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

chapter 18 Predictions

Asa's office in the Theoretical Section of Havering Memorial Institute was three floors directly above Annabelle Crowe's sprawling suite and a set of double doors north of the Pediatric Oncology ward. His office was a large room with an adjoining office for a secretary. The view was of Welfare Island across the river where Fish, holding Asa's shoulder and pointing south through the 59th Street Bridge, identified three hospitals. "That unfortunate structure on the far end is City Hospital." Fish's son had completed residency there in dermatology and syphilology. "That was in pre- penicillin times."

On Asa's first day, the foreman from Maintenance stopped in, patted the bare walls with the palm of his hand and offered Asa bookcases, blackboards or any combinations of both. Except for a small blackboard, Asa chose bookcases.

"A pencil man, I see," Solomon Perlmutter -- Sol -- observed. He was the man in the front row during Asa's first lecture, and his office was right next door. He had stopped in to introduce himself, "Formally. " he said, and to invite Asa for a glass of tea. When Asa attempted to converse in German, Sol raised his hand. "Please. I cannot abide that language any longer". Sol turned out to be a blackboard person.

Sol was a close friend of Nathan Rabinowitz, the Nate with the plaid shirt and cigar. He often brought his bag of lunch and cigar to Sol's at noon: "To mooch bad tea and good ideas." Asa joined them when he could, and lunch often became a freewheeling seminar among the three, sometimes extending into the depths of the afternoon, or until Mrs. Rowan, Asa's Secretary, would lean into Sol's doorway and remind Asa of an appointment with Dr. Adrian, Dr. Crowe or the dentist. When it came to Joyce, Asa never required a reminder, not even when he was with Sol and Nate.

The notion of a secretary had seemed absurd to Asa. Fish brought up the subject after Asa and Joyce returned from their second visit to Japan. "He works entirely too hard," Fish insisted in Joyce's presence, "and I'm also quite concerned about his high blood pressure." Besides, Fish had a problem, he said; namely, finding a suitable assignment for Mrs. Rowan. A veteran scientific secretary in her late fifties, she had spent most of her career devoted to a recently retired bacteriologist. Turning to Joyce, Fish pleaded, "Talk him into rescuing the dear woman from the purchasing department." Annabelle said she was going out of her mind trying to keep track of his whereabouts. When Asa said he really did not need the help Nate said, "You're nuts, Zook." Sol shook his head in agreement, if not with the words, certainly the idea. But when Joyce said, "Please dear," Asa agreed. In the Journal some months later, he conceded, "Mrs. Rowan has added years to my short ration of time."

Sol Perlmutter, Asa learned early on, had been a nuclear physicist. But now his work was on the statistical mechanics of biomolecules, especially DNA. And he called himself a biologist. A student of Heisenberg, Sol was from Göttingen where his father had been a music professor. As a youth, Sol had spent many hours in the university's library with Riemann's original manuscripts. [Asa's skin puckered when Sol casually mentioned Riemann.] Sol's intentions had been to go on to Berlin to work with Einstein where he had hoped to compare the atom with the cosmos. But he wanted a year or two, "Looking over the shoulder of the experimentalist." And, he confessed, he also needed a little adventure before settling down to the realm of pure theory. His formal education completed, Sol began a tour at Berkeley. But the life he had left behind vanished in his absence. "My country, my friends, my family, my boyhood dreams all ceased to exist." When war broke out, he eagerly went to Los Alamos. His senses returned after Hiroshima and Nagasaki. "And I could no longer do physics."

Abandoned physics or not, Sol Perlmutter had lost none of the habits of his renounced profession. He still solved problems in the direct, confident and economical manner of the physicist. Logic excepted, all mathematics seemed immediately at Sol's fingertips, ready to be summoned at the touch of a piece of chalk. Where Asa spent days or weeks refreshing himself on a particular method, Sol went straight for the blackboard. "I like your theory, Asa," he said early on. "Intuitively, it has the ring of validity. Unfortunately, I cannot phrase it in a mathematical way. And therefore I can offer no useful suggestions or assistance to you." Asa agreed that the theory was still far too qualitative. He would try to quantify it by parts. "Ah! By parts!" Sol said. "This was precisely Riemann's approach. He had an Orphic view of the possibilities of mathematics, saw the subject with totality. But he proceeded with great humility. He asked the humble points to yield their transcending secrets. From the elemental rules of quantity, which the humble domains around points supplied him, he constructed an abstract universe so total that it can contain the one we inhabit, as Einstein subsequently demonstrated with General Relativity theory. But had Riemann taken a grander approach, while he might have succeeded analytically, his creation would have been too remote from reality for any mind but his own to encompass and appreciate. By parts! By parts! By tiny transcendental footsteps, one at a time! If you reach your goal, Asa Zook, it too shall belong to the whole world."

