We took the walk along the beach. There was some sun, and an uncertain breeze. Winos hung around the benches, talking shop. There were fishing-boats out on the water.

The girls were beautiful. I said something to him about it. He laughed. “You should be here in the summer,” he said.

A girl on a bicycle came toward us and passed. — Consonantia. Integritas. Claritas. — I turned to look after her.

“She was smiling at you Garbonzo.” It seemed an accusation.

“Must be the hat,” I said. I tugged at it, self-conscious.


“You still smoke Camels don’t you?”

“Yes,” I said. Art and disease. “This week for some reason they’re Lucky Strikes. But usually they’re Camels. Yes.”

“And that Army jacket you used to wear. Do you still have that?”

I laughed. “I wore it to a party at Halloween,” I said.

“And when we went to Tech yesterday? How long was that?”

I laughed again. “Six years,” I said. The motion of the earth, against the fixed stars.

He shook his head. “That must have been strange,” he said.

“Yes,” I said. “It was.”


At the coffeeshop we took espresso with rolls, and talked about getting rich, or at least solvent. Teaching at the free schools seemed an obvious hustle. “Heidegger,” I said. “It was Stefano’s idea actually. The Indian stuff is about played out. So we corner the market for German idealism. It can’t miss. It’s murky, it’s Aryan, it has the vocabulary.”

“I like it,” he said thoughtfully. “I like it.”

“Come on, Richard,” I said. “’Angst’? ’Geworfenheit’?”

He laughed. “Well.”

“Come on,” I said. “’Selbstsein’? This is the fucking Age of Selbstsein.”

“Really,” he said. “Really.” He thought about it. “But why not teach a course in Wittgenstein? Seriously.”

“It is an easy name to drop,” I conceded. “But one difficult to attach to any doctrine which can appeal to the cult of self-realization. There is the contribution to the philosophical theater: the hut in Norway, the notebooks in his rucksack as the shells whistled over his head in the trenches, the retirement in Austria, schoolteacher, gardener to monks. Well and good; that works. But even this can’t sell logic and ontology.”

“True.” He frowned. “Perhaps Heidegger would be better.”

“Well.”

“But really what you should try is computer theft.”

“What?”

“No really I’m serious. Do you remember Grossmann? He was a student of mine.”

“The lapsed physicist.”

“Yes. Well, he’s some kind of computer programmer now, and he works at a bank. Not that he steals anything, I doubt he has the imagination, but anyway, I couldn’t do it, but you could. You should do it. I’m serious.”

“Right,” I said. Laughing helplessly. “Right.”

“No really you should.”

“Right,” I said. Laughing. “You handle the numbered account in Zurich. I’ll wire Exxon straight into it. We’ll buy a little country somewhere, nothing ostentatious, something with a good beach and a southern exposure. You’ll keep a villa by the sea, with a brace of Ferraris. I’ll have a Gothic castle in the mountains of the north, with a laboratory for my” — laughing; pronouncing it with difficulty: — “forbidden experiments. — a few serving-wenches, some alchemical apparatus, an assistant named Igor” —

“A graduate student of course” —

“Of course.” Laughing. “Of course. They drool, to be sure, but —”

“One can’t do without them. Really one can’t.” Curiously thoughtful. “But must he be a hunchback?”

“A polio victim perhaps. He walks with a limp. It may be he affects a cane.”

“His hair, unkempt.”

“But his brow, noble. His expression one of transcendent sadness.”

“His dress is simple.”

“Though it is intimated his descent is high; that he was raised amid wealth and every evidence of cultivation.”

“He is musical.”

“He has a gift for the harmonica. His repertoire is extensive, but he favors Bach, and Scarlatti.”

“His habitation?”

“A rude hut, not far from the castle. Nearby is a garden, where he nurtures herbs.”

Suspicion: “He doesn’t keep bees does he?”

“No.” Smiling.

“Good.” Thinking. “But no doubt he is gentle and articulate.”

“And kind with animals. It is said that he has tamed great numbers of wild birds.”

“He is fond of Schopenhauer.”

“And Heine.”

“But not Rilke.” He frowned. “No, he doesn’t like Rilke. Though I’m not sure why.”


Hands in my pockets, listening. He wanted more children. “Or at least one? You know?” She didn’t understand that. I laughed. — “What?” he asked. — “Nothing,” I said. — “Too blonde,” I said. I wiggled my toes inside my tennis shoes. — “Entirely too blonde.”


