We practiced a lot. I showed him how to throw from the stretch, figuring that a wind-up from Gregor was likely to end up in knots. And by mid-season he threw a mean curve from the stretch. We had not mentioned it to anyone else. He was wild with it, but it hooked hard; I had to be really sharp to catch some of them. It made me better at shortstop too. Although finally in one game, behind twenty to nothing as usual, a batter hit a towering pop fly and I took off running back on it, and the wind kept carrying it and I kept following it, until when I got it I was out there sprawled between our startled center fielders.

Maybe you should play outfield, Werner said.

I said, Thank G.o.d.

So after that I played left center or right center, and I spent the games chasing line drives to the fence and throwing them back in to the cut-off man. Or more likely, standing there and watching the other team take their walks. I called in my usual chatter, and only then did I notice that no one on Mars ever yelled anything at these games. It was like playing in a league of deaf-mutes. I had to provide the chatter for the whole team from two hundred yards away in center field, including of course criticism of the plate umpire's calls. My view of the plate was miniaturized but I still did a better job than they did, and they knew it too. It was fun. People would walk by and say, Hey there must be an American out there.

One day after one of our home losses, 28 to 12 I think it was, everyone went to get something to eat, and Gregor was just standing there looking off into the distance. You want to come along? I asked him, gesturing after the others, but he shook his head. He had to get back home and work. I was going back to work myself, so I walked with him into town, a place like you'd see in the Texas panhandle. I stopped outside his co-op, which was a big house or little apartment complex, I could never tell which was which on Mars. There he stood like a lamppost, and I was about to leave when an old woman came out and invited me in. Gregor had told her about me, she said in stiff English. So I was introduced to the people in the kitchen there, most of them incredibly tall. Gregor seemed really embarra.s.sed, he didn't want me being there, so I left as soon as I could get away. The old woman had a husband, and they seemed like Gregor's grandparents. There was a young girl there too, about his age, looking at both of us like a hawk. Gregor never met her eye.

Next time at practice I said, Gregor, were those your grandparents?

Like my grandparents.

And that girl, who was she?

No answer.

Like a cousin or something?

Yes.

Gregor, what about your parents? Where are they?

He just shrugged and started throwing me the ball.

I got the impression they lived in another branch of his co-op somewhere else, but I never found out for sure. A lot of what I saw on Mars I liked-the way they run their businesses together in co-ops takes a lot of pressure off them, and they live pretty relaxed lives compared to us on Earth. But some of their parenting systems-kids brought up by groups, or by one parent, or whatever-I wasn't so sure about those. It makes for problems if you ask me. Bunch of teenage boys ready to slug somebody. Maybe that happens no matter what you do.

Anyway we finally got to the end of the season, and I was going to go back to Earth after it. Our team's record was three and fifteen, and we came in last place in the regular season standings. But they held a final weekend tournament for all the teams in the Argyre Basin, a bunch of three-inning games, as there were a lot to get through. Immediately we lost the first game and were in the loser's bracket. Then we were losing the next one too, and all because of walks, mostly. Werner relieved Thomas for a time, then when that didn't work out Thomas went back to the mound to re-relieve Werner. When that happened I ran all the way in from center to join them on the mound. I said, Look you guys, let Gregor pitch.

Gregor! they both said. No way!

He'll be even worse than us, Werner said.

How could he be? I said. You guys just walked eleven batters in a row. Night will fall before Gregor could do that.

So they agreed to it. They were both discouraged at that point, as you might expect. So I went over to Gregor and said, Okay, Gregor, you give it a try now.

Oh no, no no no no no no no. He was pretty set against it. He glanced up into the stands where we had a couple hundred spectators, mostly friends and family and some curious pa.s.sersby, and I saw then that his like-grandparents and his girl something-or-other were up there watching. Gregor was getting more hangdog and sullen every second.

Come on Gregor, I said, putting the ball in his glove. Tell you what, I'll catch you. It'll be just like warming up. Just keep throwing your curveball. And I dragged him over to the mound.

So Werner warmed him up while I went over and got on the catcher's gear, moving a box of blue dot b.a.l.l.s to the front of the ump's supply area while I was at it. I could see Gregor was nervous, and so was I. I had never caught before, and he had never pitched, and bases were loaded and no one was out. It was an unusual baseball moment.

Finally I was geared up and I clanked on out to him. Don't worry about throwing too hard, I said, just put the curveball right in my glove. Ignore the batter. I'll give you the sign before every pitch; two fingers for curve, one for fastball.

Fastball? he says.

That's where you throw the ball fast. Don't worry about that. We're just going to throw curves anyway.

And you said you weren't to coach, he said bitterly.

I'm not coaching, I said, I'm catching.

So I went back and got set behind the plate. Be looking for curveb.a.l.l.s, I said to the ump. Curveball? he said.

So we started up. Gregor stood crouched on the mound like a big praying mantis, red-faced and grim. He threw the first pitch right over our heads to the backstop. Two guys scored while I retrieved it, but I threw out the runner going from first to third. I went out to Gregor. Okay, I said, the bases are cleared and we got an out. Let's just throw now. Right into the glove. Just like last time, but lower.