Nate had majored in physics and chemistry at CCNY but had shifted to electrophysiology in graduate school, at Columbia. He had an intuitive grasp of theoretical physics and approached all experiments with the aid of mathematics. At first, he confessed, he thought Zook was just one more bullshit artist. Still, where Sol looked for a theory's generality and consistency, Nate demanded, "Cows that give real milk." In addition, for physiologist Rabinowitz, "The experiment must tell how much milk." When Nate came to shake Asa's hand after Annabelle's lecture, he'd said, "What you need now, Zook, is a prediction with some numbers in it."

Asa had thought off and on about tests Nate's lab could conduct. But it was actually Joyce who precipitated the critical notion. They were reading in bed one evening, he the new issue of Mind, she the Congressional Record when: "What does this ECS -- this electroconvulsive shock do to the brain, Asa?" He described its amnesiac consequences to her and was about to say the actual physiological disruption was not known when...

"Of course," he shouted, kissed her passionately and bounced out to get the Journal.

"What was that all about, Asa?"

"You've just shown me how to give Nate his numbers. Julio's Mamaluchee involves at least two distinct behaviors First, there is the response of looking up after the snap of the comb, and, secondly, the feeding itself. Two sets of memories, Joyce, and two distinct phaseograms. Recovery from amnesia should take longer in one than the other. Intuitively, I can see how to predict the differences from the effects on of ECS on salamanders." When he said he would have to go down to the beach for a couple of day, and when he took down his long slide rule, Joyce threw her arms about him and begged him to let someone else do it. "There is no one else, dear," he replied.

It was a Tuesday morning when Asa dropped a note in Nate's mailbox. "Find the minimum shock frequencies necessary to induce amnesia for the Looking- up. Do the same for Feeding reaction. The convolution function of the two shock values will be the reciprocal of the separate recovery (regeneration) times of the two different behavioral traits -- and ipso facto, the two underlying phaseograms."

Ten days later, Asa received a message. "After frying a few of Annabelle's ugly bastards to determine our parameters, we find that, statistically, Zook is right on the experimental money. Congrats! Rabino--" The "witz" was illegibly Nate's.

Nate sometimes stopped by during the late morning, "Just to shoot the shit about science." On one such occasion, he wondered why Asa did not take a stab at his theory with the ponderomotive equations of general relativity. "Let's drag Solly in if he's awake," Nate suggested. They went next door, and Sol fixed tea.

Asa put forth his reason for avoiding well formed physical theories. "They are meant for extreme levels," he insisted. Relativity might lead to a satisfactory description, Asa further conceded. But he suspected that the equations might not apply directly and immediately to the living brain. The same was true of quantum wave theory, he thought. He had, in fact, spent some weeks attempting to fit the phaseogram into Schroedinger's equations; but none of the corollaries yielded anything testable in a biological system. The problem was analogous to bridge building.

"You've got me absolutely stymied on that one Zook. Explain!"

Sol obliged. "My dear and brilliant Nathan. Can you imagine using Riemannian geometry to design a suspension bridge? Given that the engineer had ever heard of the subject, what foreman would be able to carry out his instructions? There is a right solution for the right problem. And the methods of physics, Asa maintains, are not the correct ones for living memory.

"There is also this," Sol went on, gesturing offers of more tea with hands and eyebrows. "If I correctly gauge Asa's intent, if and when his theory is scientifically complete, he also wants it to be philosophically revealing, as well. Is that true, Asa?"

"It is."

"Philosophy!" Nate grumbled. Then he smiled, clamped his cigar between his molars and winked at Asa.

"But there is also this," Asa added. "I do not seek a theory -- or even a metaphysics -- of everything."

