Brani Vidakovic, professor of statistics at Duke University in Durham, North Carolina, will be visiting the Indian Statistical Institute (ISI) in Calcutta next year. I met him at the SPIE conference in San Diego in July. He initially mistook me for another Kumar, a professor at the University of Illinois at Urbana-Champagne, after a quick glance at my name-tag. 

    SPIE is not a society of people that go snooping around in other peoples' business, however much fun that might sound like to you. Rather, it is some fancy French acronym for the International Society of Optical Engineers. I go attend the Mathematical Imaging part of this conference every year to keep up with new research, to talk to old friends, and to chair a session or two of the wavelet transform sequence of conferences. This conference is always held in the beautiful city of San Diego, California, in late July, over a period of five days, except last year, when it was held in the fine city of Denver, Colorado. It has become the wavelet conference for the North American continent. I look forward to it all year long. 

    This is just the sort of event to go to in order to see the engine of western science and technology build up steam. I remember as a child pausing by the side of a locomotive at a small wayside station in Rajasthan. I can call up that beautiful evening at will: the calm that descends with the setting sun, the curtain falling on a blazing hot day, the fresh breeze that brushes you gently and wakes up everything in your body. There are very few people on the solitary platform, two stray goats, a peanut vendor, a frayed red flag fluttering outside the stationmaster's cabin, dust swirling in the wind. And, except for the unintrusive hiss of superheated steam, silence. If there is peace and beauty in the world, it is here. My father was a railwayman, then an Assistant Signaling and Telecommunications Engineer (ASTE) attached to the Kota Division of the Western Railway. He worked on new constructions, and little trips across Rajasthan in an "officer's carriage" were not infrequent for the family, especially when I was home from boarding school in Delhi, on vacation. A steam engine is technology become flesh. It is at once sensuous and profound. 

    Mathematics is also like that. Bit less flesh, but lots more bang. How is it that we are able to read so much meaning in a few silly symbols? I am particularly interested in transforms. You start with a bunch of numbers, millions and billions and trillions of them, and from that bunch of numbers you calculate another bunch of numbers. Then you call that second bunch of numbers a "transform" of the first bunch. That is all there is to it. Your formulas may look terrible, but that's no big deal. A machine will do all the calculation for you in very short order, so you can make them as beastly as you wish. So long as everything converges. That is the important thing. That machine becomes like a steam engine. It will inhale the insubstantial vapor of mathematics and it will make the earth move. 

    Another thing you do is give a transform a name. Something French or Scandinavian, and sonorous, like Fourier or Laplace or Langendre or Laguerre or Frazier-Jawerth is de rigueur. The purpose of the name is to ignite a certain holy terror in an undergraduate's heart, or in the heart of anyone who is not your pal, and does not belong to your own sacred priesthood. You can't have the dirty and the unwashed muscle in on your special deal. Also the people that fork over cash are mesmerized by the name. More, they are terrified by the intimidating cloud of sigma's and pi's, the uncompromisingly uppity attitude of the Greek alphabet, and the even more dangerous-looking old-German. Much too ornate, and given to such a dizzying profusion of superfluous curves and sharp chiseled angles that you'd rather ride a roller-coaster to work. A person can spend a few janmas just learning to write that old-German. I use Hindi letters sometimes, and that really blows the mind of the natives. 

    In Hindu mythology they say that the Universe is all the dance of Shiva. That is baloney of course. The truth is that the Universe is a dance of atoms and photons. That is what I tell my little Buramai. That is what you'd say if you were given to physics. If your religion were mathematics, on the other hand, you'd say that the world is a dance of numbers. We calculate in order to understand. We calculate in order to extract meaning from a big bunch of numbers that appear, at first sight, void of sense and pattern. It is like drawing juice from a lemon. Like growing a flower on a vine. Like milking a cow. Meaning and pattern and sense plucked right out of nothing. Religion is that to which you would tie your goat. That is what I think. 

    Talking of dance, we cooked one up called QED-101. Also called "Move Over Jitterbug". The cast consists of JEJ-1 (Annandita Tatabai Kumar), JEJ-2 (Abha Varma), and POP-1 (Arun Kumar). JEJ stands for Jiggling Electron Jelly. POP is Poor Old Photon. The POP travels along straight lines forever (sometimes along other arbitrary trajectories if it is a more modern kind of photon) until it passes close to a jiggling JEJ. 

    The POP swings its right arm around to signal its color. It's angular velocity tells the energy. I go all the way from 1/2 Hz to a few THz. If the arm hits a door-frame, it is time-out time. Even show-out time, depending on how much it hurts. The left hand signals the polarization. A JEJ will (probabilistically) eat a POP. Then the POP should disappear. Here I crave the indulgence of my audience. Disappear, exactly speaking, I cannot. On account of my considerable bulk. 

