the fixed point of Asa Zook/paul pietsch -- copyright 1996 by Paul Pietsch

chapter 15 Waves of Regeneration

Asa worked on his lecture after Joyce fell asleep, pausing from time to time to tiptoe to the bed, watch her and marvel, then return to his desk as refreshed as from a full night's slumber.

He was looking forward to the lecture and would use the occasion for his first public pronouncement on the fundamental principle of memory. Most of in audience, he believed, would know something of the controversial work of Karl Lashley. The chemists and physiologists present, doubtless, would know the properties of waves. But the physicians would need information their premedical physics courses had not covered, the very topics that were keys to the engram. He had had lantern slides prepared of interference fringes for a previous papers on diffraction. He examined the slides to the desk light. The were excellent, he judged. He also had a slide showing an X- ray diffraction pattern of DNA with which he would illustrate some of his main points. He had not had time, though, to prepare illustrations of Gabor's new hologram and, therefore, would have to resort to blackboard diagrams to convey the principle.

Half way into the night, after he'd completed his rough draft of the lecture and was beginning a rewrite , he stopped. "No, I shall not read the paper," he muttered silently completing the thought: I'll present it without notes, and from only a brief outline on one side of a 3 by 5 index card. For I can envisage the entire lecture with total clarity. The presentation will be the description of a living event. "It is alive," he whispered, "Alive and whole within my mind." Which is how I shall keep it.

He loaded the night's yield into his brief case, went to the window for a quick chestful of air and then settled beside Joyce.

Joyce was still asleep when he awoke, and he would not have disturbed her, except that she had said something about a crucial subcommittee hearing, today. He coaxed her to consciousness with light kisses on the neck and shoulders. She protested and fought wakefulness. But he gently persisted, managed to get her up, showered, dressed and down to the kitchen. Poppa had long since gone to the fields; Ray had left for work; the older children waited for the school bus across the road; and Millie's and the younger children's singing voices were coming from the library. Asa prepared a quick breakfast which, except for the juice and coffee, Joyce totally ignored. She'd said her good- byes the previous evening. But she paused at the library door for a last round of hugs and kisses for the children; and for a prolonged, tight embrace of Millie who, Asa could not help noticing, seemed exceptionally cheerful. Joyce said nothing during the trip north, except that Asa should not show any outward signs of affection in the airport. "Call me," was all she said as the line for the Washington shuttle began to move. After he checked in her rented car, he caught the airport limousine to Forty- Second Street and set out on foot for Havering Institute.

Asa thought he had once seen the Civil War era brick building on 14th Street that originally housed Havering, but he was sure he had never seen the institute's new facilities on midtown Manhattan's east side. At Second Avenue, he supposed it was the mountain of glass and Bedford limestone standing tall above the surrounding tenements. At First Avenue, he became even more sure. At York Avenue a sign confirmed his hypothesis: Havering Memorial Institute for Oncological Research.

In spite of his love of untampered- with Nature, Asa did not despise cities, not even New York. Cities were people, after all. But, although he forgave urban architecture, he could not rid himself of the idea that New York's skyline, and its mimics elsewhere, proclaimed a degree of linearity living creatures cannot long endure, a Euclidean geometry, convenient for the engineer but alien to Nature's grand design. He saw in the city's structural theme the essential message of the vandal. It seemed ugly.

Havering Institute immediately conveyed something quite different to him. Its components had once belong to the bedrock of southern Indiana. Quarried from their origins with skill and care, the stones had been aggregated as a good writer articulates the elements of a language: know the source and let the elements mean what they must! Havering's splendid form had once lived on the great subjective plain of a vast human imagination and, here and now, the architect's proclamation was instantly clear to Asa: BE!

Asa waited for the traffic light to change, then crossed York Avenue, entered Havering's main entrance through a welcoming bank of glass doors, obtained directions from a gray- uniformed security guard at the information desk, and proceeded to get lost --first in the children's out- patient clinic; then in the scrub room of Surgery B and finally in a biochemistry laboratory where a gracious (and attractive) technician personally escorted him to the correct elevator, where she waited with him until the car arrived. Her face was shaped like Joyce's. And when her lower lip protruded just a bit, and when her smile at him extended to her eyelids, he would have asked her if he might buy her a glass of beer, except for Joyce.

He was soon walking into a large, busy office complex and standing at attention before a desk whose name plate read, "Mrs. Jennifer Gibson." The desk seemed like a sentinel post behind which were two doors, one marked, "Fisher Adrian, M. D., Director"; the other, blank. The presumptive Mrs. Gibson looked up at Asa, and he had the urge -- which he resisted -- to snap to attention and announce, 'Private Zook reporting as ordered, ma'am.'

