So he did. He threw the ball at the batter, and the batter bailed, and the ball cut right down into my glove. The umpire was speechless. I turned around and showed him the ball in my glove. That was a strike, I told him.
Strike! he hollered. He grinned at me. That was a curveball, wasn't it?
Damn right it was.
Hey, the batter said. What was that?
We'll show you again, I said.
And after that Gregor began to mow them down. I kept putting down two fingers, and he kept throwing curveballs. By no means were they all strikes, but enough were to keep him from walking too many batters. All the balls were blue dot. The ump began to get into it.
And between two batters I looked behind me and saw that the entire crowd of spectators, and all the teams not playing at that moment, had congregated behind the backstop to watch Gregor pitch. No one on Mars had ever seen a curveball before, and now they were crammed back there to get the best view of it, gasping and chattering at every hook. The batter would bail or take a weak swing and then look back at the crowd with a big grin, as if to say, Did you see that? That was a curveball!
So we came back and won that game, and we kept Gregor pitching, and we won the next three games as well. The third game he threw exactly twenty-seven pitches, striking out all nine batters with three pitches each. Walter Feller once struck out all twenty-seven batters in a high school game; it was like that.
The crowd was loving it. Gregor's face was less red. He was standing straighter in the box. He still refused to look anywhere but at my glove, but his look of grim terror had shifted to one of ferocious concentration. He may have been skinny, but he was tall. Out there on the mound he began to look pretty damned formidable.
So we climbed back up into the winner's bracket, then into a semifinal. Crowds of people were coming up to Gregor between games to get him to sign their baseballs. Mostly he looked dazed, but at one point I saw him glance up at his co-op family in the stands and wave at them, with a brief smile.
How's your arm holding out? I asked him.
What do you mean? he said.
Okay, I said. Now look, I want to play outfield again this game. Can you pitch to Werner? Because there were a couple of Americans on the team we played next, Ernie and Caesar, who I suspected could hit a curve. I just had a hunch.
Gregor nodded, and I could see that as long as there was a glove to throw at, nothing else mattered. So I arranged it with Werner, and in the semifinals I was back out in right-center field. We were playing under the lights by this time, the field like green velvet under a purple twilight sky. Looking in from center field it was all tiny, like something in a dream.
And it must have been a good hunch I had, because I made one catch charging in on a liner from Ernie, sliding to snag it, and then another running across the middle for what seemed like thirty seconds, before I got under a towering Texas leaguer from Caesar. Gregor even came up and congratulated me between innings.
And you know that old thing about how a good play in the field leads to a good at bat. Already in the day's games I had hit well, but now in this semifinal I came up and hit a high fastball so solid it felt like I didn't hit it at all, and off it flew. Home run over the center field fence, out into the dusk. I lost sight of it before it came down.
Then in the finals I did it again in the first inning, back-to-back with Thomas—his to left, mine again to center. That was two in a row for me, and we were winning, and Gregor was mowing them down. So when I came up again in the next inning I was feeling good, and people were calling out for another homer, and the other team's pitcher had a real determined look. He was a really big guy, as tall as Gregor but massive-chested as so many Martians are, and he reared back and threw the first one right at my head. Not on purpose, he was out of control. Then I barely fouled several pitches off, swinging very late, and dodging his inside heat, until it was a full count, and I was thinking to myself, Well heck, it doesn't really matter if you strike out here, at least you hit two in a row.
Then I heard Gregor shouting, Come on, coach, you can do it! Hang in there! Keep your focus! All doing a passable imitation of me, I guess, as the rest of the team was laughing its head off. I suppose I had said all those things to them before, though of course it was just the stuff you always say automatically at a ball game, I never meant anything by it, I didn't even know people heard me. But I definitely heard Gregor needling me, and I stepped back into the box thinking, Look I don't even like to coach, I played ten games at shortstop trying not to coach you guys. And I was so irritated I was barely aware of the pitch, but hammered it anyway out over the right field fence, higher and deeper even than my first two. Knee-high fastball, inside. As Ernie said to me afterwards, You drove that baby. My teammates rang the little ship's bell all the way around the bases, and I slapped hands with every one of them on the way from third to home, feeling the grin on my face. Afterwards I sat on the bench and felt the hit in my hands. I can still see it flying out.
So we were ahead 4–0 in the final inning, and the other team came up determined to catch us. Gregor was tiring at last, and he walked a couple, then hung a curve and their big pitcher got into it and clocked it far over my head. Now I do okay charging liners, but the minute a ball is hit over me I'm totally lost. So I turned my back on this one and ran for the fence, figuring either it goes out or I collect it against the fence, but that I'd never see it again in the air. But running on Mars is so weird. You get going too fast and then you're pinwheeling along trying to keep from doing a faceplant. That's what I was doing when I saw the warning track, and looked back up and spotted the ball coming down, so I jumped, trying to jump straight up, you know, but I had a lot of momentum, and had completely forgotten about the gravity, so I shot up and caught the ball, amazing, but found myself flying right over the fence.
