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

chapter 24 Science

"I can't honestly complain," Fisher Adrian said. "The rule has been set aside so many times for me that if it's done again the policy won't exist if and when it's really needed." He gestured no thank you as Millie's new girl offered him lemonade. He crossed his thin legs, virtually wrapping one around the other, and, although his mouth wore a smile, the rest of his face bore the signs Asa knew were of pain. He'd continue to hold the title of director emeritus. Although he'd have no staff, he'd still have a laboratory. "What the heck. I always liked to do my own fiddling around, anyway." His career had reached a milestone with the testing of Asa's predictions about coppermycin. The work had come along at a time in his life when he'd long since given up hopes of ever doing anything really significant, himself. "Suddenly, there it was. Has Ace told you that we've receive twenty- five hundred reprint requests for our article in Nature ?" He had not, Joyce responded.

"What about your special people, Fish?" Joyce asked.

He sighed. "That is a true source of grief, my dear. Nate Rabinowitz hasn't published a paper in three years nor received a grant in five. They can't fire him. But they can strip him of his technicians and assign him to a broom closet."

"And you can't do anything about that?" Joyce asked.

"Only during the transition period. Only until the new director realizes just how absolute his authority really is."

"And then?"

"I don't really know. I tried to wangle a medical school job for him."


"'Up yours, Fish,' he said. No academic trash heap for him. He wants to die at the bench still going after the big ones."


"She'd survive, I do believe. But she's not going to try. She's quitting. Wants to have a baby. Ap finally talked her into marrying him."

"Do you think she'll be back?"

"I don't think so Joyce. A person doesn't step in and out of pure research. The jobs are simply too few. She might end up in Podunk's anatomy or zoology department. But I'd say her days as a scientist are over the moment she closes Havering's doors behind her. As far as returning to Havering, never. Not unless she decides to become a secretary. It's still very much a man's world, in spite of everything you and Asa forced me to do. And when I move downstairs, the policies will revert to pure verbiage."

He sighed and glanced from Asa to Joyce. "I suppose you're waiting for me to tell you about Asa's situation. His formal status at the moment is special consultant to the director. That will cease. But he can collaborate directly with me, which will give him access to the Big Burr under my name. He'll receive no remuneration. And he won't have Mrs. Rowan. But should the time arrive for clinical trials of coppermycin, I still have many uncollected debts among our oncology people. If Asa can lay out a coherent plan for arresting neoplastic growth, I'm sure we can get a first rate test out of those folks. Things are never quite as bad as they appear." He unwound his legs, reached forward and gathered Lovey into his lap. The discussion turned to politics. Soon Fish and Joyce were talking about a war in Indochina. Asa excused himself and walked out toward the compost piles.

He had slept virtually not at all in several weeks and had had a blinding headache for some days. Sol's theory! He had taken it many times to what he thought was the brink of a solution. But for months now, a path would begin full of promise only to end up in a cul- de- sac.

Asa addressed Deep Brain: "I am convinced Sol's theory and the Möbius H are related in some fundamentally inextricable way, that the fixed point is the key to it all. What is your opinion, old friend?" But Deep Brain no longer spoke to him. "Have I failed you too, in the end?" He expected nor received a reply. "You never wasted time on worthless talk, and I shall not ply you further, now."

Asa looked toward the porch. Was that Raymond standing before Joyce? He removed and wiped his glasses on the tail of his shirt. After putting the glasses back on, he squinted. No. It was Timothy. Of course, it was Timothy. There was the old green Chevy pickup truck. "May I put it in running order, Uncle Asa?" the boy had asked. It would be Asa's pleasure. Asa had forgotten the subject until Joyce called his attention to Timothy backing the Chevy up to the gasoline pump. He reminds me of myself in some ways, Asa thought now as he watched.

Lovey climbed from Fish's lap, took Timothy's hand and led him to the truck. Has the boy discovered a new piece of Nature somewhere? Timothy hoisted Lovey into the cab.

"Yes he has," Asa answered himself. "And he has an appreciative little person with whom to share it.

"My darling Lovey. How I neglect you! Yet you remain tolerant. 'Daddy, Daddy,' you'll often say, taking my chin and directing my gaze to you. My darling has been speaking to The Mauer, which I am becoming. But your lips on my cheek still reassure me against my shortcomings. You do not withhold your love, nor punish me, as you would have every right to do.

"And my Joyce, whom I fail more than all else combined." For months she had been asking about the proof of the Möbius H theorem. I am further from it now than ever.

He recalled an incident not many days before. It was morning, and Lovey's fingertips reminded him of the need for a shave. The contours of the lather on his face evoked recall of the mashed potato paradigm, which, like the H proof, he had never solved either. Joyce entered the bathroom just about then. She gently touched him on the back as she passed. The sudden high frequency whine of urination drew his attention her way. Her face, directed to his, as beautiful as ever before, deflected his thoughts from the mashed potatoes and the H proof. She was already dressed for work, in a tan, tweed suit and forest green blouse. Her lipstick, which she wore every day now, was a hue he admired on her mouth but could not name. She smiled as he prolonged his gaze. "I love you, Asa," she said softly. I love you too Joyce, he wanted to reply. But his vocal apparatus did not cooperate with his will. As he fought to bring words out of himself, she seemed to read his thoughts. "I know you do dear," she said.

