Over this damp grave I speak the words of my love.…
Jacob Goldmann’s neural research sends Jeremy into realms of mathematics that he would otherwise have explored cursorily, if at all, and which now, during these last months before Gail’s illness begins, fill and change his life.
Chaos math and fractals.
As with most modern mathematicians, Jeremy has dabbled in nonlinear mathematics; as with most modern mathematicians, he prefers the classical, linear mode. The murky field of chaos mathematics, less than two decades old as a serious discipline, had seemed tentative and strangely sterile to Jeremy before the interpretation of Goldmann’s holographic data sent him plunging into the realms and study of chaos. Fractals had been those clever things applied mathematicians had used for their computer graphics—the brief scene in one of those
Now he dreams chaos math and fractals.
Schrödinger wave equations and Fourier analyses of human holographic thought models had led him into this forest of chaos and now Jeremy finds that he is comfortable in these woods. For the first time in his life and career, Jeremy craves computer time: he finally brings a powerful CD-ROM-boosted 486 PC into the sanctum sanctorum of his study at home and begins petitioning for time on the university’s mainframe. It is not enough.
Jacob Goldmann says that he can get Jeremy’s chaos program run on one of the MIT Cray X-MPs, and Jeremy lies awake nights in anticipation. When the run is complete—forty-two minutes of computing time, a veritable eternity of a Cray’s precious time—the solutions are partial, incomplete, exhilarating, and terrifying in their potential. Jeremy realizes that they will need several Crays and more than one gifted programmer. “Give me three months,” says Jacob Goldmann.
The scientist convinces someone in the Bush administration that his work on neural pathways and holographic memory function has relevance to the air force’s longstanding “virtual reality” improved-cockpit research, and within ten weeks he and Jeremy have their access to linked Crays and the programmers to prepare the data.
The returns are coded in pure mathematics—even the diagrams are unreadable by anyone below the status of research mathematician—and Jeremy spends summer evenings in his study, comparing his own equations with the elegant Cray diagrams of Vague Attractors of Kolmogorov looking like dissected tube worms from the Mindanao Trench, but showing the same quasi-periodic interferometer patterns, chaos seas, and resonance islands that his own feeble math had predicted.
Jeremy does Poincaré sections of probability waves crashing and collapsing, and the Cray machines— moving through fractaled regions that Jeremy never hopes to understand—return hard data by the bale and computer images that look like photographs of some distant water world where indigo seas are mottled with sea- horse-shaped islands of many colors and infinite topological complexity.
Jeremy begins to understand. But just as it is coalescing for him … just as Jacob’s data and the Cray fractal images and the beautiful and terrible chaos equations on his chalkboard begin to converge … things in the “real” world begin to fall apart. First Jacob. Then Gail.
It is three months after their first visit to the fertility clinic when Jeremy visits his own doctor for a periodic physical. Jeremy happens to mention the tests that Gail has been going through and their sadness at not having a child.
“And they did just the one semen analysis?” asks Dr. Leman.
“Mmmm?” says Jeremy, rebuttoning his shirt. “Oh, yeah … well, they suggested I come back for a couple more, but I’ve been really busy. Plus, the first one was pretty conclusive. No problem.”
Dr. Leman nods, but he is frowning slightly. “Do you remember the sperm count?”
Jeremy glances down, inexplicably embarrassed. “Uh … thirty-eight, I think. Yes.”
“Thirty-eight million per milliliter?”
“Yes.”
Dr. Leman nods again and makes a gesture. “Why don’t you keep your shirt off, Jerry? I’ll run another blood pressure test here.”
“Was there a problem?”
“No,” says Dr. Leman, adjusting the cuff. “Did they tell you at the fertility clinic that they like a count of forty million per milliliter with at least sixty percent of the sperm showing good movement with forward progression?”
Jeremy hesitates. “I think so,” he says. “But they said it probably was a little below average because Gail and I … well, we hadn’t abstained quite the full five days before the tests and—”
“And they told you to come in for some averaging tests, but told you that there almost certainly wasn’t anything for you to worry about, that the problem probably lay with Gail?”
“Right.”
“Lower your shorts, Jerry,” says Dr. Leman.
Jeremy does so, feeling the slight embarrassment that men suffer as the doctor handles his scrotum.
“Take your hand and pinch your nose and mouth shut,” orders Dr. Leman. “Yes, that’s right … no air getting through at all … now bear down as if you’re trying to have a bowel movement.”
Jeremy starts to remove his hand to make a joke, but decides not to. He bears down.
“Again,” says Dr. Leman.
Jeremy winces at the pressure the doctor is exerting.
“All right, relax. You can pull up your shorts.” The doctor goes to the counter, removes the plastic glove, drops it in the trash, and washes his hands.
“What was all that about, John?”
Leman turns slowly. “That was known as the Valsalva maneuver. Did you feel that pressure where I had my finger on the vein on either side of your testicles?”
Jeremy smiles and nods. He had felt it, all right.
“Well, by pressing down there, I could feel the flow of blood going through your veins … going the wrong way, Jerry.”
“The wrong way?”
Dr. Leman nods. “I’m fairly certain that you have varicose spermatic veins in both the left and right testicles. I’m surprised that they didn’t check for that at the fertility clinic.”
Jeremy feels a wave of tension and clamminess wash over him. He thinks of all the embarrassing tests Gail has gone through in the past few weeks … all of the tests still awaiting her. He clears his throat. “Could these … these varicose veins … could they be hurting our chances for having a child?”
Dr. Leman leans against the counter and folds his arms across his chest. “They could be the whole problem, Jerry. If it is a bilateral variocele, then that could very well be dropping the motility of the sperm, as well as the actual count.”
“You mean the thirty-eight million at the clinic was an anomaly?”
“Probably,” says the doctor. “And my bet is that the motility study was done poorly. I’d wager that less than ten percent of the sperm were moving properly.”
Jeremy feels something like anger growing in him. “Why?”
“A variocele—one of these varicose veins in your testicles—is a malfunction of one of the valves in the spermatic vein that causes the blood to flow backward from the kidneys and adrenals into the testicles themselves. That raises the temperature in the scrotum—”
“Which lowers sperm production,” finishes Jeremy.
Dr. Leman nods. “The blood also carries a high concentration of toxic metabolic substances such as steroids, which further inhibit sperm production.”
Jeremy stares at the wall where there is only a cheap Norman Rockwell print of a country doctor listening to a child’s heartbeat. Both the child and doctor are rosy-cheeked caricatures. “Can you fix a variocele?” he asks.
“There’s an operation,” says Dr. Leman. “With men having sperm counts over ten million per milliliter … a category which you seem to qualify for … there’s usually a quite dramatic improvement. I think the figure’s around eighty-five or ninety percent. I’d have to look it up.”