I came down and rolled in the dust and sand, and the ball stayed stuck in my glove. I hopped back over the fence holding the ball up to show everyone I had it. But they gave the other pitcher a home run anyway, because you have to stay inside the park when you catch one, it's a local rule. I didn't care. The whole point of playing games is to make you do things like that anyway. And it was good that that pitcher got one too.
So we started up again and Gregor struck out the side, and we won the tournament. We were mobbed, Gregor especially. He was the hero of the hour. Everyone wanted him to sign something. He didn't say much, but he wasn't stooping either. He looked surprised. Afterwards Werner took two balls and everyone signed them, to make kind-of trophies for Gregor and me. Later I saw half the names on my trophy were jokes, "Mickey Mantle" and other names like that. Gregor had written on it "Hi Coach Arthur, Regards Greg." I have the ball still, on my desk at home.
The Blind Geometer
When you are born blind, your development is different from that of sighted infants. (I was born blind. I know.) The reasons for this difference are fairly obvious. Much normal early infant development, both physical and mental, is linked to vision, which coordinates all sense and action. Without vision, reality is… (it's hard to describe) a sort of void, in which transitory things come to existence when grasped and mouthed and heard; then, when the things fall silent or are dropped, they melt away, they cease to exist. (I wonder if I have not kept a bit of that feeling with me always.) It can be shown that this sense of object permanence must be learned by sighted infants as well—move a toy behind a screen, and very young babies will assume the toy has ceased to exist—but vision (seeing part of a toy [or a person] behind the screen) makes their construction of a sense of object permanence fairly rapid and easy. With the blind child, it is a much harder task; it takes months, sometimes years. And with no sense of an object world, there can be no complementary concept of self; without this concept, all phenomena can be experienced as part of an extended "body." (Haptic space [or tactile space, the space of the body] expanding to fill visual space…) Every blind infant is in danger of autism.
But we also have
, and know that we have, the capacity of complete freedom to transform, in thought and phantasy, our human historical existence…
Edmund Husserl, The Origin of Geometry
My first memories are of the Christmas morning when I was some three and a half years old, when one of my gifts was a bag of marbles. I was fascinated by the way the handfuls of marbles felt: heavy, glassy spheres, all so smooth and clickety, all so much the same… I was equally impressed by the leather bag that had contained them. It was so pliable, had such a baggy shape, could be drawn up by such a leathery drawstring. (I must tell you, from the viewpoint of tactual aesthetics, there is nothing quite so beautiful as well-oiled leather. My favorite toy was my father's boot.) Anyway, I was rolling on my belly over the marbles spread on the floor (more contact) when I came against the Christmas tree, all prickly and piney. Reaching up to break off some needles to rub between my fingers, I touched an ornament that felt to me, in my excitement, like a lost marble. I yanked on it (and on the branch, no doubt) and—down came the tree.
The alarum afterward is only a blur in my memory, as if it all were on tape, and parts of it forever fast-forwarded to squeaks and trills. Little unspliced snippets of tape: my memory. (My story.)
How often have I searched for snippets before that one, from the long years of my coming to consciousness? How did I first discover the world beyond my body, beyond my searching hands? It was one of my greatest intellectual feats—perhaps the greatest—and yet it is lost to me.
So I read, and learn how other blind infants have accomplished the task. My own life, known to me through words—the world become a text—this happens to me all the time. It is what T. D. Cutsforth called entering the world of "verbal unreality," and it is part of the fate of the curious blind person.
I never did like Jeremy Blasingame. He was a colleague for a few years, and his office was six doors down from mine. It seemed to me that he was one of those people who are fundamentally uncomfortable around the blind; and it's always the blind person's job to put these people at their ease, which gets to be a pain in the ass. (In fact, I usually ignore the problem.) Jeremy always watched me closely (you can tell this by voice), and it was clear that he found it hard to believe that I was one of the co-editors of Topological Geometry, a journal he submitted to occasionally. But he was a good mathematician and a fair topologist, and we published most of his submissions, so that he and I remained superficially friendly.
Still, he was always probing, always picking my brains. At this time I was working hard on the geometry of n-dimensional manifolds, and some of the latest results from CERN and SLAC and the big new cyclotron on Oahu were fitting into the work in an interesting way: It appeared that certain subatomic particles were moving as if in a multidimensional manifold, and I had Sullivan and Wu and some of the other physicists from these places asking me questions. With them I was happy to talk, but with Jeremy I couldn't see the point. Certain speculations I once made in conversation with him later showed up in one of his papers, and it just seemed to me that he was looking for help without actually saying so.
And there was the matter of his image. In the sun I perceived him as a shifting, flecked brightness. It's unusual I can see people at all, and as I couldn't really account for this (was it vision, or something else?) it made me uncomfortable.
But no doubt in retrospect I have somewhat exaggerated this uneasiness.
The first event of my life that I recall that has any emotion attached to it (the earlier ones being mere snips of tape that could have come from anyone's life, given how much feeling is associated with them) comes from my eighth year, and has to do, emblematically enough, with math. I was adding columns with my Braille punch, and, excited at my new power, I took the bumpy sheet of figures to show my father. He puzzled over it for a while. "Hmm," he said. "Here, you have to make very sure that the columns are in straight, vertical rows." His long fingers guided mine down a column. "Twenty-two is off to the left, feel that? You have to keep them all straight."