Mrs. Gibson deferentially introduced herself, said she had been expecting him, arose and escorted him through the marked door. Inside was a very large room featuring a deep- nap carpet, a massive oak and onyx desk, overstuffed horsehide furniture and bookshelves bearing morocco- bound classics. The office was empty, but an inner door at the far end was open, and Asa followed Mrs. Gibson through it.

"Come in, come in, Ace," Fisher Adrian said as they entered. He had been seated at a neatly organized but heavily encumbered roll top desk in the corner, writing on a yellow legal pad. But he stood as he spoke, walked to Asa and shook hands. Asa thanked Mrs. Gibson but declined her offer of coffee. She smiled again and left the way they'd entered. "Here, Ace," Fish said, taking Asa's brief case and gesturing to a chair beside a large steel desk near the window. "Let's sit over here and enjoy a little of the Lord's sunshine.

The room was in a corner of the building, and its banks of windows, at right angles to each other, presented a synoptic view of either the East River or of Yorkville. Stacks of unshelved, unclosed books competed with unfiled folders and unopened mail for all but the scarcest bit of elbow room on the surface of the steel desk. "Mrs. Gibson runs me out of here once a month to find where I've misplaced my wits," Fish said. "You're a mite early, Ace. Do you want to use my show office to collect your thoughts or go over notes?"

"No thank you, Fish."

"Okay, Ace," Fish rocked forward on his chair and used the desk's elbow room. "What's my answer? Is a non- screwball principle of life's universal and particulars a possibility?"


Fisher Adrian stared and waited and then asked, "That's all? Just yes?"

"For the present."

Fish grinned. "Well, that's precisely what I asked you for, and all you promised to deliver. But you're really not going to play Merchant of Venice with a poor old man, are you Ace?"

"No, Fish. I'm not sure of the details. But intuitively, I know there exists a unified general and particular principle of life. My lecture will be about the pivotal idea."

"Will you keep me dangling in suspense until then, Ace?

"No, Fish. The key is memory."


"Memory in its most catholic sense of the word. Psyche might be a better term."

Fish leaned back, rotated 180 degrees on his chair, extended his short legs to the windowsill, crossed his ankles and laced his fingers together atop his head. "Memory? I'm struggling with that, Ace. But I'm having trouble bringing it down to earth. It sounds almost mystical."

"No. It is not at all mystical, Fish."

Fish turned quickly back to Asa. "I didn't use mystical in a pejorative way. Forgive me if I seemed snide or sarcastic. I wouldn't do that, not with you, Asa."

"I'm not insulted, Fish. But I am not a mystic. It is a mistake to confuse theory with mysticism."

"Of course, of course. Mysticism didn't create the H- bomb. Theory did. But Ace, I'm really not at all put out by mysticism with reference to the living process. Life seems very mysterious to me, and sometimes mystical -- in the wee hours of the morning or on the toilet seat. My only proviso is that the final outcome of the thought be first rate experimental data. How one arrives at the results, I confess, is not very important to me. But Ace, I am struggling mightily to fit memory or mind into my empirical metasystems."

"I have very little use for mysticism," Asa replied, "if one is serious about it. As a self- imposed game, I occasionally indulge in it, myself. But only as a... a game. Mystery, yes. Nature is a vast mystery. And there is little of importance about her that we can know directly. But while my meanings are abstract, when I say memory, I am being quite literal. I'm being theoretical, not mystical. And I intend, ultimately, to be predictive with my theories, not speculative." Fish rested his thin elbows on the desk and pressed his knuckles against his lips. Asa continued.

"By focusing on memory, I believe I will be able to formulate a statement about Nature's first, life- giving principle. To stipulate what memory is is to define that first principle. Articulate memory in sufficiently general terms, and we predict the necessary and sufficient conditions for life to continue -- or to terminate. I am far from sure of the whole picture, the complete theory, the overall working model. But I am in a position to be very precise about the meaning of memory; about the elemental character of the psyche. I shall present the latter in my lecture today."

"Stop, Ace, I don't want to hear any more about your lecture, not right now. It might spoil the fun of listening to you unravel the story. But can you say anything at all about what's always zinging around in the back of my noodle? About mitosis? About...cancerous growth?"

"I would need several days to explain the entire argument, and the time is getting short. Therefore, let me simply mention the copulative notion. It is regeneration."

"Regeneration is memory?"

"Regeneration is the protoplasmic counterpart of remembering, Fish."

Fish stood, thrust his hands deep into his pants pockets and looked at the East River. "Ace, would you object if I attempt to put my own words to it to see if I'm getting the message?"

"I do not object."

