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

chapter 25 Philosopher's Point

"Thank you," Joyce said. When Asa said it was he who should thank her, she kissed him lightly. "I was actually thanking Nature, Asa." That said, she snapped on the light, bounded to his desk, bare feet thumping, and returned with a copy of the Möbius H and an a pair of scissors. "I'm astonished at the proof's simplicity, Asa. I should have seen it myself." She snipped the crossbar. "Proof!" she declared. "'Cutting through PHILOSOPHY subtracts the fixed axis, destroys the Möbiusness and divests our system of the continuity it is otherwise guaranteed.' That's what I've written, Asa. It's still awful stiff, and I have to play with it. But I do like it. The illustration of the proof, that is.

"I see something else, sweetheart. If we paste the crossbar back together -- if we regenerate PHILOSOPHY -- we restore continuity! Can we reconstruct an individual life..."

The startled look on her face told him she fully apprehended the implications of the discovery she had just made. "If and only if our theory is truly general, Joyce," Asa replied. "But we have a long way to go before we can claim that." She seemed to accept his assertion, which surprised him. He turned off the reading light.

He told her he had been to the sea. She immediately tensed. He talked about his deep, progressively worsening depression, its insidious onset; its inexorability once he had stopped doing philosophy. The surge out, he believed, had been akin to a manic bout; the trauma of seeing his grandparents was analogous to convulsive shock therapy. He had not been depressed in the physiological sense of the word, he believed, but he could now extrapolate from his own agony to the inner hell of his manic- depressive patients. He had always had sympathy for them. But he had failed as their doctor because he lacked empathy. He went on to describe his induced fantasies. Subtract his willful control, and his own subjective became a working model of hallucinations. He now appreciated things he had never grasped when he practiced.

"I used to believe the memory aspect of our theory held the most potential for practical good, Joyce. I am sure of it now."

"But you can never ever again put aside philosophy, Asa. And..." Joyce hesitated. "May I say something I've never allowed myself even to contemplate before, Asa?"


"I shall never let you surrender philosophy again, Asa."

"What did you proscribe before?"

"The 'let' part."

He reflected for a moment, and then kissed her.

"I'll give up the bench," she added. "We'll go back to our Möbius H and the fixed point full time."

"That would be unwise, Joyce. Some paths can never be retraced." And he wondered, immediately, if that was also true of the cut PHILOSOPHY, but quickly repressed.

Both were silent for a while. She spoke next: "You're right, Asa. But let's agree to set aside some small portion of the day for nothing but philosophy." She drew away from him, bounded from the bed, and he listened as her naked feet thumped across the floor in the direction of his desk. He flicked on the bed lamp to illuminate her return. She was already voluptuously bouncing back, carrying the Journal. Her nudity in the amber light evoked his desire.

"A minimum of one page of pure thought per day," she said. "And...uhm. None of that...until our day's work is done, Dr. uhm...Zook." Asa agreed. He described his failure with the lower caseh., of how the failure had actually triggered the idea for cutting the crosspiece. "My philosopher has returned," she observed.


Asa gradually increased his medication until the headaches disappeared. His stamina was improving, he observed late one afternoon as he and Lovey walked across the field to meet the Grossdawdy and ask if she could ride one of his horses back to the barn.

"The first maxim," Joyce had insisted, "is to avoid obsessive behavior." Life needed variety, even the life of the mind. "Second, we must budget time as we do our finite income." Their lives -- and especially his -- had to have an appropriate mixture of work and play. He would have to allow for his family's need of him. She encircled both arms around his neck and punctuated the statement with a kiss. He would have to continue doing some science, she conceded. Science was now his trade work, was how he justified himself to society. But he could confine that to the mornings, after the governess arrived, and before he broke for lunch with Lovey and the others. At lunch time, though, "Science stops!" Joyce decreed. Then came Nature's time, perhaps with the Journal, but away from the potato barn where Poppa and Raymond had rigged a work place for his DNA models. At three, after the governess left, Lovey became his personal responsibility until Joyce got home. He should impart himself to the child, and not just his feel for Nature, but languages and his vast knowledge of how things are and the way they work.

Joyce did not want to become the Zook scold, she insisted. Nor did she plan to assume a role of primacy in their family. Who was the boss of a Zook household was "irrelevant, immaterial and totally out of order." A bossy Zook was "Unphilosophical."

"You are much wiser than I am ," Asa responded. No, he assured her, after she pressed him, he would never accede to a request or demand simply because of his love for her, but "Because of the wisdom I have learned over the years to expect of your judgment."

