Similar at Every Level
Let go of your attachment to being right, and suddenly your mind is more open.
- Ralph Marston
Note: the two articles following this one expostulate more conventional ideas about fractals
In the view of Darwinists, endlessly exquisite designs of nature are the result of the interplay of two factors - random genetic mutation and natural selection. The question of "design" in nature troubled Darwin all his professional life. In the year following publication of his Origin of Species he wrote to Asa Gray: "I am in an utterly hopeless muddle. I cannot think that the world, as we see it, is the result of chance; and yet I cannot look at each separate thing as the result of design."
Darwinist Ernst Mayr said, "No consequence of Darwin's theory of natural selection was a source of greater dismay to his opponents than the elimination of design from nature." After citing examples of fantastic design in nature, Mayr goes on to say, "But when we ask how this perfection is brought about, we seem to find only arbitrariness, planlessness, randomness, and accident..."
Today, any graduate student asked to develop a paper on the subject of design in nature would invariably wind up looking into fractal geometry and mathematics. Fractal geometry, as its name implies, is a geometry focusing on the description of geometrical structures, and structuring, in fract[ion]al space. This branch of mathematics was developed in 1975.
The Elements of Euclid (circa 300 BC) summarised in thirteen volumes the mathematical knowledge of ancient Greece. Up to the 20th century, Euclid's books of geometry were taken as the final, authoritative word on the subject. They dealt with whole rather than fractional realities. Plane geometry concerns planar (one- and two- dimensional) structures, and solid geometry describes volumetric (three-dimensional) structures. Science writer and author James Gleick said new geometries occur when someone changes a fundamental supposition. He wrote: "Suppose space can be curved instead of flat, a geometer says, and the result is a weird curved parody of Euclid that provides precisely the right framework for the general theory of relativity. Suppose space can have four dimensions, or five, or six. Suppose the number-expressing dimension can be a fraction. Suppose shapes are defined, not by solving an equation once, but by iterating it [repeating it] in a feedback loop."
French mathematician Benoit Mandelbrot made a number of the above suppositions, and the result was the 1975 birth of "fractal" (fractional) geometry and mathematics (Les Objets Fractal). The original stimulus behind Mandelbrot's work was an interest in irregular (seemingly "chaotic") patterns. Cotton prices over long periods of time, frequency of earthquakes, flooding conditions - all seemed to occur with a regular irregularity. What was the principle of order within the chaos? Mandelbrot's "studies of irregular patterns," Gleick indicates, "and his exploration of infinitely complex shapes had an intellectual intersection: a quality of self-similarity. Above all, fractal meant self-similar... Self-similarity is symmetry across scale. It implies recursion, pattern inside of pattern. Mandelbrot's price charts and river charts displayed self-similarity, because not only did they produce detail at finer and finer scales, they also produced detail with certain constant measurements..."
The physical world, the explicate realm, is structured along the lines of fractal geometry. The basic underlying idea is that of repetition of structure in different scales of magnitude. The common example is a coastline: a photograph of a section of coastline from a blimp will show the same ragged contours as a photograph of the whole coast taken from a space station. A photograph of a one-foot-long section of the same coast will also show the same contours. The various coastlines are "self-similar, each like the others in shape, but different in magnitude."
Mandelbrot and those who took up the tools he provided found endless evidence of the fact that the explicate realm is designed via fractal mathematics. In light of this, the idea of Mayr and other Darwinists that the perfections of nature are the result of "planlessness" was revealed as artless. The physical realm is structured like "Chinese eggs," eggs nested within eggs.
"A decade after Mandelbrot published his physiological speculations," Gleick writes, "some theoretical biologists began to find fractal organisation controlling structures all through the body. The standard "exponential" description of bronchial branching proved to be quite wrong; a fractal description turned out to fit the data. The urinary collecting system proved fractal. The biliary duct in the liver. The network of special fibres in the heart that carry pulses of electric current to the contracting muscles...."