"Your argument is that the reconstruction of a tissue or an organ is like summoning up a shtick of memory? It's like recollection. That in, say a rat, the same forces that tell the creature which turns to take in a maze also command, for instance, the renewal of its intestinal lining or the regrowth of its hair?"

"Not forces, Fish. Logic. The confusion between energy -- force -- and logic is why biology misses what should be its point of departure from physics and chemistry. Force implies compliance with the laws of thermodynamics -- certainly within the energy levels of biological systems. Logic refers to rules of operation. Force and logic may become one and the same at velocities encountered in the cosmos or in light; but not in living matter. In fact, I can very easily show that the laws of physics break down if we insist on making force and logic one and the same for a living cell. What I mean about regeneration and remembering is that one fundamental principle is embodied in vastly different physiological activities. The remembered maze and the renewed intestine are analogs of each other, analogs in the same way that a playing phonograph recording and a person's actual voice produce analogs of each other. The two yield the same essential song by way of vastly dissimilar mechanisms -- via the same logic but different forces."

"Ace, is your system the fundamental principle?"

"The principle belongs to Nature, Fish. My system could conceivably coincide with that principle. Then again, my construct may simply parallel Nature's actual rules. I'm inclined to believe the latter."

"Why would you say that? Are you suddenly waxing conservative on me?"

"No, Fish. I merely seek to give human expression to Nature's thoughts. I'm translating. An old friend of mine, many years ago taught me to respect the limitations of translation. Something crucial always gets lost in the process."

"You're being very humble, Ace."

"I always feel humblest when closest to Nature, Fish."

"You don't play God?"

"To think is to be human, Fish. I am trying to be as human as I can be."

Fisher Adrian shifted his gaze to the East River.


Asa inspected the amphitheater from the speaker's well. The geometry of the space fit the form of all such places as this. But its geography, its details, bore the architect's vision. Its tiers, only slightly less pitched than those where Asa lectured, did not induce in him the sensation of looking up a canyon wall; nor for the audience, of perching on the edge of a cliff. Upholstered seats with fold- down desks took the place of the armless communal benches upon which his students squirmed in the vain search of comfort. He had tried viewing the lecture pit from various seats and each seemed like the very best seat in the house. Fish whispered as he was showing Asa where to find chalk and pointer that the room had no public address system, that the architect had had it written into the contract that none would be installed during his lifetime. Asa would find the acoustics equal to anything among Italy's municipal opera houses. (Asa had never been to Italy? Well, if and when he did go -- and Fish insisted that Italy was a must -- he'd have to spend some time hearing the beauty of the human voice received by Italian space.)

People were still filing in after Fish's introduction, and Asa held his opening for a moment and watched them. Many wore the intern or resident whites of Havering's clinic staff; white, gray or tan lab coats; green surgical ducks; here and there an administrator's mohair; and the inevitable dress of the working scientist: baggy trousers, faded work shirts, tieless collars, filthy lab coats. Except for two oriental men, it was a Caucasian crowd. Seven percent of the seats were occupied by women who, because they bunched together, seemed more numerous than their actual numbers. One exception was a stunning woman who took the seat beside Fish, and to whom Asa found his own attention automatically drifting. She smiled at him, and he nodded back, certain his ears had suddenly turned scarlet. Embarrassed by his disobedient eyes, he looked around the room again, rubbed his hands together and -- although a few people were still filing in -- began to speak.

"My lecture this morning is on certain theoretical properties of memory, by which term I shall mean all forms of stored neural information, irrespective of whether the information is as learned as names of the wrist bones or as innate as voiding the urinary bladder [a few giggles].

"What is the fundamental nature of the memory trace? What is the psyche?

"Let me refresh you about the work that has been going on for three decades at Harvard by Professor Karl Lashley and his colleagues. Let me summarize his prodigious attempts to isolate the engram by selectively removing portions of the brain. Lashley has not been able to isolate memory in any particular lobe or locus. Instead, his experiments have demonstrated that memory is a distributed property of the brain. Distributed as is heat in a pot of boiling water. The temperature reading does not depend on where in the pot one places the thermometer."

The woman beside Fish raised her hand, and Asa acknowledged her. "Dr. Zook?" He was surprised she knew his name. "Dr. Zook, what about brain regions such as Broca's motor speech area?"

Asa addressed his answers to the audience as a whole. Others, including Lashley, had commented at great length on questions of this sort, Asa explained. It was true that a stroke may severely impair the capacity to use memory. It was also true that certain areas of brain have been implicated in special forms of recall, in particular types of perception and in certain behaviors. Some of Lashley's recent work, in fact, showed this. Nor did Asa wish to minimize the significance of such evidence.

