Shufflebrain

by Paul Pietsch

  But once again, the calamity was only apparent. On the elevator one day, a colleague of mine, asked if it was true that I did not have a dissecting microscope. He said "hmm" when I said "yes". A few weeks later, I was busy preparing a neuroanatomy lecture when someone began kicking on the door. I opened it and there stood the colleague from the elevator, a brand new dissecting microscope in each hand and a big grin on his face. He had convinced the dean that our graduate program required dissecting microscopes. And would it be an inconvenience to store two of them in my laboratory? I still wonder if he saw the tears in my eyes.

  ***

  Unlike other species I work with, the axolotl spends its entire life in the water. Because of a genetic quirk, it fails to metamorphose into a land dweller. It does undergo internal changes as it develops into an adult, but not the drastic transformations other salamanders go through. Metamorphosis usually wipes out my stock for the season. The axolotl, however, passes into adulthood uneventfully, and lives five or six years, and sometimes longer, under laboratory conditions. By the time I was ready to experiment again, Calvin's axolotls had not only become adults but had been Looking-up for well over a year. If I had had a dissecting microscope, I would have used every last one of them much earlier, and they wouldn't have been around for what happened next.

  Shortly after my article appeared in Harper's, I received a phone call from Igor Oganesoff, a producer for the CBS News program "60 Minutes." People at CBS had liked the article, he said, and he asked if I would perform experiments in front of the camera.

  With the wrong camera angle, my experiments could easily come out looking like Grandson of Frankenstein in Indiana, which would have been unfair to Punky and Buster as well as misleading to the audience. Yet I couldn't envisage Igor Oganesoff wanting to produce a horror movie. At that time, I was an avid fan of "60 Minutes" and vividly recalled two pieces he had produced: one had portrayed the world inside a Carmelite cloister in California; the other captured an aspect of chess master, Bobby Fisher, I didn't think the world had previously suspected. I was sure Igor Oganesoff could do justice to shufflebrain. And with the opportunity to reach fifteen million people... I decided, what the heck, let's do it.

  Techniques worried me, I said, trying to imagine what would work in a visual medium. Did I remember the work done with microscopes during Walter Cronkite's "21st Century", Oganesoff asked. The cameraman Oganesoff had in mind, a man named Billy Wagner, had taken those pictures. Place a camera in his hand and Wagner becomes a genius. There was, I replied, a double-headed microscope that enabled two people simultaneously to view the same microscopic field. But I didn't have one of those expensive instruments. Details like that, Oganesoff said, were his worry. As we were talking, I thought about Calvin's large, well-trained axolotls. It was time I did some experiments with adults, anyway. Their brains could be seen even without a microscope, if worse came to worse. Yes! I thought it might be quite feasible. After a preliminary visit, Igor made plans to film the operations in July and the results in August, between the two political conventions.

  Meanwhile, I scrounged a fresh batch of axolotl larvae from Humphrey. I also carried out a few preliminary operations with adult axolotls, to work out technical nuances and get my hands back in shape.

  Calvin had graduated, and another student had taken his place. He lacked Calvin's touch with animals and couldn't seem to get the knack of weaning larvae onto liver. I undertook the chore myself, and while at it decided to study the Looking-up response carefully.

  Looking-up is surprisingly easy to induce. The quickest way is to put the larva in an opaque cylindrical container and give it a sort of tunnel view of the world above. Then, with one session a day, for four or five days, a brisk, discrete tapping of the dish, followed in a second or two by a reward, will instill the trait. After this, Looking-up behavior persists for weeks, even after the reward has been withheld. Once the animal has been trained, the Looking-up response is virtually guaranteed. I decided to put Looking-up on "60 Minutes".

