The Known, the Unknown,
and the Unknowable

Are the Boundaries of Consciousness a Fractal?

by Jonathan J. Dickau ©'99
all rights reserved

When people speak of what is known, and the realm of the unknown, they are only scratching the surface, in terms of what we can explore. There is much which appears to be known, that is questionable, or even false. There is much that many believe to be unknown, or even unknowable, which is actually part of people's everyday experience. Some of what is known to be real, however, is almost impossible to comprehend, even for brilliant minds, as it appears to conflict with common sense. So it was for Neils Bohr, one of the Fathers of Quantum Mechanics, who suggested that the quantum nature of reality was not only stranger than we imagine, but even stranger than we can imagine, and that "if it doesn't make your head spin, you're not looking at it right." The newest theories, and most recent discoveries, on the other hand, point to a description of the universe which makes quantum mechanics look almost simplistic, by comparison. If we stick to our old "world view," however, the unknown will always remain unknowable.

Part of the problem, it seems, is that we believe the universe is a reasonable place, where there must be an explanation for everything that happens, but I feel that the natural order is far more grand. The world we live in is an exceedingly magical place, and what makes it appear mundane is our limited purview. Part of the reason for this limitation is the use of guilt, fear, and intimidation, by our culture, to keep us focused upon "acceptable" ways of describing reality, which make us useful to society. The catch is that the description we cling to is a mechanistic view, left over from the 18th century, which has already been proven false! What we now know to be true, through scientific study, stands in sharp contrast to the view of the universe as a mechanism, whose behavior can be predicted by careful observation. It seems reasonable to believe that knowing the present conditions in great detail will allow us to predict the future, but this is not necessarily true.

We are taught that gathering more information will make the unknown knowable. Instead of finding that the accumulation of information makes the world more predictable, however, we are discovering that the data shows it is not so fixed as we had believed, and that many of our common-sense assumptions must be set aside. What is known as "real" today must be called into question, if we are to understand the true nature of reality better than we do now. More than this, we must learn to give wings to our flights of fancy, rather than grounding them prematurely. This is not to say that every kind of fantasy is healthy, or meaningful, but reigning in our imaginations will not bring us any closer to understanding the universe, or ourselves. The true test of a mature imagination seems to be the power to return home, and see the place with new eyes. Children have wild fantasies, and their play inspires a rapid growth in thinking capacity which our best attempts at training and conditioning could never match. The ability to direct this playful activity, however, so they return from flights of fancy to the point of departure with an expanded vision, is something we seldom teach, but it is the most useful skill we can learn.

What place does such "Reversibility Thinking" have in the "real" world? It is exactly this kind of process which allowed Albert Einstein to propound the Theory of Relativity. Mathew Maltz (in Psycho-Cybernetics) teaches that it is the best procedure to motivate ourselves to achieve our goals. Working from the goal, rather than toward it, often makes it easier to see the steps leading to successful completion. If we can "consider any state along a continuum of possibility as potentially equal to any other state," and then return to our "point of departure," as suggested by Jean Piaget, and expounded upon by Joseph Chilton Pearce, we can transcend many boundaries. By this, I mean that to be OK with any possible outcome frees us from the emotional charge of the fear of failure. If we can "imagine the worst," and be prepared to live with that, then our ability to visualize a more positive outcome takes on a far greater power, than if we need to have things work out well, in order to be happy. On the other hand, if we imagine only the worst things that can happen, and remain afraid of them, we are more likely to precipitate bad outcomes than good.

Part of the fear of the unknown, however, results from the fact that the boundary between the known and unknown (and likewise between the knowable and the unknowable) is not a simple one, but is rather convoluted. The classic Venn Diagram would depict the boundary between the known and the unknown with a circle, or oval, inside another, but reality is not like that at all. Surely, one can describe what is known as an outline within another outline which describes the unknown but knowable, and this as a figure lying within a figure representing the unknowable, but the shape of these figures is not easily described, using Euclidean Plane Geometry. I believe that the boundaries of these figures, and thus the the boundaries of consciousness itself, are a Fractal, a figure whose dimension is not a whole number, but somewhere between. The boundaries of reality, and those of human consciousness, apparently lie between dimensions, rather than having a particular dimension at all! No wonder many have a hard time understanding the world around us, or why, despite all we know, reality still doesn't make sense.