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?

d.a.m.n 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 curveb.a.l.l.s. By no means were they all strikes, but enough were to keep him from walking too many batters. All the b.a.l.l.s 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 d.a.m.ned 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 baseb.a.l.l.s. 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 ma.s.sive-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 pa.s.sable 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 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. 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 40 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. .h.i.t 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. 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 b.a.l.l.s 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 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 a.s.sume 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; self; without this concept, all phenomena can be experienced as part of an extended "body." (Haptic s.p.a.ce [or tactile s.p.a.ce, the s.p.a.ce of the body] expanding to fill visual s.p.a.ce...) Every blind infant is in danger of autism. without this concept, all phenomena can be experienced as part of an extended "body." (Haptic s.p.a.ce [or tactile s.p.a.ce, the s.p.a.ce of the body] expanding to fill visual s.p.a.ce...) 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 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, gla.s.sy 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 p.r.i.c.kly 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 a.s.s. (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 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 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 a.s.sociated 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 b.u.mpy 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? why? It doesn't It doesn't matter 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 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 emba.s.sy 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 n.o.body ever hangs out. "h.e.l.lo, 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 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 feelingly." In language, in music, most of all in the laws of geometry, I find the best ways I can to see: by a.n.a.logy 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 must be seeing; what more could it be? I believe that I see. 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 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. 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 Mobius 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?A geometry for the self-non-Euclidean, of course; in fact, strictly Nevskyan, as it has to be to help me, as I make my projections from visual s.p.a.ce to auditive s.p.a.ce, to haptic s.p.a.ce.The next time I met Blasingame he was anxious to hear what I thought of his diagram. (There could be an acoustics of emotion-thus a mathematics of emotion; meanwhile, the ears of the blind do these calculations every day.)"One drawing isn't much to go on, Jeremy. I mean, you're right, it looks like a simple projective drawing, but with some odd lines crossing it. Who knows what they mean? The whole thing might be something scribbled by a kid.""She's not that young. Want to see more?""Well..." This woman he kept mentioning, some sort of Mata Hari prisoner in the Pentagon, drawing geometrical figures and refusing to speak except in riddles... naturally I was intrigued."Here, take these anyway. There seems to be a sort of progression.""It would help if I could talk to this subject subject who's doing all these." who's doing all these.""Actually, I don't think so... but"-seeing my irritation-"I can bring her by, I think, if these interest you.""I'll check them out.""Good, good." Peculiar edge of excitement in his voice, tension, antic.i.p.ation of... Frowning, I took the papers from him.That afternoon I shuffled them into my special Xerox machine, and the stiff reproductions rolled out of it heavily ridged. I ran my hands over the raised lines and letters slowly.Here I must confess to you that most geometrical drawings are almost useless to me. If you consider it, you will quickly see why: Most drawings are two-dimensional representations of what a three-dimensional construction looks looks like. This does me no good and in fact is extremely confusing. Say I feel a trapezoid on the page; is that meant to be a trapezoid, or is it rather a representation of a rectangle not coterminous with the page it lies on? Or the conventional representation of a plane? Only a like. This does me no good and in fact is extremely confusing. Say I feel a trapezoid on the page; is that meant to be a trapezoid, or is it rather a representation of a rectangle not coterminous with the page it lies on? Or the conventional representation of a plane? Only a description description of the drawing will tell me that. Without a description I can only deduce what the figure of the drawing will tell me that. Without a description I can only deduce what the figure appears appears to mean. Much easier to have 3-D models to explore with my hands. to mean. Much easier to have 3-D models to explore with my hands.But in this case, not possible. So I swept over the mishmash of ridges with both hands, redrew it with my ridging pen several times over, located the two triangles in it, and the lines connecting the two triangles' corners, and the lines made by extending the triangles' sides in one direction. I tried to make from my Taylor collection a 3-D model that accounted for the drawing-try that sometime, and understand how difficult this kind of intellectual feat can be! Projective imagination...Certainly it seemed to be a rough sketch of Desargues' theorem.Desargues' theorem was one of the first theorems clearly concerned with projective geometry; it was proposed by Girard Desargues in the mid-seventeenth century, in between his architectural and engineering efforts, his books on music, etc. It is a relatively simple theorem, showing that two triangles that are projections of each other generate a group of points off to one side that lie on a single line. Its chief interest is in showing the kind of elegant connections that projection so often creates.