"But there is a fallacy inherent in the question, a fallacy akin to confusing the voice on the telephone with the person on the other end of the line." Laughter. Asa turned to the woman. "I was not seeking to deride you, personally, doctor. And I apologize if my remarks seemed that way. Also, let me say I believe good intentions underlie the attempts to make the form and function of the brain one and the same thing. Intentions akin to the search for the oneness of Nature.

"But the oneness of Nature is not ours to see, not with our eyes, not within the framework of daily experience, not with common sense. We can apprehend Nature's unity only if we have the humility to employ reason; only with the intellect; only when we fortify our understanding with the most powerful rational tools we can muster. Only with the lenses of mathematical theory, not those of our microscopes.

"Returning to the brain..." Laughter. "I recall well, one of my own patients, a fifty- seven year old former army sergeant who had sustained massive head injuries during the First World War. He had no left occipital lobe at all, and he exhibited the predictable neurological deficits. The opposite half his visual field was gone. But the man's cognizance of the world, and his memories, were whole. His mind was intact although his brain was not." Observations of this kind were quite common, Asa assured. For those among the audience who were interested, he wrote on the blackboard the reference to a paper by Halstead and co-workers. The woman next to Fish was intently writing when Asa glanced her way.

Asa went on. "Let me mention another patient, a man in his twenties who had the grossly enlarged head of a congenital sufferer of hydrocephalus. He was born to an inmate of a state mental institution on whose house staff I...I once served. The mother was incapable of caring for the child. Believing that the baby would soon die, administrators of the institution took no steps to have him transferred to a pediatric facility. When he did not die, he was eventually declared mentally incompetent, which relieved the state of its legal obligations to educate him. For a variety of sordid reasons, the man made his home in the institution's maximum security section where he was performing janitorial duties and other household tasks when he became my patient. Curious about why he was there at all, I examined him. I found him behaviorally and emotionally healthy, a remarkable achievement considering the unbelievably horrible conditions in which he had lived his life. Psychometrically? He scored 118 and 124 on two different nonverbal IQ tests. I discovered that, although he could not write, for he had not gone to school, he had somehow learned to read. 'Where?' I inquired. From the captions in the funny papers! He had even learned to play checkers, and I was no match for him at all." Light laughter.

"The man died of pneumonia during the subsequent winter." Asa went on to described what he saw when he observed the autopsy: "His cranial case was principally occupied, not by brain but by cerebrospinal fluid. His cerebral cortex was compressed against the interior of his skull and measured less than a tenth the normal thickness. Here again is another dramatic example of normal human intelligence within an anatomically abnormal human brain.

"I am not unaware of the great fascination Westerners have with structure. I am not unaware of the fact that entire segments of science totally ignore Karl Lashley, the very founder of physiological psychology."

He digressed to recount his personal discovery of Lashley during his first days as an undergraduate, and how he had spent weeks thinking of little else. "But when I went to medical school, I was in for a shock." He told of purchasing his first arm load of very expensive medical textbooks [laughter]; and of going outside the bookstore and setting the costly stack on the sidewalk so as to browse his neuroanatomy book, eager to find out about any new turns Lashley's work might have taken.

"To my utter astonishment, not only was Lashley's research missing from my neuroanatomy textbook, his name was not even in its bibliography. 'How?' I wondered, 'How can a book devote itself to the brain and contain not a single reference to Karl Lashley?' I have come to discover since that such is a habit not merely of neuroanatomy, but science as a whole. Confronted with an inexplicable body of knowledge, science simply ignores its very existence. It is as though innocence can somehow banish ignorance. [Laughter.]

"But Lashley's detractors will find no solace in his opus. Indeed, if a student were to ask me for an exemplar of scientific excellence, I would direct the person to Lashley's work. Indeed, I actually did just that not too many days ago." [Instantly, his mind formed the image of the student in the third tier center without her short white coat, in his office to accept his collection of Lashley's reprints. Asa wondered if she might be reading them at this very instant. What was her name?] He glanced quickly at the person beside Fish and mused momentarily at the likeness between the two young women.

Asa walked to the center of the pit and stood at parade rest, much as he did in his own classroom. "But what is the nature of the engram? Tucked away, parenthetically, among his writings, Lashley proposes a physical analog of the engram. I had almost forgotten it myself until..." He paused and cleared his throat. "Until very recently. Lashley proposes as a physical model of the engram the interference pattern: The fringes made by colliding waves. Light waves, water waves, waves of any sort, really, as I'm sure you learned in high school science.

"Phase is the essence of all interference patterns. And before we go any further I should like to give you an intuitive feel for the meaning and the implications of phase."

Asa signaled for the first slide. The lights of amphitheater dimmed to amber, and in a moment onto the screen flashed a series of vertical stripes. "Interference pattern!. The next slide, please."

