Automatically, Leonid Vitalevich gripped his wallet tight in his trouser pocket, against pickpockets. Gangs worked the trams, and you couldn’t tell which of these faces, these polite faces, aggressive faces, drunken faces, was really a pokerface, a front for a hand down below extracr it eve surplus value. He couldn’t see anything beneath chest level, so it was best to be careful; couldn’t see his feet, though he could certainly feel them, now that the fuggy warmth of the tram had thawed the crust over the annoying hole that’d appeared today on the sole of his left shoe. He had a small wad of newspaper in there, and it was turning soggy. This was the third time this winter the shoes had sprung a leak. He would have to go back to the retired cobbler Denisov this Sunday, take him another present, listen to more self-contradictory reminiscences about the old man’s adventures with women. Of course it would be much better to get a new pair of shoes altogether, or maybe boots. Who could he ask? Who would know somebody who knew somebody? He would have to think about it. He gazed through the sliver of window visible between heads, and fragments of city slid by: a patrol car parked on a corner, grand facades streaked with damage from leaking gutters, red neon flashing FIVE – IN – FOUR, FIVE – IN – FOUR, the word more on the bottom corner of a poster, which he knew at once would read in full Life has become better, more cheerful! Those posters were all over the place. The slogan advertised Soviet Champagne. Or the existence of Soviet Champagne advertised the slogan, he wasn’t sure which. But now he was looking without seeing. His thoughts had dived into his satchel, clutched tight with his other hand. Halfway down a lefthand page in his notebook, the blue ink scribble of equations broke off, and now his mind was racing on from that point, seeing a possible next move, seeing the thread of an idea elongate. Today, something had happened.
He had been doing a bit of consultancy. It went with being attached to the Institute of Industrial Construction; you had to sing for your supper every so often. And he didn’t really mind. It was a pleasure to put the lucid order in his head to use. More than a pleasure, a relief almost, because every time the pure pattern of mathematics turned out to have a purchase on the way the world worked, turned out to provide the secret thread controlling something loud and various and apparently arbitrary, it provided one more quantum of confirmation for what Leonid Vitalevich wanted to believe, needed to believe, did believe when he was happy: that all of this, this swirl of phenomena lurching on through time, this mess of interlocked systems, some filigree-fine, some huge and simple, this tram full of strangers and smoky air, this city of Peter built on human bones, all ultimately made sense, were all intricately generated by some intelligible principle or set of principles working themselves out on many levels at once, even if the expressions didn’t exist yet which could capture much of the process.
No, he didn’t mind. Besides, there was a duty involved. If he could solve the problems people brought to the institute, it made the world a fraction better. The world was lifting itself up out of darkness and beginning to shine, and mathematics was how he could help. It was his contribution. It was what he could give, according to his abilities. He was lucky enough to live in the only country on the planet where human beings had seized the power to shape events according to reason, instead of letting things happen as they happened to happen, or allowing the old forces of superstition and greed to push people around. Here, and nowhere else, reason was in charge. He might have been born in Germany, and then this tram ride tonight would have been full of fear. On his professor suit would have been a cotton star, and dark things would have looked out of people’s faces at him, just because his grandfather had worn earlocks, had subscribed to a slightly different unverifiable fairytale about the world. He would have been hated there, for no reason at all. Or he might have been born in America, and then who could say if he would even have had te two kopecks for the tram at all? Would a twenty-six-year-old Jew be a professor there? He might be a beggar, he might be playing a violin on the street in the rain, the thoughts in his head of no concern to anyone because nobody could make money out of them. Cruelty, waste, fictions allowed to buffet real men and women to and fro: only here had people escaped this black nonsense, and made themselves reality’s deliberate designers rather than its playthings. True, reason was a difficult tool. You laboured with it to see a little more, and at best you got glimpses, partial truths; but the glimpses were always worth having. True, the new consciously-chosen world still had rough edges and very obvious imperfections, but those things would change. This was only the beginning, the day after reason’s reign began.
