The Matrix of Genius:
Cognitive Neurophysics and the Development of Extraordinary Human Intelligence
Part IV and V

by Mark Evan Furman

Transmission and Recursion

We now arrive at the two final processes involved in the development of extraordinary human intelligence—genius. The first is a pattern behavior referred to as transmission, which we have alluded to before. The second, recursion, is an emergent property of all five of the pattern behaviors—incorporation, replication, cleaving, recombination and transmission, acting in concert.

Transmission is simply the isomorphic “displacement” or “propagation” of a pattern–integrity (information) through coordinate–space or different encoding mediums separated by a boundary, where information is preserved or conserved. Transmission is the way in which information “travels” or gets “exchanged” through and between mediums such as cells, organisms, water, atmosphere, etc. This displacement or propagation of a pattern–integrity (transmission) can occur in many different ways and is responsible for the enormous flexibility and variation found in the world of pattern. Without it, the diversity and beauty of nature as we know it would vanish. We will mention just some of the major ways in which this displacement can occur and then describe each in a little more detail.

Transmission can occur by solition wave (translation), rotation, involution, exvolution, vibration, expansion, contraction (in time or space, symmetrically or asymmetrically), diffraction, refraction, three–dimensional to two–dimensional, inversion, mirror image, retrogradation, inside–outing, enfoldment, and unfoldment. In each case of displacement of the pattern–integrity, information is preserved—simply shunted in space or time isomorphically. Let’s explicate each of these types of pattern transmission and highlight their relevance to the development of mind, brain, and genius.

Transmission by Solition Wave (Translation)

When transmission occurs by solition wave, also known as translation, the pattern–integrity is simply displaced in coordinate space or through and between encoding mediums in more or less a linear trajectory. This type of transmission can be readily observed when watching a wave travel along the surface of the ocean towards the shore. As alluded to earlier, the water molecules themselves do not actually travel with the wave, only the disturbance (the pattern–integrity) actually travels.

We can also see transmission by solition or translation when we look into the sky on a partly cloudy day. If you allow your eyes to follow a particular puffy cloud as it travels across the sky, the pattern (the cloud) simply changes in position from moment to moment, following what appears from the ground to be a linear trajectory. Of course from the perspective of space, we can look back at the earth and see that the cloud actually has angular, not linear, acceleration.

Messenger molecules within our body can also be seen traveling about from place to place by translation. This can be seen in the behavior of neurotransmitters as they jump from synapse to synapse between nerve cells. It can also be seen in the behavior of neuroendocrine molecules such as hormones as they travel to their target cell through the bloodstream. Transmission by solition or translation can also be seen occurring within brain and mind on a larger scale. This happens when we incorporate a particular image, such as the face of a loved one, and then close our eyes and move that image throughout our visual field from left to right, or top to bottom, without changing the image (the pattern–integrity).

Translational displacement is also a common element found in the music compositions of many great composers such as Beethoven, Mozart, and Bach. Quite often while reading a particular score, you will notice a pattern of notes that is simply displaced upwards or downwards on the staff without the relationship of each note to each other note ever changing. The key that the pattern is played in changes while the melody (the pattern–integrity) remains the same.

Transmission by Rotation

Another type of transmission is transmission by rotation. This can be found ubiquitously at all levels of nature, big and small. The pattern–integrity called planet earth is one among an untold number of planets in our universe which spin on their axis, and return to the same position periodically. As a pattern-integrity rotates in coordinate–space, it appears to change only from a particular perspective; but, in fact, as it rotates, all information is preserved. Of course, planets don’t simply rotate. The motions of planets are products of collections of many different transmission types operating in concert. As the planet earth rotates, it also revolves around the sun, tracing an angular trajectory around it. So, as it rotates, it can never really come back to the exact same place in coordinate–space.
In the world of the very small, electrons are believed to travel around their atomic nuclei by the same translational and rotational displacements in coordinate–space. And, in the world of the colossal, entire galaxies travel translationally while the individual stars that make them up travel rotationally as well as translationally in an angular acceleration forming enormous spirals of light in the evening sky. Within the human mind and brain, rotational transmission is essential for many high and low level cognitive tasks. Sometimes we see someone in a crowd we think that we might know, but we see them from an unfamiliar angle. In order to confirm our assumption, we take that incorporated image and mentally rotate it in the coordinate–space of working memory until we can make a positive identification of the face. Once we do, we feel confident in approaching that person and tapping them on the shoulder to say “hi.”

