Shufflebrain

by Paul Pietsch

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  Imagine two points, A and B in our Euclidean world, 180 degrees apart on a circle. Let's begin a clockwise journey on a circlar course. When we arrive at 180 degrees, instead of continuing on around to 360 degrees,let's extend our journey, now counter-clockwise--to maintain our forward motion--into another circularly directed dimension, eventually arriving back at the 180 degree mark and continuing on our way to the origin; we form a figure 8. (Note that the two levels share one point -- at B.)

  Notice that we "define" our universe by how we travel on it. On a curve, we of course, move continuously over all points. When we get to the 180 degree point we have to travel onto the second or lower dimension if it is there. If we don't, and elect not to count that second dimension, it may as well be "what ain't." But if the dimensions join, then a complete cycle on it is very different from an excursion around a single dimension. Notice on the 8, we must execute two 360-degree cycles to make it back to our origin. The point is that while curvature is our elemental rule, and while the relative values remain unchanged, an increase in dimensions fundamentally alters the nature of the system.

  Suppose now that we add another dimension at the bottom of the lower circle to produce a snowman. Again our basic rules can hold up, and again relative values can transform unchanged, but, again, the course and nature of our journey is profoundly altered beyond what we'd experienced in one or two dimensions. For although we have a single curved genus of figures, each universe becomes a new species.

  We could have grown additional dimensions off virtually any point on our original curve. And the sizes might vary greatly. Nor are we really compelled to remain on a flat surface. Our system might have budded like warts. And we can vary the sizes of any added dimensions. Or if we work in the abstract (as Riemann did) we can make a many-dimensional "figure" of enormous complexity. The point is that we can evolve incredible variety from a very simple rule (curvature).

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  Now let's connect hologramic theory to our discussion in this chapter.

  First, we conceive of mind as information, phase information.

  We put that information into an ideal, Riemann-like universe--into a continuum of unspecified dimensions whose fundamental rule is curvature.

  A relative phase value--a "piece of mind"--is a ratio of curvatures.

  We gave our phase ratios expression as tensors.

  The modalities and operations of mind then become tensor transformations of the same relative values between and among all coordinates within the mental continuum.

  We dispose of our need to distinguish perceptual space from Fourier transform and kindred transform space because we do not set forth a coordinate system in advance, as we did earlier. Coordinates of the mind come after, not before the transformations.

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  If you're still struggling, don't feel bad. Instead, consider hologramic mind as analogous to operations of a pocket calculator. The buttons, display, battery and circuits--counterparts of the brain--can produce the result, say, of taking the square root of 9. The calculator and its components are very much a part of the real world. But the operations--the energy relationships within it belong to the ideal world. Of all the possible coordinates that can exist in an ideal world, one coincides with experience.

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  Believe me, I appreciate the demands Riemann's ideas can place on you, reader, especially at the outset. Therefore, allow me to offer another metaphor of hologramic mind.

  Imagine a system whose rules apparently violate Riemann's curvature, a system that seems to be governed by straight lines, sharp corners and apparent discontinuities everywhere. What could epitomize this better than a checkerboard. Let's make that a giant red-black checkerboard.

  Now imagine that one arbitrarily chosen square is subdivided into smaller red-black checkerboard squares. Randomly select one of the latter sub-squares and repeat the sub-squaring operation; do it again...and then again. Appreciate that "checkerboardness" repeats itself again and again, at every level. The various levels can be thought of as the equivalents of dimensions within our curved continuum. We can subdivide any square as many times as we please. Because we can pick any square for further sub-squaring--and subdivide as often as we wish--we can make any sub-checkerboards, --or sub-sub-checkerboards--carry vastly different specific checkerboard patterns.

  Okay, to complete our metaphor of hologramic mind, all we have to do is say that our red-black sets, subsets, sub-subset represent spectra of phase variations at different levels.

  Now that we've created imagery, let's get rid of the checkerboard metaphor. But let's reason it out of the picture, instead of issuing a fiat.

  We said that the red and black squares are infinitely divisible. Assume that we subdivide until we approach the size of a single point (as we did with the hypotenuse and our pearly e 's). If the system is infinitely divisible, then there ought to be a single unreachable point-sized square at infinity. If there are really two separate squares down there, then our system is not infinitely divisible; and if it's not infinitely divisible, where did we get the license to divide it at all? Thus we must place a single indivisible square at infinity so that we can keep on subdividing to create our metaphor. But what color is the infinite and indivisible square? Red or black? The answer is both red and black. At infinity our apparently discontinuous system becomes continuous: red and black squares superimpose and, as in Riemann's universe, the one becomes part of the other. A hidden continuity underlies the true nature of the continously repetitive pattern, and it is the reason we can systematically deal with the pattern at all. Our checkerboard metaphor of hologramic mind turns out to be a disguised version of Riemann's universe. It is, therefore, an analog not a metaphor.

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  Now let's use our general theory to answer a few questions.

  How do we really account for the results of shufflebrain experiments? How could Buster's fish codes blend in smoothly with his own? How was it that Punky's salamander medulla could receive the tadpole message from the frog part of his brain? The same questions exist for "looking up." Why weren't all my experiments like pounding a square peg in a round hole? Continuity had to exist. And phase transformations had to define the coordinate system, rather than the other way around.