  ***

  The experiment I performed on camera involved three animals: two naive axolotl larvae and a trained adult "Looker-up" from Calvin's old colony. The anterior part of the trained adult's cerebrum replaced the entire cerebrum of one naive larva. Would the host become a Looker-up? The other naive larva served as a donor animal, and I transplanted its entire brain into the space left in the adult's cranium. Would the transplant "confuse" the adult? Mike Wallace eventually called the second larva "the loser". For it received no brain transplant.

  I decided not to call the viewer's attention to Looking-up, and instead focused attention on the survival of feeding after shufflebrain operations. I had no doubts about feeding. But Looking-up was still very new. Something could have turned up to change my mind. If the paradigm turned out to be a fluke, trying to correct the misinformation broadcast on television would be like attempting to summon back an inadvertently fired load of buckshot.

  Looking-up:

  Adult axolotl involved in 'swap' experiment shown on 60 Minutes. Looking-up remained intact after its cerebrum had been replaced by the entire brain of a young and naive larva. The animal in the picture had been taught to look up (to earn a juicy hunk of liver). The larva in question--the recipient of this animal's original cerebrum--became a Looker-up without any training. Larvae because of their small feed on brine shrimp, not liver. [The handwriting on the masking tape (label) is '7-3-72 Whole baby...'; the crop-off part says, '...brain #2]

  CBS broadcast the show a year later. In the interim, I had carried out enough testing and had conducted sufficient control experiments to be sure of the results. Within about one week, a previously naive recipient of a trained Looking-up animal's cerebrum becomes a Looker-up itself, without training. And these animals retain the Looking-up trait for the remaining months, or even years, of their lives. Controls, animals with transplants from the brains of naive animals, do not show this response. While the initial experiments--like those I performed on camera--were with the cerebrum, I obtained the same results with pieces of midbrain and diencephalon.

  The trained cerebrum donors were very interesting. As soon as the effects of anesthesia wore off, these animals demonstrated that they remembered the signal to look up. In other words, Looking-up memories existed in the donated as well as the retained parts of these animals' brains. What was true of innate feeding behavior also worked for Looking-up: memory wasn't confined to a single location in the brain.

  I also repeated Mike Wallace's "loser" experiment. I found that, true to the principle of independence (adding to the hologramic deck), the extra brain parts did not "confuse" the host.

  Meanwhile, a group of Israelis, working with the brains of adult newts, had demonstrated that dark-avoidance memories can be transplanted from one animal to another[1] When the "60 Minutes" show did air, I had no doubts about Looking-up. Sitting in my living room, a member of Igor's audience myself, I felt that someone else was on the screen doing my experiments. Indeed, someone else was at the microscope. The intervening year had been very full.

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  Internet contact:pietsch@indiana.edu

  chapter seven

  Waves of Theory

  UNTIL NOW, we have been investigating hologramic theory from the outside, looking at its implications in terms of what we can understand in the realm of experience, testing its predictions to see if they can possibly work, asking ourselves if the hologram mimics the living brain sufficiently to warrant a serious probe into the subject's rational core. Until now, our questions have concentrated on what a hologramic mind can do, and we have been able to pursue the answers in the world most real to us. But now we must turn to the question, What is hologramic mind? To find the answer, we must enter the ideal, abstract, unfamiliar domain of the hologram itself. And to make the journey, we need to borrow concepts from mathematics.

  What is mathematics, anyway? The American philosopher Charles Peirce, who gave contemporar
y science its philosophical backbone, observed, "The common definition ...is that mathematics is the science of quantity.[1] But, citing his own mathematician father, Benjamin Peirce, Charles went on to assert that it is actually "The science which draws necessary conclusions." Thus the numbers are not what make a mathematical statement our of 1 + 1 = 2; rather, it's the necessary conclusion forced from 1 and 1 by the plus sign. If we extrapolate Peirce's characterization to our own quest, the payoff ought to be a clear understanding not only of what we mean by "hologramic mind" but also of why hologramic mind does what it does when it does it.

