selfsame thing becoming physical law.’
‘Ahem,’ I said.
‘Okay, look. You know that everything we do, everything we build, the entire design of the western world is more or less based on parameters set forth in Euclidean geometry.’
‘I suppose I know that somewhere.’
‘Exactly. Well, mathematicians have always known that Euclidean geometry is itself based on certain approximations of reality — lousy approximations, it turns out — but they’ve always just brushed that little matter aside and stuck it under the label of “assumptions”. They’ve gone ahead and said it doesn’t matter.
‘But Euclid is the law for most of us. For two thousand years we’ve regarded those Euclidean approximations as realer than Coca-Cola. For the vast multitudes, for
‘I don’t know. It was. simpler, I guess. Smaller, more compact. Less technological, certainly.’
‘Yes!’ Klein practically jumped out of his chair. His glasses flew off his face and bounced on the table. He grabbed at them, smearing the lenses with butter, but stuck them right back on his nose.
‘Before Euclid this wasn’t a world of science and technology, it was a world of gods and magic. Euclid came along and reshaped geometry, yes, but at the same time he reshaped an entire
‘Whoa, wait a minute. Correct me if I’m wrong, but Euclid dates back to what? 300 or so BC? That cosmology of Greek and Roman gods survived him by centuries. And even then you’re talking, what, hundreds of years more before things really caught on.’
‘Of course!’ Klein shouted. ‘Because it took that long for the Euclidean conception to approach its critical mass. You couldn’t pick up a paper in ancient Rome and read about how Euclid redefined the world! There was no Page Three girl to help spread word of the invention of this neat new geometry. There wasn’t any CNN to tell the masses: Greek gods dead, film at ten.’
Klein was sort of bouncing up and down as he spoke and alternately enthralling and intimidating me. Generally excitable, he was now at the edge of something more extreme. The room had emptied out, but those still around eyed him with nervous apprehension or undisguised mirth.
‘There was no mass media. It took hundreds of years for ideas to be made real. Now it happens in no time. Or practically no time. The first work to see chaos for what it was appeared barely three decades ago. Within a few years we have theories of fractal geometry and complexity, and philosophies of deconstruction. And now it’s on Yves Saint Laurent’s bloody knickers.’
‘Take it easy, Klein. Sit down.’
Klein looked around. He was breathing hard and his glasses were so filthy he might as well have been wearing shades. He stood still for a moment, ran his tongue over his dry lips and flopped back into the chair.
‘Two thousand years ago Euclid killed the gods. What’s going to happen this time?’
I had no idea, but strongly suspected that Klein didn’t have it quite right. The other diners went back to their affairs. I started to proffer a counter-argument when Klein’s already ashen pallor went even whiter.
‘Shit,’ he said and got up. I turned around and saw Margaritte eyeing us from the door. Klein ran over to his wife, but she didn’t look happy. They started arguing almost at once, then she stormed off. He trudged after her, pressing his glasses to his face with one hand and I heard their rising voices carrying on down the hall. Shaking my head and smiling at the onlookers with a ‘well-what-can-you-do?’ kind of grin, I gathered up his books and papers and took them with me. I didn’t know what to think of Klein’s theory, but I was frankly worried for his mental health.
Rightly so, as it turned out. For I would never see him alive again.
Klein called at 4:02:35. Ah, the priceless precision of the digital age.
I grabbed the phone on the second ring. Elaine never moved. I’d neither seen nor heard from Klein for ten days following our lunch, though I’d tried to call him. In the interim I’d come across an article in the
‘Hi, Steve.’
It was a most un-Kleinlike greeting. He sounded tired and hoarse and out of sorts.
‘Hey, Klein. How are you?’
‘It looks bad, Steve. I’m frightened.’
‘What? Of what? What’s wrong?’
I glanced over and saw that Elaine was awake and watching me. I spoke softly, but there was an edge to my tone that must have got though to her. She looked groggy but concerned.
‘I’ve been running the models, Steve. Exact calculations. Thousands of iterations before the equations converged. Soon that won’t work any more, you know. Iterative processes are doomed. But for now, for a little while longer, maximum likelihood estimates don’t lie. Though I wish they did.’
‘Klein…Have you been drinking?’
Elaine’s eyebrows leapt up like grasshoppers. I’d never known Klein to imbibe anything stronger than tea with lemon.
‘A little. Margaritte keeps a supply, you know.’
I didn’t wonder. ‘Are things, you know, okay with you and Margaritte? After the other day and all?’
There was a lengthy pause with only line noise and Klein’s deviated septum to fill the silence.
‘I. that is, Margaritte. we’re approaching a threshold, too. It’s all gone to turbulence, now, and I can see the edge. I can
There was another staticky silence. I hesitated, but with my eyes fixed on Elaine’s, decided to go ahead.
‘Listen to me, Klein. You can’t always…depend on the numbers. They’re like you were saying with Euclid, you know? They’re not quite real. They’re just representations and they’re different from people. Abstract. People aren’t fixed things. Even when you think they are.’
‘I don’t know, Steve. ’
‘What I’m about to tell you, I’ve never talked about before and I…
I was talking to Klein, but looking at Elaine. She nodded back at me.
‘My first teaching position was back in the States, right out of my doctorate. It was a shit-hole of a department in a dull Midwestern town and it was horrible. Elaine was miserable. She had left behind her job and all her friends because it was the only position I could get and we were committed to staying together.
‘Well, let’s just say that things got bad. Real bad. I had a killer teaching load and the town was full of overqualified faculty spouses, so Elaine couldn’t find any work. I’d come home tired and mean and she’d be angry and bored. For a while we communicated through grunts and yells.’
‘Steve. ’
‘Just listen, Klein. It was the end of the semester and we hadn’t. been together for weeks. I was starting to browse the classifieds for studio apartments. So it’s right around finals time — and you know, I’ve got a couple, three hundred undergrads and it’s just pure chaos, you’ll pardon the expression — when this perky little sophomore comes to see me. She’s a total airhead, but with one of those teenage bodies that won’t quit. And she’s failing the course and the door’s closed and she
‘I hated myself for it and I still do. I figured for sure it was the end for us and probably my career. Hell, I thought maybe that’s why I did it. And I won’t lie to you, Klein, it got pretty bad. But it also brought stuff into focus. There was a lot of pain, but we found a way through it. Eventually. And my point is this: in the end I…we decided that it was all just a moment. Just an