Many questions on IQ tests are designed to confirm whether or not the test taker has this cognitive ability. The most common form is a set of approximately six connected blocks drawn three–dimensionally. The test taker is given the reference pattern and then asked to match it against four or five other patterns which have been displaced rotationally. If the test taker matches the reference pattern with the correct pattern, he or she is considered intelligent. Yet, when broken down in terms of pattern behavior, the question simply determines whether or not the test taker has had prior practice in the process of rotating a pattern–integrity. You can test for whether or not you currently have this capability by starting very simply. Imagine a plate with a familiar design and on top of this plate a bright red apple. Rotate the plate clockwise in your mind while at the same time rotating the apple toward you end over end. Many people cannot do this. Yet, you can train the brain to perform this process simply by doing the process physically with real objects and letting your visual system incorporate not only the content (the apple in the plate) but also the process (the clockwise and the simultaneous end–over–end rotation). Both translational and rotational displacement of mental images (pattern–integrities) were essential to the thought experiments that led to the development of Einstein’s theory of relativity.

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Transmission by Involusion and Exvolusion

Transmission by involusion or exvolusion are similar to transmission by rotation. This can be easily imagined by visualizing a doughnut. If a doughnut was symmetrically rotating toward its own hole, such that the part of it that was outside is now inside, and the part that was originally inside is now outside, we call this involusion. If the process of transmission occurs the opposite way, such as if we were to run a film of what just happened backwards, we would call this exvolusion. In a sense, there are several types of transmission occurring simultaneously in this example. There is rotation of a pattern, as well as retrogradation of the same pattern, during instances where there is a switch from involusion to exvolusion. This particular pair of pattern transmissions happens to be one way in which we can create an “inside–outing” of a pattern, which we will discuss a little later. One structure which has the capacity to involute and exvolute is called a Taurus, a pattern which occurs often in the modeling of non–linear dynamic system.

As in all other pattern behaviors, involusion and exvolusion appear to be ubiquitous in the universe. This behavior can be found in many lower level single cellular organisms that ingest their food by the process of engulfment. Black holes in space also exhibit what might be thought of as involusion of the matter and energy that come too close to its event horizon. And of course, there are those select children throughout the ages who to their parents chagrin persist in turning their eyelids inside–out to entertain their friends and siblings.

Transmission by Expansion, Contraction, and Vibration

Transmission by expansion and contraction are much more fundamental types of pattern behavior than those such as involusion and exvolusion. And, again, such behaviors of expansion and contraction can be found ubiquitously throughout the living and nonliving world. We can see both expansion and contraction occurring in the subatomic world in the behaviors of atoms. When atoms are excited by the absorption (incorporation) of photons, their electrons move from their ground state within the inner shells of the atom to their excited state where their electrons can be found orbiting the nucleus for a trice in their outer shells. This can be considered a transformation by expansion of the pattern where information (the structure of the atom) is preserved. As these electrons emit (transmit) the photons that they have previously absorbed (incorporated), they immediately return to their ground state—orbiting again within their inner shells. This can be considered a contraction of the pattern–integrity called “atom.” When expansion and contraction occur in close succession, we refer to this as vibration.

Vibration can also be seen on a slightly larger scale when atoms temporarily join together by sharing electrons. This coupling between two or more atoms is a loose one involving enough play where, together as a single pattern–integrity, the atoms can expand slightly away from each other and subsequently contract toward each other periodically as they also rotate around a common axis. A behavior quite similar to this can be seen when looking up at the heavens. On a scale many magnitudes of order larger than the last example, pulsars vibrate and revolve with such regular pattern that we can almost use them as clocks. A pulsar can be formed out of two neutron stars or “white dwarfs” as they enter each other’s field of gravitational influence. When this happens, the two stars interact precessionally (at other than 180 degree angles), expanding and contracting their orbits around a common axis.

We can also see expansion and contraction of pattern–integrities throughout all parts of the biological world. As a young child hops down a flight of stairs on the balls of his feet, the closely packed molecules of liquid and gas that make up his multifarious tissues contract upon impact and then expand upon release, creating a vibration that is transmitted throughout his entire body to such an extent that if he does it hard enough, or continues it long enough, he will end up with a headache.
Pattern–integrities can not only expand in the dimension of space but also in time. Musical forms such as fugues and cannons employ this type of pattern transformation, yielding enormous variation that results in the listener’s unending pleasure. This type of musical form was created by taking a small pattern of notes (a melody) and expanding them in time by playing them twice as slow in a different instrument voice than the first pattern is played. At the same time, another voice is assigned to play the same melody (pattern–integrity) contracted in time. In this case, it would be played twice as fast as the original melody. The type of auditory complexity that results is called recursion. Recursion is a nesting of self–similar patterns which we will be discussing shortly. It is interesting to note that in a case of music–making, the pattern–integrity which expands and contracts does so in many modalities. Auditorily, we can hear the expansion and contraction of the melody, which gives us listening pleasure. Visually, as we inspect the score, we can see the expansion and contraction of a pattern–integrity as it imbues the paper it is written on with a phantasmagoria of visual textures. At the same time, as a listener, we can feel the expansion and contraction of the pattern–integrity through the quickening and slowing of our heartbeat and respiration as it is phase-locked in forced resonance with the vibrations of the music. And finally, the performers can also feel the expansion and contraction of the pattern–integrity through their tactile and proprioceptive sensory pathways as their fingers perform the written score.