    Having consumed a POP, the JEJ becomes very excited and jumps up and down with much vim and vigor --- as Bond would say. Then (probabilistically), when it has jumped itself to the very verge of exhaustion, the JEJ spits out a new POP in a random direction, and off goes the POP again, having been "scattered". Magically, the new POP has exactly the frequency and the polarization of the POP that had earlier been eaten by JEJ. Even though it seems to me that polarization need not necessarily be conserved, and I would like to invite Prashant Valanju to the forum to weigh in on this problem here. 

    JEJ-2 (on account of her bulk) has petitioned to play the part of Inertia. But, regrettably, Lady Inertia, of the sort JEJ-2 has in mind, has no role in this dance because all the action takes place above 0 degree Kelvin. 

    Teetee is under training as a stand-in for POP-1, but he gets so continually excited with the infectious grace of the older dancers, and that with no trace of quantization, that we may have to declare him a free-electron instead. Buramani is working on the songs and the score that goes with the dance. She wants to rent a big theater, with red curtains that rise and fall, for our public performance. I suggested that we could make Daniel, 6, next door, the announcer, but Bui vetoed the plan. She said that Katie and Daniel are our only solid prospects for a ticket-buying audience. Clever of her to think of that! On my part I am trying to persuade JEJ-2 not to drop out of her role. After all, this not just about Quantum Electrodynamics. It is also (secretly) a very clever Weight Reduction Program. Try it! And don't forget to send me the before-and-after pictures. 

    Why is San Diego a bit like Calcutta? Because it has cycle rickshaws for hire! This is the first year they have appeared. You can hail one down in front of the Marriott Hotel and ride about a mile to the Fifth Street. I didn't. While on the other side of the Marriott, a huge sleek and menacing warship bristling with radars and antennae and big guns slips silently through the channel to the Pacific. This is the only place outside of India where I have seen cycle rickshaws. Which reminds me to ask: Have person-drawn rickshaws really disappeared from Calcutta? Buddi? 

    Conference evenings are party time, and sidewalk tables at the restaurants on the Fifth Street are full of strange people from god-knows where drinking quantities of wine, talking in foreign accents --- even those, like me, that have lived in the US for ever --- and waving their hands, writing math on the napkins, drawing strange pictures (no artists these), laughing, drinking much too much. A few spouses and children, but mostly a very male crowd. They clearly don't belong to San Diego, which is mostly full of "real foxy ladies," as my friend Joe Rich of Lockheed-Martin once described them, in real short skirts, legs from here to there, their breasts barely restrained by their sheer, low-cut, or half-open blouses. The weather in San Diego is always perfect. The light, like golden murkoos. Crisp. 

    Brani Vidakovic is using wavelet coefficients to synthesize probability density functions (pdf's). Not a particularly useful sport in itself. But next he plans to do this: Suppose every time you put out your hand Mother Nature were to give you a number, then we ask this question: what pdf is she plucking her numbers off? And with how much confidence can we tell? And what if the pdf changes with time. Very useful questions.

    There is lot of good work at Bell Labs being done by Wim Sweldens and his collaborators across the country. Wim and I are guru-bhais. His doctoral-advisor Bjorn Jawerth was on my dissertation committee, and in 1988 I named a transform (that they invented) after Bjorn Jawerth and Michael Frazier. Frazier and Jawerth are both mathematicians, harmonic analysts. Their work was directed at the understanding of a certain type of "function spaces" called Besov spaces. A purely mathematical problem, but then it all got hijacked by us engineers. Because engineers, unlike mathematicians, actually do something useful. We don't just waste chalk, do we? Mike Frazier is at Michigan State University now, and Bjorn was stolen from Wash U by the University of South Carolina. They were both at Wash U when I was a graduate student there. 

    Bjorn tried hard to teach me the subtleties of harmonic analysis once he realized that I really did propose to do something useful with it. But my heart wasn't in his brand of analysis. We'd sit there in a big hot classroom --- the math department was poor, as they all are, and not given to excessive air-conditioning --- and he would pace up and down before the blackboard, and I would say, "Please Professor Jawerth draw me a picture. Tell me like you'd tell a child. Don't tell me stuff I don't want to know." 

    I really learnt how to do mathematics from Professor K.K.Nambiar at Bharat Electronics in Bangalore. He is now at the Jawaharlal Nehru University in Delhi. "No, no," he would tell me as I struggled with a proof on the board, "That don't make no sense. Don't write that sort of bad equation. Look. Close your eyes. Think of a ball of wool here (shaking his left hand in the air), and another ball of wool here (shaking his right). Now connect them with one thread and suddenly one eat up the other, and they are both one ball now. Then that is a new equivalence, do you see ..." 

    And, miracle of miracles, I saw! 

    We thought about writing a book on the algebra of relations but that hardly got started. Professor Nambiar taught me that mathematics is not about symbols. It is about pictures in your head. It is about things that you would hold and touch and feel, even if only in your head. So I try and do my math the Nambiar way. "Proof by intimidation" is the principle that many professors practice, and many books practice. That is not the way to knowledge. The way to know math is to treat her like an absent lover, and to imagine how you would touch her and smell her and taste her if she were to appear this minute. She should be like clay to a potter at the wheel. She is the stuff we are made of. Was it not Surdas that wrote: "Maati kahe kumhar se, tu kyon ronde mohe. Ek din eysa aayega, mein rondoongi tohe." 