His body had refused, too, when he tried to command it to render lovin'. "I have become impotent," he had weakly managed, once.

"It will pass, darling," she'd reassured.

Now, as he watched her on the porch, and remembered back through the brief scene in the bathroom, he detected not a single sign of recovery within himself. He turned and walked a few paces out into the bean field. There he squatted to examine a new sprout whose neck was severely hammer locked by the earth. His legs were too weak to maintain the position and he fell forward onto his knees. He had never squatted well, he reflected. He directed his attention to the lone sprout. As gently as he could, he stroked the pale green shoot with the side of his little finger. "The pain of birth will soon pass. You will soon straighten to the sun and grow to the full magnificence of your beanness." As he stroked, the tiny shaft broke the soil's hold. He relaxed back, folded his hands in his lap, and watched until the little shoot slowly flex upward. "You see, my dear. Life is truly glorious. And you exhibit the law of it all." He struggled to his feet. And then he declared to the field full of sprouts: "Generate to regenerate!"

We must take our own advice, he said to himself. He looked back at the porch, at his wife and at his friend. Then forcing one foot to follow the other, he walked slowly back between the compost piles, into the garden, across the yard and to the steps.

"We were just talking vacations, dear," Joyce said as Asa eased down onto the porch steps. "I was telling Fish that one thing after another has prevented our visiting Ceylon, and..." Asa was only partially listening, in spite of himself. "Fish says that henceforth all his vacations will be in the laboratory mixing solutions and looking through the microscope. Can you imagine a man like that?" Fish was chuckling as though being tickled on the ribs. Joyce always had the perfect word for the moment. "Oh, I've come to love my Saturdays," she was saying. She stretched and panned around at the view from the porch.

"Fish?" Asa asked. Joyce stopped swinging. Fisher Adrian leaned forward.

"Yes, Asa?"

"I believe we should get some data on how a diverse variety of mouse tumors react to coppermycin. Do you have the capabilities to perform such experiments?"

"Why yes, Ace. In fact, that'll be just about my speed, now."

"There is one other request I would like to make," Asa said. "I shall continue to need model building equipment to complete Sol's work. May I keep what I have here."

"While the authority still rests with me, Dr. Zook, Havering Institute hereby makes the models your property."

Joyce and Fish were laughing lightly now. Ray and Millie soon joined them. And Asa, again, was only partly hearing what the others were saying.


Toward the beginning of summer an incident crashed into Asa Zook's Mauer and, with the freewheeling force of a loose wrecking ball, exposed his cloister to the glare of realworld light.

He had not felt physically up to travel, he told Joyce, but she and Lovey should not deprive themselves of a true vacation on his account. Joyce said Ceylon, or even Japan, would not seem right without him. She was very weary though, she admitted, simply had to escape from things for a while, but had anticipated him and had already made alternative plans. Lovey had been asking about her grandparents in Florida; this was the perfect opportunity to go down for a visit.

On the way back from Newark after seeing Lovey and Joyce off, Asa, deciding it was time to talk to the sea, aimed Joyce's Mercedes south by east.

The bungalow was in subtotal disrepair. Someone had ripped the plywood from the windows. No pane of glass remained unsmashed. One end of the porch had collapsed after a sledge hammer had battered away the stone- shell support he had built long ago with gifts from the sea. The porch screening had been assaulted with a gouging instrument of some sort. Through a side window, he noticed the stove was gone. Disarticulated stovepipe, strewn about the floor, seemed like a cubist's rendition of a dissecting table at the end of the school year. The built- in book shelves had been axed to kindling. An abandoned owl's nest in the rafters prompted him to hope the creature would someday return. The screen door of the porch had been yanked from Poppa's shimmed hinges and stomped into a tangle of wire and splinters. On the floor, just inside the bungalow door, he noticed a recently used condom. "I hope you served love," he said to the object. Where the outdoor hearth had been now rose a dune of sand. The well cap, pumpless for a long time, lay beneath the same mantle.

Asa walked down to the water. The sea was at extreme low tide. With no wind at all, the surf was tantalizingly calm. He removed his shoes and socks, tucked them under his arm and walked along the damp sand toward the breakwater. En route, a clam's brief air bubble attracted his attention as a lazy tongue of sea drew back into the easy deep. Asa dug up the creature, kissed it and returned it to its dwelling place before the next wave cycled back to the shore.

At the breakwater, he found a safe place for his shoes and socks. Then he struggled like an aged goat, up and over the angular faces of the blocks to the barrier's crest. The one ton prisms of Devonian shale glinted magenta here and there, "Where sunbeams pay the correct trigonometric tribute," he sad. What price in man and beast did the sea exact for the placement into itself of this artifactual mountain? He'd raised that question before. And he had always meant to research the methods of pier, jetty and breakwater construction in perilous waters such as this. But he had deferred the investigation until, eventually, his curiosity faded away.