Normal organismic growth is also a good example of transmission by expansion. As the heart, lungs, and other vital organs of a human being grow in size; information (the pattern–integrity), and thus proper function, is preserved or conserved.

Another example of expansion and contraction of a pattern–integrity can be found in the boiling of a cup of water in a pot. As we boil the cup of water, the resulting kinetic motion will make the pattern–integrity called “water” expand in space. It will first become steam and form a large cloud above the pot, then it will continue to expand, becoming a diffuse water vapor that fills the room as it seems to disappear. Contraction occurs when steam condenses and becomes water.

The ability to expand and contract pattern–integrities that were originally incorporated into our mind and brain is vital for problem–solving, decision–making, creativity, and the development of extraordinary intelligence. For example, it was common dogma for nearly 2,000 years since the inception of Euclidian geometry that the sum of all angles of a triangle invariably equal 180 degrees in all cases. Albeit a modicum of experimental evidence, this was somewhat of an a priori conclusion. Numerous theorists throughout the years questioned this dogma when new evidence was found suggesting that the earth was round, not flat as originally assumed. It was a priori theorized that a triangle, expanded enough so that it was drawn over a significantly large spherical surface of the earth, would clearly exhibit a sum of angles far in excess of 180 degrees. The increase in the sum of the angles would vary in direct proportion to the curvature of the earth that the triangle was drawn upon. This critical discovery spearheaded a paradigm shift in science that shook the very foundations upon which society had been built. The implications of this discovery have only begun to unfold themselves in the practice of present day science and technology. Had the human mind not had the fundamental ability to expand the pattern–integrity, this discovery would never have been made.

Expansion and contraction come in many different forms. As we have just seen, expansion and contraction of pattern–integrities can occur in both space and time. They can also occur both symmetrically and asymmetrically.

Transmission by Diffraction and Refraction

Transmission by diffraction and refraction bear many similarities to the pattern behaviors previously discussed. Diffraction is a change in direction and intensities of a group of waves after passing by an obstacle or through an aperture. Most young children have seen this phenomenon demonstrated by nature when rushing water in a stream attempts to pass between two large rocks positioned very close to one another. Diffraction and refraction are very closely related phenomena recursively built up from more fundamental pattern behaviors. As we take the pattern–integrity called a light wave, or white light, and we direct it through a prism, diffraction and refraction cause the white light to cleave into several discrete waves of different wave–length revealing all the colors of the visible electro–magnetic spectrum. For those readers who have never seen this demonstrated in a school classroom, fear not. The next time you look up into the sky and see a beautiful rainbow, you can rest assured you have seen the combined behavior of diffraction and refraction at work.

Refraction is the spreading, slowing, bending of a wave due to passage from one medium to another. In both diffraction and refraction, we can witness a bending of a pattern–integrity called a wave. This is referred to as a change in direction which tends to also result in a spreading or expansion of a pattern as is seen when white light is passed from air through a prism, producing a spectrum. The same phenomenon can also be seen occurring in sound waves, as well as waves in other mediums such as water. The slowing of a wave during refraction, means that the wave or pattern–integrity has changed velocity (light travels at different velocities through different mediums such as air, water, and glass). This slowing can simply be understood as an expansion of a pattern–integrity in “time.” As you can see, diffraction and refraction are complex pattern behaviors which are assembled from simpler ones on one level and result in both simpler and more complex pattern behaviors on other levels. The ability to represent such patterns as these in mind was critical in the development of Einstein’s theory of special relativity, as well as his theory of general relativity. The mental representation of these pattern behaviors are also critical for engineers involved in acoustics technology. This is the type f technology that might be employed to make sure that every listener in a concert hall has an equally pleasurable experience no matter where they are sitting. The engineering genius, R. Buckminster Fuller, employed the mental representation of this, as well as many other pattern behaviors, in order to develop the theory of synergetics which has become indispensable knowledge in the field of engineering.

Transmission between Dimensions

Transmission of a pattern–integrity can also occur between dimensions such as the second and third dimensions of space. A simple example of this comes from our ability to recognize a close friend or relative from a photograph. If you look at a 3x5 photograph, and have this feeling of instantaneous recognition, it is really quite a remarkable achievement since the pattern–integrity you call “your friend” has not only been significantly contracted in space, but has also been transmitted from three dimensions to two dimensions, while at the same time conserving enough information for you to recognize this new transformation as “your friend.”

A much more complex example of dimensional transmission is employed by nature in the opposite direction (from 2D to 3D) during the manufacturing of proteins from DNA. Both DNA and the primary structure of a protein (a string of articulated amino acids) can be thought of as structures having only one or two dimensions (depending how small a measurement you use). As a protein folds itself, this two dimensional string of articulated amino acids rapidly becomes a three dimensional molecular machine able to perform complex tasks throughout living organisms. This three dimensional folding pattern is said to be the protein’s tertiary structure.