(It is also true that this theorem is reciprocal; that is, if you postulate two triangles whose extensions of the sides meet at three collinear points, then it is possible to show that the triangles are projections of each other. As they say in the textbooks, I leave the proof of this as an exercise for the reader.)But so what? I mean, it is a beautiful theorem, with the sort of purity characteristic of Renaissance math-but what was it doing in a drawing made by some poor prisoner of the Pentagon?I considered this as I walked to my health club, Warren's Spa (considered it secondarily, anyway, and no doubt subconsciously; my primary concerns were the streets and the traffic. Washington's streets bear a certain resemblance to one of those confusing geometrical diagrams I described [the state streets crossing diagonally the regular gridwork, creating a variety of intersections]; happily, one doesn't have to comprehend all the city at once to walk in it. But it is easy to become lost. So as I walked I concentrated on distances, on the sounds of the streets that tended to remain constant, on smells [the dirt of the park at M and New Hampshire, the hot dog vendor on 21st and K]; meanwhile, my cane established the world directly before my feet, my sonar shades whistled rising or falling notes as objects approached or receded... It takes some work just to get from point A to point B without getting disoriented [at which point one has to grind one's teeth and ask for directions] but it can be done, it is one of those small tasks/accomplishments [one chooses which, every time] that the blind cannot escape)-still, I did consider the matter of the drawing as I walked.On 21st and H, I was pleased to smell the pretzel cart of my friend Ramon, who is also blind. His cart is the only one where the hot plate hasn't roasted several pretzels to that metallic burnt odor that all the other carts put off; Ramon prefers the clean smell of freshly baked dough, and he claims it brings him more customers, which I certainly believe. "Change only, please," he was saying to someone briskly, "there's a change machine on the other side of the cart for your convenience, thanks. Hot pretzels! Hot pretzels, one dollar!""Hey there, Superblink!" I called as I approached him."Hey yourself, Professor Superblink," he replied. (Superblink is a mildly derogatory name used by irritated sighted social service people to describe those of their blind colleagues who are aggressively or ostentatiously competent in getting around, etc., who make a is a mildly derogatory name used by irritated sighted social service people to describe those of their blind colleagues who are aggressively or ostentatiously competent in getting around, etc., who make a display display of their competence. Naturally, we have appropriated the term for our own use; sometimes it means the same thing for us-when used in the third person, usually-but in the second person, it's a term of affection.) "Want a pretzel?" of their competence. Naturally, we have appropriated the term for our own use; sometimes it means the same thing for us-when used in the third person, usually-but in the second person, it's a term of affection.) "Want a pretzel?""Sure.""You off to the gym?""Yeah, I'm going to throw. Next time we play you're in trouble.""That'll be the day, when my main mark starts beating me!"I put four quarters in his callused hand, and he gave me a pretzel. "Here's a puzzle for you," I said. "Why would someone try to convey a message by geometrical diagram?"He laughed. "Don't ask me, that's your department!""But the message isn't for me.""Are you sure about that?"I frowned.At the health club I greeted Warren and Amanda at the front desk. They were laughing over a headline in the tabloid newspaper Amanda was shaking; they devoured those things and pasted the best headlines all over the gym."What's the gem of the day?" I asked."How about 'Gay Bigfoot Molests Young Boys'?" Warren suggested."Or 'Woman Found Guilty of Turning Husband into Bank President,'" Amanda said, giggling. "She drugged him and did 'bemod' to him until he went from teller to president."Warren said, "I'll have to do that for you, eh, Amanda?""Make me something better than a bank president."Warren clicked his tongue. "Entirely too many designer drugs, these days. Come on, Carlos, I'll get the range turned on." I went to the locker room and changed, and when I got to the target room Warren was just done setting it up. "Ready to go," he said cheerily as he rolled past me.I stepped in, closed the door, and walked out to the center of the room, where a waist-high wire column was filled with baseb.a.l.l.s. I pulled out a baseball, hefted it, felt the st.i.tching. A baseball is a beautiful object: nicely flared curves of the seams over the surface of a perfect sphere, exactly the right weight for throwing.I turned on the range with a flick of a switch and stepped away from the feeder, a ball in each hand. Now it was quite silent, only the slightest whirr faintly breathing through the soundproofed walls. I did what I could to reduce the sound of my own breathing, heard my heartbeat in my ears.Then a beep beep behind me to my left, and low; I whirled and threw. Dull thud. "Right... low," said the machine voice from above, softly. behind me to my left, and low; I whirled and threw. Dull thud. "Right... low," said the machine voice from above, softly. Beep Beep-I threw again: "Right... high," it said louder, meaning I had missed by more. "s.h.i.t," I said as I got another two b.a.l.l.s. "Bad start."Beep-a hard throw to my left-clang! "Yeah!" There is very little in life more satisfying than the bell-like clanging of the target circle when hit square. It rings at about middle C with several overtones, like a small, thick church bell hit with a hammer. The sound of success. "Yeah!" There is very little in life more satisfying than the bell-like clanging of the target circle when hit square. It rings at about middle C with several overtones, like a small, thick church bell hit with a hammer. The sound of success.Seven more throws, four more hits. "Five for ten," the machine voice said. "Average strike time, one point three five seconds. Fastest strike time, point eight four seconds."Ramon sometimes. .h.i.t the target in half a second or less, but I needed to hear the full beep to keep my average up. I set up for another round, pushed the b.u.t.ton, got quiet; beep beep throw, throw, beep beep throw, working to shift my feet faster, to follow through, to use the information from my misses to correct for the next time the target was near the floor, or the ceiling, or behind me (my weakness is the low ones; I can't seem to throw down accurately). And as I warmed up I threw harder and harder... just throwing a baseball as hard as you can is a joy in itself. And then to set that bell ringing! throw, working to shift my feet faster, to follow through, to use the information from my misses to correct for the next time the target was near the floor, or the ceiling, or behind me (my weakness is the low ones; I can't seem to throw down accurately). And as I warmed up I threw harder and harder... just throwing a baseball as hard as you can is a joy in itself. And then to set that bell ringing! Clang! Clang! It chimes every cell of you. It chimes every cell of you.But when I quit and took a shower, and stood before my locker and reached in to free my shirt from a snag on the top of the door, my fingers brushed a small metal wire stuck to an upper inside corner, where the door would usually conceal it from both me and my sighted companions; it came away when I pulled on it. Fingering the short length I couldn't be certain what it was, but I had my suspicions, so I took it to my friend James Gold, who works in acoustics in the engineering department, and had him take a