  The reader probably can think of many specific examples, though, in which adding one thing to another does not necessarily yield two (even when we keep apples and oranges straight). With scrambled eggs, for example, combining two beaten yolks produces one entity. Bertrand Russell helps us with problems like this, and in so doing furnishes us with an essential caveat: "The problem arises through the fact that such knowledge [mathematical ideas] is general, whereas all experience [egg yolks or salamander brains] is particular.[2]

  Our search will uncover hologramic mind not as a particular thing but as a generalization. We will begin the quest in this chapter with a theoretical look at waves. And we will continue our search through the next two chapters. It is important to know in advance that our objective will not be the geography, but the geometry of the mind. Ready? "And a one-y and a two-ey..." as my children's violin teacher used to say.

  ***

  The central idea for our examination of waves originated in the work of an eighteenth-century Frenchman, Pierre Simon, Marquis de Laplace. But it was a countryman of Laplace who in 1822 explicitly articulated the theory of waves we will call upon directly. His name was Jean Baptiste Joseph, Baron de Fourier.

  In chapter 3, I mentioned that in theory a compound irregular wave is the coalesced product of a series of simple regular waves. The latter idea is the essence of Fourier's illustrious theorem.[3] The outline of a human face, for example, can be represented by a series of highly regular waves called sine waves and cosine waves.

  Such a series is called a Fourier series, and the Fourier series of one person's face differs from that of another person's face.

  We're not just talking about waves, however. As, J. W. Mellor wrote in his classic textbook, Higher Mathematics, "Any physical property--density, pressure, velocity--which varies periodically with time and whose magnitude or intensity can be measured, may be represented by Fourier's series."[4] Therefore, let's take advantage of Fourier's theory, and, to assists our imagery, let's think of a compound irregular wave as a series of smaller and smaller cycles ; or better, as wheels spinning on the same axle; or perhaps even better still, as the dials on an old-fashioned gas or electric meter. Waves, after all, are cycles. And wheels and are circles. Now imagine our series with the largest wheel--or slowest dial--as the first in line, and the smallest or fastest back at the tail end of the line. The intermediate wheels progress from larger to smaller, or slower to faster. Or the faster the dial, the more cycles it will execute in, say, a second. In other words, as we progress along the series, frequency (spins or cycles per second) increases as the cycles get smaller.

  If we were to transform our cycles back to wavy waves, we would see more and more wavelets as we progressed along the series. In fact, in a Fourier series, the frequencies go up--1, 2, 3, 4, 5, 6... and so on.

  But wait! If the frequencies of your face and mine go up 1, 2, 3, 4, 5, 6...how can our profiles be different? What Fourier did was calculate a factor that would make the first regular wave a single cycle that extended over the period of the compound wave. Then he calculated factors, or coefficients, for each component cycle--values that make their frequencies 1, 2, 3, 4, 5, 6... or more times the frequency of the first cycle. The individual identities of our profiles, yours and mine, depend on these Fourier coefficients. The analyst uses integral calculus[5] to determine them. Fourier analysis (what else!) is the name applied to the analytical process. Once all the coefficients are available, the analyst can represent the compound wave as a Fourier series. Then the analyst can graph and plot, say, amplitude versus frequency. A graph can be represented by an equation. And an equation using Fourier coefficients to represent a compound wave's amplitude versus frequency is called a Fourier transform, which we'll discuss in the next chapter.

  But wait! Isn't there something fish about coefficients? Isn't Fourier analysis like making the compound wave equal ten, for instance, and then saying 10 = 1+2+3+4? If the components don't come out just right, we'll just multiply them by the correct amount to make sure the series adds up to the sum we want. Mellor even quotes the celebrated German physician and physicist, Ludwig von Helmholtz as calling Fourier's theorem "mathematical fiction."[6] But this opinion did not stop Helmholtz and many in his day from using Fourier's theorem. Fourier's ideas gave new meaning to theoretical and applied mathematics long before the underlying conditions had been set forth and the proofs established. Why would anyone in his or her right mind use an unproved formula that had shady philosophical implications? The answer is very human. It worked!