Slowly, song and mirth returned to the "Zookery," as Timothy called the homestead. All at the supper table laughed.

Timothy was indeed a remarkable boy, Asa observed. More so than his brothers and sisters, he had an affinity for things of importance to Asa.. The DNA models intrigued him. After Asa transferred model building to the potato barn, Timothy increasingly became a presence in his life. "Wouldn't you have more fun playing?" Asa asked his nephew one Saturday morning.

"This is playing, Uncle Asa," Timothy said as he popped a methyl group on a thymidine. Soon Asa began to realize that the boy's sense of spatial relationships, far superior to his own, were moving Sol's theory along.

"I may soon have this done," Asa informed Joyce. "After I have kept my faith with Sol, I shall devote all my scientific inquiries to the illness of the mind. I may practice medicine after Sol's theory is complete," he said one morning in the bathroom as he admired the blend of a novel fragrance with a new beige cotton suit and a canary yellow blouse. "On a limited scale, of course. But I may be of some use, now." No, no! he insisted, they did not have to discuss it this morning. He did not want her to be late or have to rush. They could take up the subject with the entire family during supper. Their practical insight would be useful.

At the car, after he had lifted Lovey for a final hug, and had leaned in for his own good- bye, Joyce said, "Our lives are becoming complete, Dr. Zook."


Fisher Adrian called to say he had bad news. He wanted Joyce present when he told what it was. He'd drive down on Saturday, if that did not seriously disjoin what he realized were their precious times together as a family. "It is very important, Asa," he stressed.

On Saturday, Lovey went on a previously planned picnic with Poppa and the others, and Joyce, Fish and Asa went into the library. Fish admired the woodwork and inquired about Poppa's techniques for mitering. "Stalling will not make it sting any less," Joyce eventually said.

Fish removed several data sheets from his attaché case and spread them out on the reading table. "It didn't work, Asa," he said. "With only one exception, coppermycin had no effects on the growth of any tumor. Not the leukemias, melanomas, adenocarcinomas. Only the muscle tumor responded. I've repeated the experiments again and again. And I've been carrying this sad tale around in my heart for too many days."

Asa's head began to throb.

"I fail to see...the urgency," Joyce said. Her voice cracked halfway through the sentence.

Fish spoke. "The problem is that now we don't know how valid our other experiments were. We don't know if the coppermycin attacked DNA in some fundamental way, as Asa predicted, or if it acted against something unique to muscle."

Now Asa spoke. "The problem has to do with the experimental nature of the research, Joyce. It is not a matter of being right or wrong. It is that we have generated empirical uncertainty about the generality of the test. Either we explain the results directly from the fixed- point H theory or we admit that the theory is not general. And if the latter statement is true the fixed- point theory may have only an incidental and not a necessary relationship to the logic of Nature." Asa could feel the beginnings of depression. But he continued. "What about the mechanisms of the antibiotic, Fish?"

"Virtually unknown, Asa. And to make matters worse, the chemical structure hasn't yet been worked out."

"This is terrible," Joyce exclaimed. She immediately covered her mouth and looked at Asa. And in what she said next, and for the first time in their lives together -- indeed for the first time in his recollections -- Asa Zook believed he was being lied to: "...I meant about the chemistry," she added. "I'm sure the theory is still as sound as a drum. And Fisher Adrian, I'm going to bet you a steak dinner that..."

Asa heard no more. Her totally uncharacteristic use of clichés convinced him she lied to spare him. He stood, walked to the window and looked toward the compost piles. Then he shifted his gaze to the potato barn. The DNA models! I must go to them. He was only vaguely aware of Fish's departure or what else he had said. As soon as Fisher Adrian drove off, Asa excused himself and walked away from Joyce.

"Please dear," she followed him part way across the yard, "You're making a mountain out of a mole hill." ['Sound as a drum.' 'Steak dinner.' 'Mountain out of a molehill.'] She was lying to protect him from some utter disaster her quick intelligence had instantaneously apprehended.

"And with far greater clarity than all of us combined," he declared when he was by himself.

"Deep Brain, what have you to say about all this?" Of course, Deep Brain gave no answer. "I shall speak for all of us, in that case. Our only salvation is to explain the failure of the experiments from the very heart of the theory.

"Assume that the H is not general. Then how do we explain the Mamaluchee? Independence?" Asa paused in hopes that Deep Brain would comment. Of course, it did not.

"Again, I shall answer. The H would be a special theory, applicable only to the situations I have enumerated. Moreover, our theory would be a consistent part of a larger theory, as Einstein's theory of special relativity is part of general relativity.