With practice, human minds and brains can also be taught to transmit information isomorphically between the second and third dimensions. In the human brain, the cerebral hemisphere is divided into two parts that we refer to as the left and right hemispheres. The visual pathways in the right hemisphere of right–handed people are equipped with special cells which are able to represent previously incorporated images in 3D. These visual pathways are referred to as magnocellular pathways (Davidson and Hugdahl, 1995; Gazzaniga, 1995; Kandel, et al., 1991). To use these pathways for image representation, a normally organized right–handed person would move the image to their left visual field in working memory (Furman, Nov. 1996; Dec. 1996). This is considered a transmission by solition or translation. The visual pathways in the left hemisphere have a greater preponderance of parvocellular representation medium. Unlike magnocellular pathways, which are made up of large, overlapping cells, parvocellular pathways are made up of relatively smaller, non–overlapping cells. This cellular matrix does not allow for the representation of visual information in three dimensions. Instead, we see the same image represented in two dimensions. You can experiment with this by visualizing a familiar room in your home, including all its contents, using your left visual field. Then simply slide the image over to your right visual field, and you will notice it will become flat. Thus, the transmission of visual information from magnocellular to parvocellular pathways allows a pattern–integrity to be represented variously in three dimensions or two dimensions. Another interesting fact about parvocellular pathways is that, since they form a non–overlapping, cellular matrix, a visual image held in working memory in the right visual field can much more easily be cleaved into parts and the recombined in new ways (Furman, Nov. 1996; Dec. 1996; Jan. 1997), allowing for greater creativity and problem–solving skills.

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Transmission by Inversion and Retrogradation

Transmission by inversion and retrogradation are closely related pattern behaviors found ubiquitously in mind and nature. A simple form of inversion can be visualized if we go back to our example of the photograph of your friend. In addition to contracting your friend and transmitting him or her from three dimensions to two, you can also invert the pattern–integrity simply by turning the photograph upside down. This is the simplest form of inversion. Notice that you can still recognize your friend and pick his or her photograph out of a collection of many others with relatively little difficulty.

Many speed–reading courses make use of inversion by having participants turn their reading materials upside down and asking them to read them. This helps them gain the mental flexibility to learn how to process the same code in very different ways. It is interesting to note that the images contained on this page which you are currently reading are automatically inverted as they pass through the convex side of your ocular lenses, and are subsequently represented by your retinal sheet upside–down. Through many stages of processing, these images are finally seen by you in their original orientation.

A more complicated form of inversion is employed in music when a composer takes a core pattern–integrity (a melody) and inverts it by making the high notes low and the low notes high, by the same intervals. Such a simple transformation has created a myriad of beautiful compositions by composing geniuses such as Bach, Beethoven, Chopin, and Mozart. It is also useful to note that from certain frames of reference, rotation and inversion can appear to be one–in–the–same.

Transmission by retrogradation can be thought of as another form of inversion with the only difference that this inversion does not just occur in space but also in time. Retrogradation simply defined is backward motion. If we get in our car and drive a few yards and then shift into reverse and exactly retrace our trajectory, we have employed retrograde motion or the retrogradation of a pattern–integrity. Many speed–reading courses also employ retrogradation by having the reader read line 1 of a passage from left to right and then, rather than wasting the saccadic motion necessary to return the eyes to the beginning of line 2, the course instructor will have the reader actually read line 2 backwards; thus doubling the speed of the reader.

Retrogradation is also very often employed by composers who increase the complexity and beauty of their compositions by assigning counterpunctal melodies to two different instrument voices such as piano and violin. These interwoven melodies are actually the same melody except for the fact that one of the voices plays the melody backwards.

In the world of molecular biology, we can also see retrogradation at work in the behavior of ribosomes. Ribosomes are large proteins that read mRNA and in turn assemble proteins out of the correct amino acids specified by the mRNA. Ribosomes have the capability of reading mRNA in either direction (in forward or retrograde motion) in order to produce the proteins used by living organisms.

Retrogradation is one of the keystone pattern behaviors employed by the field of NLP in the construction of the now–famous V/K Disassociation method for eradicating long–standing phobias and traumas. For those who are not familiar, the method works like this. The subject is asked to make a representation of the traumatic event in the form of a movie. The subject is then asked to watch the movie from beginning to end in a disassociated fashion as if they are in a movie theatre watching themselves watching the movie of themselves, from the perspective of the projection room (sometimes referred to as double disassociation). What this first step does is simply contract the pattern–integrity called “traumatic event” in space such that, when the subject thinks about it in working memory, it takes up a relatively insignificant amount of the visual field compared to the way the subject normally represents the event to himself. This contraction of the pattern–integrity in visual working memory also corresponds to a contraction of the neural network or number of neurons needed to represent the traumatic event. This is called population coding (Furman, May 1996). This pattern transmission by contraction of the number of neurons which transmit the traumatic event results in an attenuation of the emotional pain normally experienced by the subject.

