grange in Co. Meath. This design pre-dates the arrival of Christianity in Ireland by some 3,000 years. It is thought to be the oldest Celtic symbol and is supposed to represent the 3 stages of man: Birth, Death, Eternity. (www.bodhran.com/designs.html)

Notice how this pattern is a phosphene composite, made from three identical phosphene images.

Phosphene Motifs in Paleoart

In the search for 'deep patterns' or patterns that may be hardwired in the brain, I've come across the concept of 'phosphenes' (Robert G. Bednarik). Phosphenes are created through electrical stimulation, pressure on the eyeball, a blow to the head or certain hallucinogens.

Phosphene forms are the fifteen known standard form constants of phosphenes -- and most of these are found in the earliest engravings and petroglyphs.

There are concentric circles, oblong eye shapes, parallel horizontal and vertical lines, adjacent wavy lines, spirals, grids, dot patterns in a grid/matrix arrangement, screens or meshes, radiating star shapes, stars enclosed within a circled, irregular closed shapes, the shape of a hand and a burst shape like a spray of grass.

Remarkable!

Here are some interesting quotes from research papers:

"There is a good reason why our visual system finds repeated marks such as parallel lines, geometric shapes and certain patterns appealing. It is because they resonate with patterns already integral to the visual cortex, they are related to the way its neurons process visual input. Artistic 'primitive' motifs are of interest to us not because they reflect the properties of the external world, but because they stimulate properties of the visual system."Bednarik (1984)
"It is thought that features are detected by cortical cells forming the bottom layer of a hierarchy of cells that respond progressively to increasingly abstract geometric features" (Barlow 1972).

Hodgson deduces that cells in higher layers could respond to simple geometric patterns (Livingstone and Hubel 1995).

The main references for the above quotes are from research papers by Robert G. Bednarick and Derek Hodgson about Phosphene Theory (Bednarik 1984, 1987, 1990; Hodgson 2000).

While this may be presumptive, I think it would be a good idea -- if one were to be developing a machine that simulates the workings of the neocortex -- to prime this machine with some phosphene motifs, rather than making it learn everything from scratch.

Protoglyphs - Patterns in the Mind

I have an idea. An educated guess. A partial theory that is beginning to take shape. I started thinking about this in the early 1990s, kept thinking about it while completing my MSc in Cognitive Science and finally, nearly 10 years later, I'm still thinking about it. I can't stop thinking about cognition.

As I learned more about Cognitive Science, I became very determined to discover what was known and what wasn't yet known about the mind and how we think. There were still some very big mysteries to solve. And many, many questions to be asked to properly explain the workings of the human mind. I was truly shocked to discover there wasn't even a unified definition of a concept, let alone an agreed-upon theory of how the entire mind actually worked. Perception seemed fairly well understood; how we get information from the world around us into our minds. But then what happens? How is that information encoded in our minds? There are many theories. And after the information is encoded, how is it remembered? Again, there are many theories for this. And what about the ability to be creative? How did this happen cognitively?

Cognitive Science seems largely divided into two main camps (or attitudes) that represent two quite different approaches. A student in cognitive science had to make a critical decision. Was your research orientation going to be 'hard' or 'fuzzy'? Was it 'top-down' or 'bottom-up'? The top-down approach encompassed artificial intelligence and rule-based systems. It was about developing an overriding structure, or framework, and organizing data within this framework. This approach had worked remarkably well to store and retrieve data (and is now used in contemporary computer operating systems), but it certainly isn't flexible enough to represent the way the mind actually works. The other approach - bottom-up - encompasses neural networks. This approach has some intrinsic advantages, because it starts out simple and evolves into higher levels of complexity through adaptive learning. This dynamic is very similar to real human learning. The somewhat perplexing disadvantage of this approach is its inability to evolve a syntax of any kind. At what point does structure appear? How does a framework evolve? How are rules determined?

A simple way to think about these two approaches is to imagine a solid cookie cutter and a piece of rising dough. The top-down approach is to take the cookie cutter and press it into the dough. Any dough outside the cookie cutter is simply not included. If the dough wants to rise beyond the boundary or top of the cookie cutter, it can't. The bottom-up approach is to watch the dough rise up to (somehow) assume the shape of the cookie cutter, before it even reaches the cookie cutter. How does the dough know to self-organize itself into the cookie cutter shape? Quite simply, it doesn’t. It's needs some guidance. It needs some foresight or some preliminary instruction.