Instantly the stripes vanished and two diagrams appeared, one a simple wavelet and the other a circle. "Let me remind you that a wave and a circle incorporate identical logic. If you are unaware of that, simply take my word for it until you have a chance to check your textbooks. Recall, we often refer to waves as 'cycles.' For the rise and fall and return of a wave embodies the same principle as the excursion around and around a circle -- or cycle" He called attention to shaded areas in both diagrams on the screen. Shading was in the first quarter of the circle. In the wave shading extended from the origin to the peak. "These shaded areas are equivalent zones," he said tapping the rubber tip of the pointer alternately at the wave and circle. "And they give us an intuitive idea of the meaning of phase.

"Phase is sometimes defined as the fraction of a wave or cycle where we find a particular point at any given instant. The phase represented on my diagrams is the equivalent of 90 degrees -- 90 degrees with reference to the origin, the zero on the wave, twelve o'clock if the circle were the face of a wrist watch. Of course, I could have chosen 60 or 48 or 17 degrees."

He licked his lips and rolled the shaft of the pointer between his palms. "Notice the terms we employ in speaking about phase -- angles. Angles or functions of angles, such as sines or cosines. Now let me pose this rhetorical question. What is the absolute size of an angle?

"Obviously, the answer is that an angle has no absolute size. And the same statement is true of phase. Phase has no absolute size. Phase is relationships of entities, relationships of changes And an interference pattern is a record of the phase differences between two sets of interacting waves. The shadows are a memory of the combined phases of the two sets of waves.

"For our discussion, the critical thing to keep in mind is that phase lacks absolute properties. Technically speaking, phase is of arbitrary size, which is true of angles and functions of angles in general.

"Of course, we cannot have pure phase, not in physical waves. The wave's mass or energy is a function of its amplitude, which we measure at the wave's crest. But the precise location of the crest -- or any physical part of a wave -- is a function of phase. Given any amplitude, phase will completely define the profile of the wave.

A mohaired sleeve went up. Asa paused to acknowledge the question. "Doctor, your diagrams show a simple sine wave. How can we extrapolate to, say, the profile of a face?" Snickers erupted from among several younger members of the audience.

"No, please," Asa raised his open hand to the snickerers. "It is a legitimate question. These matter are very opaque in the textbooks. Possibly because the author himself does not believe the profound implications. Or possibly the implications of phase seem to bear the germ of embarrassing conflicts with some dogmas of science." Laughter, again. "But back to the question of the simple versus the complex wave. "

Asa described Fourier theorem for those of the audience who might have forgotten the principle. Then, facing the person in mohair, he reasserted, "A compound wave is merely the sum of simple waves. It is as though a series of the simple waves interfered with each other to create the compound wave. Thus a compound profile is a spectrum of phases.

"But let me again emphasize the relative nature of the phase spectrum. Olden Havering's statue in front of the building is many times the size of the original object [light laughter]. Yet the same stern message is transmitted to us independent of the absolute physical proportions [more light laughter]."

Now someone boomed at Asa from the left side of the room. The voice belonged to a large man in a plaid shirt and hematoxylin- smeared khaki trousers; he was on his way to a portable auxiliary blackboard to one side of the screen. Asa increased the blackboard illumination. "What you're talking about, Zook, doesn't apply to waves with multi- valued functions -- like this!" The man began drawing a figure with hairpin loops. "How would you handle something like this?"

"There are several ways, the most efficient would be as a Riemann surface," Asa answered while the man's chalk was still screeching. The man stopped, grinned, took a cigar from his shirt pocket, touched it to his forehead and returned to his seat.

"Back to phase," Asa went on. "I refer to waves and circles only for illustrative purposes. But phase is inherent in all harmonic events, in all actions and reactions of a continuous and cyclic character. And it would be an error to envisage waves, literally, in the remarks I am about to make." He dimmed the lights. "Next slide, please."

On flashed a composite picture of several sets of stripes, the stripes of each set varying in thickness. "These are interference patterns of different frequencies -- different numbers of stripes per millimeter. The different spacings represent different phase angles between the sets of waves used to create the interference patterns. I show this slide to emphasize the intimate relationship of pattern to phase. For phase strictly and minutely determines each pattern. This is another way of saying that the interference pattern is a memory of the interacting waves.

"If we postulate that interference is an analog of memory -- as Lashley does -- then we are left with the obvious corollary that phase is the essence of memory. Phase is the fundamental element of the psyche. Indeed, I make the latter assertion here and now. Mind is fundamentally phase. And everything the engram is, does or can do depends upon the mathematical properties of phase.