Anyway. Today he had had a request from the Plywood Trust of Leningrad. ‘Would the comrade professor, etc. etc., grateful for any insight, etc. etc., assurance of cordial greetings, etc. etc.’ It was a work-assignment problem. The Plywood Trust produced umpteen different types of plywood using umpteen different machines, and they wanted to know how to direct their limited stock of raw materials to the different machines so as to get the best use out of it. Leonid Vitalevich had never been to the plywood factory, but he could picture it. It would be like all the other enterprises which had sprung up around the city over the last few years, multiplying like mushrooms after rain, putting chimneys at the end of streets, filling the air with smuts and the river with eddies of chemical dye. All the investment that hadn’t gone into new clothes and everyday comforts had gone into the factories: they were what the tired people on the tram had got instead. At the plywood factory, he supposed, there would be a raw brick barn, cold enough inside at this time of year to turn the workers’ breaths to puffs of steam. He guessed that the machinery would be the usual wild mixture. Aged pre-revolutionary presses and stampers would be running alongside homegrown products of the Soviet machine-tool industry, with here and there a silky import, efficient but hard to maintain. Together, under the exposed girders of the roof, this mismatched orchestra of devices would be pouring out a discordant symphony of hisses, treadlings, clunks and saw-edged whines. The management wanted help tuning the orchestra up. To be honest, he couldn’t quite see what the machines were doing. He had only a vague idea of how plywood was actually manufactured. It somehow involved glue and sawdust, that was all he knew. It didn’t matter: for his purposes, he only needed to think of the machines as abstract propositions, each one effectively an equation in solid form, and immediately he read the letter he understood that the Plywood Trust, in its mathematical innocence, had sent him a classic example of a system of equations that was impossible to solve. There was a reason why factories around the world, capitalist or socialist, didn’t have a handy formula for these situations. It wasn’t just an oversight, something people hadn’t got around to yet. The quick way to deal with the Plywood Trust’s enquiry would have been to write a polite note explaining that the management had just requested the mathematical equivalent of a flying carpet or a genie in a bottle.
But he hadn’t written that note. Instead, casually at first, and then with sudden excitement, with the certainty that the hard light of genesis was shining in his head, brief, inexplicable, not to be resisted or questioned while it lasted, he had started to think. He had thought about ways to distinguish between better answers and worse answers to questions which had no right answer. He had seen a method which could do what the detective work of conventional algebra could not, in situations like the one the Plywood Trust described, and would trick impossibility into discling useful knowledge. The method depended on measuring each machine’s output of one plywood in terms of all the other plywoods it could have made. But again, he had no sense of plywood as a scratchy concrete stuff. That had faded into nothing, leaving only the pure pattern of the situation, of all situations in which you had to choose one action over another action. Time passed. The genesis light blinked off. It seemed to be night outside his office window. The grey blur of the winter daylight had vanished. The family would be worrying about him, starting to wonder if he had vanished too. He should go home. But he groped for his pen and began to write, fixing i
n extended, patient form – as patient as he could manage – what’d come to him first unseparated into stages, still fused into one intricate understanding, as if all its necessary component pieces were faces and angles of one complex polyhedron he’d been permitted to gaze at, while the light lasted; the amazing, ungentle light. He got down the basics, surprised to find as he drove the blue ink onward how rough and incomplete they seemed to be, spelt out, and what a lot of work remained.
And now, on the tram, he was following his thought into implications, into what he was suspecting might be a world of implications. Clearly, the world had got by quite well until now without this idea. In the era before half past two this afternoon, the people arranging the flow of work in factories had been able to do so with a fair degree of efficiency by using rules of thumb and educated intuition, or else the modern age would not be as industrialised as it was: would not have trams and neon, would not have airships and autogyros thronging the sky, would not have skyscrapers in Manhattan and the promise of more in Moscow. But a fair degree of efficiency was very far removed from a maximum degree of efficiency. If he was right – and he was sure he was, in essentials – then anyone applying the new method to any production situation in the huge family of situations resembling the one at the Plywood Trust should be able to count on a measurable percentage improvement in the quantity of product they got from a given amount of raw materials. Or you could put that the other way around: they would make a measurable percentage saving on the raw materials they needed to make a given amount of product.
He didn’t know yet what sort of percentage he was talking about, but just suppose it was 3%. It might not sound like much, only a marginal gain, an abstemious eking out of a little bit more from the production process, at a time when all the newspapers showed miners ripping into fat mountains of solid metal, and the output of plants booming 50%, 75%, 150%. But it was predictable. You could count on the extra 3% year after year. Above all it was free. It would come merely by organising a little differently the tasks people were doing already. It was 3% of extra order snatched out of the grasp of entropy. In the face of the patched and mended cosmos, always crumbling of its own accord, always trying to fall down, it built; it gained 3% more of what humanity wanted, free and clear, just as a reward for thought. Moreover, he thought, its applications did not stop with individual factories, with getting 3% more plywood, or 3% more gun barrels, or 3% more wardrobes. If you could maximise, minimise, optimise the collection of machines at the Plywood Trust, why couldn’t you optimise a collection of factories, treating each of them, one level further up, as an equation? You could tune a factory, then tune a group of factories, till they hummed, till they purred. And that meant –
‘Watch what you’re doing!’ cried the short woman. ‘Take your head out of your arse and watch what you’re doing, why don’t you?’ The big man had seized the chance, s rast time they all shuffled up the tram, to free his hand and light a cigarette. But as it hung at the corner of his mouth, cardboard holder pinched in two dimensions to act as a filter, a jolt from the track had knocked the whole burning load of tobacco out of the paper tube at the end, and it had fallen, smouldering, onto her shoulder. Her arms were pinned.