There are problems with both of these approaches. The top-down approach superimposes a structure. It does not adapt to information that was not originally anticipated in the initial design. It doesn't learn. The bottom-up approach tries to evolve a structure. The bottom-up approach has a problem emerging some type of overriding framework, structure or form, within which to contain itself. A superimposed structure is too rigid. And a self-evolving structure is so chaotic as to be practically non-existent. It doesn’t have any rules. The truth must lie somewhere in between.

I started to wonder if something was happening in between these two approaches. Some middle process. Some transitional layer that could tie these two approaches together. There had to be some form of cognitive representation that was missing, that people just weren’t thinking about, even though clues about the existence of this mysterious area seemed to be everywhere, in different forms, in many different disciplines.

I started looking for clues. And in a very gradual, roundabout fashion, the clues began to point to an area that may answer many questions, and perhaps begin to unify the many micro-theories about cognition.

This is my idea. I think there is an area of knowledge representation in cognition that I have named 'protoglyphic'. Proto: ‘indicating the first or earliest or original’. Glyph: ‘a symbol, icon, pictograph, etc. that is used as a graphic representation’. I think the mind may have a set of protoglyphs that it uses at the very roots of cognition. These protoglyphs may be encoded at the very deepest level in the mind, just above the level of the neurons. Protoglyphs may be patterns that act as a categories and subcategories to give ‘structure’ or shape to information. Protoglyphs are not visual patterns, necessarily, but are better thought of as SPATIAL form patterns. Information is mapped onto these patterns. Protoglyphs act as the encoded structure for information. These patterns can be represented as a visual pattern, or a physical structure, or a temporal structure. There is a linear quality to protoglyphs. They are perceived over time in a linear fashion. Whether through visual sampling, tactile sampling, or auditory sampling, the perceived samples are ‘pieced together’ into a larger pattern. Protoglypic patterns are spatial. They are created by linear data sampling, and then superimposing (sharp and fuzzy) data samples together to form a pattern. This re-creation of the sampled bits relies on memory.

What are protoglyphs like?

I think protoglyphs are partly fuzzy, partly solid; like outline drawings of very basic patterns such as a spiral, a matrix (grid) or an arrangement of descending or ascending horizontal or vertical bars (some people theorize that these types of primary patterns are hard-wired in the brain), or protoglyphs can be made of more complex pattern fields, such as hexagonal shapes that are interlocking, or triangular shapes (Similar to the images seen in quilts!!). I think protoglyphic patterns are the fundamental underpinnings of cognition. These patterns are the structure onto which we map our knowledge categories. And oddly enough, I think the highest level mathematics echoes these low level patterns. As above, so below. Strangely enough, a mind must advance to a certain level of development, must acquire the ability to abstract, before it can ‘look back’ on itself, to examine its own patterns. By externalizing mathematical formulas, and applying them to other things in our world, we are essentially applying our own mental patterns that are originally derived from nature, back onto nature. Our mind makes an internal blueprint (from its observations and experiences with nature), abstracts the blueprint (in terms of principles and formulas), and then applies that blueprint back onto the external world to produce artifacts. Truly a strange process indeed, to be human.

My personal protoglyphs are like wireframe images. They’re just lines that represent a pattern. They can move in space, or be static. They’re like a set of templates and I map information onto them. Most people think the only way to organize information is using a tree structure, a DAG (directed acyclic graph). But some information, especially if it is associatively or temporally organized, does not easily map onto a tree structure. A tree structure cannot show simultaneity very well (or things happening in parallel) ??.

Some protoglyphs may be hard-wired, and some may be individually crafted. There is evidence to support both types. Some visual patterns seem common to all people. Others are entirely unique. For example, a concept of time. Some people think of time as a line. Some think of it as a shifting window, or moving interval. I think of time as a spiral, where each ‘loop’ is one year and the months map around the loop with January to the east and June to the west. My spiral starts at the bottom, with a small loop and gets larger every year as it moves upwards. I've spoken to other people who also represent time as a spiral, but theirs begins at the top and moves downward. Some people might call this a mental model of time. And it is. The protoglyph is the spiral pattern shape that is independent of any information mapping.

So what’s the difference between a ‘mental model’ and a protoglyph, you ask? Ah! Protoglyphs may be smaller components of mental models. Protoglyphs may act as a sort of alphabet for mental models. And mental models may act as the syntax for protoglyphs. Or, the protoglyph may be the actual pattern itself, independent of any information. It is a prototypical graphical pattern structure onto which information is mapped.