“But don’t you like this place?” he asked.

“Yes,” I said. “I have a love for these hippie coffeehouses, man: the wood all over, the posters hung up, the stereos, the views. This place reminds me a bit of the Sundance cafe.”

“Where’s that?”

“In Nederland, twenty miles west of Boulder. It’s almost nine thousand feet there, cool even in the summer. They have a deck, with a view, you know, of real mountains, bare rock and glacier ice.”

“Perhaps you should live there.”

I laughed. “Perhaps.”

A pause. On the stereo, an old Beatles’ tune: Things we said today.

“But really we should go to Guatemala,” he said.

I laughed. “All right.”

“No really we should. I have family there you know, though I haven’t seen them in a long time. There are German colonies all over South America, and you’d love it there, you really would.”

“But do you speak Spanish?” I asked. “I mean their Spanish. Because I don’t. Though I suppose I could learn.”

“Oh yes. I do. You could. No, we should do it. We really should.”

“All right.” Laughing.

“But where do you live now? Do you live in the mountains?”

“Not really. At the foot of one.”

“Because I’ve been there you know, though not in a while. Diane’s sister lives there. Melissa goes to visit her every summer.”

“Really? Where does she live?”

“I don’t know. But it is beautiful, I remember that. But you don’t live in the mountains?”

“No.” Laughing. “Though perhaps I should.”

“Yes,” he said. Curiously thoughtful. “Perhaps you should.”

“Though town may well suffice.”

“Suffice?”

“That’s the intent,” I said. “To Mellow Out.”

“Really?” He laughed. “But have you?” He examined me. “You seem better.”

“Yes. I am.”

“It is beautiful.”

“Yes. It is.”

“The city’s right beneath the mountains isn’t it.”

“Yes,” I said. “It is.” Thinking. “I remember that that struck me first about it, that the mountains start there all at once. The city sits beneath what was a wall of naked rock.”

“Yes,” he said. “I remember that, that struck me too.” He smiled. “That is strange isn’t it? I’m sure you can explain it though.”

I laughed.

“Come on. You have an explanation for everything Garbonzo.”

I shrugged. “The motion of the plates,” I said.

He smiled. Waiting. Which was part of the game.

I laughed. “The motion of the plates,” I said, “represents an attempt to impose a smooth vector field upon the surface of the sphere. But the sphere admits no smooth global vector field. So the field can be smooth on patches only, and the patches must meet on curves on which the flow is discontinuous.”

Suspicion: “Really Garbonzo.”

I laughed.

“But Diane’s rich now you know,” he said. “She’s an architect, she finished at UCLA after we split up, and she got in on some real estate deals, I don’t know how. I can’t believe the money she makes.”

“Really?” — Toy houses on the table, when Scott and I had come to dinner, balsawood and paper. — Very thin, small nervous: horrified when Melissa had come in out of the dirt, producing a slug from her clothing.

“Yes, and it’s that much worse, you know, because, you know, I have these teaching jobs, but none of them is really very stable, I send out resumes all the time, but what can you do? it’s not like Caltech, I mean they paid really well, no matter how weird the place was (How could you stand it? though of course I guess you couldn’t), and we owned that house in fact, though of course we sold it, and now I don’t know, I really don’t. It’s all right being a janitor isn’t it? I mean it leaves you time to think.”

I assured him that it did.

“Because I wonder about that,” he said. “I mean, what I could do. But then finally it occurred to me that I could always be a chauffeur. You know? Wear a uniform, and drive some rich guy around. Because I know Los Angeles like the back of my hand, I’ve lived here all my life, and I could do that, I really could.”

“Yes,” I said. Thinking; laughing. “A friend of Scott’s did that once. It didn’t sound bad.” I paused. “He repeated his mantra, you know, he had some guru, and he did it all the time, for the positive karma, right, and that was what came of it, he got that job.” Laughing. “It was funny because he talked about it as if these were the cash benefits of meditation, right, but it didn’t sound bad. Once in a while he’d have to drive his millionaire somewhere, but the rest of the time he’d sit there in the car, you know” — patting at the top of my head — “with his little cap on, I mean, I saw the uniform, but he’d sit there in the car and smoke dope. I liked the sound of it. You could write.”

“He smoked dope?”