"Just life itself," Nate laughed. He stood, rubbed his abdomen with both hands, looked at his wrist watch and announced, "Feeding time, gents."

Asa was about to say he could not join them when Mrs. Rowan's head appeared in the door way. "You and Mrs. Zook have a luncheon engagement with Dr. Adrian today."


Asa was to meet Joyce in Fish's quarters. The two were in the big office, Joyce holding a Morocco-bound volume and reading an A. E. Housman poem to Fish when Asa arrived. Annabelle would be joining them in the lobby, Fish said. In the elevator, Fish told them that a broadcaster friend had introduced him to a restaurant on Eighth Avenue with arguably the fastest waiters in New York. Lunch was the specialty of the house, and while it was still new and exciting to him Fish wanted to share the place with his favorite people. Joyce gestured Fish a kiss.

Joyce and Annabelle greeted each other with an embrace, as they usually did. The four took a taxi across town (Asa would have preferred the walk). "Where is it?" Joyce asked after the cab let them out. Fish merely grinned and led them to the side door of a tenement building. The door was covered with sheet lead and proved deceptively heavier than it looked. Inside, they followed Fish up a flight of stairs and into a realm no one would have suspected from the street. "White oak," Asa announced about the exposed beams in the ceiling. "Cut and rubbed a hundred years ago, I judge."

"Poppa would love it here," Joyce said. Asa smiled, shook his head in the negative and looked toward the bar. Joyce grinned in agreement.

The headwaiter led them to a center table, asked if they would care for cocktails before ordering, and then politely called, "Garçon!"

Asa addressed Garçon in Tagalog. Fish ordered three dry martinis and a black coffee. Except for Joyce and Annabelle, the patronage was exclusively male. Several men said, "Hello, Mrs. Zook," on their way in or out, and one stopped at their table to shake Joyce's hand. "Well you've finally broken into our exclusive world," he said to her.

"Turnabout is only fair play, Mr. Applington," Joyce answered. "I'd like you to meet my husband, Dr. Asa Zook and two of his colleagues, Drs. Annabelle Crowe and Fisher Adrian."

"Please don't stand up folks," Mr. Applington insisted. "Reporters aren't accustomed to deference." His gaze kept drifting to Annabelle. Fish invited him to join them. "No thank you, sir. I've got to skidaddle in a minute."

"Do you know him, Ap?" Joyce asked in hushed tones, indicating with her gaze a man seated alone by the wall.

"Ed? Sure. Want an introduction, Mrs. Zook? I'm pretty sure he wants to meet you. And would you believe that an old salt like that is painfully shy?" Joyce excused herself, but this was someone whose hand she simply had to shake. She and Ap walked to Mr. Ed's table. He stood up, snuffed his cigarette out in a saucer and accepted Joyce's hand.

"He's a great human being," Fish said, and Annabelle agreed. He was thin with a long, sad face, large widely spaced eyes, distinct eyebrows and dark, plastered- down hair. Mr. Ed nodded their way, and Asa returned the gesture with a smile. "He may have saved this nation," Fish said to Joyce as she returned. She agreed.

Ap, who had paused at Mr. Ed's table, stopped on his way "back to the grist mill." Again, he seemed quite interested in Annabelle. From the blush on her face, Asa postulated that she was also interested in Ap. Joyce winked at Annabelle after Ap departed.

Asa asked Joyce to select something light for him. Then Joyce, Fish and for a brief while Annabelle discussed politics, while Asa admired a collection of tooled silver platters and pewter ale tankards on shelves behind and adjacent to the bar.

Annabelle soon dropped out of the political conversation, and turned her attention to Asa. "When do we start talking in earnest about the blastema?" she said.

"We can talk now if you would like," he answered.

"What is the blastema?" Joyce turned away from Fish to ask.

Annabelle replied, "It's a little bud of cells -- what the regenerating limb of a salamander starts out as."

