The Hollow Man

EYES

Of all the new concepts that Jeremy has brought to me, the two most intriguing are love and mathematics.

These two sets would seem to have few common elements, but, in truth, the comparisons and similarities are powerful to someone who has experienced neither. Both pure mathematics and pure love are completely observer dependent—one might say observer generated—and although I see in Jeremy’s memory the assertion by a few mathematicians like Kurt Gödel that mathematical entities exist independently of the human mind, rather like stars that would persist in shining even if there are no astronomers to study them—I choose to reject Gödel’s Platonism in favor of Jeremy’s stance of formalism: i.e., numbers and their mathematical relationships are merely a set of human-generated abstracts and the rules with which to manipulate these symbols. Love seems to me to be a similar set of abstracts and relation-of-abstracts, despite their frequent relationship with things in the real world. (2 apples + 2 apples did indeed = 4 apples, but the apples are not needed for the equation to be true. Similarly, the complex set of equations governing the flow of love does not seem dependent upon either the giver or recipient of that love. In a real sense I have rejected the Platonic idea of love, in its original sense, in favor of a formalist approach to the topic.)

Numbers are an astonishing revelation to me. In my former existence, prior to Jeremy, I understand the concept of thing but never dream that a thing—or several things—have the ghost echo of numerical values sewn to them like Peter Pan’s shadow. If I am allowed three glasses of apple juice at lunch, for instance, for me there is only juice … juice … juice, and no hint of quantification. My mind no more counts the juices than my stomach would. Similarly, the shadow of love, so attached to a physical object yet simultaneously so separate, never occurs to me. I find that property connected to only one thing in my universe—my teddy bear—and my reaction to that one thing has been in the form of pleasure / pain response with the bias toward the pleasurable, so that I “miss” teddy when he is lost. The concept of “love” simply never enters the equation.

Jeremy’s worlds of mathematics and love, so often overlapped before he comes to me, strike me like powerful lightning bolts, illuminating new reaches to my world.

From simple one-to-one correspondence and counting, to basic equations such as 2 + 2 = 4, to the equally basic (for Jeremy) Schrödinger wave equation that had been the starting point for his evaluation of Goldmann’s neurological studies:

All is revealed to me simultaneously. Mathematics descends upon me like a thunderclap, like the Voice of God in the biblical story of Saul of Tarsus being knocked off his horse. More importantly, perhaps, is that I can use what Jeremy knows to learn things that Jeremy does not consciously know. Thus, Jeremy’s basic knowledge of the logical calculus of neural nets, almost too elementary for him to remember, allows me to understand the way that neurons can “learn”:

Not my neurons, perhaps, given Jeremy’s rather frightening understanding of holographic learning functions in the human mind, but the neurons of … let’s say … a laboratory rat: some simple form of life that responds almost exclusively to pleasure and pain, reward and punishment.

Me. Or at least me, pre-Jeremy.

Gail does not care about mathematics. No, that is not quite accurate, I realize now, because Gail cares immeasurably about Jeremy, and much of Jeremy’s life and personality and deepest musings are about mathematics. Gail loves that aspect of Jeremy’s love of mathematics, but the realm of numbers itself holds no innate appeal for her. Gail’s perception of the universe is best expressed through language and music, through dance and photography, and through her thoughtful and often forgiving appraisal of other human beings.

Jeremy’s appraisal of other people—when he takes time to appraise them at all—is frequently less forgiving and often downright dismissive. Other people’s thoughts, on the whole, bore him … not out of innate arrogance or self-interest, but due to the simple fact that most people think about boring things. Back when his mindshield—his and Gail’s combined mindshields—could separate him from the random neurobabble around them, he did so. It was no more a value judgment on his part than if another person in deep and fruitful concentration had risen to close a window to shut out distracting street sounds.

Gail once shared her analysis of Jeremy’s distance from the common herd of thoughts. He is working up in his study on a summer evening; Gail is reading a biography of Bobby Kennedy down on the couch by the front window. The thick evening light comes through the white cotton curtains and paints rich stripes on the couch and hardwood floor.