“Oh yes. Certainly. In fact I think it was the millionaire’s dope. But I never saw this guy without a joint in his hand.” The Fabulous Furry Freak Brothers. “I wonder what became of him.” Laughing. “Maybe he works in a bank too.”

“Really,” he said. “Really.” Thinking. “But we should go to Guatemala Garbonzo. I’m serious.”

“All right,” I said.

“Really,” he said. “We can get a van and drive down there. You’d love it there. You really would.” A pause. “But if we’re going to do this we’re going to have to get a couple of women Garbonzo.”

I laughed. I thought I could take care of the van.


Staring out the window then: the world floated on the water. Like the fishing-boats: toys, and their receptacle. — Laughing.

“What?” he asked.

“Nothing.” Laughing. “Who built the shore so near the ocean?”

He smiled. “That must have been strange,” he said.

I looked at him; established reference; looked away again. “Yes,” I said. “It was.”

He smiled and said nothing. After a moment I looked back at him and grinned. My teacher still; he knew I could do better.

A name need not have unique denotation. Thus Richard might be Fagley: in the cafeteria, in the ninth grade; done with another gruesome lunch, we sat at our table and played games with strips of paper. — Stefano to one side, making comment, obscene, original. Perhaps it had been this time that he had read aloud from my Latin book, the rape of the Sabine women, mispronouncing with such ludicrous effect. — Here Christiansen came walking by, pausing to look over our shoulders: that petulant expression, that callow self-important scowl, pursing those bloodless lips, trying to decide whether this was some kind of dirty joke that would allow him the petty satisfaction of busting us for detention. -— Ignoring him, innocent precocious dorks absorbed in our game: cut the loop in half, you get one longer loop; cut it along in thirds, you get two, one twice the length of the other, and these two linked. Fagley bet me that I couldn’t guess, and he was right. — Christiansen gave up; paused to lay a hand upon Stefano’s shoulder and murmur a few words of encouragement — for, mysteriously, Stefano was one of his favorites. — “Yes sir,” Stefano said; waited until he’d walked out of earshot and added, “Asshole.” — We laughed. Christiansen looked back, scowling, but we’d put our straight faces back on, and he had to keep upon his rounds. — Fagley bet me again. This time I stared at it a while, and this time I got it right.

— Gamov? most brilliant dilettante, now poured into his grave. — I muttered something.

“What?” he asked. Smiling.

“Nothing.” My love is of a birth so rare. “Have you ever heard of a Klein bottle?”

“No.”

“Well.” A pause. “It’s the simplest example, or nearly, of a nonorientable manifold.”

“Well,” he said. A patient smile.

I laughed. “A manifold is just a space.”

“A space?” The indefinite article.

“A set of points. A bag of shit, a bunch of grapes. It doesn’t matter. Though you say a little more about the bagginess, the bunchiness, than you have to a priori: something about closeness, about one point’s lying in the neighborhood of another. Then it becomes topology.”

“Well.” He frowned. A certain resistance to the method of abstraction.

I laughed. “Come on man. We’ve been through this before.”

“All right,” he said. “But I don’t like it.”

Go on, said D’Alembert, and faith will come to you. “That’s still too general to be nice,” I said. “There are pathological examples of topological spaces. But a manifold is a nice space. Something smooth, like you might paste together out of sheets of paper. Or mold from clay.”

“Really,” he said. Abstracted. “From clay.”

“Though it might be best to think of figures blown from glass. For that suggests the essence of the shape, you know, the shape alone, with no thought for its size, or what it holds, what stuff it is that fills it out.”

“All right,” he said.

“You might think of the surface of a sphere,” I said. “Or that of a coffee cup.” With the obvious gesture.

“A coffee cup?” Amused. “With the handle on it I suppose.”

“Oh certainly,” I said. “The handle’s quite the best of it.”

“Why?” Puzzled. Regarding the object at hand.

“The hole,” I said. The finger through it, waggling. “You can’t get rid of the hole.” Holding the cup up; staring at it. “You classify things — shapes, spaces in the abstract — up to smooth deformations. So a coffee cup is any other coffee cup, or a doughnut, for that matter, or inner tube, and a sphere is any other sphere, or flattened sphere, or plate, or bowl. But the coffee cup can’t be deformed into a sphere, or into a vase, say, with two handles on it, or: — a pretzel, say, blown out of glass, with as many handles as you please. For in the simplest case, the case implicitly at hand, you’ve classified the surface if you simply count the handles. Because when you make the handle, when you make the puncture in the clay, you work a certain violence on the object, you do something that isn’t smooth. You make one thing into another.”