"How did nature manage to evolve such complicated architecture?" Gleick asks. "Mandelbrot's point is that the complications exist only in the context of traditional Euclidean geometry. As fractals, branching structures can be described with transparent simplicity, with just a few bits of information..." Fractal mathematics is a branch comprised of simple formulae by which conversions are made - fractal to fractal.
The seemingly infinite complexity of the Mandelbrot set is based on the simple formula z'=z2 + c. Take a number, multiply it by itself, and add the original number.
"By the 1980s, Gleick writes, a home computer could handle arithmetic precise enough to make colourful pictures of the [Mandelbrot] set, and hobbyists quickly found that exploring these pictures at ever-greater magnification gave a vivid sense of expanding scale. If the set were thought of as a planet-sized object, a personal computer could show the whole object, or features the size of cities, or the size of buildings, or the size of rooms, or the size of books, or the size of letters, or the size of bacteria, or the size of atoms. The people who looked at such pictures saw that all the scales had similar patterns, yet every scale was different. And all these microscopic landscapes were generated by the same few lines of computer code."
A decade or so after the publication of Les Objets Fractal, as Gleick observes, a number of biologists (and not just "theoretical biologists") began the work of re-understanding the body in terms of fractal engineering. Today, the fractal approach is being used to better understanding every component of the human body.
Neuroscientist Ary Freeman, for instance, maintains that a kind of "ordered unpredictability" lies at the heart of the brain's ability to perceive the world. "Studying the electrical activity of the brains of rabbits trained to recognise various smells, Freeman finds that the animals' brain waves shift to a different pattern of chaotic activity as each smell is inhaled...
Paul Rapp of the University of Pennsylvania has found similar results in humans. When his subjects were asked to count backward from 100 by sevens, their brain-wave patterns s uddenly shifted into a chaotic state that marked intense concentration.
The Freeman and Rapp references are from a recent article titled "The Mathematics of Human Life," by William F Allman. Allman says of the full dimensions of the fractal phenomenon: "The body's overall structure bears the signature of the chaotic processes that shape it - right down to the DNA molecule that serves as its genetic blueprint. The fractal nature of DNA appears to play a role in its ability to pass on biological information that controls development of the various parts of the body. Because fractals represent a midway point between randomness and predictability, DNA's fractal structure may represent a compromise between encoding the maximum amount of information, while still being extremely resilient to damage."
In the early '80s, the Darwinian orthodoxy still reigned supreme, and consequently it was assumed that the secrets of biological evolution would be discovered as the result of research in genetics. Most biologists interested in evolutionary process were guided (or misguided as it were) by the doctrine of the primacy of DNA. For these researchers, fractal geometry was of interest only as it might apply to understanding the nature and workings of DNA. Among the more unorthodox biologists interested in fractal mathematics was University of Virginia - trained anatomist and cell biologist Dr Bruce H Lipton.
Improvements in electron microscopy during the '50s made it possible for researchers to really look at the cellular membrane. Lipton's career as evolutionist began when he concluded that consciousness is not something encoded in the genes (the position of the orthodoxy) but something "transduced" by the IMP system of the cell membrane. The biological basis of consciousness, Lipton maintains, is the integral membrane protein (IMP) unit, a stimulus-response mechanism in which the "receptor" is the stimulus receiver and the "effector" the response activator. "So," Lipton says, "we get into an interesting understanding of consciousness here. The fundamental consciousness unit happens to be a combination protein receptor and effector. If you separate either of these two proteins from each other, then that unit of perception is not made. If you cut the receptor off, no signals come in, or if you cut the effector out then there's no response to the signal. In either case, you break the perception pathway."
If the IMP receptors are cut off, then the cell goes comatose and dies, whereas if the nucleus is taken out of the cell, the cell continues to operate normally, until such time as it requires new parts. Lipton says this indicates the biological primacy of the membrane over the DNA.