‘Sorry, sister,’ said Big Chin, trying to flap the embers off her and down.
‘What good is sorry, you big lummox? Get it off me. Oh, look at my coat. There’s a hole right through –’
– and that meant that you could surely apply the method to the entire Soviet economy, he thought. He could see that this would not be possible under capitalism, where all the factories had separate owners, locked in wasteful competition with one another. There, nobody was in a position to think systematically. The capitalists would not be willing to share information about their operations; what would be in it for them? That was why capitalism was blind, why it groped and blundered. It was like an organism without a brain. But here it was possible to plan for the whole system at once. The economy was a clean sheet of paper on which reason was writing. So why not optimise it? All he would have to do was to persuade the appropriate authorities to listen.
Suppose that the Soviet economy could be made to grow by an extra 3% a year – an extra 3% year after year, compounded. It would mount up fast. After only a decade, the country would be half as rich again as it would have been otherwise. Quicker than anyone imagined yet could come the golden age whose promise was implicit in the rhythm of every production line, but which had still to free the world from scarcity; the golden age the Party promised, but said it could not deliver till the heavy work of construction was done, except in the symbolic form of Soviet Champagne. Seen from that future time, when every commodity the human mind could imagine would flow from the industrial horn of plenty in dizzy abundance, this would seem a scanty, shoddy, cramped moment indeed, choked with shadows, redeemed only by what it caused to be created. Seen from plenty, now would be hard to imagine. It would seem not quite real, an absurd time when, for no apparent reason, human beings went without things easily within the power of humanity to supply, and lives did not flower as it was obvious they could. Now would look like only a faint, dirty, unconvincing edition of the real world, which had not yet been born. And he could hasten the hour, he thought, intoxicated. He gazed up the tram, and saw everything and everybody in it touched by the transformation to come, rippling into new and more generous forms, the number 34 rattlebox to Krestovsky Island becoming a sleek silent ellipse filled with golden light, the women’s clothes all turning to quilted silk, the military uniforms melting into tailored grey and silver: and faces, faces the length of the car, relaxing, losing the worry lines and the hungry looks and all the assorted toothmarks of necessity. He could help to do that. He could help to make it happen, three extra percent at a time, though he already understood that it would take a huge quantity of work to compose the necessary dynamic models. It might be a lifetime’s work. But he could do it. He could tune up the whole Soviet orchestra, if they’d let him.
His left foot dripped. He really must find a way to get new shoes.
Notes – I.1 The Prodigy, 1938
1 Without thinking about it, Leonid Vitalevich: Leonid Vitalevich Kantorich (1912–86), mathematician and economist, nearest Soviet equivalent to John von Neumann, later (1975) to be the only Soviet winner of the Nobel Prize for Economics (shared with Tjalling Koopmans). Calling someone by first name and patronymic expresses formal esteem, in Russian; he is mostly referred to that way here, to suggest that he is being viewed with respectful acquaintance but not intimacy. With fictional elaboration, this scene on the tram is true to his history, for which see his Nobel Prize autobiography, in Assar Lindbeck, ed., Nobel Lectures, Economics 1969–1980 (Singapore: World Scientific Publishing Co., 1992); and the collection of his letters and articles, with colleagues’ memoirs, in V.L.Kantorovich, S.S.Kutateladze and Ya. I. Fet, eds., Leonid Vitalevich Kantorovich: Chelovek i Uchenii (‘Man and Scientist’) (Novosibirsk: Siberian Branch of the Russian Academy of Sciences, vol. 1 2002, vol. 2 2004); and S.S.Kutateladze, ‘The Path and Space of Kantorovich’, talk at the international Kantorovich memorial conference, Euler International Mathematical Institute, St Petersburg, 8–13 January 2004.
2 Gangs worked the trams: for 1930s crime and 1930s streetcars, see Sheila Fitzpatrick, Everyday Stalinism: Ordinary Life in Extraordinary Times (OUP, Oxford 2000), pp. 52–3.
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