confidential look at it."It's a little remote microphone, all right," he said, and then joked, "Who's bugging you, Carlos?"He got serious when I asked him where I could get a system like that for myself.John Metcalf-"Blind Jack of Knaresborough"-(17171810). At six he lost his sight through smallpox, at nine he could get on pretty well unaided, at fourteen he announced his intention of disregarding his affliction thenceforward and of behaving in every respect as a normal human being. It is true that immediately on this brave resolve he fell into a gravel pit and received a serious hurt while escaping, under pursuit, from an orchard he was robbing... fortunately this did not affect his self-reliance. At twenty he had made a reputation as a pugilist. (!)Ernest Bramah, Introduction,The Eyes of Max CarradosWhen I was young I loved to read Bramah's stories about Max Carrados, the blind detective. Carrados could hear, smell, and feel with incredible sensitivity, and his ingenious deductions were never short of brilliant; he was fearless in a pinch; also, he was rich and had a mansion, and a secretary, manservant, and chauffeur who acted as his eyes. All great stuff for the imaginative young reader, as certainly I was. I read every book I could get my hands on; the voice of my reading machine was more familiar to me than any human voice that I knew. Between that reading and my mathematical work, I could have easily withdrawn from the world of my own experience into Cutsforth's "verbal unreality," and babbled on like Helen Keller about the shapes of clouds and the colors of flowers and the like. The world become nothing but a series of texts; sounds kind of like deconstructionism, doesn't it? And of course at an older age I was enamored of the deconstructionists of the last century. The world as text: Husserl's The Origin of Geometry The Origin of Geometry is twenty-two pages long, Derrida's is twenty-two pages long, Derrida's Introduction to the Origin of Geometry Introduction to the Origin of Geometry is 153 pages long; you can see why it would have appealed to me. If, as the deconstructionists seemed to say, the world is nothing but a collection of texts, and I can read, then I am not missing anything by being blind, am I? is 153 pages long; you can see why it would have appealed to me. If, as the deconstructionists seemed to say, the world is nothing but a collection of texts, and I can read, then I am not missing anything by being blind, am I?The young can be very stubborn, very stupid."All right, Jeremy," I said. "Let me meet this mysterious subject subject of yours who draws all this stuff." of yours who draws all this stuff.""You want to?" he said, trying to conceal his excitement."Sure," I replied. "I'm not going to find out any more about all this until I do." My own subtext, yes; but I am better at hiding such things than Jeremy is."What have you found out? Do the diagrams mean anything to you?""Not much. You know me, Jeremy, drawings are my weakness. I'd rather have her do it in models, or writing, or verbally. You'll have to bring her by if you want me to continue.""Well, okay. I'll see what I can do. She's not much help, though. You'll find out." But he was pleased.One time in high school I was walking out of the gym after P.E., and I heard one of my coaches (one of the best teachers I have ever had) in his office, speaking to someone (he must have had his back to me)-he said, "You know, it's not the physical handicaps that will be the problem for most of these kids. It's the emotional problems that tend to come with the handicaps that will be the real burden."I was in my office listening to my reading machine. Its flat, uninflected mechanical voice (almost unintelligible to some of my colleagues) had over the years become a sort of helpless, stupid friend. I called it George, and was always programming into it another p.r.o.nunciation rule to try to aid its poor speech, but to no avail; George always found new ways to butcher the language. I put the book facedown on the gla.s.s; "Finding first line," croaked George, as the scanner inside the machine thumped around. Then it read from Roberto Torretti, quoting and discussing Ernst Mach. (Hear this spoken in the most stilted, awkward, syllable-by-syllable misp.r.o.nunciation that you can imagine.)"'Our notions of s.p.a.ce are rooted in our physiological physiological const.i.tution'" (George raises his voice in pitch to indicate italics, which also slow him down considerably). "'Geometric concepts are the product of the idealization of const.i.tution'" (George raises his voice in pitch to indicate italics, which also slow him down considerably). "'Geometric concepts are the product of the idealization of physical physical experiences of s.p.a.ce.' Physiological s.p.a.ce is quite different from the infinite, isotropic, metric s.p.a.ce of cla.s.sical geometry and physics. It can, at most, be structured as a topological s.p.a.ce. When viewed in this way, it naturally falls into several components: visual or optic s.p.a.ce, tactile or haptic s.p.a.ce, auditive s.p.a.ce, etc. Optic s.p.a.ce is anisotropic, finite, limited. Haptic s.p.a.ce or 'the s.p.a.ce of our skin corresponds to a two-dimensional, finite, unlimited (closed) Riemannian s.p.a.ce.' This is nonsense, for R-s.p.a.ces are metric, while haptic s.p.a.ce is not. I take it that Mach means to say that the latter can naturally be regarded as a two-dimensional compact connected topological s.p.a.ce. Mach does not emphasize enough the disconnectedness of haptic from optic s.p.a.ce-" experiences of s.p.a.ce.' Physiological s.p.a.ce is quite different from the infinite, isotropic, metric s.p.a.ce of cla.s.sical geometry and physics. It can, at most, be structured as a topological s.p.a.ce. When viewed in this way, it naturally falls into several components: visual or optic s.p.a.ce, tactile or haptic s.p.a.ce, auditive s.p.a.ce, etc. Optic s.p.a.ce is anisotropic, finite, limited. Haptic s.p.a.ce or 'the s.p.a.ce of our skin corresponds to a two-dimensional, finite, unlimited (closed) Riemannian s.p.a.ce.' This is nonsense, for R-s.p.a.ces are metric, while haptic s.p.a.ce is not. I take it that Mach means to say that the latter can naturally be regarded as a two-dimensional compact connected topological s.p.a.ce. Mach does not emphasize enough the disconnectedness of haptic from optic s.p.a.ce-"There came four quick knocks at my door. I pressed the b.u.t.ton on George that stopped him and said, "Come in!"The door opened. "Carlos!""Jeremy," I said. "How are you?""Fine. I've brought Mary Unser with me-you know, the one who drew-"I stood, feeling/hearing the presence of the other in the room. And there are times (like this one) when you know know the other is in some odd, undefinable way, the other is in some odd, undefinable way, different different, or... (Our language is not made for the experience of the blind.) "I'm glad to meet you."I have said that I can tell dark from light, and I can, though it is seldom very useful information. In this case, however, I was startled to have my attention drawn to my "sight"-for this woman was darker than