He made his way carefully seaward along the jagged crest. At the spot where he had come up, he paused and sat. He let his memory reconstruct the feel of the submerged blocks Deep Brain had advised him to find on the sea floor. Now his imagination was mathematically transforming the tactile reminiscence into a visible scene of the invisible depths. As only the eye of the mind can see, he saw himself in the lightlessness crawl hand over hand, slowly ascend, and then with his last moment of breath wait beneath the surface for the poet's gift of stillness between two waves of sea. His mind showed him his naked image zooming into the air, vaulting, then crawling and squirming up the blocks to flop like a spent mackerel

Asa stood up and peered over the edge to watch the sea lap at the water mark. "Even in your most gentle moments, you hate me.

The sea does not hate you, Asa!

Deep Brain! "Oh, please repeat that. Please."

But the Deep Brain did not answer.

"No matter," Asa tried to address the question to all parts of himself. "Deep Brain only speaks truth." He realized he was involuntarily repressing his fantasies. "Do not go away my gentle madness..." he started to add: I cannot be left alone.

But he was not a lonely, wordless void. His mind was turning over serious thoughts. Nor were they the accursed facts, facts, facts of science either. Nor poetry. Nor anything but...but, "Yes! Philosophy!"

He made his way to the seaward end of the crest. "How can I model the proof of H? Shall I phrase H as a tensor. Maybe I can execute a contraction to covert H to h? He smiled as he constructed an imaginary dialog with Joyce. 'But dear,' she'd declare. 'Doesn't that mathematical gobbledygook simply take us further away from where we want to go? I mean, don't we really want to prove the theory by philosophical induction -- with words -- so everybody can understand it?' And he would become horny. Which he was at this very moment, he realized.

Joyce, of course, would be correct. "Why do I feel so close to the H as I stand here looking at the waves of the sea? What is it about waves?


And then he saw it. So simple, so close at hand, so uncomplicated that he dropped to his knees and laughed and laughed.

"It is so simple, sea!" he shouted. The analytical proof, he had shown with symbols, asserted NOT- fixed point equaled NOT- continuity. To model NOT all they needed was a pair of scissors. "Like Riemann!"

If they cut through the crosspiece of the H, they would obliterate Möbiousness, and thereby continuity. The scissors would do in the real world what NOT- Möbius would prove in the abstract. He bent his head and laughed again. And now his nose began to bleed.

He stuffed bits of handkerchief into each nostril and staggered to his feet. "I must get back to the Journal."

Judiciously, bare toes gripping the rocks with a new found purpose for stealth, he made his way back, scooped up his shoes and hobbled as fast as he could to the car. His head still ached, terribly so, but his nosebleed had stopped. His thoughts were clear. And for the first time in a long time he was Asa Zook, philosopher.


Millie and Poppa came running as Asa pulled into the driveway. "Something awful's happened, Asa," Millie cried out. Asa gripped the steering wheel and clenched his teeth. Poppa told it. A state trooper had come by less than ten minutes ago. "Brace yourself, son," and Poppa pinned Asa's shoulder against the back of the seat. "It's your grandparents. That's who the authorities think they are, anyhow." Asa sagged. How readily, he would reflect on the plane, how willingly the mind accepts -- veritably greets -- a terrible tragedy as a substitute for the utterly unendurable. Had Poppa said 'Joyce' or 'Lovey'...There were no symbols for his thoughts. "Grandparents" had produced instantaneous relief. I am only mortal, he would consoled himself.

And mortal indeed. With a mortal's responsibilities. Raymond had taken a crew beyond reach by telephone. Poppa, clearly, was not the one to go. The responsibility was Asa's and Asa's alone.

Meticulously following every instruction, Asa presented himself at the information counter as soon as he arrived in the airport terminal. The young woman picked up the telephone and drawled, "Mister Zook is here, sir." In a moment, two men approached, one wearing a brown uniform, the other dressed in a charcoal gray suit and carrying a light gray fedora in his hand. The civilian held up a card laminated in clear plastic and identified himself as an agent of the Federal Bureau of Investigation. The agent introduced the uniformed man as Sheriff John Bishop.

Asa rode in a police car with Sheriff Bishop. The agent and another civilian followed in an unmarked Plymouth sedan.

The morgue was in the basement of the Forsythe County Courthouse. They brought Gramma out first and an attendant laid back a heavy canvas shroud. She was naked. Most of her lower face was missing, and she had what appeared to be two obliquely directed bullet holes in just above her right breast. An autopsy had not been conducted on her.

Grampa had been subtotally decapitated. The base of his occipital bone remained attached to the stump of his neck. Pieces of his face were bundled in cheesecloth, which the morgue attendant unwrapped. Asa recognized Grampa's nose and identified a gold- filled left superior first premolar tooth in a piece of maxilla.

"You a doctor or something?" Sheriff Bishop asked. Asa said he held an MD degree. The sheriff handed Asa his grandparents driver's license, "They them?" he asked. After Asa answered, "Change the Does to Overfields," he said to his secretary. "Now let's see if'n he knows the nigrah." They went to another section of the morgue, and the attendant wheeled out the body of teenage girl whom Asa did not know.

Joyce and Lovey were on the porch when Asa got home. He took both into his arms. And then he cried.

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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