Low buzzing spread throughout the audience. Asa took a breath and continued. "Now an ordinary interference pattern does not supply the intuition with a sufficient analogy. The problem is that two monotonic wave fronts such as those used to construct the patterns on the screen -- two regular wave fronts -- do not carry an intuitively meaningful message. Our intuition demands what I technically call a non- zero message. The next slide, please.

"This slide shows an X-ray diffraction pattern. It happens to be a diffraction pattern of DNA -- a paracrystalline pattern, technically speaking. The shadows, although exceedingly complex, nevertheless embody and obey the same logic as in the fringes of a simple interference pattern, I showed earlier. Hidden in what we see on the screen are spectra of phase information. And if the crystallographer were able to deduce those phase spectra from the data we see, he would be able to tell us every detail of the internal anatomy of the DNA molecule. The diffraction pattern, in other words, is a memory of how the DNA's atoms collectively diffracted -- bent -- the X-rays as they passed through the crystal."

Fisher Adrian raised his hand. "Dr. Zook, did I hear the caveat 'if' in your remarks? Wasn't that done to deduce the double helix?"

"Not quite. Certain features of the diffraction pattern suggest that DNA is helical. But phase has been a genuine problem for the crystallographer, and especially so in paracrystalline patterns such as on the screen. Those who are now intensively analyzing such data must take the double helix as a given."

Someone raised an objection. Before Asa could reply, a man in the front row, turned around and answered with a Swabian accent. "The X-ray data do not give the double helix. Intuition produced it, not calculations. Forgive me, Dr. Zook." The man's friendly face beamed at Asa, and Asa smiled back.

"I merely use DNA," Asa continued, "as a actual example of a complex spectrum of phase information. But in what you see on the screen, phase information is distributed -- repeated whole, again and again, in different sectors of the diffraction pattern. The crystallographer forces his data to yield phase by mathematics. Calculating is the crystallographer's analog of remembering."

Now the woman next to Fish raised her hand. "I'm really sorry to keep interrupting you, Dr. Zook..."

"No, please do not apologize," he responded. Her lower lip came forward slightly, she blushed but continued her question.

"You model memory with the X- ray pattern -- physically-- and remembering with mathematical calculations. Wouldn't you want something truly physical for remembering? After all, the remembering brain would have to rely on physical circumstances for calling memory out of storage, wouldn't it?"

The question delighted Asa. She was not only beautiful. She was also brilliant. For she had anticipated the very next point he was about to make.

"Yes. You are correct. We do need a physical precedent in our model for utilizing phase information. One actually exists. It appeared in the literature not long ago in an article in Nature by a D. Gabor. It is called the hologram.

"Gabor's hologram is not very spectacular. Yet I am quite surprised that physicists have paid it so little attention, thus far. For Gabor has shown that not only can a complex phase spectrum be recorded -- as the hologram -- but the original wave front can be reconstructed from the record."

"I don't believe it," said the large man in the plaid shirt who was now vigorously chewing one end of his unlit cigar.

"It occurred, Nate," the Swabian gentleman looked over his shoulder and reassured.

Nate protested. "But Sol, that would violate the Uncertainty Principle."

"NO!" Sol and Asa replied in unison. Sol smiled up at Asa and yielded.

Asa explained to the audience that the hologram recorded not phase itself, but a memory of phase. "Reconstruction of an image from it," he went on, "is the regeneration of phase, not merely the simple decoding of it." If one kept the subtle distinction in mind, the Uncertainty Principle was "completely safe." Asa and Sol smilingly shared a private moment of mirth.

Asa moved to the lectern and looked at the audience. "Regeneration is the key word in understanding how a hologram remembers. Unfortunately, no light source exists of sufficient coherency to illustrate the theoretical capabilities of Gabor's hologram."

Sol raised his hand. "Such a source may be available within a few years, Dr. Zook, a source of highly coherent light in which photons will be emitted in pairs as identical twin pairs.. Excuse me, Dr. Zook, but I was merely attempting to head off some of my colleague Nate's nominalistic objections." Asa looked at Nate who, grinning from ear to ear, had eaten half his cigar.

"I am very much obliged, sir," Asa said. "For in that case, let us imagine a hologram with the distributive properties of an X- ray diffraction pattern. In such a hologram, every point would contain a complete memory of the entire visible object. And even if we destroyed large areas of it, the surviving portions would still be able to reconstruct the entire object. For every fragment of our hypothetical hologram would contain a complete record of the original wave front's phase spectrum."

"I'm confounded by that one Dr. Zook," Fisher Adrian broke in. "You're implying that every geometric point contains a whole record. How, pray tell, can that possibly be?"

"Phase is without absolute size," Asa answered. "And therefore any surviving fragment will contain a complete memory. In this respect, the preserved memory in the hologram is analogous to the surviving memory among Lashley's rats. It is also analogous to the wholeness of the minds of my patients whose brains were decidedly not whole.