other people, she was a sort of bundle of darkness in the room, her face distinctly lighter than the rest of her (or was that her face, exactly?).A long pause. Then: "On border stand we n n-dimensional s.p.a.ce the," she said. Coming just after George's reading, I was struck by a certain similarity: the mechanical lilt from word to word; the basic incomprehension of a reading machine... Goose b.u.mps rose on my forearms.Her voice itself, on the other hand, had George beat hands down. Fundamentally vibrant under the odd intonation, it was a voice with a very thick timbre, a ba.s.soon or a hurdy-gurdy of a voice, with the buzz of someone who habitually speaks partly through the sinuses; this combined with over-relaxed vocal cords, what speech pathologists call glottal fry glottal fry. Usually nasal voices are not pleasant, but pitch them low enough...She spoke again, more slowly (definitely glottal fry): "We stand on the border of n n-dimensional s.p.a.ce.""Hey," Jeremy said. "Pretty good!" He explained: "Her word order isn't usually as... ordinary as that.""So I gathered," I said. "Mary, what do you mean by that?""I-oh-" A kazoo squeak of distress, pain. I approached her, put out a hand. She took it as if to shake: a hand about the size of mine, narrow, strong fat muscle at base of thumb; trembling distinctly."I work on the geometries of topologically complex s.p.a.ces," I said. "I am more likely than most to understand what you say.""Are within never see we points us.""That's true." But there was something wrong here, something I didn't like, though I couldn't tell exactly what it was. Had she spoken toward Jeremy? Speaking to me while she looked at him? Bundle of darkness in the dark... "But why are your sentences so disordered, Mary? Your words don't come out in the order you thought them. You must know that, since you understand us.""Folded-oh!-" Again the double-reed squeak, and suddenly she was weeping, trembling hard; we sat her down on my visitor's couch, and Jeremy got her a gla.s.s of water while she quaked in my hands. I stroked her hair (short, loosely curled, wild) and took the opportunity for a quick phrenological check: skull regular and, as far as I could tell, undamaged; temples wide, distinct; same for eye sockets; nose a fairly ordinary pyramidal segment, no bridge to speak of; narrow cheeks, wet with tears. She reached up and took my right hand, squeezed it hard, three times fast, three times slow, all the time sobbing and sort of hiccupping words: "Pain it, station. I, oh, fold end, bright, light, s.p.a.ce fold, oh, ohhh..."Well, the direct question is not always the best way. Jeremy returned with a gla.s.s of water, and drinking some seemed to calm her. Jeremy said, "Perhaps we could try again later. Although..." He didn't seem very surprised."Sure," I said. "Listen, Mary, I'll talk to you again when you're feeling better."After Jeremy got her out of the office and disposed of her (how? with whom?) he returned to the seventh floor."So what the h.e.l.l happened to her?" I asked angrily. "Why is she like that?""We aren't completely sure," he said slowly. "Here's why. She was one of the scientists staffing Tsiolkovsky Base Five, up in the mountains on the back side of the moon, you know. She's an astronomer and cosmologist. Well-I have to ask you to keep this quiet-one day Base Five stopped all broadcasting, and when they went over to see what was wrong, they found only her, alone in the station in a sort of catatonic state. No sign of the other scientists or station crew-eighteen people gone without a trace. And nothing much different to explain what had happened, either."I hmphed hmphed. "What do they think happened?""They're still not sure. Apparently, no one else was in the area, or could have been, et cetera. It's been suggested by the Russians, who had ten people there, that this could be first contact-you know, that aliens took the missing ones, and somehow disarranged Mary's thought processes, leaving her behind as a messenger that isn't working. Her brain scans are bizarre. I mean, it doesn't sound very likely...""No.""But it's the only theory that explains everything they found there. Some of which they won't tell me about. So, we're doing what we can to get Mary's testimony, but as you can see, it's hard. She seems most comfortable drawing diagrams.""Next time we'll start with that.""Okay. Any other ideas?""No," I lied. "When can you bring her back again?"As if because I was blind I couldn't tell I was being duped! I struck fist into palm angrily. Oh, they were making a mistake, all right. They didn't know how much the voice reveals. The voice's secret expressivity reveals so much! so much!-the language really is not adequate to tell it; we need that mathematics of emotion... In the high school for the blind that I briefly attended for some of my cla.s.ses, it often happened that a new teacher was instantly disliked, for some falseness in his or her voice, some quality of condescension or pity or self-congratulation that the teacher (and his or her superiors) thought completely concealed, if they knew of it at all. But it was entirely obvious to the students, because the voice (if what I have heard is true) is much more revealing than facial expressions; certainly it is less under our control. This is what makes most acting performances so unsatisfactory to me; the vocal qualities are so stylized, so removed from those of real life...And here, I thought, I was witnessing a performance.There is a moment in Olivier Messiaen's Visions de l'Amen Visions de l'Amen when one piano is playing a progression of major chords, very traditionally harmonic, while on another piano high pairs of notes plonk down across the other's chords, ruining their harmony, crying out, Something's wrong! Something's wrong! when one piano is playing a progression of major chords, very traditionally harmonic, while on another piano high pairs of notes plonk down across the other's chords, ruining their harmony, crying out, Something's wrong! Something's wrong!I sat at my desk and swayed side to side, living just such a moment. Something was wrong.When I collected myself I called the department secretary, who had a view of the hall to the elevator. "Delphina, did Jeremy just leave?""Yes, Carlos. Do you want me to try and catch him?""No, I only need a book he left in his office. Can I borrow the master key and get it?""Okay."I got the key, entered Jeremy's office, closed the door. One of the tiny pickups that James Gold had gotten for me fit right under the snap-in plug of the telephone cord. Then a microphone under the desk, behind a drawer. And out. (I have to be bold every day, you see, just to get by. But they didn't know that.) Back in my office I closed and locked the door, and began to search. My office is big: two couches, several tall bookcases, my desk, a file cabinet, a coffee table.... When the part.i.tions on the seventh floor of the Gelman Library were moved around to make more room, Delphina and George Hampton, who was chairman that year, had approached me nervously: "Carlos, you wouldn't mind an office with no windows, would you?"