The reason I think protoglyphs exist is based on my research into the two primary ways we represent cognitive information. The most common way is known as top-down knowledge representation. It is hierarchical and rule-based. This is how computer software is designed. The rules are designed from the top-down. Nested hierarchies of rules that call each others’ functions. The second most common way to represent knowledge is known as bottom-up. Fuzzy and incomplete knowledge is cycled through a neural network until a prototype or ‘best instance’ can be formed. This form is predominately associative (relational) and based on fuzzy data clusters that produce category prototypes.

There are clues as to why something like the Protoglyphic Layer must exist in cognitive representation. Whether the protoglyphs are a layer in cognition, or a relay switch between two different systems, I don’t know right now. If you look at the circumstantial evidence, the clues I’ve included below, maybe you too will conclude what I’ve concluded. There is an area in cognition, the protoglyphic layer, that we need to investigate and research, if we are ever to truly understand the way in which our minds really work.

Clue No. 1 - Human learning is concrete, then abstract
We know that humans first learn associatively, and then evolve their learning to more rational forms that enable abstraction and complex symbol manipulation. And we know that this process takes about 12 years. There is a learning continuum in cognition that we all experience from a concrete one-to-one literal mapping/correlation with real world objects, to the ability to later abstract internally. We go from outside, to inside. It takes a while for our internal ‘world’ to develop. It is not fully developed until we are 11 or 12. And then it’s as if we quite literally do have our own personal world mapped out inside our head.

Clue No. 2 - A visual aspect to cognition
Scientists and thinkers the world over have indicated there is some visual aspect of thinking, some internal manipulation of ‘hidden forms or references’ where connections are made and rearranged at some deep level. There’s the famous discovery of the Benzene ring, the snake biting its tail dream. Einstein said there was a visual aspect to his thinking. Visual metaphors somehow imply that there is a deep level that represents knowledge, that can be accessed through visualization, dreams, somehow associating two seemingly un-related things. A deep-level visual structure explains how a person can think of a sunset and it is evocative of a song, or a poem, or even a mathematical formula that describes a physical descent, all as items that possess a similar structure.

Clue No. 3 - Underlying similarities in Art, Music, and Math
Common structures and patterns underpin all knowledge disciplines. Its as if the ‘bedrock’ is the same, at the deepest level, for all disciplines, for all forms of human knowledge. This implies that there is a common form of representation at some deep level in the human mind.

Clue No. 4 - Limitations of traditional software
Traditional software does not properly model the workings of human thought. It is not creative, adaptive or predictive.This implies that a hierarchical top-down approach is not the whole story of cognition. Neural network software is good for image/pattern recognition, but it offers no method to represent relationships between objects.

Clue No. 5 The artifacts of art, crafts and technology
The products produced by women and men seem to reflect predominantly different thinking styles. (Perhaps the focus here should be more on the different thinking styles and less on the genders that embody these styles.) As with most things, both genders exemplify both styles of thinking in varying degrees, both the logical and the creative. This has been proven in research, behavioural and physiological. It is perhaps best shown by the artifacts produced by the different genders. An interesting thing to note is that whenever there is a technological boom where the men are making profound advances in science and technology, there is a similar boom in the arts and crafts of women. You might think this is a backlash effect, but I think it is something else. I think classic, fundamental protoglyphic patterns have been recurrent throughout the history of peoplekind, predominantly in the arts of women. I think the artifacts of mena and women are parallel activities, offering expressions through different modes.

Clue No. 6 - Fractals in nature
What we know about fractals is that a simple formula that is reproduced can create a beautiful form that is identical at different resolutions or scales. Ferns, shells, trees, branches, flowers, mountains, clouds; forms in nature seem to be based on the repetition of a single, relatively simple mathematical formula.

Clue No. 7 - Nature does not have straight lines
Nature does not have straight lines. But mathematics (the notation of humans to quantify their world) does. A line is an ‘average’. It does not exist anywhere in nature. This is because a purely straight line cannot emerge, cannot grow in a world that is interconnected and constantly changing and subjected to cycles and seasons. Imagine a plant growing in the ground. Each day it is subjected to fluctuations in temperature, sunlight, rainfall, wind, the random meanderings of insects and animal, some predators, some egg-layers. And all the while it is attempting to grow upwards. Its growth cannot be straight, as it adapts to all of these outside influences. You will never, ever see a straight plant! Or tree, or river. Look around you. Nothing in nature is straight. (Note: I attribute this interesting point to my uncle Dr. Stephen Vonder Haar, a hydrogeologist in Berkeley, CA) If you think about this a bit more, you’ll realize that it’s rather odd that people come from a natural environment that is not straight, is not geometric, but we build geometric things. Where is this geometrical ordering coming from? Is it our mind’s unique way to efficiently record and organize information? I think it is. I think the Platonic view of the world is not something that exists ‘out there’ for us to discover. I think it is an efficient system our mind has evolved to make sense of fuzzy data out there in the natural, moving world.