Jerry, here’s something I want you to see.

??? Mild irritation at being removed from the flow of the equation he is scrawling on the chalkboard. He pauses.

Bobby Kennedy’s friend Robert McNamara said that Kennedy thought the world was divided into three groups of people—

The world’s divided into two groups of people, Jeremy interrupts. Those who think the world’s divided into groups, and those who are smart enough to know better.

Shut up a minute. Images of the pages fluttering and Gail’s left hand as she searches for her place again. The breeze through the screen smells of newly mown grass. The thick light deepens the flesh tones of her fingers and gleams on her simple gold band. Here it is … no, don’t read it! She closes the book.

Jeremy reads the sentences in her memory as she begins to structure her thoughts into words.

Jerry, stop it! She concentrates fiercely on the memory of root-canal work she’d suffered the summer before.

Jeremy retreats a bit, allows the slight fuzziness of perception that passes for a mindshield between them, and waits for her to finish framing her message.

McNamara used to go to those evening “seminars” at Hickory Hill … you know, Bobby’s home? Bobby ran them. They were sort of like informal discussion sessions … bull sessions … only Kennedy would have some of the best people in whatever field there when they talked about things.

Jeremy glances back at his equation, holding the next transform in his mind.

This won’t take long, Jerry. Anyway, Robert McNamara said that Bobby used to sort of separate people into three groups.…

Jeremy winces. There are two groups, kiddo. Those who—

Shut up, wise guy. Where was I? Oh, yes, McNamara said that the three groups were people who talked mostly about things, people who talked mostly about people, and people who talked mostly about ideas.

Jeremy nods and sends the image of a hippo yawning broadly. That’s deep, kiddo, deep. What about those people who talk about people talking about things? Is that a special subset, or can we create a whole new—

Shut up. The point is that McNamara said that Bobby Kennedy didn’t have any time for people in the first two groups. He was only interested in people who talked about … and thought about … ideas. Important ideas.

Pause. So?

So that’s you, silly.

Jeremy chalks the transform in before he forgets the equation that follows it. That’s not true.

Yes, it is. You—

Spend most of my waking hours teaching students who haven’t had an idea in their heads since infancy. QED.

No … Gail opens the book again and taps long fingers against the page. You teach them. You move them into the world of ideas.

I can barely move them into the hall at the end of the class period.

Jerry, you know what I mean. Your removal from things … from people … it’s more than shyness. It’s more than your work. It’s just that people who spend most of their thinking time on anything lower than Cantor’s Incompleteness Theorem are boring to you … irrelevant … you want things to be cosmological and epistemological and tautological, not the clay of the everyday.

Jeremy sends, Gödel.

What?

Gödel’s Incompleteness Theorem. It’s Cantor’s Continuum Problem. He chalks some transfinite cardinals onto his blackboard, frowns at what they have done to his wave equation, erases them, and scrawls the cardinals onto a mental blackboard instead. He begins framing a description of Gödel’s defense of Cantor’s Continuum Problem.

No, no, interrupts Gail, the point is only that you’re sort of like Bobby Kennedy that way … impatient … expecting everyone to be interested in the abstract things that you are …

Jeremy is growing impatient. The transform he holds in his mind is slipping slightly. Words do that to clear thinking. The Japanese at Hiroshima didn’t think that E = mc² was particularly abstract.

Gail sighs. I give up. You’re not like Bobby Kennedy. You’re just an insufferable, arrogant, eternally distracted snob.

Jeremy nods and fills in the transform. He goes on to the next equation, seeing precisely now how the probability wave will collapse into something looking very much like a classical eigenvalue. Yeah, he sends, already fading, but I’m a nice insufferable, arrogant, eternally distracted snob.

Gail does not comment, but gazes out the window at the sun setting behind the line of woods beyond the barn. The warmth of the view is echoed by the warmth of her wordless thoughts as she shares the evening with him.