The second part of the technique requires the subject to view the movie backwards from the end to the beginning several times very rapidly. This part of the technique employs transmission by retrogradation as well as a contraction of the original pattern–integrity in time since the subject is viewing it much faster than it is normally represented. The combination of retrogradation and both types of contraction (space and time) employed by the technique is what imbues it with its tremendous power to eradicate traumas and phobias. The original pattern–integrity is irreparably disrupted by these competing pattern behaviors resulting in an increase in entropy within the neurocognitive system—opening a doorway to positive change (Furman and Gallo, 2000).

Transmission by Mirror–Image

The isomorphic transmission of information by mirror–image is quite interesting indeed. In a way we can think of this as a form of inversion since things appear to be reversed by their mirror images. If you look at yourself in a mirror, or at your reflection in the water, and you raise your right arm, it appears that the pattern–integrity looking back at you, called “the mirror–image reversed you,” is raising their left arm. Had this image been an actual person staring back at you, that would be the case.


Transmission by mirror–image was employed by the scientific geniuses who discovered how DNA was able to copy itself. DNA in human beings consists of two strands of nucleotides approximately 3 billion in length. The nucleotides are strung together like beads, and this string of beads has only a four letter alphabet, T, A, G, C. T and A are known to bind only to each other. And G and C form a similar partnership. It was found that the two strands of DNA are in a sense mirror–images of each other. If a T exists on the first strand, an A exists in the same position on the second strand. In the same regard, if a G exists on the first strand, its partner C occupies the same position on the second strand. In this way, the complex codes incorporated within this string of 3 billion nucleotides can be replicated by the mirror-image strand. This amazing feat is performed by employing enzymes that break the bonds between partners and “unzip” the double helix into two separate templates. The process of unzipping can be understood as the pattern behavior of cleaving. Once unzipped, specialized enzymes recombine the nucleotides on each template with their corresponding partners; but in this case, their corresponding partners are selected from free–floating nucleotides. When this process of recombination is complete, DNA has effectively replicated itself by employing a mirror–image template for its construction of two identical double helixes. As you can see, DNA replication is a highly complex process employing many of the pattern behaviors previously discussed.

It is important to note here that nature had been employing mirror–image pattern–integrity transmission for quite some time before the human mind discovered how it was done. However, in order to make this discovery, the human mind first had to learn how to transmit pattern–integrities in mirror-image reverse in order to form the testable hypothesis that determined the correct experimental design, which in turn led to the discovery of how DNA replication worked.

Transmission by Enfoldment and Unfoldment

Transmission by enfoldment and unfoldment in its simplest form can be understood by taking a piece of paper, drawing a picture on it, folding it in half and then in half once again. If the picture that we drew represented a pattern–integrity, the folding of the piece of paper into four equal parts, and thus the enfoldment of the pattern–integrity, resulted in a transformation of that pattern–integrity such that it disappeared from sight. Yet, even though it disappeared from sight, information was conserved since we can simply unfold it and the resulting pattern-integrity stands as clear evidence. Had we folded the paper in the opposite direction, such that part of the pattern–integrity could be seen from the outside instead of being completely hidden as in the first example, we would have ended up with a pattern significantly different than the one we started with. In the same regard, if we simply unfold that which was enfolded, we would see that the pattern–integrity—the original picture we drew—remains the same.

Some pattern–integrities when enfolded enough, can not so easily be unfolded; such as when we scramble an egg or blend the ingredients of a cake mix, yet the information is conserved. The pattern behaviors of enfoldment and unfoldment were used as a model by the physicist David Bohm, to explain how subatomic particles such as electrons can “appear” to move in coordinate space when, in fact, they may not be moving at all, but simply appearing in rapid succession as a result of the enfolding of one particle which makes it seem to disappear and the corresponding unfolding of nearby particle which makes it seem to appear out of thin air. If the enfolding and unfolding of the corresponding particles happens quickly enough, it creates an “apparent motion” (Bohm,1995). This type of visual illusion is often seen when the individual lights on a commercial sign or Christmas tree are turned on and off in close succession.

