Thinking In Structure

That Serve!

Written by

Paul Higham

in

[Author’s note:
This is a short work of fiction.]

First off, I suppose I have to explain why I decided to e-mail Dr. Petalman at all, what with him being the most famous mathematician on the planet and me just a nineteen year-old college drop-out.

Contrary to a lot of current gossip, it wasn’t the million dollars. In fact, I knew he didn’t have the million dollars. I was aware he had refused it. So it wasn’t that.

And it certainly wasn’t because of the math. Let me get that straight from the get go. Back then, I hated math.

And I didn’t want him to help pick a winning horse in the four thirty at Leyton Plains, or give me the number of next week’s Powerball, or the name of a tech stock to invest in, or any other of the crap you might have read on the internet.

Really, I just had a question about table tennis. I was nationally ranked, but the coach had a grudge against me and wanted me off the team. So I needed Petalman’s advice.

But I can understand that you might not accept that, so let me explain properly.

I first saw Dr Petalman playing ping pong on NOVA, this science documentary they have on Saturday nights on PBS – fifty minutes of high-brow gobbledygook that my sister, Courtney, likes to watch in the hope that some of it will rub off and she’ll grow a brain and not fail integrated science.

Most times it’s on, I’ll be outside in the yard practising with the table pushed against the wall, but that night I was in the front room – I had the daily Sudoku to finish and I didn’t want to do it in the kitchen because Dad was there, eating his tuna sandwiches, making the place reek to high heaven.

So I sat with the newspaper in front of me, half a wary eye on the T.V., watching it distractedly – really there was no other way, because this NOVA episode seemed to consist mostly of a procession of bizarre computer images : brightly colored rubber balls spinning on gray backgrounds and then twisting into spirals and exploding, and fields of little arrows like a thousand tiny weather vanes swimming on a giant chin, and numbers, everywhere numbers, tsunamis of numbers, swarming over strange, bent shapes that looked like mutant vegetables.

“Are you really watching this crap?” I said to Courtney.

It was like something out of Alice in Wonderland.

“Shut up and do your Sudoku,” she said.

“Because there’s football on the other side.”

“It’s math. It’s fascinating.”

Fascinating is a Courtney word. It means she doesn’t get something, but she wishes she did.

When the trippy animation stopped, they showed eccentric-looking men talking straight to camera. They subtitled them, and Courtney read out the names in her sing-song voice – Professor Cornelius Crackhauser, Head of Abstract Geometry at MIT; Simeon Turnip, Emeritus Professor of Quantum Loop Gravity at UCLA; Dr David Bonkbasher, Reader in Abstracted Riemannian Surfology, St John’s College, Cambridge and so on – all these oddballs mumbling baloney at the interviewer, scratching their heads and showering the lens with dandruff.

I tried not to watch. I put my elbows on the coffee table and my head between my hands, hoping by ducking down I would streamline the flight of high-faluting bullshit as it soared over the top of my head.

But something kept drawing my eyes back to the screen.

This show was about mathematics? That’s what Courtney had said. But wasn’t mathematics arithmetic and algebra and numbers and things? If the show really was about mathematics it was mathematics like I’d never heard of – insane mathematics, ninja mathematics, mathematics in fifty nine dimensions and thirty seven different color schemes, mathematics with cubes and pyramids and tesseracts and floaty things that dissolved into shimmering metallic matrices that had four sides of Greek letters and another six in hieroglyph; mathematics that spun and whirled and flashed before your eyes. In short, coked-up math for tripped-out crackheads.

A man in his thirties came on the screen. He looked like his head had been stuck on his neck upside down – a great shaggy arc of a beard grew on his chin, the top of his head was totally bald and, to cap off the effect, the wires of beard re-emerged in huge, disconnected tufts right over his eyes to form eyebrows thick as hedgerows.

“Dr Misha Petalman,” said Courtney slowly, reading the sub-title with difficulty because at the same time she was texting, maybe even sexting, who knows these days with Courtney. “Lecturer in Advanced Differential Geometry, Slakov Institute, Moscow.”

And then they showed something really astonishing – footage of Dr Petalman playing ping pong at some academic conference with another mathematician. The two of them hammered away at each other while the narrator told us that they were geniuses, but that even geniuses must have outside interests and Petalman’s was table tennis.

That really got my attention.

I could see right away he was very good. He hit the ball with enormous sweeps of his hairy arms, dashing about the table in a fury, his eyes blazing with rage. He would move right up close to the table and then play dinky little lobs to the back line with huge spin on them so that the ball would curve away at impossible angles, bamboozling his opponent.

But it was really his serve that had me fascinated. There was something very strange about it. It seemed to be a variant of the back-spin cross-table, but Petalman was not pushing his arm forward and spinning the ball clockwise like I’d been taught – he was throwing it up a huge distance and then chopping it vertically.