Many natural objects (trees, lakes, clouds, etc.) have boundaries which do not lend themselves to a simple description using normal geometry, but are fairly easily modeled by using Fractal Geometry instead. The work of Michael Barnsley shows that the information contained in images of natural scenes can be compressed to a small fraction of its normal size, by using fractals, and it suggests that doing so allows us to reconstruct the underlying order. We can take a grainy image, and applying fractal algorithms to detect the shapes which created that image, actually generate a sharper, higher-resolution image. An article by Benoit Mandelbrot, in the February '99 issue of Scientific American, shows that money also follows a fractal order. It suggests that fluctuations in financial markets can be far more accurately modeled by a multifractal approach, than with the conventional interpolation and extrapolation techniques of modern economics. The implications of this are staggering! These examples are compelling proof of the fractal nature of objects, and phenomena, in the natural world, and a substantial step away from the simplicity of common-sense descriptions of the world.

Another well-known example of the complexity of nature arises from the study of weather forecasting. A man named Edward Lorenz, at MIT in the '60s, used an analog computer programmed with partial differential equations (arising from the laws of thermo- dynamics) to model circulation of air in a convection cell, and discovered something very interesting. After a run of calculations was interrupted, he wanted to resume the process from an earlier point, and found that, after a time, the results of his calculation were completely different! Starting the process from the middle, with the same input (the result at that point), created a result which diverged greatly from the initial run of the program. He thought that he had made a mistake, but instead discovered the "sensitive dependence on initial conditions," which has come to be known as the Butterfly Effect. I believe that it was first called this, because the figure produced by this process, the Lorenz Attractor (which is a fractal), is shaped a bit like a butterfly. The popular reformulation of this is that the flapping of a butterfly's wings in California can change the weather in New York.

The implication here is that no amount of information about present conditions, or the exact immediate state of reality, will allow us to see forward, backward, or sideways, with absolute accuracy. In fact, the Hubble Telescope, and other observational instruments, seem to indicate that what we thought were universal constants of reality (e.g. - the speed of light, fine structure constant, & possibly Planck's constant) are fixed only in our local area of space. The evidence is there, that our consensus of what constitutes reality is flawed, and can actually keep us from seeing things as they really are. The foundation for many concepts of a mechanistic view of the universe was disproven near the start of the 20th century. So why do we still cling to the illusion of a mechanical reality? Perhaps it's because we would like the universe to be simple, or that we "need" things to make sense, in order to accept them as real. Perhaps the fact that many things do adhere to a pattern mechanically has lulled us into a false sense of security. Whatever the reason, the real world doesn't have to make sense to us, in order to be the way it is. It does need to be consistent with itself, but it need not conform to our verbal-semantic definitions, nor does the underlying order need to be as simple as common-sense would dictate, in order to be real.

So is language the problem? To some extent, I believe that this must be true. Some langauges are worse than others, but the dependence upon any language, at all, tends to have an obscuring effect on our perceptions of reality. The founder of General Semantics, Alfred Korzybski was fond of saying "The word is not the thing." to signify that our maps, or the grids, by which we define reality, are not the same as those things they designate. Chinese Patriarch Sen T'san went much futher, exhorting us to "Stop talking, stop thinking, and there is nothing you will not understand." The English language, for all its power to describe, is particularly subject to the illusions of word-based thinking, and the problems of objectified consciousness. English is great at describing things, but it is somewhat limited, in describing events where the "things" involved are not the key players.

Native American languages, and most Oriental languages, are far more "process" oriented than English, and better reflect the tone of Quantum Mechanics, Relativity, and other modern Sciences. English, and other Indo-European languages, make an explicit separation between subject and object, even in those cases where the two are inextricably interlinked. This is not strictly real, but it is often mistaken for reality, nonetheless. Worse yet, people often insist that it "has to be that way," in order to make sense, but this is lunacy. Inventor/Philosophers Buckminster Fuller and Arthur Young often expressed dismay that we are taught to focus on objects and interactions, rather than processes and forces, and said that this creates illusions of reality. General-semanticist Robert Pula stated that it might be more accurate to talk not of "things" changing, for example, but of changes "thinging." This is an elegant expression of how language-induced assumptions have crept into our way of thinking, and adversely influenced our observations of what is known.

Some things that are now known can't be put into words, at all! Other things must be grasped as a "gestalt," if they are to be understood, and must be seen as a part of the system, or ecology, to which they belong, to be accurately perceived. Living beings are a prime example of this, but ironically, and somewhat tragically, the so-called Life Sciences are particularly prone to a mechanistic view of reality. The evidence is accumulating that the body, and living systems in general, are not mechanical at all. When the heart's rhythm is somewhat chaotic, and it dances between different rhythmic states, this is an indication of health, but when it becomes too regular, this is an indication of impending death. The same is true of the brain; when it is healthy and functional, its impulses have a fractal nature, and appear to follow a chaotic attractor, but when they become totally regular, this is known as an epileptic seizure. To assert that the body, or other living organisms, are mechanical, is a travesty, but many feel it is unscientific to believe otherwise.