Transmission by Inside–Outing

Probably the most complex and interesting of all of the pattern behaviors found in nature is the isomorphic transmission of a pattern–integrity (information) by inside–outing. The simplest way to envision inside–outing and its far–reaching implications is to imagine a rubber glove; the type of rubber glove that you might use for house cleaning will due fine for this thought experiment. Imagine that we are holding in our hand a yellow–colored, right–handed rubber glove. Now imagine placing your right hand inside the glove. Incidentally, the inside of the glove is colored green. Once your right hand has slipped into the rubber glove, you can easily verify that it is a right–handed glove, since it fits perfectly over your right hand. Now imagine grabbing the edge of the rubber glove while simultaneously holding your fingers tightly together so that, in one quick motion, you can turn the glove completely inside–out. The resulting transformation of information is profound. First you will notice that as you were pulling the glove inside–out, you were employing the pattern behavior of involusion and exvolusion. Once the glove has been turned completely inside–out, you will notice that its pattern-integrity has been inverted. Since the fingers of the glove are now pointing toward your fingers, and the end that you slip your hand into is pointing away from you—the pattern–integrity is completely upside–down. Upon closer inspection, you will notice that the inversion that occurred is no simple inversion. You are actually looking at what could be a mirror–image of the original glove. If you now perform one additional transformation, this time a transformation by counter–clockwise rotation, you will notice immediately that you no longer have in your hand a yellow, right–handed glove. Instead, you are now the proud owner of a green, left–handed glove. The right–handed glove has disappeared from sight. Simply by slipping the glove over your left hand, you can confirm that it is, in fact, a left–handed glove.

This may not seem so miraculous to you, as you have probably done this before at some time in your life. But, for a moment, let’s imagine that you were not privy to the transformations that were made. Let’s instead imagine that you were originally given a yellow, right–handed glove as a gift from a friend. You open the box in front of your friend, try on the glove and confirm that it is, in fact, a yellow, right-handed glove. You then proceed to close the box up with glove inside, and set it on the counter. When you awake the next morning, you decide to use your new yellow, right–handed glove for some spring cleaning. You open the box, and to your surprise, you instead find a green, left–handed glove. Try as you may, it does not fit your right hand. Imagine how shocked you would be if you were unaware that nature had the power to perform this information–preserved transformation.

This is probably the exact same feeling many scientists had when the engineering genius, Buckminster Fuller, suggested that subatomic particles previously believed to be able to disappear in thin air, don’t actually do so. He suggested instead, that they simply turn inside–out and become their mirror–image reverse. From the outside, scientists who are unaware of nature’s ability to transform a pattern–integrity in this way, would assume they are seeing two different particles, when in fact they are just seeing one particle radically displaced in coordinate space by an inside–outing transmission. In the future, this may explain how it is possible that an electron and its anti–particle, the positron, can “annihilate” each other and become two photons; as well as how two photons can annihilate each other to become an electron and positron pair (Feynman, 1985). It may also explain what happens when a star implodes and becomes a black hole, two of the most profound enigmas left in the field of physics.

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PART V in the October, 2000 issue begins here:

Recursion, Nested Loops and the Genesis of Self-Reference

Up until now, we have discussed each of the processes that make up the matrix of genius in somewhat of an isolated fashion, in order to define them. Although they had to be defined separately, it would be a grave mistake to think that they exist separately in nature. They do not. All the behaviors of pattern interact with one another. The principle that appears to govern their interaction is called recursion.

Recursion is somewhat slippery and difficult to define but it can be thought of as the incorporation by a pattern–integrity (structure or process) of exact or modified copies of itself or more commonly, isomorphic transformations of itself, where information has been preserved. Recursion is sort of a “nesting” of copies of a pattern, structure or process yielding a self-similarity on multiple levels. Every complex structure and process experienced in nature develops out of the recursive interaction of the five behaviors of pattern (incorporation, replication, cleaving, recombining and transmission). The result of recursion on these five behaviors is the birth of complexity, diversity, adaptation, beauty, nested information loops, fractals and self-–reference to name just a few (Hofstadter, 1980; 1999; Mandelbrot, 1977; Margulis and Sagan, 1986; Loewenstein, 1999).

One way to think about recursion is simply to imagine the nesting of stories inside stories, movies within movies, paintings within paintings, parenthetical comments inside parenthetical comments, Russian dolls inside Russian dolls, Chinese boxes within Chinese boxes, subroutines within computer programs or processes within processes (Hofstadter, 1980; 1999). This is the world we live in, the world of mind, brain and nature, where patterns incorporate other patterns and processes incorporate other processes, in order to build the universe around us and within us. Even a casual glance at a head of broccoli reveals the self-similarity on multiple levels--a contraction of a pattern-integrity in space that is ever-diminishing as we move our eyes from bottom to top. You can separate the smallest branch of a head of broccoli near the very top and when you hold the branch that you separated under a magnifying glass, you might be startled to find that it looks just like the head of broccoli that you separated it from. Recursive processes yield fractal structures. This is the stuff that lungs, brains, vascular systems, coast lines, and clouds are made of.