  Consider another question, now that I've mentioned salamanders and mixing species. How can we explain the similarities and differences between them and us? Hologramic mind, constructed as a version of Riemann's universe, supplies the answer in two words: curvature and dimension. We share with all living creatures the rule of curvature, but we and they are vastly different universes by virtue of dimension. (I will return to dimension in the next chapter when discussion the cerebral cortex.)

  And how can we sum together phase codes of learned and instinctive origins, if fundamentally different abstract rules govern, say, a reflex kick of a leg and a 6/8-time tarantella? We'd move like jack-jointed robots if our inner universe were a series of bolted-together but discontinuous parts. How could we condition a reflect if we couldn't smoothly blend the new information with what's already there?

  Speaking of robots, we are different from the digital computer in more than the obvious ways. The computer's mind is a creature of the linear, Euclidean world of its origin. It was invented to be just that. Its memory reduces to discrete bits. A bit is a choice (usually binary)--a clean, crisp, clear, no-nonesense yes-no, on-off, either-or, black-white (or red-black) choice. And it is efficient. A computer's memories are clean, crisp, clear, linear arrays of efficient choices. By definition! By design!

  By contrast, the hologramic mind is not linear; not either-or; not efficient. Hologramic mind acts flat and Euclidean and imitates the computer only when the items of discrete, discontinuous data are few. We're quickly swamped when we try to remember or manipulate an array of, say,100 individual digits, a simple task for the computer. Yet ask the digital computer to distinguish between your face and a dozen randomly sampled faces--with and without e
yeglasses, lipstick and mustaches, and from various angles and distances--and it fails. Brains and computers operate on fundamentally different principles, and they mimic each other only when the task is trivial.

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  Now consider the problem that arises in perceptual vis-à-vis physical time and space. People, the author included, have reported dreaming ten-year scenes within the span of a few minutes. The reverse is probably more common: a horror lived during a second of physical time can protract into a very long perceptual interval. To the scuba diver who runs out of air, a few minutes hardly seem like a few. And time compresses during a race to the airport when we're just a few of those minutes behind schedule.

  Space can do some wacky things, too. A character in a Neil Simon play tells how, during a bout of depression, he couldn't cross the street because the other side was too far away.[14]

  What do we do about subjective phenomena, anyway? Discount them from Nature because they're "only in the mind."

  In Fourier (and kindred) transforms, the time-dependent features of relative phase became space-dependent. But the relationships in transform space obey what time-dependent ones do in perceptual space: the axes don't contract and expand. Tensors, on the other hand, aren't constrained by presumptions about coordinate axes. In the curved continuum, time-dependent ratios may turn up on an elastic axis. And because the hologramic universe is a continuum, we lose the distinction between perceptual and some other kind of space; or we may have the conscious impression that time is expanding or that distances will not close. Yes, it's ideal, subjective, illusory. Subjective time and space are informational transforms of what the clock gauges and the meter stick plots. The constraints on the clock and meter stick are physical. Constraints on the transformations of the mind are ideal. But both belong to Nature.

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  But hologramic theory suffers a major deficit, and we will have to correct it. Our construct is too perfect, too ball-bearing smooth, too devoid of errors, for twig missing from the nest or the freckles on a face. We can't see ourselves in the picture. We must account in our theory for what doesn't transform, what won't remain invariant in all other coordinates. Our pictures requires precisely what the pure theoretician goes to great pains to get out of the way--parochial conditions, particular features, local constants! Physiologist E. Roy John, recall (from chapter 2) identifies local constants as noise. I believe we must also put amplitude among our local constants. (Experimentation may uncover others.)

  Local constants make perception distinct from recollection of the original percept. They make a kiss different from a reminiscence of it. They put subtle but critical shades of difference on the spoken versus the written word. (Notice some time when you're listening to a correspondent deliver the news from a script the subtle change that occurs when he or she shifts to the ad lib to answering of questions from the anchor person.) Local constants become essential when the general becomes the particular; when the ideal, abstract, informational hologramic mind transduces into experiences; where theory stops and experiments take over.

  Because they are strictly parochial, the local constants necessarily vary with each individual. And the more dimensions a mind uses, the greater the impact of local constants on the collective behavior of the species. Hologramic theory, thus, is a self-limiting theory.

  We should not underestimate a theory's implications merely because the theory limits itself (as any scientific theory eventually must). A little humility can actually go a long way, as Riemann found. The latter is true of hologramic theory. Let me illustrate what I'm driving at by calling upon the checkerboard metaphor.

  To the red squares, let's assign relative phase tensors and everything else we explicitly use in hologramc theory. To the black squares, let's assign our local constants--which we can't directly treat from hologramic theory. To guarantee that the theory continues to restrict itself, let's maintain the rule that we cannot enter a black square from a red square, and vice verse. With this rule in mind, let's subdivide squares again and again, as we did before, and let's pose the same question: is the infinite square red or black? Just as before, it has to be both red and black. We still can't enter the infinite square. But this time, it's not the math book that bars us from infinity. It's our own rule. Both black and red exist at infinity. If one up from infinity is red, and we're there, we can't enter the next set (infinity) because it contains black and is off limits. (Note that how red and black got to infinity in the first place isn't our affair. We didn't put infinity there, since we couldn't reach it in the first place.) Thus the infinite square precludes hologramic theory (red) from using local constants (black) and vice versa.