It seems likely that the desire to take refuge in a mechanistic view is often prompted by fear of being "caught" with an incomplete understanding, or a lack of predictability, which might result in the loss of a job, or of funding for ones pet project, because real progress is often too tough to measure. Instead we are compelled to find "reasons" why things behave as they do, and are rewarded for having explanations, even if they are overly simplistic, and unreasonable in the long run. The truth is often far more elusive than our overseers would like to believe, but "I don't know," or "it requires more study," are usually deemed unacceptable answers, both in research and in problem-solving. The application of simplistic answers, however, can do more harm than good, and is often worse than no answer at all. Having answers is taken as evidence that we are being methodical, even if our answers are not correct ones.

An additional complication arises from the fact that having the right answer, and being able to show how you got there, are very different, and sometimes mutually exclusive. The development of Neural Network Computers has shown that the circuitry designed to provide the quickest, and most accurate, solutions to real-world problems cannot often be easily utilized to show how a solution was arrived at. A neural-net system can be "trained" to settle on the correct response much more quickly than conventional computers (with far less complexity, and little or no programming), and they are therefore great at handling real-time processes, such as production line automation. Unfortunately, there is no way the same system can tell us how its result was arrived at, or why things went wrong. They are far too "human," in this respect, but unlike real human beings they are incapable of rationalizing, in order to make "excuses".

Research into the action of various parts of the brain, in response to stimuli or in problem-solving activities, has shown that our decisions are often made fairly quickly, and quite subliminally, even when our awareness of, and apparent participation in, the process of deciding, takes far longer. In other words, we decide things right away (in deep areas of the brain), but take a long time to rationalize our decisions, before we are comfortable enough to take action, or announce our decision. So how can we avoid undue rational- ization, and think more clearly? Can we learn to step aside, and cooperate with the natural process? According to Korzybski, "If we 'think' verbally, we act as biased observers," and "remain in our rut, ..making keen, unbiased, observations and creative work well-nigh impossible," but by thinking without words, "we may discover new aspects and relations on silent levels," and yet use words to describe them. He states that "Practically all important advances are made that way." Perhaps "the Place of Silent Knowledge," to which Carlos Casteneda journeys in "The Power of Silence," is a worthwhile place for all of us to visit.

In that book, don Juan describes how we get there as crossing "the Bridge of Pure Understanding," and this makes perfect sense, in the context of Korzybski's views. In many cases, the truth is un-approachable from successive approximations, but knowable, as a whole, either by itself or in combination with its environment. When experiencing "silent knowledge" or "knowingness," one just knows, and there are no reasons to speak of; it just is, and that is all that can be said about it. To reason and to know may be mutually exclusive phenomena, where knowing is a matter of direct perception. Although this may seem irrational, or even counter-productive, this view is largely a matter of conditioning, and it is not shared by most of the world's greatest thinkers.

What makes the unknown unknowable, to a large degree, is the extent of our cultural conditioning, and not the inherent limitations of our brains, or other neural apparatus. It is the act of clinging to rational thought which makes direct, intuitive, or non-ordinary, perceptions unreal. The fear of the unknown can keep us from looking beyond the "shadows on the wall of the cave," and stepping out into the light of day. There are times when we must abandon Aristotelian logic, and embrace paradoxical logic instead. Either- Or thinking doesn't always work, but the anxiety we experience over an indefinite result can often get the best of us. On the other hand, sometimes the answer is not one, or the other, but both, neither, or some higher concept of which the apparent choices are only a projection, a "shadow on the wall." Although the universe appears to be three dimensional, for example, scientists now believe that we inhabit a space with quite a few more dimensions, and that theories based on a 3-D construct convey only limited understanding of what truly comprises our reality.

There will always be intractable problems, which no amount of logic, reasoning, or understanding will solve. Some things will always be unknowable, in the sense of being impossible to express, except as the forms or phenomena which naturally exist, of themselves. This does not mean that all of these things are unknowable forever, even if we can't be the ones to know them. In some cases, it means that only beings with a higher order of evolution can ever hope to possess such knowledge. In other cases, the ability to know certain information is due to the physical or energetic limitations of that which is being studied, the tools we are using to study things with, or the fragility of the matrix which holds the information we desire. It has been known, since the early 20th century, that making direct measurements of some quantities will influence the value of others, and that this can prevent us from ever knowing what they were. According to the uncertainty principle, the greater the accuracy with which we know some things, the less accurately we can know others. Fortunately, we are now learning that (at least in some special cases) it is possible to make interactionless measurements, getting around even this problem.