I laughed. All of the full professors had offices on the outer perimeter of the floor, with windows.

"You see," George said, "since none of the windows in the building opens anyway, you won't be missing out on any breezes. And if you take this room in the inner core of the building, then we'll have enough s.p.a.ce for a good faculty lounge."

"Fine," I said, not mentioning that I could see sunlight, distinguish light and dark. It made me angry that they hadn't remembered that, hadn't thought to ask. So I nicknamed my office "The Vault," and I had a lot of room, but no windows. The halls had no windows either, so I was really without sun, but I didn't complain.

Now I got down on hands and knees and continued searching, feeling like it was hopeless. But I found one, on the bottom of the couch. And there was another in the phone. Bugged. I left them in position and went home.

Home was a small top-floor apartment up near 21st and N streets, and I supposed it was bugged too. I turned up Stockhausen's Telemusik Telemusik as loud as I could stand it, hoping to drive my listeners into a suicidal fugal state, or at least give them a headache. Then I slapped together a sandwich, downed it angrily. as loud as I could stand it, hoping to drive my listeners into a suicidal fugal state, or at least give them a headache. Then I slapped together a sandwich, downed it angrily.

I imagined I was captain of a naval sailing ship (like Horatio Hornblower), and that because of my sharp awareness of the wind I was the best captain afloat. They had had to evacuate the city and all the people I knew were aboard depending on me. But we were caught against a lee sh.o.r.e by two large ships of the line, and in the ensuing broadsides (roar of cannon, smell of gunpowder and blood, screams of wounded like shrieking seagulls), everyone I knew fell-chopped in half, speared by giant splinters, heads removed by cannonball, you name it. Then when they were all corpses on the sand-strewn splintered decking, I felt a final broadside discharge, every ball converging on me as if I were point 0 at the tip of a cone. Instant dissolution and death.

I came out of it feeling faintly disgusted with myself. But because it actively defends the ego by eradicating those who attack its self-esteem, Cutsforth calls this type of fantasy in the blind subject healthy. (At least in fourteen-year-olds.) So be it. Here's to health. f.u.c.k all of you.

Geometry is a language, with a vocabulary and syntax as clear and precise as humans can make them. In many cases definitions of terms and operations are explicitly spelled out, to help achieve this clarity. For instance, one could say: Let (parentheses) designate corollaries.

Let [brackets] designate causes.