The cell's Parts Department - the genome - functions as a supplier of new parts. Lipton feels that consciousness does not originate in the genome (the "ghosts in the machine" hypothesis of the Darwinists), it originates in the environment and is transduced (processed) by the cellular membrane. Various of the signals so processed activate creative processes in the genome. If the cell were viewed as a stimulus-response mechanism, a kind of super IMP, then the cellular membrane would be the stimulus-receiver component and the genome the bottom-line response component.
Consciousness refers to a process that occurs in any organism, from the prokaryotic cell to the human being - the process of receiving signals (from outer environment and inner domain) and translating those signals into appropriate biological responses.
Lipton indicates there is a wide spectrum of awareness, "from the hypothetical organism that can see one percept - meaning it would have just one receptor and effector, so it can see only one thing, to a human being, who has an enormous range of awareness and enormous versatility in terms of response."
Many orthodox biologists define consciousness as a strictly human phenomenon. Others don't. There are great differences between the signal reception-response expressed by a unicellular organism and the signal reception-response expressed by the human being, but these differences do not justify the hypothesis that there is no relationship between awareness at the cellular level and awareness at the human level. Indeed, from the point of view of methodology, such a "negative hypothesis" is invalid. It's possible to prove that which is, but how is it possible to find evidence for the non-existence of something? ["God does not exist, and here's the proof..."?]
Darwinism taught that evolution expresses continuity with change. First there is a something, and then the something becomes something else. The exact nature of the something else is determined by the nature of the something and by certain other factors that come into play to modify the something. By the standard of continuity with change, so convincingly expressed by Darwinism, we would suppose not that human consciousness is a "special phenomenon" (an idea which smacks of the Biblical doctrine that man is a special creation), but that human consciousness is an evolved form of lower consciousness. Why not presume that human consciousness is an evolved expression of cellular consciousness? (Itzhak Bentov believes humans operate via two distinct consciousnesses the rudimentary consciousness which is the collective cell consciousness, and the higher consciousness which is an emanation of a higher self.) Lipton identifies three primary means by which consciousness evolved from unicellular consciousness to human consciousness.
The first means was increase of cellular membrane surface area. Nature made the prototype cell (the prokaryote) into a smarter cell - a cell with greater consciousness capability. How? The cellular mechanism of perception, the IMP network, requires access to the external environment and to the inner domain, and thus they cannot be stacked. The cell membrane contains only one layer of IMPs. This means that if the IMP (consciousness) capability of the cell were to be increased, then the surface area of the membrane had to be increased. This expansion of cell membrane surface area was accomplished in two ways: through the development of an internal skeleton (the prokaryotic cell has an exo[outside]skeleton) and through the internalisation of all systems not requiring a face-to-face contact with the external environment. In the case of the prokaryote, all systems (including the DNA) are on the membrane surface; in the case of the eukaryote (final stage cell), only the "nervous system" is on the surface. The other systems are internalised as organelles. And how are organelles formed? Lipton: "In evolution, functional groupings of plasmalemmal [membrane] IMPs invaginated and detached from the cell surface. These internalised portions of the plasmalemma provided for the formation of discrete membranous organelles, including the nucleus. Organisation, functional integration, and mobility of the organelles was provided by the cytoskeletal matrix."
What the evolution of consciousness next required, as part of its "membrane expansion program," was the development of the optimal program for the integration of inputs. The IMP receptors receive signals (inputs) and the effectors activate the output functions that transduce the signals into behaviour. In addition to receptors and effectors there is an intermediate protein called a processor protein, or "G protein." Processor proteins interface between receptors and effectors, and, given their positions, they had great potential for directing and re-directing incoming frequencies. In the words of Bruce Lipton: "A processor can hook a receptor to one output, and another processor can hook the same receptor to a different output - so that one incoming signal can be split by the processor into multiple functions. Over evolution the processor proteins are co-ordinated, or co-ordinate themselves, in such a way that the processor sub-system has tremendous versatility in terms of its ability to 'get the most' out of incoming signals. The sub-system might be able, for instance, to use just one incoming signal to provide a wide variety of biological functions." What the processor protein sub-system represents, Lipton says, is "a mechanism of expanding the consciousness not just by increasing the numbers of receptors and effectors, but by integrating them into functional biological repertoires."