Clue No. 8 - The Laws of Thermodynamics and Minimal Lexical Attachment.
All systems tend to disorder. All systems tend to lose energy. The natural state of a system with a high state of order (or energy) is to become disordered and disorganized. This dovetails nicely with the interworkings of nature. I think this is more an attribute of nature trying to establish equilibrium amongst. In cognition, there is a theory in language called Minimal Lexical Attachment. Given two ambiguous paths in a sentence structure, this theory describes how the mind will always recall the path that costs the least amount of energy to ‘traverse’. The best example is when a sentence has an ambiguous structure, when it can be grouped in two different ways with two different prepositional phrases. The mind will choose the shortest path as the most obvious way to interpret the sentence. The important point here is that the organization of knowledge within the mind is done with efficiency in mind. Nature, by nature, is not wasteful with energy. And neither are our minds. Our minds organize information in a way that is efficient and straightforward.

Clue No 9 - Modality independence
While vision is our dominant modality for getting information from our environment, we also have auditory and tactile information (along with olfactory, of course). Note here: how the deaf use sign language to create ‘forms’ in space that convey information. If you were to photograph the ‘trails’ of the hands over time through space during deaf signing, they create a 3-dimensional shape. A protoglyph is not a visual pattern, necessarily, although if one is pre-dominantly visual, it will manifest itself as a visual pattern. If one is blind, it may manifest as an auditory, tactile or olfactory pattern. Other clues here are in synaesthesia (The Man who tasted shapes)

Clue No 10 - Autism
Autism and Temple Grandin. Her explanation of the strengths and weaknesses of being autistic. The video player in her head. The primitive emotions. Visual thinking. A bottom-up approach. How she forms prototypes and categories.

Clue No 11 - We're pattern makers.
We’re not just pattern recognizers. We’re also prolific pattern makers. I think this ability may be attributed to the fact that we are pattern encoders – spatial pattern encoders. Because we have protoglyphic patterns encoded in our minds, we can produce and reproduce patterns. A pattern is a module that is repeated. Repetition is an action that occurs over time. Patterns are a function of time. We are pattern-makers.

Clue No. 12

Humor is an indication of the way the brain may represent patterns. Normally we go along the main track and suddenly the punch-line makes sense and we’re taken to the sidetrack and in hindsight it’s perfectly logical. The essence of humour is you’re taken to a different position and from that position looking backwards, it’s perfectly logical.

(Sharon Mascall/Susan Mackie – Are we hardwired for creativity? DeBono Institute)

Clue No. 13

Mental Models (from Wikipedia)

A mental model is an explanation in someone's thought process for how something works in the real world. It is a kind of internal symbol or representation of external reality, hypothesised to play a major part in cognition. The idea is believed to have been originated by Kenneth Craik in his 1943 book The Nature of Explanation. After the early death of Craik in a bicycle accident, the idea was not elaborated on until much later. Two books, both titled Mental Models, appeared in 1983 [1]. One was by Philip Johnson-Laird, a psychology professor at Princeton University. The other was a collection of articles edited by Dedre Gentner and Albert Stevens. See Mental Models (Gentner-Stevens book). Since then there has been much discussion and use of the idea in human computer interaction and usability by people such as Donald Norman and by Steve Krug in his book Don't Make Me Think. Walter Kintsch and Teun A. van Dijk, using the term situation model (in their book Strategies of Discourse Comprehension, 1983), showed the relevance of mental models for the production and comprehension of discourse. These are just a couple of examples among many, many others.

Clue No. 14

The work of artists...like Paul Klee. Why do his paintings in the Guggenheim museum that are celebrated as masterpieces look like handmade quilts made by women? Klee was searching to represent ‘the reality behind visible things’. So why then does so much of his work look like the arts and crafts of women throughout history?The rugs, patchwork quilts, paintings made by the Australian aboriginals?

Patterns and Symmetry

Patterns are intrinsically symmetrical.