Let {braces} designate...

But would it be true, in this other language of the heart?

Next afternoon I played beepball with my team. Sun hot on my face and arms, spring smell of pollen and wet gra.s.s. Ramon got six runs in the at-bat before mine (beepball is a sort of cricket/softball mix, played with softball equipment ["It proves you can play cricket blind" one Anglophobe {she was Irish} said to me once]), and when I got up I scratched out two and then struck out. Swinging too too hard. I decided I liked outfield better. The beepball off in the distance, lofted up in a short arc, smack of bat, follow the ball up and up-out toward me!-drift in its direction, the rush of fear, glove before face as it approaches, stab for it, off after it as it rolls by-pick it up-Ramon's voice calling clearly, "Right here! Right here!"-and letting loose with a throw-really putting everything into it-and then, sometimes, hearing that beepball lance off into the distance and smack into Ramon's glove. It was great. Nothing like outfield. hard. I decided I liked outfield better. The beepball off in the distance, lofted up in a short arc, smack of bat, follow the ball up and up-out toward me!-drift in its direction, the rush of fear, glove before face as it approaches, stab for it, off after it as it rolls by-pick it up-Ramon's voice calling clearly, "Right here! Right here!"-and letting loose with a throw-really putting everything into it-and then, sometimes, hearing that beepball lance off into the distance and smack into Ramon's glove. It was great. Nothing like outfield.