Once nature perfected the cell, which is to say maximised its capability for receiving and processing signals, then there was, according to Lipton, a momentary pause in the evolutionary process. If nature was to continue with the work of building greater and greater consciousness capabilities into the biological realm, there had to be a new format as the cell format had been completed. What would be the next step?
Dr Lipton recalls the moment in 1983 when he discovered the answer to that question: "I was sitting in my laboratory looking at a eukaryotic cell through an electron microscope. I was reiterating in my mind the common understanding that all the physiologic systems that can be found in the human being are in the eukaryotic cell when it really struck me... the cell I was looking at was a fractal of the human being. Alternatively, the human being is a fractal of the cell - a version on a greater order of magnitude." From that moment, Lipton the anatomist and cell biologist became Lipton the evolutionist.
"Evolutionary process is not that very very long uninterrupted upward inclined plane that the Darwinists suppose it is," Lipton says. "In terms of simple structures, evolution is more like a ladder - a fractal ladder which takes us, 'us' being the material realm, into higher and higher consciousness. The single cell - from prokaryote to eukaryote - is one rung of the ladder. After this rung was completed, nature took a bunch of state-of-the-art [eukaryotic] cells and combined them into the first multicellular organism. That first organism was the beginning of a new fractal rung, a rung that is completed with the completion of the human being. We humans are the eukaryotes of our fractal level."
In the years following his realisation, Lipton accumulated more and more information supportive of the hypothesis that fractal mathematics and geometry are at the formative heart of biology and evolution. "The story of evolution at the level of the single cell is largely the story of cell membrane expansion," Lipton says. "The more membrane surface, the more IMPs can be packed in. At the level of the multicellular organism, the maximising of cellular membrane surface area is achieved through 'fractal packing.' The way to get the most surface area into any given three-dimensional space is by means of fractal structuring."
The third primary means of consciousness expansion, Lipton reasons, is the combination of fractal-rung end products into the proto-products of the next fractal step. The eukaryote is the end product of the single cell fractal rung. When it was completed, the next step was the combination of eukaryotic cells into the first multicellular organism. Human beings are the end products of the multicellular rung. What marks the completion of this rung? Level of consciousness is the measure. Probably, the key marker of completion is the development of "creator consciousness," the understanding that we "create our own realities."
Currently, we (humans) are very much in the process of discovering the facts of our "creation consciousness," the various programs (paradigms) on which we run. What we call Darwinism is a basal paradigmatic program, one on which Western civilisation has operated on for over 100 years. It is not so much a scientific program as a political program. If the masses are convinced that existence is without purpose or plan, that "anything goes" and "anything can happen," then of course what is needed is strict top-down control. Thus was born the so-called "New World Order," which is understood by many as an elitist conspiracy to control the world through control of economics, politics, and ultimately genetics and thought.
In endeavouring to explain the origins of New World Orderism, critics invariably point to secret societies, some of which have been around for a very long time. But the bottom-line source of whatever problems we might have as a civilisation is the basal paradigm(s) we operate upon. Look at the paradigm, not at the people. People are in a real sense merely puppets of their paradigms. At least, this has been the case until recently. Now, civilisation seems to be really getting the idea that we and the creator energy are in some sense synonymous. Yes, we are fractals of the Creator. This is the meaning of the idea that man is made "in the image" of God. This is the message of Christ (and of other great spiritual leaders) - a message that humankind has historically not been ready to receive.
Embracing the understanding that what we call physical existence is, as it were, like a computer modelled by means of fractal mathematics, is a key to the reconciliation of Western religion and science - of metaphysics and physics. Whatever label we might care to give the implicate order doesn't really matter, so long as we have a reasonably accurate understanding of "the way it all works." The Christ message and the New Physics message point in the same direction, toward "participatory Creatorism."