Ian Stewart has said that symmetry is the key to nature and cognition. If this is true, then there's some type of clue here (about what yet, I'm not exactly sure). If we search for symmetry, for balance, and we gravitate toward or look for repetition or sameness, (as one of the primary principles of Gestalt Perception), this offers us a sense of certainty. It enables us to predict 'what comes next'. Any irregularities we find in a pattern requires us to make adjustments in our understanding of the pattern field. We identify, adapt and learn. Humans are highly sensitized to irregularities. We notice 'what's different' far more easily and quickly than we can match up what is the same. We strive for sameness, continuity and closure (Gestalt Principles of Perception). This gives us certainty in 'knowing' about our world. Differences are disruptive and require adaptation and change. And this costs energy. Cognitive energy.

Musings on Pattern Maps

A pattern can offer instructions. It can act as a 'map' for thinking and behaviour, if a person, or a quasi-intelligent 'thing' can 'see' or receive the information of the pattern in an intelligible way.

What if our brains record pattern maps in their neuronal trees (exactly how a brain does this biochemically, we we don't need to worry about right at the moment) and then these pattern maps act as guides for cognition and behaviour?

Are there pattern maps in cognition? And what might they 'look' like?

The reason I started thinking about this is because we know that the mind records information similar to the way a neural network records patterns. But it's not known exactly how this information is recalled or "re-membered". Some memory specialists theorize that each time we remember something, it is slightly different, because human memory is thought to be an active process of re-membering or re-associating, and that it is context-sensitive. Each time a brain remembers something, it's in a different predisposition, or state. What if a memory is stored -- fundamentally -- as a pattern image. A pattern is a very efficient way to store information.

I started to wonder what it would be like if a pattern map was used to give something or someone instructions. How would this work? Maps are good for instructions in a spatial context. And we live and move through space, right?

Someone can look at a map (after knowing their own orientation – eg. 'You are HERE') and follow it to move to another place, in another space – using n-s-e-w coordinate orientation. Go up 2 and left 1 . Go up 4 and right 6. This movement can be represented as a directional path and can be drawn as a picture.

When people were first trying to give robots instructions, they'd write out the directions (in code the robot could understand) and the robot would follow it. But the instructions were fixed, linear in structure and lengthy. If a robot had an image that it could refer to and follow, how would this be different than what we already have? Would this be an improvement? What if computers and/or robots could follow maps without step-by-step instructions? What if they could traverse an image for instructions? How might this change things?

The first step is to have devices that can learn images and recall them accurately. (See Numenta www.numenta.com) The next step is to provide visual maps to these devices so that they can do things in various situations-- and yet learn in such a way as to adapt their 'understanding' of a space and self-modify their maps. For example, if a robot were given a map of a room to clean (and had a movement algorithm to traverse the space), it would first actively explore to verify the physical space matched the virtual map. Then it would do its cleaning job. If a new piece of furniture was put into the room, it would adapt its movements as needed. It could learn. If an object was in the room that wasn't there before, it would be discovered, and the robot would navigate around it and make a note in its room map.

I know there are small robotic vaccuum cleaners that many people have in their homes right now. But I think their behaviour is fairly localized. They interact with whatever is directly in front of them. I don't think these little robot vaccuums can reproduce a map of the room they've just cleaned. But I may find soon enough that they can.

Pattern Makers by Kim Vonder Haar

I've always been fascinated by patterns.

So, this is the beginning of a research project about patterns, and perhaps eventually, a book.

Questions I hope the book will answer:

1. How have patterns evolved throughout human history? Have they evolved alongside cognitive development? When have we seen surges or lulls in patternmaking throughout history?

2. Why do we make patterned objects? Are we attempting to replicate natural structures? To recreate what we see in nature? What is our motivation? What do patterns represent to a person?

3. What are the simplest patterns and why do we make them more complex? Show examples of simple and complex patterns. What about evolutionary or transformational patterns? Morphing patterns?

4. What does a study of patterns tell us about our cognitive and creative processes? What clues does this study give us about how we perceive and think about or process our worlds? Is there a grammar for patterns? A syntax? A structure of rules? Is pattern-making unique to humans? (No...beehives) So, how does pattern-making differ in humans when compared to insects/animals/plants/geological formations?

5. What might a pattern grammar tell us about the creative process? The arts? How is pattern-making different in the arts when compared to the sciences?

6. How is a pattern defined? Is pattern-making gender-biased? How do patterns made by women compare to those made by men?

7. Is there a spiritual component to pattern-making?

Notes:
People like to make things. Pattern-making is an active process of deliberate creation.
Patterns as Context, Environments, Domains, Frameworks. Patterns as the underlying framework for metaphors. Similar pattern domains give rise to a proliferation of multi-modal metaphors in art, science, poetry.

People as Pattern Makers

There's something about patterns, the making of patterns, that offers clues about how we think.