Nonetheless, there are some details known to exist which we may never be able to get to, no matter what the process of measurement or calculation. The Mandelbrot Set, a fractal which may be the most complex form possible to generate through Mathematics, is a good example of this. It is known to contain such a richness of detail that some areas appear to have unending complexity. By this, I mean that one can zoom in on some areas of this figure, again and again, finding more and more detail the farther you go. It is not possible to get to the "end" of the detail, by any means whatsoever, since zooming in on the most complex part will always allow you to discover yet more detail. The real issue is the time and energy required to make the detail apparent. With real-world phenomena, there is a natural limit, in terms of a particular grain or dimension possessed by a given entity, and this offers hope that we will eventually see them, but for the fundamental components of reality, the energy required to perceive their nature is very high indeed. For this reason, quarks (the constituents of sub-atomic particles) are very difficult to observe, especially certain flavors of quarks, and we are only now building machines powerful enough to probe their qualities at all.

In a similar way, there is an energy requirement which must be satisfied in order to perceive, or represent, any number of natural objects and phenomena. The process of seeing into the world of the very small, or very complex, requires tools which can generate and/or direct large amounts of energy. In addition, the body and brain of the perceiver must be able to withstand, and maintain, high energies or vibrations, in the process of conceiving of details, in order to encompass the complexity. This can be illustrated by placing some sand on a drum head, and then applying a tone to vibrate it. Different patterns emerge, as one changes the frequency, or pitch, of the tone being applied. A low frequency tone will produce patterns which are relatively simple, and regular, but as the pitch is increased, the detail and complexity of the pattern also increases. A high enough vibrational state is required to allow a particular level of organization to be manifested, or perceived. The story is similar, for waves in the brain, but there is a limit to what is safe to manifest in a living brain, or in any kind of electronic circuit. One cannot just keep turning up the clock speed of the processor, without burning something out. For this reason, some details can only be expressed in situ, as the objects or events themselves.

Of course, this brings us to the greatest unknown of all, and the question of whether it is unknowable. There are things which seemingly cannot be known to the living, or by using tools which are manifested in material substance, but does this mean that they are forever beyond our grasp? Does our consciousness end with the physical? We know that objects are made from energy, but most of us are not cognizant of the fact that matter remains a manifestation of energy, even while possessing form, and very few are directly aware of it, as an entity of itself. Energy is real! It is, perhaps, more real than matter since it is that from which matter is formed, and that to which matter must return. While matter is real, energy continues to play a part in our daily lives, and in all of the activities of matter throughout its life. Although energy can dissolve matter, causing our death, it is also energy which brings life to matter, animating substance. The substance of our thought is energy, as well, since the carrier of thoughts is not matter, but energy.

Energy can never die, and it is not lost, when form passes away. Energy can only be transformed, or transmuted, and it is therefore immortal! The unknown is unknowable, at least in part, because we are fixated on substance, and not upon energy. We are reluctant to look beyond matter, because we identify with it, even if it is not who we really are. Most of us believe strongly that we are the body, and this is part of what makes the unknown scary. The body can die, and we don't want to risk this. Much of what keeps us from knowing the unknown, therefore, is simply the fear of death. Death seems utterly final, although we can't know for sure. Death has long been used as a symbol representing the unknown, and for good reason. Without dying, we can never know, in a definitive way, what lies on the other side. And if we do die, how can we come back to tell anybody? If we no longer had a living body, how could we prove to anyone else that we are alive? It would seem that death is the ultimate enemy. It is the nemesis of all life!

Death can also be a friend, however, in our struggle to survive, or in our quest to discover the unknown. If we learn how, we can use it as an ally. Having death as an advisor can be useful, since death stalks us ruthlessly, and with great cunning, and sometimes these qualities are what we need to see things clearly. Using death to stalk oneself, making it a tool for evolving the courage to become cunning without conceit, and ruthless without being overly self-important, is certainly possible. If we "die daily," or undertake the process of "little deaths," in order to allow ungainly parts of our lives to pass away, and preserve what is more vibrant and real, we may actually extend the life of the physical body. I believe that we must overcome the fear of death, to see things as they are, but this need not make us foolhardy. To live ones life as if every day could be the last can give one new meaning and purpose. It can bring a lightness to our step, making us seem carefree, but it can also give us the courage to peer fearlessly into the heart of the unknown.

©'99 Jonathan J. Dickau - all rights reserved

Single copies of this document are allowed,
for reference or personal use, but reproduction
for commercial purposes is not permitted.

Return to
Feature Articles

Return to
Fractal Cosmos

Return to
Independent Thinking

Check Out Related Work
Dan Winter's
Monitoring of Heart
Is Attention
Itself Fractal?

Posted on
March 10, 1999

Updated on
August 20, 2005

©'99 Jonathan J. Dickau - all rights reserved