If you’ve ever pointed a T.V. camera at its own monitor, for a short time you can witness the nested pattern of televisions within televisions ad infinitum. The resulting image appears like a long hallway of T.V. monitors ever decreasing in size—one nested inside the other. To create such a complex and compound pattern, the pattern must loop back upon itself over and over again, allowing for self–mirroring or self–reflection. In the same regard, the neural matrix of our brains is capable of modeling the world around us. Since approximately one half our brain interfaces with the outside world of sensory stimuli (the external information field), and the other half of our brain connects with itself, thus interfacing with the internal information field, our neural architecture loops back upon itself in ever-increasing complexity. These nested information loops in the neural matrix are what make it possible to make models of the world and in turn be consciously aware of the models that we make. As certain neural networks within our brain incorporate and represent visual, auditory, tactile, olfactory and gustatory information from the outside world, other neural networks mirror those neural networks and then finally mirror themselves, making possible conscious awareness of what we are currently experiencing.

As alluded to in many of the previous examples used to describe pattern behaviors, complex behaviors such as DNA replication do not involve replication alone but instead, the complex, recursive enumeration of all of the behaviors of pattern occurring simultaneously on multiple levels of scale. We see such properties as these emerging in the activity of our immune systems, in the activity of individual cells and even in the behavior of stars in galaxies.

Recursive enumeration is a process by which new things emerge from old things by fixed rules such as the energy shunting processes of incorporation, replication, cleaving, recombination and transmission, and the symbol shunting processes of topographical number theory and music. Recursion produces surprises-- unexpected results from the interaction of elements governed by a set of fixed symbol shunting or energy shunting rules. Suitably, complicated, recursive systems such as human brains, or even subsystems of a single human brain, are strong enough to break out of any predetermined patterns of behavior that seem initially to be imposed by these fixed rules. It is this phenomenon that is one of the most important, defining properties of genius—the development of extraordinary human intelligence.

AI pioneer, Douglas Hofstader, has made an elegant distinction between those systems possessing the capacity for “true thought” and those that do not (1980; 1999). Those that are capable of the type of thought that result from complex, recursive processes are said to be operating in I–mode. If a system is operating in I–mode (intelligence mode), it continually breaks out of predetermined, predictable patterns of behavior even though it is operating from a collection of simple, fixed rules (symbol shunting or energy shunting rules). If a system is operating in M–mode (machine mode), the system has not developed enough recursive complexity (self–referential, information loops) to perform any behavior other than what it was programmed to perform. Here is the difference. If two children are both given sets of numbers along with their combinatory rules, such as addition, subtraction, multiplication and division, to be performed in a certain order and sequence, the child operating in M–mode will be able to follow the combinatory rules and produce the correct answer. This child need only have incorporated and replicated the numbers and their combinatory rules. The child operating in I–mode, however, cannot only perform the behaviors dictated by the combinatory rules and get the correct answer, but can also think “about” the rules, thereby creating short–cuts, and developing new formulas and algorithms for symbol shunting. Such children are capable of applying meta-mathematics.

As we mentioned before, the incorporation and replication of patterns which are the quintessence of M–mode system operations, are sufficient for getting A’s in school math courses. But, there is a world beyond the classroom that stubbornly chooses not to obey such conventions and pays rather handsome rewards to those who can create and innovate. In order to work out his theory of relativity, Albert Einstein, had to break out of M–mode and think about the “rules” of mathematics as well as the “laws” of physics extant in his time, when he finally realized that the “accepted” use of those rules and laws would be insufficient to accurately model the real world. Many great scientists before him, found the necessity to develop new mathematical systems--new symbol shunting rules in order to describe the portion of reality of interest to them. For example, calculus had to be developed in order to fully describe laws of motion and non–linear differential mathematics had to be developed in order to describe the behavior of systems over time. Such developments could never have been made by blindly following the current dogma. Rather, each genius in his time had to prolong an apostasy in order to show that the development of new rules and laws would increase our ability to describe reality thus advancing our understanding and appreciation of nature.

Multiply embedded states of motion are ubiquitous throughout nature. Cells, organs and organ systems incorporate, replicate, cleave, recombine, and transmit patterns (information) in order to sustain life--a delicate balancing act between the opposing tendencies of pattern and entropy. The matrix of genius is subserved by both the pattern behaviors of our cellular information encoding mediums as well as the behaviors of information itself. The patterns and processes which we incorporate throughout life, forcibly deploy our pattern encoding bioarchitecture, resulting in the dynamical development of our information encoding mediums, both neurophysical and biophysical. Information shapes the encoding medium that it passes through—it in–forms that medium, imbuing it with new functions. This is why both “content” and “process” are critical elements of early educational training. When the human mind learns a new process, the human brain learns to connect a new way. The degree of recursion that can be found within our brain tissue, determines the degree of recursion, ergo genius, that can be produced by mind. Nowhere in our educational mediums are these properties of pattern more thoroughly exploited than in high–level mathematics, music and art.

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Recursion in Music

Composers of the Baroque and Classical eras are notorious for their recursive employment of incorporation, replication, cleaving, recombination and transmission. Although we have briefly discussed some of these examples earlier, it is important to note that the structure of these musical forms bear a great influence on the minds of composers, performers and listeners alike since their action literally shape the brain tissue and biophysical systems that process these pattern–integrities. Cannons and fugues, two musical forms developed during the Baroque era, make use of the sheer elegance and complexity of recursive pattern–integrities.