Impatiently I pulled my hand away, and the flood of frustration began its tidal wash through me (most familiar of sensations, felt scores of times a day); my voice tightened to a high whine: "But why? It doesn't matter—"
"Yeah it does." My father wasn't one for unnecessary neatness, as I already knew well from tripping over his misplaced briefcase, ice skates, shoes… "Let's see." He had my fingers again. "You know how numbers work. Here's twenty-two. Now what that means is two twos and two tens. This two marks the twenty, this two marks the two, even though they're both just two characters, right? Well, when you're adding, the column to the far right is the column of ones. Next over is the column of tens, and next over is the column of hundreds. Here you've got three hundreds, right? Now if you have the twenty-two over to the left too far, you'll add the twenty in the hundreds column, as if the number were two hundred twenty rather than twenty-two. And that'll be wrong. So you have to keep the columns really straight—"
Understanding, ringing me as if I were a big old church bell, and it the clapper. It's the first time I remember feeling that sensation that has remained one of the enduring joys of my life: to understand.
And understanding mathematical concepts quickly led to power (and how I craved that!), power not only in the abstract world of math, but in the real world of father and school. I remember jumping up and down, my dad laughing cheerily, me dashing to my room to stamp out columns as straight as the ruler's edge, to add column after column of figures.
Oh, yes: Carlos Oleg Nevsky, here. Mother Mexican, father Russian (military advisor). Born in Mexico City in 2018, three months premature, after my mother suffered a bout of German measles during the pregnancy. Result: almost total blindness (I can tell dark from [bright] light). Lived in Mexico City until father was transferred to Russian embassy in Washington, D.C., when I was five. Lived in Washington almost continuously since then; my parents divorced when I was fifteen. Mathematics professor at George Washington University since 2043.
One cold spring afternoon I encountered Jeremy Blasingame in the faculty lounge as I went to get a coffee refill—in the lounge, where nobody ever hangs out. "Hello, Carlos, how's it going?"
"Fine," I said, reaching about the table for the sugar. "And you?"
"Pretty good. I've got a kind of an interesting problem over at my consulting job, though. It's giving me fits."
Jeremy worked for the Pentagon in military intelligence or something, but he seldom talked about what he did there, and I certainly never asked. "Oh, yes?" I said, as I found the sugar and spooned some in.
"Yes. They've got a coding problem that I bet would interest you."
"I'm not much for cryptography." Spy games—the math involved is really very specific. Sweet smell of sugar, dissolving in the lounge's bad coffee.
"Yes, I know," Jeremy said. "But"—an edge of frustration in his voice; it's hard to tell when I'm paying attention, I know (a form of control)—"but this may be a geometer's code. We have a subject, you see, drawing diagrams."
A subject. "Hmph," I said. Some poor spy scribbling away in a cell somewhere…
"So—I've got one of the drawings here. It reminds me of the theorem in your last article. Some projection, perhaps."
"Yes?" Now what spy would draw something like that?
"Yeah, and it seems to have something to do with her speech, too. Her verbal sequencing is all dislocated—words in strange order, sometimes."
"Yes? What happened to her?"
"Well… here, check out the drawing."
I put out a hand. "I'll take a look."
"And next time you want coffee, come ask me. I do a proper job of it in my office."
"All right."
I suppose I have wondered all my life what it would be like to see. And all my work, no doubt, is an effort to envision things in the inward theater. "I see it feelingly." In language, in music, most of all in the laws of geometry, I find the best ways I can to see: by analogy to touch, and to sound, and
to abstractions. Understand: To know the geometries fully is to comprehend exactly the physical world that light reveals; in a way one is then perceiving something like the Platonic ideal forms underlying the visible phenomena of the world. Sometimes the great ringing of comprehension fills me so entirely that I feel I must be seeing; what more could it be? I believe that I see.
Then comes the problem of crossing the street, of finding my misplaced keys. Geometry is little help; it's back to the hands and ears as eyes, at that point. And then I know that I do not see at all.
Let me put it another way. Projective geometry began in the Renaissance, as an aid to painters newly interested in perspective, in the problems of representing the three-dimensional world on a canvas; it quickly became a mathematics of great power and elegance. The basic procedure can be described quickly: When a geometrical figure is projected from one plane to another (as light, they tell me, projects the image on a slide onto a wall), certain properties of the figure are changed (lengths of sides, measures of angles), while other properties are not—points are still points, lines lines, and certain proportions still hold, among other things.
Now imagine that the visual world is a geometrical figure, which in a way it is. But then imagine that it has been projected inward onto something different, not onto a plane, but onto a Möbius strip or a Klein bottle, say, or onto a manifold actually much more complex and strange than those (you'd be surprised). Certain features of the figure are gone for good (color, for instance), but other essential features remain. And projective geometry is the art of finding what features or qualities survive the transformations of projection…
Do you understand me?