Annabelle had recently told Asa about an interesting experiment she had first heard about up at Woods Hole and that had recently been confirmed and extended by a young man at Pennsylvania. "The dogma," she'd said was that, except for nerves and skin, the new tissues of the regenerated limb all develop from the cells of the blastema; that the cells are initially uncommitted; and that their fate is progressively sealed by factors in the local tissue environment. "The current gospel," she'd said, had replaced an older theory, proposed most notably by Thomas Hunt Morgan. "Morgan believed the new tissues of the regenerated part grew directly from the preexisting tissues of the stump. This recent experiment suggests that Morgan may have been right all along." Asa had been intrigued and had pondered the issue off and on for some weeks.

"It may be," he said between bites of a toasted cheddar sandwich, "that..." He washed down the morsel with a swig of coffee. "...That particular tissues regenerate, in principle, as specific engrams remember."

"Would you repeat that, please, Asa. " Fish had halted his conversation with Joyce and now stared at Asa.

"We may be able to show that regeneration and remembering are analogs of each other by focusing on the differentiation of specific tissues. Nate was able to separate particular memories with electroconvulsive shock. He was able to do so because particular phaseograms are independent of each other. Now suppose there are independent memories for, say, regrowth of muscle versus regrowth cartilage. Suppose further that a phase- like distribution of cellular or genetic factors is unique for the musculature versus the skeleton of a regenerating salamander limb."

Annabelle finished the thought: "Then new skeleton and new muscles would be analogous to the separate acts of Looking- up versus Feeding."

"Correct. But the two memories are independent of each other. Now if regeneration is indeed remembering, then the development of muscle and skeleton should also be independent of each other. The test would be to alter the development of one while concomitantly holding the other constant. Is that feasible?" Asa sat back and awaited Annabelle's answer.

"I know precisely the experiment," Annabelle declared. She lifted her purse and took out a mechanical pencil.

"Wait a minute," Fish broke in, "Neither the Havering nor the Adrian budget can afford this priceless linen." He placed a protective hand over a patch of tablecloth Annabelle had just brushed clear. She blushed and grinned at Fish, winked at Joyce and accepted the spiral note pad Asa had just slipped from his shirt pocket.

Annabelle sketched as she described experiments with limbs grafted to the eye socket in place of the eye. "Muscles originally attached to the eyeball grow into the transplanted limb. And the muscle changes its patterns for a distance out along the shank of the grafted limb. But the transplanted limb's skeleton remains perfectly normal."

Fish broke in: "Why that's the perfect paradigm for Asa's Independence Principle. Just amputate the transplant. If Asa's right, the newly regenerated piece of limb will have normal skeletons but abnormal muscles right?. But what about controls?"

"Fish, you're a genius," Annabelle declared. Then drew two hasty salamanders, each with one eye. "Beyond a certain distance, the muscles in the transplant remain normal. So all we have to do is make some transplants long and others short. If Asa is right, cutting through the normal regions of the longies won't produce abnormalities. It'll be cutting through the abnormal shorties that will show the changes in regeneration. Isn't that right, Asa?"


Joyce posed a question. "Wouldn't it be worthwhile to amputate some of your longies right up close to the eye socket where they're abnormal?"

"That's a very good idea, Joyce," Annabelle said. "That'll give us controls for the level of amputation. Of course, Joyce's longies will produce abnormal muscles; because the muscle will have changed in the region of amputation."

"You'll be able to guarantee the change," Fish offered "by microscopically examining the piece you amputate. "

"Yes," Annabelle responded.

"How reliable are the criteria for judging the results?" Asa wanted to know.

"Idyllic," Annabelle answered, turned to a blank page and presented a thirty minute discourse on the anatomy of the salamander's limbs.

"Well!" Fish reacted when she was through, "It looks as the phaseogram is really on the line." Joyce smiled and winked at Annabelle.

"I know it'll work," Joyce asserted . Asa said nothing.


Annabelle Crowe put her entire crew to work on the Independence Project, as Joyce dubbed it. "I absolutely refuse to speculate about experiments in progress," Annabelle had said at the outset of their collaborations. "Theories and experiments just don't mix when either is actively going on." Only when the results were in and polished up would she sit down and ponder them. When the Independence Project formally began, she firmly declared, "I don't want to see you at all until the whole story is finished, Asa. Not even for lunch. It's too important to be messed about." And as he had so often done merely to survive, Asa Zook completely banished Independence and Annabelle Crowe from his conscious thoughts.