Another important implication of fractal biology and evolution is that at long last, we have solid support for the Gaia hypothesis that the planet is one organism. The human being is a fractal of the single cell; the planet is a fractal of the human being. If existence is structured along fractal lines, then it is very difficult to avoid the conclusion that Earth is a single organism. [With a consciousness?]
If our planet is a single organism, then what is Homo sapiens? What is the role of humans? Their probable role with regard to the planet is akin to the role of immunity cells in the body - "to serve and protect." The Biblical idea that humans are meant to be the "stewards" of the planet is an early expression of Lipton's current understanding that humans are immunity cell equivalents.
It is important to note that immunity cells are not simply the "cops" of the body. They are, in the words of Bruce Lipton, "the cells of evolution." They have the ability to embrace the new things - the unknown - to learn those new things. They are the experts - the Sherlock Holmeses. Further, they are little creators ... the creators of genetic blueprints for organisms that can protect the body against antigens - even extraterrestrial ones.
Source: Condensed from © 1995 Ted D Hall & LEIRG [Leading Edge International Research Group]. It appeared in a Leading Edge book titled Avoiding Extinction
Julia set for the mapping Eλ = λ exp(z) where (left) λ < 1/e and N = 50; (centre) λ > 1/e and N = 50; (right λ > 1/e and N = 200. Note the explosion into colour as λ increases past 1/e, indicating the burst into chaos.
Julia sets of the function Cλ(z) = iλ cos z. (Left) λ is approximately 0.67; (right) λ is slightly larger.
Julia sets of the function Sλ(z) = (1 + λi) sin z. (Left) λ = 0, there is a large basin of attraction (black) consisting of points attracted to 0; (right) λ > = 0, the basin is destroyed and the entire screen fills with colour, suggesting a burst into chaos.
Source: Science Vol 235 16 January 1988
Click to play
Source: fractal-recursions.com This is the first one listed at the site; there are 13 others equally lovely on this site - a fractal lover's dream.
Of Springs, Crowds, Crinkles and the Price of the Yen
After years of decorating bedroom walls, adorning t-shirts and illuminating trendy nightclubs, fractals are starting to become useful
How long is a coastline? This was a question much asked a decade ago by science journalists trying to explain the fad for fractal mathematics in the 1980s. The answer depends on how long the ruler is that you are trying to measure it with. As you look closer to the point where the land meets the water, a coastline gets longer as more and more kinks are seen in it. In fact, the small-scale view looks surprisingly like a miniature version of the large-scale one. It is, in the jargon, self-referential.
Dealing with this, and similar problems (what is the surface area of a cloud?) is the province of fractal mathematics, or the algebra of partial dimensions. A coastline is too non-linear to be a line one dimension but not substantial enough to be a surface (two dimensions). It is somewhere in between - one and a bit dimensions.
Back in the 1980s, it all seemed curious, but not, perhaps, all that useful (except for working out how clumpily matter is distributed in the universe or for modelling the growth of red algae). Like catastrophe theory, another of that decade's crazes, fractals strutted and fretted their hour upon the stage and then were heard no more. They are now making a comeback, as a combination of better mathematics and faster computers puts them in reach of people other than cosmologists and botanists.
The best developed fractal application is image compression. Even with computer memories doubling in capacity every 18 months or so, there is still a premium on space. So when pictures to be stored digitally can be cajoled into taking up less space on a hard disk than they might otherwise need, money can be made. Traditional compression methods can squeeze pictures only so far. For example, a maximum of 72 minutes of video can fit on a CD-ROM. Fractal compression can put more than two hours of film on to such a disk. It may soon allow movies to be transmitted over the Internet at something approaching their proper speeds.