"I shall henceforth refer to the memory trace as the phaseogram. And I assert here and now that the phaseogram is the fundamental unit of the psyche, which is implicit in my remarks thus far.

"But I should like to make a prediction. The phaseogram exists independent of the brain's anatomical organization. Therefore, memory ought to survive the randomization of the brain's parts. Given intact sensory and motor mechanisms, the psyche will endure the scrambling of the brain's structure.

"Thank you," Asa said, and he rested against the lectern in anticipation of questions. But the audience sat in silence, as though waiting for him to continue. When he did not, they began talking in muted tones and slowly filing out. There were no questions, whatsoever.


Asa's was the clam chowder, wasn't it? the waiter was asking. "Nuttin' to drink, right, sir?" Asa tried to listen to the conversation. When was Havering going to get its own electron microscope, Dr.___ [he'd failed to register her name] was asking. Fish was saying that "Annabelle" could spend money faster than he could raise it. But, seriously, he added, they really were going to get an RCA at the end of the fiscal year when one of their NIH grants came into effect. Speaking of grants, Fish turned to the man on his right, had he heard anything from NSF? The man stopped the progress of a forkful of Wiener schnitzel and grinned, presumably in the affirmative. Fish turned and asked Asa for his opinion. About what? The value of electron microscopy in biological research. Asa had no opinion.

Dr. Annabelle rummaged through her chef's salad, speared a miniature bell tomato and transferred it, whole, into her mouth. Her lips struggled to remain pressed together. Asa's headache began to abate as he watched and became mildly amused by her motile mouth. She looked at him, smiled and attempted to talk over the sound- quenching morsel. "I hope you weren't just being gallant." She swallowed, and her clear mezzo- soprano returned amid the next sentence. "I hope my questions didn't distract you.

"They did not," Asa replied. The chowder was too salty, and he laid down the spoon.

"I'm utterly exploding with a billion questions," she said, "Questions about the phaseogram. Your predictions, especially. How do you plan to tackle the experiments?"

"I do not maintain a laboratory," he answered. She stared at him, and her smile disappeared. "I'm strictly a theoretician," he added. "I would not know where to begin the testing my predictions, not experimentally."

Fisher Adrian had been saying something to a young man across the table about tickets to the Polo Grounds. But he broke off and turned diagonally to address Dr. Annabelle and Asa simultaneously. "I'd like you to see Dr. Crowe's lab this afternoon, Ace.

"I would not want to insinuate myself into your routines," Asa said.

"Nonsense." She blushed. "I really love showing others my research."

"What is your research Dr. Crowe?

"Please call me Annabelle.

"My name is Asa.

"She's an experimental embryologist, Ace," Fish inserted, raising his beer stein, "And one of the most skillful I've ever seen." Her blush deepened.

"I transplant things," Annabelle said. "Little things."

"For example?

"Pieces of salamander. Limbs, tails. Heart, recently. I've been observing, lately, what happens after I transfer minced up ventricular muscle to the gelatinous tissue of the larval salamander's tail fin."

"What does happen?"

"I'm not totally sure yet, but I think the pieces reconstruct a miniature heart, which hooks up with host vessels and begins pumping blood right there in the fin."

"You did say larvae?"

"Yes. The axolotl. Ambystoma mexicanum. We rear them in my lab."

"The operations must demand great dexterity," Asa observed.

"Indeed they do, Ace," Fish injected.

Annabelle wrinkled the skin on the bridge of her nose. "Not awfully much, really." She transferred her attention to something within her salad bowl.

"Say Zook," Nate called from the far end of the table. He furiously sawed at Bratwurst as he spoke. "Just where does phase fit into the electrophysiology of the brain?" Several conversations at the table stopped.

"The entire nervous system from the single neuron up to the brain as a whole is organized to communicate phase information. The all- or- none firing of nerve impulses makes amplitude modulation a poor means for generating neural signals. Effectively, the brain cannot make a message by varying the strength of signals, that is by modulating amplitude. Frequency modulation is the signaling mode of the nervous system.

"Like an FM radio?" Someone at the middle of the table had posed the question. Not sure who, specifically, Asa leaned forward and addressed his answer in the general direction. "Yes," he said. "Frequency modulation -- FM -- is a physical way of varying phase.

Nate shoved his plate aside, propped his elbows on the table, bit off and spat out the tip of a fresh cigar and spoke. "What would you use as the equivalence of a coaxial cable, Zook?

"Parallel tracts. Two or more tracts connecting relay stations. Two or more parallel pathways that either conduct at different velocities, or have different path lengths.