  An extremely complicated wave may be the product of many component waves. How many? An infinite number, in theory. How, then, does the analyst know when to stop analyzing? The answer suggests another powerful use of Fourier theorem. The analyst synthesizes the components, step by step--puts them back together to make a compound wave. And when the synthesized wave matches the original profile, the analyst knows it's time to quit adding back components. What would you suppose this synthesis is called? Fourier synthesis, what else! Now when Fourier synthesis produces a wave like the original, the analyst knows he or she has the coefficients necessary to calculate the desired Fourier transform; that is, the equation of the compound wave.

  Conceptually, Fourier synthesis is a lot like the decoding of a hologram. But before we can talk about this process, we must know more about the hologram itself. And before that, we must dig deeper still into the theoretical essence of waviness.

  ***

  The first regular wave in a Fourier series is often called the fundamental frequency or, alternatively, the first harmonic. The subsequent waves, the sine and cosine waves, represent the second, third, fourth, fifth, sixth... harmonics. Computer programs exist that will calculate higher and higher harmonics. In the pre-microchip days, nine was considered the magic number; even today, nine harmonics is enough to approximate compound waves with very large numbers of components. As the analysis proceeds, the discrepancy between the synthesized wave and the original wave usually becomes so small as to be insignificant.

  These terms may seem very musical to the reader. Indeed, harmonic analysis is one of the many uses of Fourier's theorem. Take a sound from a musical instrument, for example. The first component represents the fundamental frequency, the main pitch of the sound. Higher harmonics represent overtones. There are odd and even harmonics, and they correspond to sine and cosine waves in the series. I present these terms from harmonic analysis only to illustrate one use of Fourier's theorem. But the theorem has such wide application that it has become a veritable lingua franca among persons who deal with periodic patterns, motions, surfaces, events...and on and on. I see no particular reason why the reader should dwell on terms like "fundamentals" and "odd-and-even harmonics." But for our purposes, it is highly instructive to look into why the component waves of Fourier series bear the adjectives, "sine" and "cosine."[7]

  The trigonometrist uses sines and cosines as functions of angles, "function" meaning something whose value depends on something else. A function changes with variations in whatever determines it. Belly fat changes as a function of too many peanut-butter cookies changes location from plate to mouth. Sines and cosines are numerical values that change from 0 to 1 or 1 to 0 as an angle changes from 0 to 90 degrees or from 90 to 0 degrees. The right triangle (with one 90 degree angles) helps us to define the sine and cosine. Sine is the side (Y) opposite an acute angle (A) in a ri
ght triangle divided by the diagonal or hypotenuse (r): sin A=Y/r. The cosine is the side (X) adjacent, or next to, an acute angle, divided by the hypotenuse: cos A=X/r.

  The famous Pythagorean theorem holds that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the two other sides (r2** = X2** + Y2**, where 2** is square). Suppose we give r the value of 1. Remember that 1 x 1 equals 1. Of course r2** is still 1. Notice that with X2** at its maximum value of 1, Y2** is equal to 0.

  Thus when the cosine is at a maximum, the sine is 0, and vice versa. Sine and cosine, therefore, are opposites. If one is odd, the other is even.

  Now imagine that we place our right triangle into a circle, putting angle A at dead center and side X right on the equator. Next imagine that we rotate r around the center of the circle and make a new triangle at various steps. Since r is the radius of the circle, and therefore will not vary, any right triangle we draw between the radius and the equator will have an hypotenuse equal to 1, the same value we assigned it before. Of course angle A will change, as will sides X and Y. Now the same angle A can appear in each quadrant of our circle. If angle A does, the result is two result is two non-zero values for both sine and cosine in a 360-degree cycle, which would create ambiguity for us. But watch this cute little trick to avoid the ambiguity.