"Can I discover the larger theory? Do I have time?" The impolite left side of his mind took the dais: You must realize, Asa, that if H is not really general, you will never find Nature's law.

Not necessarily! the Deep Brain finally spoke.

"Oh please tell us more, Deep Brain," Asa begged. But Deep Brain had said its piece. Now it was for his lesser selves to speak for themselves. "Did you hear that left side? Did you? Let me interpret for the illogical among us. Deep Brain means that Nature still has a chance against God. But if -- and only if -- the valid special theory incorporates regeneration. If and only if Nature's rule entails memory."

And having so said, Asa Zook terminated his fantasies and threw himself full force into Sol Perlmutter's theory of DNA synthesis.


The crisp air would have gratified his lungs except for the sulfurous East River. A rat rode by aboard a raft of garbage. Asa leaned over the steel railing and called to it. "There are many opportunities for escape between here and the open sea. But it will be up to you to recognize them." A young couple strolling arm- in- arm quickened their pace as they walked behind him. Silently, Asa told them he loved them and wished them all the happiness love had brought into his life.

He had been here since late afternoon, since Julio had walked with him to Havering's main entrance, and he had needed a place to think. Asa had hand- carried the last of Sol Perlmutter's theory into Havering and had waited in the anteroom of the Comp Lab for Big Burr's verdict. "Too much complex curvature, Ace," Julio had said. "I wish I knew what to suggest."

A stout boy skated awkwardly by, his steel wheels resounding against the octagonal asphalt tiles and mimicking Japanese machine- gun fire from within a stone building. He will grow up to be lean and agile, Asa assured himself.

A tugboat passed. The cook, one foot on the railing of the galley deck, waved. Asa waved back. A ruler held to the eye would have measured the cook as four inches tall. The thought cued recollection of a classic paper of Karl Lashley's: how does the cognition allow us to recognize a four- inch cook on a twelve- inch tugboat? "Phase is sizeless," Asa said. Lashley would have loved the phaseogram.

Another tug passed, this one too far away for its microscopic crew to respond to an invisible landlubber. Asa waved anyway. "Got a couple of spare dimes, Mack?" a man was asking over Asa's left shoulder. Asa gave him a ten dollar bill.

Asa looked across the rapidly moving estuary. "It is not a true river," he had read in one of the first books Miss Rouelle had recommended. "Miss Rouelle."

Welfare Island formed the opposite bank. Its buildings recapitulated the essence of the Mauer. Asa turned for a glimpse at Havering some blocks north. Its proud profile, partially visible in the day's last light, rose above its neighborhood. Havering's beauty was as willful as the ugliness across the river was contrived. "Why do you thus choose ?" Asa shouted out. A man in a dark blue overcoat stopped, turned and walked briskly in the other direction. "I apologize, sir," Asa whispered.

When the last light of day passed, Asa pushed himself away from the rail and headed north. He would use Fish's lab. He veered left, and not until he was irrevocably close did he realize he had intruded upon love in progress on one of the benches. "Please forgive me," he said as he hastened onto the cobblestone apron of East River Drive. As he waited for the traffic to thin, he let his mind's voice bid the lovers twenty feet behind him: Please do continue! Then he heard his voice saying to the boy. "Be a nice GI."

As he crossed the street in the interval between two speeding taxicabs, he suspended all conscious thoughts. And he was hurrying up the block, signing in at the night desk and fumbling for his key to Fish's quarters.

He had left his briefcase on Fish's desk. And now he spread its contents over the big work island in the center of the lab. He had one slide rule in the briefcase, but not the big one. No matter. He rummaged through Fish's desk and found the circular slide rule he knew had remained there in disuse since Big Burr. Paper! "I need paper."

Asa decided to take a running start at the calculations. He would back up to already solved parts, to what he could partially verbalize. Words would let him generate the momentum he needed before...And he could feel himself approaching the theory's unknown frontier almost as one approaches sleep. And in the next instant his mind deverbalized.


Even approximately how long he had been going, Asa had no idea whatsoever. But he heard himself shout, "Wait!" Wait? A powerful intuitive net had snared something his equations were not showing. Could never possibly show! WAIT! was the sharpest verbal summons his soul could execute. And suddenly, Asa was not calculating.

"I have been working on the wrong assumption. I had believed that Sol's theory would subsume ours. But I clearly see that it is the other way around. And I see much more, too. Sol's is a special variant of ours. Sol's is the geometry of DNA. Ours is the plan of life itself. And life cannot be reduced to DNA. I need no calculations. I philosophical induction. And I need predictions."