"Give me a for- instance." Nate lit his cigar with a Zippo lighter.

"The auditory system has co- terminal pathways of different lengths. The voluntary motor system is another. The limbic system has them. Indeed, I know of no major exception. Do you?"

Fish entered the discussion. "I think Dr. Zook uses the term 'parallel' in a much more general way than we're accustomed to. You don't mean parallel in a straight- line sense, do you Dr. Zook? If I understand you, by co- terminal you mean that the tracts in question begin together, say at station A, and then end, for instance, on B. Is that correct?"

"Yes!. I think it is best to think of coaxial pathways as geodesics of somewhat different curvatures."

"I'm lost back at stations A and B, Asa," Annabelle said.

"Would you mind, Ace, if I attempted the answer?" Fish asked.

"Not at all."

Fish signaled for the head waiter. "Anton, I'm going to ruin another tablecloth. Please put it on my personal tab, not the Institute's." Anton seemed familiar with whatever was coming. He snapped his fingers and a coterie of bus boys rushed forward to clear the table. "I'll keep those, please," Fish said, retrieving a partially filled water goblet and two teaspoons from a bus tray.

Fish set the goblet at the middle of the table. On the white field of linen where his plate had been, he drew a small circle and labeled it with the letter A. "Call the goblet, station B," he said. From A to the goblet, he drew two arcs, one much wider than the other. Now he lifted the two teaspoons and held them over A. "Observe!" Fish said. He moved the spoons out over the separate arcs toward the goblet. Ding! and Ding! the goblet resounded upon the separate arrival of each spoon. "The interval between the two dings depends on the difference in the two path lengths. The difference is analogous to the phase difference Dr. Zook is talking about. Relative phase is embodied in the variation between the two paths and is manifest in the two dings." Fish winked at Asa. "Virtually from your article on coaxial communication in the British Journal for the Philosophy of Science, Ace." Asa returned Fish's grin.

"The dingbat theory! Dingdong! Dingdong! Dingdong!" announced the Polo Ground man, laughing

The smile instantly vanished from Fisher Adrian's face. He stared at the young man. It was a wire- haired paratrooper's stare. Silence spread up and down the table. And except for Nate and Asa, the others began examining either the tablecloth or a target elsewhere in the room.

Asa spoke. "No," he said. "Ding- ding is more parsimonious, I would say, and we should invoke Occam's Razor whenever we can."

Laughter erupted from Nate and progressed throughout the table, excepting Fish. "Moreover," Asa added, "A spectrum of ding dings! Dingaling Theory might be a more suitable title." Now Fish joined the laughter.

Annabelle looked at Asa. Her lips parted, the lower member of the carmine pair protruding just a bit. A nibbly bit. And then she spoke. "I like that Dr...Asa. Seriously. I mean, a spectrum of dings would add up to music. Can you fit memory explicitly into the neural pict-- No! I won't mix the metaphor with 'picture,' Asa. Can you connect the phaseogram to the neural symphony?"

"If we take Fish's spoon and tablecloth nervous system, the memory is built into the curvature difference between the two arcs extending from A to the goblet. The phaseogram is anything -- any medium -- that can preserve the phase variations of the original message. Anything that can, potentially at least, regenerate the original ding- dings when we activate the memory. Opening up the coaxial pathway is analogous to perception. The song itself is the counterpart of behavior. The phaseogram links perception to action.

"Think of the three modalities -- perception, memory and behavior -- as three connected but independent mathematical spaces. What must be generated for the perceptual signal is a phase spectrum. What must be stored as memory is the phaseogram itself. What must be read out during remembering is a facsimile of the original phase spectrum. That spectrum when transduced into actions and reactions among muscle groups yields behavior. Movement of information from one abstract space to another is analogous to mathematical transformation."

"I like that, Zook," Nate announced with a grand swoop of his free hand. "I like it a whole lot. In essence what you're saying is that memory preserves the variational relationships between input and output."

"Yes. Nor must tracts, per se, carry the phaseogram. The medium could in theory take the form of harmonic motion among charged particles in the cell's membrane; or even resonance within chemical bonds within molecules of the cell. I don't maintain that memory necessarily exists at such levels. But keep in mind that phase is of arbitrary size. And the same phaseogram could conceivably exist on molecules and simultaneously throughout the brain as a whole. But just which media support the phaseogram is really an experimental, not a theoretical issue."

Nate signaled his intent to speak again. "Yes, Zook, I really like your phaseogram theory a lot. But there's one thing wrong with it. No data!" He crushed his cigar between his molars and said not another word.

Copyright, 1996 by Paul Pietsch, all rights reserved. May be copied for personal, educational or other non-commercial "fair-use" purposes, as defined by U.S. copyright law.

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