It looked impossibly difficult but Petalman was like an automaton, whacking serve after serve and never missing the chop.

“You see him do that?” I said to Courtney. “I could never do that.”

“Because you’re dumb, Dennis. This is higher math. You can’t even add up a till roll.”

“Not the math. They’re not even talking about the math. Look, it’s table tennis. And watch the way he’s serving. That is awesome. The way he’s taking the ball and tucking it in the back of his hand and then slicing the bat down. He’s winning every point on that serve.”

“The show is end-to-end educational mathematics and the only part that interests you is the ping pong.”

“Because this guy, Petalman, is AMAZING at ping pong…” I said, and pushed the newspaper to one side so I could watch him properly, as he gave this astonishing exhibition of tip-top, high precision, technically perfect ball bashing.

Later, I googled Dr. Petalman.

Wikipedia was not helpful – the entry was long, all about his proof of the Poindexter Conjecture the year before, and how he had refused the million dollars Clay Prize, saying that he had no need for money and that the proof itself was reward enough. Nothing about the ping pong.

At the bottom of the entry, however, was a link to an academic paper, and at the bottom of that, below a mass of Greek symbols, was his e-mail address.

I know it was presumptuous and perhaps a little crazy, but I figured what the hell, I would really like to know the secret of that serve.

So I sent him an e-mail.

This was what I wrote:

I sent the e-mail off and the truth is I didn’t think too much about again. At that time I had a lot on my mind, what with the team being selected on Tuesday, and Coach Grant being such a hard-arse about practice and everything, so really I forgot all about the e-mail to Dr Petalman. Until the next evening when I saw this in my inbox:

“RE: That Serve!!!! petalman@slakov.ru”

I didn’t immediately open it. I figured it was just some sort of automated response, or maybe an assistant at the university had got round to clearing the doctor’s inbox.

When eventually I clicked on it, this is what it said:

‘Feign’ I had to look up.

Then I replied:

One day later I got this:

So that’s how we started. Dr Petalman telling me about this wild man, the ingenious yeti with too much time on his hands, and urging me to think deep and not fast– to take the slow path, the less-travelled road, and above all else to concentrate on just this one problem, the problem of the ping pong serve, to the exclusion of everything else.

After I had made the commitment, it was just a matter of time.

I don’t want to tell you too much about the specifics of Dr Petalman’s program except it was conducted by Instant Messenger and webcam (any doubts I had that I might be speaking to a fake Dr Petalman were immediately dispelled when I first caught sight of his extraordinary and unique upside down face on the screen of my computer).

The program was also extremely practical.

To give you some small flavor, here are a few of the tasks he set me:

  • Combing the hair on a spherical dog (we used a real Alsatian).
  • Parallel transportation of the connection of a vector field around a closed manifold (plastic arrows and assorted rubber mattresses).
  • Winding number of loop integrals (homing pigeons).
  • The n-Sphere – (n plus one space hoppers and industrial sewing equipment).

We worked together for six months.

Initially the sessions were no more than thirty minutes, but as we continued and I began to make progress, they extended longer and longer, until more often than not we worked through the night – Dr Petalman explaining a new idea; my trying to understand it; Dr Petalman urging me onwards, schooling me through his practical experiments; the first inklings of comprehension; then a growing confidence and a final cataclysmic aha! moment when at last I grasped the concept in the whole – an extraordinary catharsis, more powerful than orgasm.

Thoughts of that table tennis serve that had initiated the tuition rapidly became subsidiary to the beauty of the math he was showing me. I felt he was guiding me through a new and wonderful world previously hidden to me – a multiverse of vectors and tensors and multi-dimensional manifolds, a dancing jamboree of pure abstracted thought.

Then one day, about six months into the program, after we had completed an extraordinary session on the perturbation expansions of Yang-Mills Quantum Field Theories involving copious use of tightly wound plastic hoses, Dr Petalman leaned forward into his webcam and said softly, “Dennis, you have been a wonderful student. It has been a pleasure working with you.”

“Thank you, Dr Petalman. But honestly really the pleasure has been all mine. You have been the most extraordinary teacher.”

“Truly you have worked hard. I think now you are ready.”

“Ready for what?

“The serve, Dennis.”

“The serve. Yes. I had forgotten about the serve.”

‘We were leading up to it.”

“Yes. We were.”

He moved back from the camera and I could see that the matt green blur that had always been present in the furthest corner of his room was now pulled into focus and resolved into the unmistakable shape of a ping pong table.

The doctor moved towards it and then pulled a bat and a ball from inside his tweed jacket.

He didn’t hesitate. He threw the ball high, giving it the extraordinary spin I had seen so many months before on the NOVA program, and then he slashed at it with his bat.

In that one motion, as the bat hit the ball, all became clear to me. All the teaching of the past six months filled my mind and flashed into clear focus. Immediately, I understood.