Many times a single piece of music will start off as nothing more than a short pattern of note sequences (a melody). This melody will be considered the core or the tonic for the piece. The rules by which the piece expands to full length, are in essence, the pattern shunting behaviors of incorporation, replication, cleaving, recombination and transmission, and it is done so recursively—one isomorphic transformation of the core pattern nested inside another. For example, the core pattern may consist of just eight notes. Then the eight notes are replicated so that they appear several times throughout the piece. Incorporated within this replication might be a contraction in time, of the core pattern which means that it is played twice as fast. The contracted pattern would then be assigned to another instrument voice. In another part of the score, the reverse may take place. The core pattern would be expanded in time and played only half as fast. To develop the cannon or fugue further, the core melody may be played several times throughout the piece in retrograde (back wards). This too, would be assigned to a different instrument voice to increase the beauty of the piece. The next section of the musical score may change in texture completely as it might contain an inversion of everything that was done so far. It is also very common to cleave the core pattern into pieces such that when the first part of the pattern is played, it creates a tension in the listener which lasts until the last part of the cleaved part is played. This cleaved core pattern could be separated by many other isomorphic transformations of the core pattern. If you would like to be able to experience just what such a piece of music sounds like, I would suggest to the reader a collection by Johan Sebastian Bach called the Musical Offering. The Musical Offering is a mirror of nature’s most fundamental processes for the creation of beauty and complexity from a set of simple rules.

Epilogue

What is genius? Genius is the ability to produce new things of great complexity from a set of fixed simple shunting or energy shunting rules. Genius is the ability to step outside those rules and think about them, question them, modify them, in order to produce that which has never been produced. Where does genius come from? Genius comes from nature—and her five behaviors of pattern. Genius comes from the recursive enumeration of these pattern behaviors in mind and brain. What is the difference between those who have extraordinary human intelligence and creativity and those who do not? The difference is that as a result of incorporating and utilizing the five behaviors of pattern recursively, the mind of a genius can more closely model reality. The mind of a genius can step outside a set of fixed rules and create new rules. Where can the tools and rules for modeling genius be found? They can be found in nature’s patterns. Is genius learnable? By now the answer to that question should be self–evident. Can genius be explicitly taught? Absolutely! It can be explicitly taught when designers of educational materials take into account the critical need for fusing process and content together. Recursive enumeration of the five behaviors of pattern can be taught explicitly, content notwithstanding. Such processes can be taught in mathematics, English and science as easily as it can be taught in music and art. The term for such an educational system that employs all of what has been previously discussed within this paper is an Intelligent Learning System (ILS).

Genius is not an all-or-nothing phenomenon. It is not something we have or do not have. It is instead something that we develop by degree as a direct result of the patterns that we choose to incorporate as well as how we learn to incorporate those patterns and use them once we can replicate them. To the degree that our life experiences—our changing information field—imbues our neural matrix with the essential ingredients; the contents and processes that we have previously discussed in this paper, we will exhibit the characteristics so commonly defined by humanity as genius. The matrix of genius is a process template—a blueprint for designing a mind and brain capable of great acts of erudition far beyond that which is made possible by the haphazard incorporation of “content”—a template with which we can consciously influence our own design if we so choose

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Mark Evan Furman -- email: neurosci@gate.net
International Society for Cognitive-Neurophysics
Director of Education & Research, The Keys to Success, Inc.
Mr. Furman is an internationally respected scientist, author and lecturer. By the age of 37 he and his pioneering work became the subject of historical, biographical record, reported within the pages of the 17th Edition of Marquis’ Who’s Who in the World and the 5th Edition of Marquis’ Who’s Who in Science and Engineering . He is recognized for his significant contributions to the fields Cognitive-Neurophysics and Education Neuroscience, his prolific published works and international public speaking. He is the developer of Human Performance Modeling and Engineering, NeuroPrint and Intelligent Learning Systems (ILS). He has recently completed his second book entitled The Neurophysics of Human Behavior: Explorations at the Interface of Brain, Mind, Behavior and Information, which will be released in June of 2000. He has lectured both in the U.S. and Europe and his pioneering work in the field of neuroscience has been published in 42 countries. Furman is certified by The Society of NLP as a practitioner, he is also a member of The New York Academy of Sciences, The Cognitive Science Society, The American Society for Training and Development (ASTD), and The American Association for the Advancement of Science (AAAS).
Mr. Furman has been a featured guest on several radio talk shows and his work has been the subject of a numerous feature interviews and articles appearing in national business journals. Mr. Furman is an affiliate member of the International Society for the Study of Peace, Conflict & Violence, Division 48, American Psychological Association, Washington, D.C. He may be reached via
e-mail at: neurosci@gate.net
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