“But you do that when you shape the clay.”

“Not in the same way. There is a distinction.”

“Yes,” he said. “I see that there is.” Staring at the coffee cup. — Philosophy begins with wonder; and therefore, learn to gape.

“But these,” I said, “the surface of the sphere, that of the coffee cup, are orientable manifolds. They have an inside and an outside.” A pause. “This has to do with the distinction between the right hand and the left. There’s mention of the problem in the ’Tractatus’, a reference to Kant. It’s a kind of paradox, because the right hand and the left are congruent, mirror images” — I held them up for his inspection [Where had the tremor gone? this time last year they would have shaken] — “but no motion in space can carry the one into the other. If you’ve a right-hand glove, and you want to put it on your left hand, you have to turn it inside-out. You can’t just take it behind your back, and then put it on. You have to cheat. You can’t walk through the looking-glass, at least it doesn’t seem you can. So ordinary space, the space we grew up in, is orientable.”

Staring at his hands. “Have you been reading Kant?”

“Handedness is called ’parity’, in theoretical physics. — No. Not really. That was your advice. You said to wait.”

Looking up, surprised. “I did?” Thinking. “But that was good advice.”

I laughed.

“But perhaps you should now.”

“Perhaps I shall.”

“There are parallels with Wittgenstein you know.”

“I know.”

“You might write something about that.”

“I’d thought about it.” A pause. “But it’s just what they held in common that disturbs me.” Der Satz kann die logische Form nicht darstellen, sie spiegelt sich in ihm.

“Really?”

“Yes.” A pause. “There’s a misapprehension, I guess you could say, of the problem of representation. It seems like a simple lack of mathematical imagination. Everything Wittgenstein said was impossible a priori, Gödel and Tarski accomplished ten years later. You don’t find any direct recognition of this in the philosophical literature, but it’s true. I mean, really, man, I do believe that, that the philosophy of logic is the proper successor to metaphysics. But the whole thing is bound up with questions of mathematical form.” Staring at my toe: the fabric of logical space.

“Did you read Chihara’s book about Gödel?”

“Once. I had meant to try again.” As had perhaps Chihara.

“I know Chihara.”

“I remember that you told me that.”

“You should try to write something about this.”

“Yes. I suppose that I should.”

Remembering his hands, still curiously posed before him. “Space.”

I laughed, and patted at the breast pocket of my jacket. — Brown battered leather, the gift of Tommy, Dottie’s boyfriend, the Jewish lawyer. It must have been fashionable once, or he never would have owned it; it must have fallen out of fashion, or he never would have given it up. Since then I’d been relentlessly wearing it down to punk. — In the pocket I kept a small black notebook. There was a blank sheet of paper folded up and bound into the back with a paper clip. I took it out, smoothed it upon the tabletop, and introduced a new and sharper fold which allowed the removal of a long rectangular strip. Then I held the strip up between the thumbs and middle fingers of each hand, and gave him the look, roughly, that Bullwinkle gave to Rocky: Nothing up my sleeve.

“I take this strip of paper,” I said, “and identify the ends in the obvious fashion.” They merged. “I have a section of a cylinder. You see?”

“I see,” he said.

“But,” I continued, “if I pull the ends apart, and interpolate half a twist before I put them together again, I have something rather different.”

“Yes,” he said. “How curious.” Staring.

I made the join fast with the paper clip. — Bloodless lips that man had had. And Fagley. Had he ever come back from Canada?

“What?” he asked.

“Nothing.” I hung the loop upon my finger, and let him look at it. “This is a Möbius strip, which is, roughly, half a Klein bottle. I’d have to be able to paste two of them, together to exhibit that explicitly, though, and I can’t do that in three dimensions.”

He smiled. “I suppose you can in four.”

“Yes.” I put the strip down in front of him, and made a sketch on the remainder of the sheet of paper. Then I thought better, and made a second one. “Suppose a sort of chemist’s flask, with a long neck coming out the top and a hole left in the bottom. Then there are two ways to run the neck around and close the surface. One way” — pointing — “you end up with a torus, just an inner tube again, with a bulge in it. The other way you take the neck around to the wall of the flask, step around the wall” — pointing, laughing — “and run the neck through to the inside of the flask, and match the hole in the opposite sense.”

