Physics in Carouge

Geneva — Before the advent of this trendy but expensive craze of hanging out in Starbucks coffee shops, I discovered a most effective way of isolating myself in cafés to do some work. I am quite sure that many theorists and mathematicians have long practiced café hopping, pretending to work, but in my case, lately, it has assumed a certain routine.

Our studio in the Old Town, some 500 years old, is quite small. To sleep, my wife and I would bring down a Murphy’s bed from a wall, the French call it a “lit au mur.” As I am an early riser, I would sometimes gather up the laundry and pack it in a bag with my laptop as well. I then take Tram 12 (Ce tram roule de electricite d’origin hydraulique), which means what it sounds, in the direction of Bachet. I have always wondered whether the Swiss named that village after the number theorist; I have never felt motivated enough to research the matter. Some 10 stops later, in the village of Carouge, I would get off at Ancienne, walk over to one of the two public laundry shops I know in Geneva, load my laundry, go to Café Choco, then order a café-au-lait and a croissant. I would then read the Journal de Geneve. After minutes of frustration — I generally forget to pick up my little dictionary — I will then resume my physics work.

In the past few weeks, the subject is to prove that it is not possible to produce turbulence autonomously from the Navier-Stokes equation, a 200-year-old proposition. An hour later, still in frustration, I would walk back to the laundry shop, asking the “patron” to please watch my laptop. An hour and 15 minutes later, I would dry the laundry. Why so long? The Swiss laundry machine cycle uses time gently for the detergent to act, unlike American ones which use brute force for a few minutes of agitation. I say, the Swiss understand chemical action better, detergents take time to act, something called reaction rates. Anyway, I then transfer my laundry to the dryer expecting to return in 30 minutes to pick up the dry laundry. I would not worry if I am late, the other users will set my laundry aside to use the dryer. Back to the café. There I will call my wife who has already awakened, to fold the laundry — she insists that she organizes the clothes better — and join me for lunch at Café de l’Aigle, a Spanish restaurant which serves “tortilla,” my comfort food from my mother’s kitchen. We come to lunch rather late, I could then order espresso and stay on for two hours more, attempting to do physics. Gloria, my spouse, goes out for a walk and does some shopping. The laundry stays on my side discreetly.

Let me explain why Gloria likes to take charge of folding my T-shirts. From childhood, I learned to remove my shirt by pulling it over my head, inside out. When cleaned, I would put it back head first, reversing the process of undressing. Result? An economy of moves, at no point would it be necessary to reverse the shirt. Any other wife may result in an inverted clean shirt in my person. Why this lesson in elementary topology? Because ultimately, I think, to solve the problem of turbulence, one must use two branches of mathematics, complex variable theory and topology.

Recently, with the help of Alfonso Albano and Pascal Getreuer, we published a paper that showed the possibility of turbulence, analytically, from a post-Navier-Stokes equation of my own invention, from 10 years of knocking my head on turbulence. The analytic solution has the topology of a doughnut, (did you know that a T-shirt and a doughnut have different topology?) the real part of the solution for the velocity field is multi-valued, the first such demonstration of a velocity field with many possible values. Compare this with single-valued solutions in regular or laminar flow. That’s it, for details, the interested reader will have to write me at [email protected].

But this little note is all about coffee shops and physics. Indeed our paper was partly written at Choco Cafe, and maybe some other café that Alfonso and Pascal frequent. Alfonso and I have never personally met Pascal, our collaboration was done through the Internet. Someday, we will meet in another coffee shop, just like that time when my late mentor Max Dresden and I spent a few hours together at coffee shops in Prague. The coffee was expensive, more than $2 each, but that includes rent for the ambience.

In its proper context, I must add that nearly all of my theory papers on turbulence were written in Carouge, where I used to live in a “sous-toit” apartment, literally under the roof, much like artists’ quarters in the attics of Paris. Well, Geneva is not quite like Paris, it’s quiet and more predictable, as in Café de la Poste, still in Carouge, where I wrote some of my longest papers.

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Amador Muriel has officially retired, but is busier than ever with his research, a physicist vagabond who organizes experiments in Hong Kong, Germany, Massachusetts, and Novosibiisrk, Siberia. He is a Corresponding Member of the National Academy of Science and Technology. He will soon join the Philosophy Department of Harvard University to explore the Kuhnian paradigm of scientific revolutions, which his quantum theory of turbulence is supposed to exemplify. His book, “Quantum Nature of Turbulence” will be published this year by Nova Science Publishers. This article is based on an excerpt from another book in progress, “Dialogues from the Third World,” to be completed at Harvard. In 2011, he will be editor of a new series, “Modern Turbulence.” E-mail at [email protected]