    That was perhaps a non sequitur. But it does remind me to mention that Abha recently bought us a fine CD of Surdas ji's bhajans sung by Kishori Amonkar called "Ghat Ghat me Panchhi Bolta". The first song in that is the bhajan of the title. And it is wonderful, and so wonderfully sung. "Aap hi dundeei. Aap taraju. Aap hi baitha tolta. Ghat ghat me panchhi bolta."

    Then I learnt more math from Mike Frazier. We would stand and work at the same blackboard in his office, I to the left and he to the right till everything came out as it should. There is a light that suddenly comes on in the upper story. Then mathematics flows freely as water. 

    My very old friend Andrew Laine is moving from the University of Florida at Gainesville to Columbia University in New York, where he is charged with the job of setting up a new department of medical imaging. He has been working on the detection of nodes and microcalcifications in mammograms, the signals of malignancy. Andy and I were office-mates at Wash U, and I first introduced him to the subject. He would help me write up code, and in exchange I helped him with the math. And we both ate quantities of popcorn. Brenda, Andy's girlfriend, won't be moving to Manhattan with him. I was walking by her side, behind Andy, on our way to the Fifth when she told me how Andy doesn't think it necessary to get engaged and that therefore she won't be moving with him. Andy's ears turned red, and he sheepishly looked back at us. Whenever he is in trouble his ears turn red like that lamp on your disk drive. She was wearing a very nice short black dress. She's good-looking, a very friendly lady with a wide all-American smile. Andy had better change his mind. 

    Panos Kudumakis of King's College, London, said that he last year taught himself wavelet transforms from my dissertation. That made me very happy. To know that the tome is serving some purpose even after this many dusty years. Panos is working on audio source-coding for the Internet. 

    The wonderful team of Akram Aldroubi and Michael Unser is breaking up. For a number of years they worked together at the National Institutes of Health (NIH) in Maryland, Virginia, turning out first-rate work. Akram is a mathematician (real analysis) and Michael an electrical engineer (signal processing). Just the right sort of a team. Like yin and yang. Now Akram is moving to the math department at the Vanderbilt University in Nashville, Tennessee, where he will be working with Doug Hardin, who was also there at SPIE with his wife. Akram is the most fun guy of all the wavelet crowd. He is like a big round untidy unruly bear, whose handwriting it is impossible to read. He has a huge big laugh. He is originally from Iraq, but did his masters in Zurich and his PhD in France. Michael Unser and his wife and 10 month old baby were flying almost directly from San Diego to their new home in Switzerland, where Michael will be a professor at EPFL (Ecole Polytechnique Federale at Lusanne). Martin Vetterli, ex of Columbia U and UCB, has already been at EPFL for a couple of years. He didn't show up this year. 

    Klappi and Fred, two young students from the Technical University of Karlsruhe, discussed their problem with Manos Papadakis (harmonic analysis), professor at the Military Academy of Greece, and me. They are designing a chip, and want to do away with all division in their algorithm. If you do division in hardware, it costs you plenty of Silicon real-estate. If you do it in microcode, it costs you clock cycles, and that is not healthy for the real-time performance of long calculations. This is an old problem that needs to be tackled anew with every new class of techniques. They would like to do their arithmetic in a ring of integers they said. I said that I think that is impossible. I suggested that they try and do arithmetic over the ring of dyadic rationals instead. And guess what, back home in Austin, I invited Dong Wei, doctoral candidate the University of Austin, to come and give us series of three talks on his work, and he has exactly the dyadic rational thing all neatly worked out. I will send mail to Fred and Klappi today and let them know, and stick a copy of Dong Wei's paper in the mail. It's a fat one. Dong Wei was a student of Professor Burrus and is now a student of Professor Al Bovik here at the University of Texas in Austin. 

    Research is all about people. That is one thing that I have learnt. It is the people you like to get together with. Who talk your language. Who want to know exactly what you want to know also. What is the stuff the world is made of? How does it come together? And how does it dance? It is a race between friends. Conferences are rare in India. You hardly ever get to meet someone from a few miles away that works in your area. Hotels are too expensive for 850-rupees-wallahs. It is hard to get train reservations. Arrey baba, you can read it all in that book by Gurrburr Baba, why go all the way. That doesn't work. Research is a contact sport. Where there is no coming together, there can be no research. Of that I am convinced. This is one lesson I have learnt from America. 

    Coming back to Brani. He is very excited about his forthcoming trip to the Indian Statistical Institute. "It will be a pilgrimage," he says in his soft and round east-European voice. His face is creased with fifty lines. "You know, every single person I have met from there is a first rate statistician. No exceptions. Zero. Each and every one! How do they do it? There is nothing like that anywhere else in the world." 

    So you see Radha, you made a mistake by not sticking to ISI. I have asked Brani to have a few kala jamuns for me, but not to complain if they lay him down with diarrhea.