Fractal compression, developed by Michael Barnsley of Iterated Systems, in Atlanta, Georgia, makes use of self-referential information in the pictures. Recurring patterns in an image are identified, regardless of size, and a single copy is stored. Information about their actual size and position is held elsewhere. The result is a particularly efficient method of packing pictures away.
Fractals have also started to earn their keep in more humble industries than the movies. Making springs, for example, is beset by a recurrent problem. Since spring makers have no reliable way of telling whether a particular batch of wire will make a good spring. they have had to test each batch separately by coiling it into springs. Wire that fails this test is coiled again using more lenient settings until it passes or until it is judged too poor for spring making.
A device called the "fracmat" should do away with this batch-processing. Developed in Britain by Ian Stewart, his team at Warwick University and the Spring Research and Manufacturers Association, this allows single wires to be tested quickly and reliably. Fracmat comprises a pair of motors, a long rod and a laser micrometer all wired into a personal computer.
Wrapping a sample wire around the rod produces a long coil whose individual turns are variably spaced. This spacing is the tell-tale sign of the wire's quality: low quality wire is randomly spaced, higher grades more regularly. Plotting the distance between adjacent turns against the distance between the immediately preceding pair of turns produces a fractal which mimics the underlying structure of the wire - self reference again. Perfect wire would have turns with exactly the same separation, and the resulting fractal shape would be a point - which has no dimensions. Messy wire produces a smeared-out shape, which is wider and taller.
One of Dr Stewart's students, who missed out on the joys of spring making, was Keith Still. Mr Still has developed his own breed of fractal - the "orchid" - which can be used to model the way in which crowds leave confined spaces such as rock concerts and sporting events.
It is hard to model a crowd using traditional mathematics. Though a single person will leave a room simply by walking in a straight line to the door, it is much harder to say how 500, let alone 50,000, people will leave a football stadium. Traditional mathematics tends to collapse when faced with so many variables. The problem rapidly becomes too complex to solve in a reasonable time.
Basic orchid fractals behave like a well-ordered, rational crowd - one without the inherent confusion caused by people moving at different speeds, walking in the wrong direction or simply standing about. Of course, crowds are hardly models of good behaviour, so Mr Still added random elements, to simulate human characteristics, back into the system. The result is Legion, a system that can simulate a crowd of up to 250,000 people using orchid fractals.
Mr Still found what security managers at large events have long known: that those on the edges of a crowd surging to an exit will get to it more quickly. However, he also found that a triangle-shaped gridlock, with one apex at the door, spreads rapidly back into the room. Earlier models of crowds, which treated them as if they were solid lumps, or worse, fluids, had failed to spot this feature. So, surprisingly, had stadium designers. In fractal-speak, this triangular dead zone is awake, a point of stability in the sea of complexity. Dead zones can be moved - or new wakes created - and crowd movements increased by, counter-intuitively, adding barriers such as handrails or pillars.
The most speculative use of fractals is in foreign-currency markets. For many years, mathematicians have tried and failed to capture the intricacies of financial markets in mathematical models. But fractals do have some plausibility as a tool. Market movements seem to demonstrate the fractal trait of self-similarity. And the dealers themselves - a group of people all attempting to do the same thing (maximise profit, while minimising loss) look suspiciously, at least in mathematical terms, like a crowd of people making for the same exit.
Like a crowd, the individual actions of most buyers and sellers make little difference to the market as a whole. But big perturbations - central-bank intervention, for example - can act like pillars, creating a different fractal wake. So, in just the same way that Legion is used to predict how a virtual crowd will leave an as-yet-unbuilt stadium, Mr Still's system might be used to predict underlying trends in, for example, dollar-yen transactions.
Mr Still found that by piping 1994 and 1995 yen and dollar transactions through his fractals he could distil some kind of underlying order from the chaos of the market. Dramatic falls and rises - known, technically speaking, as discontinuities - in dollar-yen prices were anticipated by a jitter in his orchid fractals. Like a fire spreading through a building, bad news takes time - even if only a fraction of a second - to respond to. Those closest to the fire respond quickly, but the crowd as a whole takes time to adjust.