Before he could set his intentions to the paper, he began to feel very dizzy and in need of air. His ears were ringing. And his left visual field was blurred. He rested back in Fish's chair. And.... the next thing he knew, Fish was gently patting his shoulder.

"So this is where you've been," Fish was saying. Fish picked up the telephone and hammered the switch hook. "Damn that switchboard. Hello, hello...Please get me an outside line. Damnit, I know what the hell time it is. This is Dr. Adrian speaking." Fish covered the mouthpiece and said something Asa did not make out. Then he handed Asa the receiver. It was Joyce, but the sound faded in and out.

"I am all right, Joyce," Asa said. Fish took the phone, said something and hung up. "Can you perform the following experiments, Fish? The first group involve bacteria. A simple broth culture, I'd even be able to run myself if I weren't so exhausted. I would suggest Bacillus subtilis. Let the culture start growing. Then add many times the lethal dose of coppermycin. Prediction: the bacteria will not stop growing as they would if you added, say, cyanide. Growth will continue and level off smoothly after a complete cycle for the culture as a whole."

"Yes, Asa."

"If that works, repeat the mouse tumor experiments; use leukemias, which kill quickly. Divide the animals into about eight groups. Vary frequency, dose and the time of day for treatment among the groups. Some groups will significantly outlive the untreated controls; others will not. Survival will not depend on increasing the bulk amount of antibiotic but on the frequency of administration.

"More! There is no a priori way to say just which group will outlive the rest. Just that some groups will outlive the others. Can you conduct these experiments, Fish?"

"Yes, Asa."

"Please take me home now, if you can, Fish."

Fish called the security guard and asked him to bring a wheel chair. Asa vaguely sensed the guard helping him into Fish's car in the basement parking garage. Just before he fell asleep, Asa realized that he was partially blind.


Asa vaguely remembered being helped from the car and carried upstairs by Poppa and Raymond. Joyce was there, and she was in the room when he went back to sleep. Now as he opened his eyes and daylight danced cheerfully about him, she was there again, leaving her rocking chair and coming to sit beside him on the bed. His vision had partially cleared. But his ears rang as they had after he first fired the M1 rifle. For a moment he feared he would be unable to hear her. But she said, "Good morning, darling," and the softness of her voice reassured him.

"Joyce," he whispered. "The general fixed- point theory is valid. The H tells us how coppermycin reacts with and affects DNA and thus provides a rational explanation of coppermycin's apparent failure. It is the experiment that failed, not the theory. It is as you said it would be."

"I did not lie to you, Asa."

"You never lied to me." He gestured for her hand. "It would have been unphilosophical, which my Joyce has never been."

"Are you hungry, dear?" she asked "No. But I have much to tell you. Please get the Journal." He talked deep into the night, told her all he could and stopped when they were exhausted. Fish called the following morning to tell Joyce that the bacteria had obeyed Asa's prediction. In three weeks, Joyce relayed, Fish would have the data on the leukemias. It would not matter, Asa told her. Their theory was philosophy now.

"And our H" she said, "is part of eternity."

Fish should expect certain nuances in the tumor tests, Asa instructed, especially if he conducted repeat series. Again, she should remind Fish that some groups of mice would appreciably outlive others. But Fish would not be able to predict just which ones from earlier runs.

By late afternoon he had told her all he knew how to tell. All but one thing, which he had saved until the end. She wept at first. But then she dried her eyes and smiled. She extended her hands to his, one palm up, the other down, and they complemented each other's finger tips. "When the one is part of the other," she said. "My Asa Zook." They rendered the solemn kiss.


He awoke in total darkness, aware of Joyce from the scent of her. And his tactile senses weakly registered the rhythm of her breathing on the bed somewhere near. But he could not hear her now. I love you, he would have said aloud. You made the love of Nature live in my soul. I truly agree, the Deep Brain said. Thank you, Deep Brain. I know you speak only truth. And here we all are, all of us, our essence still coherent within my ruined head: All of us our own final piece of proof. Nature, please be kind in your triumph. Be merciful to God. Forgive Him. For your love is the stronger force. Nature is the stronger! the Deep Brain asserted. Thank you for saying that, Asa replied. I must leave you soon Asa, Deep Brain said. Good-bye Deep Brain. I loved you. I loved you all. All. Asa quickly thought of Momma, Poppa, Raymond, Timothy, Lovey. Then he fixed his mind on the person somewhere near him. Joyce. Joyce. Joy...

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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