  When we're on the red square, the "mechanism" that inhibits our movement into the infinite square is the corresponding black square, also a step up from infinity. Ironically, the very self-limiting nature of hologramic theory establishes the existence--the Existenz--of the domain with our local constants.[15]

  In formal terms, the incompleteness of hologramic theory makes local constants an existential necessity. The term existential refers to existence.

  The very incompleteness of the theory allows us to use it to resolve the mind-brain conundrum. Hologramic theory deals explicitly with mind. Yet it can do so only because it implicates local constants. And local constants exist in the brain. In other words, hologramic theory must work within a mind-brain system. A corollary of the last statement is that the source of the mind-brain conundrum was the fallacy, inherent in holism and structuralism alike, that a unipolar view can let us comprehend the mind-brain cosmos. Once we remove this fallacy and allow mind and brain to get back together again, the conundrum vanishes. Mind endows brain with the abstract universe in which to contain the realm of thought. But brain, in turn, gives life to the mind.

  We must reach outside hologramic theory to give perspective to our conclusions. And I know of no system of thought more perfectly suited to our needs than Hegelian dialectics, in which a thesis merge with its antithesis to create a synthesis.

  What is the mind-brain synthesis? You and I are! They are! It is general and ideal, as we all are. And it is particular and real, as we are too.

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  Internet contact:pietsch@indiana.edu

  chapter ten

  Microminds and Macrominds

  WE RETURN TO THE IMPERFECT but comfortable realm of experience. In chapters 5 and 6, we sought out predictions in hologramic theory. Now we shift emphasis to explanations, to the use of hologramic theory for making rational sense of certain equivocal and seemingly unbelievable observations. And we start with the behavior of bacteria.

  Bacilli, rod-shaped bacteria, propel themselves through fluid with whip-like appendages called flagella. flagellar motion depends on a contractile protein hooked to the base of each microbial appendage. An individual flagellum rotates, in the process executing wave motion. Locomotion of a bacillus, therefore, is an algebraic function of the phase and amplitude spectra collectively generated by its flagella. We might even regard the overt behavior of a bacillus as a direct consequence of periodic activity--the phase and amplitude spectra--reflecting the rhythm of its contractile proteins. Thus if a hologramic mind exists in the bacillus, it shows up literally and figuratively right at the surface of the cell.

  But is there really a mind in a creature so primitive? We can describe a stretching and recoiling spring with tensor transformation. But our intuitions would balk, and rightfully, if we tried to endow the back porch door with hologramic mind. Thus before we apply hologramic theory to the bacillus, we need evidence only experiments and observations can supply.

  Single cells of many sorts can be attracted or repelled by various chemicals. The reaction is called chemotaxis. In the 1880s, when bacteria was still a very young science, a German botanist named Wilhelm Pfeffer made an incredible observation in the common intestinal bacillus, Escherichia coli (E. coli)-- more recently of food-poisoning fame. Other scientists had previously found that
meat extract entices E. coli whereas alcohol repels them: the bacteria would swim up into a capillary tube containing chicken soup or hamburger juice but would avoid one with ethanol. What would happen, Pfeffer wondered if he present his E. coli with a mixture of attractants and repellants? He found if concentrated enough, meat juice would attract E. coli even though the concentration of ethanol was enough, by itself, to have driven the bacteria away.

  Did Pfeffer's observations mean that bacteria make decisions? Naturally, the critics laughed. But in comparatively recent times biochemists have begun to rethink Pfeffer's question. And in rigorously quantified experiments with chemically pure stimulants, two University of Wisconsin investigators, J. Adler and W-W Tso came the conclusion, "apparently, bacteria have a 'data processing' system." Courageous words, even within the quotations marks. For in a living organism, 'data processing' translates into what we ordinarily call thinking.

  Adler and Tso established to important points. First, the relative--not absolute--concentrations of attractant versus repellent determines whether E. coli will move toward or away from a mixture. Second, the organisms do not respond to the mere presence of stimulants but instead follow, or flee, a concentration gradient. And it was the consideration of concentration gradient that led biochemist D. E. Koshland to establish memory in bacteria.

  Koshland became intrigued by the fact that a creature only 2 micrometers long (.000039 inches) could follow a concentration gradient at all. The cell would have to analyze changes on the order of about one part in ten thousand--the rough equivalent of distinguishing a teaspoon of Beaujolais in a bathtub of gin, a "formidable analytical problem," Koshland wrote.

  Did the cell analyze concentration variations along its length? To Koshland's quantitative instincts, 2 micrometers seemed far too short a length for that. Suppose, instead, the bacterium analyzes over time, instead of space (length)? What if the cell could remember the past concentration long enough to compare it with the present concentration? Koshland and company knew just the experiment for testing between the two alternative explanations.