A basic principle of financial economics is that it is impossible, in any market that assimilates information efficiently, to predict the future price of a security on the basis of its past price. Nonetheless, says Mr Still, inefficiencies do remain: by looking at the behaviour of orchid fractals it may be possible to detect jitters that occur just before a discontinuity is reflected by the market, even though currency traders, surrounded by television screens and computer terminals, are inundated by real-time information. It is in that impenetrable forest of information that Mr Still hopes his orchids of knowledge will flourish, by telling people the only two things they actually need to know. When things are going up, and when down.
Source: The Economist 13 April 1996
by Paul Pietsch
It seemed almost the setting for a seance or an exorcism. "Please step this way!" I was ushered through darkness, to a stool in front of an emerald-green shaft of laser light. One of the experimenters inserted a photographic plate in the path of the laser beam. Suddenly, from nowhere, suspended in cosmic black space before me, there appeared a dissected human brain. But I knew for a certainty that the specimen could not possibly be there. It was one of my own class demonstrations. And I'd locked it up in a cabinet across the hall.
Yet I was seeing no photograph. When I shifted over to the left, I could see a side of the brain not visible from the front. Over on the right, or standing up, I got different perspectives. Moving in close, almost expecting to smell strong formaldehyde fumes, I could make out fine gridlike indentations that had been impressed by cheesecloth while the brain was still fresh and soft. Finally, I had to reach out and try touching the brain to convince myself that the thing itself really wasn't there at all. I wasn't hallucinating or witnessing trick photography. Nor was the image an optical illusion, either. It was an image reconstructed from a hologram (indiana.edu).
A hologram encodes for the height of waves and how quickly points on the wave move from one place to the next. Called phase and amplitude, the two properties determine all else about waves, including any images or messages the waves may be transporting. (Photographs contain information only about amplitude.) I understood what was going on in that room. I even knew the mathematical reasons why. It was science, not magic or supernatural laws at work. Yet the human being in me kept asking over and over again just what reality really was, anyway. For it wasn't only the uncanny hologram. It was the thought that before me might lie the basic secret of how that pickled brain across the hallway had once stored a living mind.
Theories are what make scientific revolutions happen. And we may just be in the early and uncertain rounds of one right now. For the abstract principles of the hologram form the basis of a theory to explain the brain's most elusive properties. Hologramic theory, an editor of mine once named it, And that's what I'll call it here. Hologramic theory was first proposed by physicists, not psychologists, physiologists, or anatomists. But the theory has been used by a number of behavioural and biological scientists during the past few years to account for many diverse paradoxes about the brain. The theory has predicted incredible results in many laboratories, including my own, and has led to new and unsuspected possibilities of brain and mind. And physical holograms may be used to motel many features of mind that once seemed totally beyond the ken of science.
A generation ago, psychologist Karl Lashley found that he could dim the recollections of laboratory animals by destroying parts of their brains. But it wasn't where he cut, it was how much. Lashley concluded that the engram, or memory trace, is distributed and repeated throughout the brain. He could never isolate the engram. People's engrams have been equally elusive, although Lashley's doctrine may be too simplistic to cover the complex brains of humans, apes, and, perhaps, dolphins and whales. But his basic idea works, even in us. And his beliefs have been sustained by many different kinds of experiments, some conducted even by his critics. A physiologist named E Roy John and his colleagues have learned how to detect active memory signals in the living brains of rats and cats; the same signals recur in vastly different regions of the brain, just as Lashley's doctrine predicts. And would you believe that shuffling a salamander's brain does not scramble the animal's mind? I might not, either, except that I did the research myself.
The diffuse hologram makes no more common sense than the brain itself. Cut the hologram in half and both halves still regenerate a whole scene. Try quarters, eighths - and it's the same thing! The reason is that a whole code exists at every point in the medium. The reasons are mathematical. But, basically, the hologramic code depends on ratios established within the medium, not absolute values. Like an angle, the code is relationships, abstract relationships, really.