The upcoming election preoccupied Joyce unlike anything Asa had previously seen. Her own campaign concerned her very little. But one of her party's candidates for the presidential nomination, "has utterly captivated me," she told Asa. "He'll restoreth our soul." On the increasingly rare occasions when they were together, she talked of little but politics, and, as she reflected herself, "with renewed vigor."

Asa regretted his ignorance of Joyce's world. "I am unfair to you," he said after she had returned full of enthusiasm from a speaking tour in West Virginia.

"How so, darling?" She was puzzled. She had made herself an integral part of his life, he said, but he had not reciprocated.

"It's very simple my dear philosopher," she replied. "I can but you can't. Your work and life are indistinguishable. Mine aren't. I wouldn't want to, but I could survive as plain old Missus Asa Zook who tends the six kids, four pigs, eighteen chickens and one philosopher. But I couldn't survive without your love. And no work, no Asa Zook. Ergo..." she kissed him on the mouth. "You vote for my man, and we're even."

And Asa had something to say to Joyce. "Without your love, I would not have my work." He offered to stuff and type envelopes for "her man" as a show of support. She laughed, hugged him around the chest but declined.

But an entirely new area of interest opened up for Asa Zook, and in a tragic way.

Sol Perlmutter came into Asa's office early one morning. Could they talk over in his place? He wanted to use the blackboard. He did not offer Asa a tea.

Sol had been spending virtually all his time, nowadays, on the synthesis of DNA, he said. He had recently given a lecture to the staff of Havering on the thermodynamics of the double helix and had demonstrated that, when placed in water, the two strands of the molecule cannot remain rigidly and everywhere fused together. "For the helix to remain double, overall, locally some complementing bases must be randomly separating or rejoining at all times," he'd said. Others had shown this to be true, experimentally, he told Nate and Asa back in his office, and he had showed them his own detailed calculations. "The geometry of the double helix is deceptively regular. But the DNA molecule is highly dynamic, always in a state of flux. And the analytical problem is decidedly nonlinear."

From almost the beginning of his own work on DNA, Sol said, he had a hunch that the key to the control of cancerous growth was hidden in the dynamics of the DNA molecule itself. His hope was to lay a theoretical foundation for the design of new classes of drugs, drugs that would grip DNA, prevent the two stands from coming apart and thus serving as templates for new DNA molecules. The idea fascinated Asa. This morning, though, something seemed to be distracting Sol.

"I was thrilled when Fisher Adrian said you would join us, Asa. 'There is the man who can make physics and biology one science,' I thought as I listened to your remarkable lecture. 'There is the mind capable of peering simultaneously into the very different worlds of the two. The philosopher. The pursuer of implications.'

"I have carried my analyses of DNA a long way since you arrived here Asa. And often my progress has been a direct result of our informal conversations. But my work is still incomplete. As such, it is merely a glorified heap of rubbish, not even worth publishing. I shall never complete my work, Asa. I will be dead first." Asa covered his mouth with a hand and neither said nor asked anything.

Sol continued: "Just yesterday, I learned that I have acute myeloid leukemia. I do not fear death at all. If I had returned to Germany on schedule, I probably would have died with my family. Nor am I bitter. Indeed, it is almost just. I have never lamented the deaths from cancer of my many former colleagues at Los Alamos. For the same reason, I cannot bring myself to rue my own fate. But my unfinished work is of potential importance and could benefit many. I want you to take my calculations, Asa. I do not know if or whether you can complete them. I cannot even recommend the specific approach you should take. Or even if you should attempt the problem at all. But I would like you to have them, if you will."

"I will accept your calculations," Asa replied. Forty days later, Asa Zook and Nathan Rabinowitz silently watched their friend Sol Perlmutter die.


Sol had operated strictly in the abstract, and his analyses were confined exclusively to what he could formulate into equations. Asa's first task was to convert his friend's opus into words, and he struggled to do so late into the summer of the following year. To assist his imagery, he relied more and more on molecular models of DNA, the most elaborate of which took more than two weeks to construct. "It's sexy," Joyce pronounced when he brought her in to the office to see it. "I mean, dear, there's a kind of abstract voluptuousness about it. Sort of the Platonic idea of sensuality. Say! I'll probably become jealous thinking about you all alone in a room with it."