“No.”

I laughed. “I’ll admit the glassblower might not like it.”

“No,” he said. “You can’t even visualize that.”

“Geometric intuition is something more than visualization,” I said. “Kant was wrong. Remember? And you can draw it. Sort of.” Hand waving at the sketch.

“Maybe,” he said. Staring at the drawing. “Klein didn’t drink did he?”

“Not from one of these.” Sleeping-draughts for overwork. One of those classic nineteenth-century breakdowns. Not unlike my own.

“No,” he said. Staring. “That is strange.”

“Yes,” I said. “For instance you think it of a surface that it has to have two sides. But a Klein bottle has only one.”

“Yes.” Staring at the strip, the drawing. “How curious.”

“And so you can’t say which side is the inside, which the outside. Thus ’nonorientable’.”

“Yes,” he said. He understood it.

“You can see that on the strip,” I said. I held the join between the thumb and finger of one hand, and traced a path with the forefinger of the other. “If I begin here, say, and move along the surface to my starting-point again, I find I’m on the other side. But twice around” —

— “And you return,” he said. Staring at it. “How extraordinary.”

“Suppose the strip were glass,” I said. “So that we identified the points, as it were, on the one side and the other. If I write something on the strip, a letter ’a’, let’s say” — in fountain pen I did; it ran through and you could read it from both sides — “and walk it around the loop, it returns after one circuit to its starting-point, but upside-down and backwards. It becomes its mirror image.”

Suddenly suspicious: “Do you think about this kind of thing all the time Garbonzo?”

“No.” Laughing. “I pass my evenings mooning after pussy, just as you do.”

“All right,” he said.

“And I’m not even married.”

“All right,” he said.

“But,” I said (laughing), “to continue,” I said [laughing], “suppose this letter were a little clock sent round this little world. It would come back running — well, backwards; with its figures all reversed.”

“Could that really happen?” Intrigued. “If you went around the universe? Could you come back with your time running backward?”

“I don’t know,” I said. “There’s a problem with causality.”

He frowned. “I never liked causality.”

I laughed.

“But could that really happen? Could something like this happen?”

“One usually assumes it can’t. Left- and right-handedness get mixed up in some kinds of elementary particle interactions, but not like this. It’s not like you walk round the world to wind up through the looking-glass.” The distinction between global and local. “That would be cosmology; that would be different. But there are some weird cosmological models. There’s one of Gödel’s, for example, that allows time-travel. Or seems to.”

“Really?” Startled. “Gödel again?”

“Yes. He wrote a little piece about it, for the Schillp volume for Einstein. You’d love it. He begins by citing McTaggart on the unreality of time.”

“Really?” Thinking; shaking his head. “I don’t believe these people.”

“Yeah,” I said.

Thinking. “You should write something,” he said.

“Oh, maybe,” I said.

A pause.

“So,” he said.

“So,” I said, “it’s like that. As if we’d gone round separate ways, and met again. Congruent with our former selves, but changed, you know, in parity. Her heart is on the other side. We’re strangers now.”

“Yes,” he said. “I see.”

I had tucked my right foot up under my left knee, and forgotten it; it was now half-asleep. I stumbled slightly as I got up.


We walked back along the beach. He had a favorite bookstore too. We leafed through little magazines, exchanging small opinions.

Then we sat by the pier for a while, and had a piece of the local color to tell us the story of his life. He wore an old green Army jacket; I thought he always should. The pockets were capacious, and held many cans of Coors. His tale might have proved a dull one, but his sense of plot was sure, and he varied, as our several moods required, the name of the woman, the label on the bottle. His twenty years upon the beach were thus as many minutes, perhaps a few more ounces, when quite suddenly he caught sight of a friend who bore a paper bag, and left as abruptly as he had come; warning us, over his shoulder, against the police. “Pigs,” he said. “Right, man,” I said. “Watch your back.” “I hope you got that down,” Richard said.

Then we tried a couple of galleries. Large colored shapes, like infant’s toys. We carried posters away.

I thought of my playpen, the letters and the numbers hung up upon a string, bright plastic reds and blues. The past was a receptacle; a bottle holding nothing now.

So I saw somebody famous putting up his show. But I didn’t see the girl on the bicycle again.