And next inning I hit one hard hard, and that's great too. That feeling goes right up your arms and all through you.Walking home I brooded over Max Carrados, blind detective, and over Horatio Hornblower, sighted naval captain. Over Thomas Gore, the blind senator from Oklahoma. As a boy his fantasy was to become a senator. He read the Congressional Record Congressional Record, joined the debate team, organized his whole life around the project. And he became senator. I knew that sort of fantasy as well as I knew the vengeful adolescent daydreams: All through my youth I dreamed of being a mathematician. And here I was. So one could do it. One could imagine doing something, and then do it.But that meant that one had, by definition, imagined something possible possible. And one couldn't always say ahead of the attempt whether one had imagined the possible or the impossible. And even if one had imagined something possible, that didn't guarantee a successful execution of the plan.The team we had played was called Helen Keller Jokes Helen Keller Jokes (there are some good ones, too [they come {of course} from Australia] but I won't go into that). It's sad that such an intelligent woman was so miseducated-not so much by Sullivan as by her whole era: all that treacly Victorian sentimentality poured into her: "The fishing villages of Cornwall are very picturesque, seen either from the beaches or the hilltops, with all their boats riding to their moorings or sailing about in the harbor. When the moon, large and serene, floats up the sky, leaving in the water a long track of brightness like a plow breaking up a soil of silver, I can only sigh my ecstasy"-come on, Helen. Now (there are some good ones, too [they come {of course} from Australia] but I won't go into that). It's sad that such an intelligent woman was so miseducated-not so much by Sullivan as by her whole era: all that treacly Victorian sentimentality poured into her: "The fishing villages of Cornwall are very picturesque, seen either from the beaches or the hilltops, with all their boats riding to their moorings or sailing about in the harbor. When the moon, large and serene, floats up the sky, leaving in the water a long track of brightness like a plow breaking up a soil of silver, I can only sigh my ecstasy"-come on, Helen. Now that that is living in a world of texts. is living in a world of texts.But didn't I live most (all?) of my life in texts as least as unreal to me as moonlight on water was to Helen Keller? These n n-dimensional manifolds... I suppose the basis for my abilities in them was the lived reality of haptic s.p.a.ce, but still, it was many removes from my actual experience. And so was the situation I found myself confronted with now, Jeremy and Mary acting out some drama I did not comprehend... and so was my plan to deal with it. Verbalism... words versus reality.I caressed my glove, refelt the knock of bat against beepball. Brooded over my plan.The next time Jeremy brought Mary Unser by my office, I said very little. I got out my "visitor's supply" of paper and pencils and set her down at the coffee table. I brought over my models: subatomic particles breaking up in a spray of wire lines, like water out of a showerhead; strawlike Taylor sticks for model making; polyhedric blocks of every kind. And I sat down with the ridged sheets made from her earlier drawings, as well as the models I had attempted to make of them, and I started asking very limited questions. "What does this line mean? Does it go before or behind? Is this R R or or R prime? R prime? Have I got this right?" Have I got this right?"And she would honk a sort of laugh, or say, "No, no, no, no" (no problem with sequencing there), and draw furiously. I took the pages as she finished them and put them in my Xerox, took out the ridged, b.u.mpy sheets and had her guide my fingers over them. Even so they were difficult, and with a squeak of frustration she went to the straw models, clicking together triangles, parallels, etc. This was easier, but eventually she reached a limit here too. "Need drawing beyond," she said."Fine. Write down whatever you want."She wrote and then read aloud to me, or I put it through the Xerox machine marked translation to Braille translation to Braille. And we forged on, with Jeremy looking over our shoulders the whole time.And eventually we came very close to the edge of my work, following subatomic particles down into the microdimensions where they appeared to make their "jumps." I had proposed an n n-dimensional topological manifold, where 1<>< infinity,="" so="" that="" the="" continuum="" being="" mapped="" fluctuated="" between="" one="" and="" some="" finite="" number="" of="" dimensions,="" going="" from="" a="" curving="" line="" to="" a="" sort="" of="" n="" n-dimensional="" swiss="" cheese,="" if="" you="" like,="" depending="" on="" the="" amounts="" of="" energy="" displayed="" in="" the="" area,="" in="" any="" of="" the="" four="" "forms"="" of="" electro-magnetism,="" gravity,="" or="" the="" strong="" and="" weak="" interactions.="" the="" geometry="" for="" this="" manifold-pattern="" (so="" close="" to="" the="" experience="" of="" haptic="" s.p.a.ce)="" had,="" as="" i="" have="" said,="" attracted="" the="" attention="" of="" physicists="" at="" cern="" and="" slac-but="" there="" were="" still="" unexplained="" data,="" as="" far="" as="" i="" could="" tell,="" and="" the="" truth="" was,="" i="" had="" not="" published="" this="" work="" i="" had="" not="" published="" this="" work.so="" here="" i="" was="" "conversing"="" with="" a="" young="" woman="" who="" in="" ordinary="" conversations="" could="" not="" order="" her="" words="" correctly-who="" in="" this="" realm="" spoke="" with="" perfect="" coherence-who="" was="" in="" fact="" speaking="" about="" (inquiring="" about?)="" the="" edges="" of="" my="" own="" private="" work.the="" kind="" of="" work="" that="" jeremy="" blasingame="" used="" to="" ask="" me="" about="" so="" curiously.i="" sighed.="" we="" had="" been="" going="" on="" for="" two="" or="" three="" hours,="" and="" i="" sat="" back="" on="" the="" couch.="" my="" hand="" was="" taken="" up="" in="" mary's,="" given="" a="" rea.s.suring="" squeeze.="" i="" didn't="" know="" what="" to="" make="" of="" it.="" "i'm="" tired.""i="" feel="" better,"="" she="" said.="" "easier="" to="" talk="" way-this="" way.""ah,"="" i="" said.="" i="" took="" up="" the="" model="" of="" a="" positron="" hitting="" a="" "stationary"="" muon:="" a="" wire="" tree,="" trunk="" suddenly="" bursting="" into="" a="" ma.s.s="" of="" curling="" branches.="" so="" it="" was="" here:="" one="" set="" of="" events,="" a="" whole="" scattering="" of="" explanations.="" still,="" the="" bulk="" of="" the="" particles="" shot="" out="" in="" a="" single="" general="" direction="" (the="" truths="" of="" haptic="" s.p.a.ce).she="" let="" go="" of="" my="" hand="" to="" make="" one="" last="" diagram.="" then="" she="" xeroxed="" it="" for="" me,="" and="" guided="" my="" hands="" over="" the="" ridged="" copy.once="" again="" it="" was="" desargues'="" theorem.at="" this="" point="" mary="" said,="" "mr.="" blasingame,="" i="" need="" a="" drink="" of="" water."="" he="" went="" out="" to="" the="" hall="" water="" dispenser,="" and="" she="" quickly="" took="" my="" forefinger="" between="" her="" finger="" and="" thumb="" (pads="" flattening="" with="" an="" inappropriate="" pressure,="" until="" my="" finger="" ached)-squeezed="" twice,="" and="" jabbed="" my="" finger="" first="" onto="" her="" leg,="" then="" onto="" the="" diagram,="" tracing="" out="" one="" of="" the="" triangles.="" she="" repeated="" the="" movements,="" then="" poked="" my="" leg="" and="" traced="" out="" the="" other="" triangle.="" then="" she="" traced="" down="" the="" line="" off="" to="" the="" side,="" the="" one="" generated="" by="" the="" projection="" of="" the="" two="" triangles,="" over="" and="" over.="" what="" did="" she="" mean?jeremy="" returned,="" and="" she="" let="" my="" hand="" go.="" then="" in="" a="" while,="" after="" the="" amenities="" (hard="" handshake,="" quivering="" hand),="" jeremy="" whisked="" her="" off.when="" he="" returned,="" i="" said,="" "jeremy,="" is="" there="" any="" chance="" i="" can="" talk="" to="" her="" alone?="" i="" think="" she's="" made="" nervous="" by="" your="" presence-the="" a.s.sociations,="" you="" know.="" she="" really="" does="" have="" an="" interesting="" perspective="" on="" the="" n="" n-dimensional="" manifold,="" but="" she="" gets="" confused="" when="" she="" stops="" and="" interacts="" with="" you.="" i'd="" just="" like="" to="" take="" her="" for="" a="" walk,="" you="" know-down="" by="" the="" ca.n.a.l,="" or="" the="" tidal="" basin,="" perhaps,="" and="" talk="" things="" over="" with="" her.="" it="" might="" get="" the="" results="" you="" want.""i'll="" see="" what="" they="" say,"="" jeremy="" said="" in="" an="" expressionless="" voice.that="" night="" i="" put="" on="" a="" pair="" of="" earplugs="" and="" played="" the="" tape="" of="" jeremy's="" phone="" conversations.="" in="" one="" when="" the="" phone="" w