To write grant applications is important. It forces you to structure your thoughts and can be rewarding. But, let’s be honest, it’s also dull. The format is strict, with little room for animation. Every so often, while struggling to fit a minimal text to multiple evaluation criteria, weird sentences pop up in my head, and I begin to daydream about handing in an altogether unconventional proposal.

TURBULENCE – A RESEARCH PROPOSAL

Photo by Didssph on Unsplash

1. Survey of the field

I’ll tell you, more or less, how the research came about. The story begins at the University of Munich, at the Physics Department, in the office of Herr Prof. Dr. Arnold Johannes Wilhelm Sommerfeld. He needed a challenging problem for an annoyingly talented student, called Berg, perhaps, he couldn’t quite remember. “Werner”, in either case, was his given name.

–Turbulence!, Herr Prof. Dr. roared. That is the right problem for you Werner.

The young student, not called Berg but Heisenberg, was terrified. His thoughts on the matter were chaotic, entangled in each other so to speak, with no end to it. He even developed an allergy towards the problem, so bad he couldn’t stop sneezing. To recover he went to Helgoland, as it turned out a blessed place to forget about turbulence and such things. Heisenberg instead took measures to pursue his own ideas. And soon enough he came up with an exciting theory. He went to his friend Max Born in Göttingen.

–Look, Max, I found these mathematical tables. You can sort of multiply them, but, its funny, AB is not BA.

–Oh, you mean matrices? Max said.

Heisenberg was devastated again. For the second time he had failed, and this time with embarrassment.

–Matrices, he thought, if only they could be eliminated!

Max, on the other hand, was curious.

–But Werner, my good friend, how did you find the tables?

–Oh, I observed them in the spectral lines, Heisenberg muttered.

Somehow Max Born was intrigued by this reply, and he wanted to know more, but Heisenberg was altogether downhearted. He was uncertain his theory would ever yield anything precise.

In retrospect, it is only fair to say that Heisenberg’s idea was not entirely useless. It did, after all, lead to “un-dead cats” and “God particles”, and, more importantly, inspired the title of a decent James Bond movie. With time, Heisenberg also grew fond of his theory. And he lived his life among Max Born and like-minded who also appreciated it. However, even at old age he couldn’t forget about the “right problem” assigned to him. On a high-spirited occasion, he told his friends:

–When I meet God, I’m going to ask him two questions: why quantum mechanics? And why turbulence? I really believe he’ll have an answer for the first.

Let’s now fast-forward, past when even the music industry had realized that AB-BA is something to reckon with. Turbulence, though, was still an open problem. The physicists had given up on it since long. Well, maybe not entirely true, they did claim it “the most important problem in classical physics”. But who wants classical when you can rock to AB-BA!

Mathematicians, however, usually slow on the uptake, were still trying to grasp turbulence. One of them was Vladimir Arnold. He enjoyed skiing and this day he was out. In a whirlwind he double-poled his way over the hills, seeking the shortest path to his destination. And then he thought of something. An infinite number of skiers trying their best to get to their destinations without running into each other. So the theory of geometric hydrodynamics was born.

Now, let’s pause for a second and give a thought to the often twisted, chaotic paths that lead to scientific discoveries. From the outset, Heisenberg’s theory involving matrices had little to do with hydrodynamics and turbulence; certainly for Heisenberg himself, his ideas from Helgoland came in active pursuit of forgetting about turbulence, as I have already explained. But – perhaps Gods reply to his impious remark – it happened one day that a second Vladimir, by the name Zeitlin, established a deep connection between Heisenberg’s matrices and turbulence. At the time, even mathematicians, really quite slow on the uptake, had begun to enjoy AB-BA, although in a strictly formal setting. A paper on the matter landed on Zeitlin’s desk. Well acquainted with optimal skiers, he then found that the hydrodynamic equations where turbulence arise can be approximated by Heisenberg’s matrices; a matter of replacing the well-known AB-BA by the obscure WP-PW.

At the time Zeitlin made his discovery, I was in elementary school struggling with fractions, with no real ambition. Not until after I had grasped the irrational nature of things at university, did I first encounter Zeitlin’s model. Even many years later, I was in my office awaiting a student. Milo was his given name, but I couldn’t quite remember his family name. “Viviano” or something – perhaps they live far from here. In either case, Zeitlin’s model was on my mind as the student, Milo, suddenly stepped in and asked for a suitable thesis topic.

–Turbulence!, I roared.

2. Aims and purposes

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