At any rate, with very tiny pieces of a diffuse hologram, the regenerated image does blur, as did the memories of Lashley's animals. But the information itself doesn't degenerate. It's in the communication of it; the loss of fidelity is an effect of "noise" on the very weak signal a tiny piece of hologram generates; it's like what static does to a weak radio signal or snow to a dim TV picture. Physiologist John believes that signal-noise differences account for specialised functions in particular parts of the brain.
A subtle dilemma pops up in work such as Lashley's. If engrams are distributed everywhere, how does the same brain house more than a single memory? Holographers have produced what are called multiple holograms - codes of many different scenes superimposed one on top of the other right in the very same medium! How can this be? In theory the individual code can be made almost as small as a single geometric point. Thus on any piece of medium, the number of individual codes may approach infinity, in theory. In practice, multiple holograms actually exist. In multiple holograms, the holographer keeps different scenes straight by manipulating such properties as colour or the angle of the construction beam. Then, during decoding, by making comparable adjustments, the holographer can cause one whole scene to go off and another to come on - like an actor forgetting Othello so he can play Hamlet.
Consider, though, what happens if the holographer doesn't make adjustments during the coding process! During decoding, the holograms might act as though they had an imagination: scenes might merge that had never coexisted in physical reality at all. Or, depending, on the scenes, the holograms might also act as though they were producing delirium tremens or were taking a trip on LSD.
The abstract principle in the hologram easily accounts for my shufflebrain experiments. Each code is not only whole, it is also independent of other codes - although codes cooperate in regenerating the image. Shuffling parts of the salamander's brain was like scrambling a deck of identical cards. But this independence principle would also allow new information to be fed into the deck. I've tested this prediction by transplanting brain parts. An operation can give a salamander thoughts originally taught to another salamander - or even the instincts of fishes or frogs.
Actually, some 200 reports exist alleging that memory may be transferred in chemical form from one rat to another - or even from a rat to a hamster! This is a very controversial subject, and it would take me a book to do justice to both sides. But one big imponderable used to be how a tiny molecule might store all the information required to make a memory. Hologramic theory doesn't settle the controversy. But holograms would have no trouble fitting on a molecule, in theory, at least. There is evidence of memories on molecules. The most convincing ease has come from studies of decision-making and memory in bacteria, believe it or not, organisms that don't even have brains. But there's this major obstacle against reducing mind to molecules - and this extends to the chemical transfer of memory, too: the facts. Some physiologists have found no chemical changes associated with learning. Hologramic theory suggests reasons for such discrepancies, some mathematical, others that can be seen by way of physical simulation. Let's look at an example of the latter.
There are acoustical holograms - holograms made from sound instead of light. The information is gathered with a microphone and the code is displayed on a tv tube. It's possible to photograph the hologram for permanent storage, should someone pull the tv plug or change scenes. Short- and long- term memory might work analogously. Or the transition from visual to some other mode might be modelled as follows: it is possible to shine a light through the photograph and visually regenerate a scene originally encoded by sound. But consider this question: Where is the hologram? In the air near the microphone? In the vibrations of the microphone? In the electronics of the set? On the tube? In the photographic film? The answer is that it is in all these places. For the hologram is information. It is abstract relationships. The same code can exist in vastly different kinds of media and depend on different mechanisms - just as an angle of 30º may be formed from ivory, mahogany, or extruded aluminium.
Hologramic theory does not free mind from media. It is no new variant of mind- body dualism. But the theory's most far reaching implication is that many different mechanisms and media can store the same codes. Stored mind is not thing. It is abstract relationships produced by things. In the sense of ratios, angles, square roots, mind is a mathematic. No wonder it's hard to fathom.
Paul (Andrew) Pietsch, Phd
Based on an article in the November/December issue of the magazine, Quest/77 in a special feature on brain function, edited by Tony Jones.
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