My insight was devastating.

The Petalman Program: Serve Dynamics

Active Manifold: Semi-Riemannian non-commutative Lie algebra
Status: Waiting for serve…
Δ(Serve) = Yang–Mills term + mass gap

“You should write it up,” he said later, when he had gone over my interpretation three times, making small corrections here and there

“How do you mean write it up, Dr Petalman?

“Write it up as an academic paper. It is important work.”

“I can’t write up a scientific paper. I’m a college drop-out.”

“It is just a question of embellishing the original arguments. I will guide you.”

So I spent the next three weeks, with Dr Petalman’s help, writing up the results.

When we had finished, Dr Petalman decided it was good enough to upload to Arxiv.org, the mathematicians’ website, and when that was done, he announced his program complete, and told me he would be unavailable for tuition for the immediate future.

The paper caused quite a stir, and I’m afraid Dr Petalman may have encouraged it. Titling it, “Proof of Yang Mills and Mass Gap”, when really it was a simple little exercise in the interpretation of the dynamics of a closed physical system in three dimensions (the flight of a ping pong ball in fact) was, in retrospect, something akin to a red rag to a bull. The math community was lining up to laugh at it. But Dr Petalman had taught me well, and when the trivial rebuttals failed, the heavyweights took an interest.

Professor Lau at Harvard put his best team onto it and, unfortunately for me, after a year of going at it they announced to the world (through the New York Times) the proof was correct. The International Math Union called, begging me to accept a new Clay Prize.

I had no idea what to do. I felt like a complete fraud. The paper was mine and I had written its arguments, but only because I had followed the Petalman Program. When the world found out, I would be exposed and ridiculed. My sister Courtney, especially, would have a field day.

I urgently needed to speak to Dr Petalman, but every night I logged into hotmail, his status was offline.

Until exactly a year after he had logged off – it was now August 2014 – he came back online.

“Dr Petalman,” I typed furiously. “Thank God, I’ve gotten hold of you. The Millennium Prize Institute has been in contact. They want to award me a Clay Prize. It is a disaster. You have to help me out. You have to tell them what really happened.”

“But, Dennis, it is as they say. You produced a work of genius. You established the existence of the Yang-Mills theory with a mass gap. ”

“But it was not original work. I was only following your program.”

“In mathematics, as in so many other fields, almost nothing is truly original. We all, even the greatest of us, build on the work of others. How did Sir Isaac Newton put it? ‘We stand on the shoulders of giants.’ It was the same for me, following Goffendiek. And Goffendiek only followed Weyl. And Weyl, Riemann. And Riemann, Gauss. All the way back to Pythagoras. (Pythagoras followed somebody too, only the somebody’s name has been lost to history.)”

“But I can’t accept a Clay Prize.”

“Why not?”

“It doesn’t seem right. I’m not worthy. I haven’t paid my dues.”

“These are not valid reasons to refuse. You must accept.”

“How can you say that? When you were offered the Prize, you didn’t accept.”

“And it was the greatest mistake of my life. Goffendiek was relying on it. He owed money to Weyl.”

An uncomfortable suspicion came over me.

“You set me up for this, didn’t you, Dr Petalman?”

“Not at all. Your research was a natural extension of mine. It solved a second great mystery. I was merely your guide to fertile mathematical ground. You dug the truffle.”

“You want the money, don’t you? I’m supposed to give you some of the money, right?”

“Let’s call it a tuition fee.”

“You want the money but you don’t want to be seen accepting it. It would be terrible for your image. You’re famous for having turned the prize down after all.”

“I do want some money, yes, Dennis. My mother is sick and has medical bills. And it would be difficult, after getting so much publicity when I refused the original prize for me to now decide to accept it. It is not so much a matter of pride as a matter of practicality. I fear the storm created would destroy what little privacy I now enjoy.”

By now I was seriously angry. Who was Dr Petalman to use me like this? What manner of a man was he?

I stared long and hard at his hairy avatar and turned the computer off in disgust.

I refused the Clay Prize and I guess that is how you’ve heard of me. I’ve been told I upset a lot of mathematicians doing that. But actually that is something I’m sort of proud of.

Petalman vanished off the internet completely. He may be walking the Andorran Alps with Professor Goffendiek.

Courtney passed Integrated Science.

Now, here’s the pitch.

You may like to know I am still very keen on table tennis. I have a few videos up on YouTube – you could take a look at my channel if you like (DennisNutsPingPong). There is one wicked serve I am particularly proud of and if you take a look and think it’s cool, I would be very happy to teach it to you.

I figure right now, what with this recession and everything, you might have a lot of time on your hands.

I warn you though, the explanation is going to be complicated and it will require some work on your part to get the hang of it. But I do guarantee it will be worth your while to complete the program…

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