She became serious as her curiosity took hold. What represented which atoms? What were these flattened little guys with the brass hooks? And why were they white like the hydrogens? Oh! They too were hydrogens! What made the strands helical? When Asa said "entropy," and she asked for a definition, and when he mentioned the Second Law of Thermodynamics, she immediately insisted on a minilecture, which he paused to render.

"What about the mad dog reactions, Asa?"

"The what?"

"The ones you called hydrophobic. Where are they on the model?"

When he stopped laughing, he explained that most were not represented, that many chemists did not consider hydrophobic interactions as true bonds. Why? After he explained the concept, she looked at him.

"Darling?" She put her hands around his neck, and her playfulness disappeared. "Is all this related to your philosophical system? Or are you digressing from your main goal?"

"DNA is closely related to my work, and what I am trying to do now may one day be pivotal to it." He took her hands. As he had first done with his own while overlooking the ocean on the eve of their first meeting, he turned one of her palms up and the other down, pressed her middle finger tips gently together and asked her to let the others touch. "Your hands are a model of my philosophical universe, Joyce. Together they represent an Hegelian synthesis. The logic of DNA is also Hegelian."

"Like our love, Asa?"

"As is our love."

"Wait, Asa!" Joyce took her hands apart and offered them to him, one palm up, the other down. They complemented each others' finger tips. "As our love, Asa. As our life."


"Off your ass Zook," Nate announced, leaning into the doorway and hoisting his crumpled lunch bag, "We're going for a walk over to Central Park."

A light snow had cleared the air but the flakes had dissolved instantly on contact with the ground, leaving the pavement dry enough for the fast pace Nate usually set. Asa also enjoyed a brisk midday walk. Sol had been averse to any activity more strenuous than hefting a blackboard eraser. With Sol now gone, Asa and Nate transferred their noonday communions to the sidewalks of New York. Occasionally, they exchanged a technical word or two. But mostly they walked and watched the world on whose extreme periphery both existed. On this day, Nate said nothing at all, even as they sat on a bench and ate their sandwiches.

When Asa got back to his office, Annabelle Crowe was sitting beside his desk drinking from one of Mrs. Rowan's vast collection of exotic coffee cups. On his desk lay a Manila folder. Annabelle did not speak, nor did her face reveal any emotion.

Asa sat. A neatly typed sticker on the folder's tab read "Independence Ms., Draft 1.1"; he opened the folder, and read its contents. When he looked up, Annabelle was smiling. She leaned over the edge of the desk and firmly kissed him on the mouth.

"Has Fish seen these results yet?" Asa asked. She shook her head, no. "Shall we take them up together?"


Fish silently read through the manuscript. Then he shook his head from side to side. A slow grin began at the corners of his mouth and eyelids and spread until all his muscles of facial expression were contracted. Turning the pages back to the beginning, he reread the title aloud, "'Independence of the Development of the Musculature and the Skeleton in the Regenerating Limb of the Larval Salamander.'

"By- the- gum, this calls for celebration." Then his smile receded. He sagged back into his chair. "Imagine being in Mother Nature's place at this moment and beholding what two of your darlings have accomplished. If there is such a thing as a miracle, I declare the human race is it."

Asa's neck muscles flexed at 'miracle.' Instead of objecting, he replied: "The human mind is a stupendous universe. Nothing quite like it may exist anywhere else in the cosmos." Annabelle thought the manuscript needed considerable polishing, and a few interesting ancillary questions had cropped up about muscle, per se. But as far as she was concerned, "Asa's predictions have come to pass without one solitary hitch." At the moment, though, she was one totally exhausted human being. She was on her way to Jamaica for how long she didn't know. She stood, kissed Asa again, let Fish kiss her and departed humming the 'Battle Hymn of the Republic.'

Asa stood to leave, but Fish touched his arm and asked him to hang around a few minutes so that an old man wouldn't have to sip his whiskey alone. After reiterating his joy, Fish became serious. "Asa, I don't quite know how to tell you this. But my wise old nose tells me you and Annabelle are in for some hard knocks ahead. If my assessment is correct, Independence will ruffle some might powerful feathers in Annabelle Crowe's field. It may become tough, especially on her. Very tough!"

After Fish's whiskey was gone, Asa returned to his office and telephoned Joyce.

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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