e pur si muove

Spring is Here, originally uploaded by Elia Diodati.

Unmistakeable signs of life teem at the base of a dogwood tree on campus. That, plus today’s 68°F (20°C) weather. Quite a heat-wave!

How important is higher maths anyway? We live in a stupid world. A world in which the most intricate machines and living organs are created by a stupid process called evolution. There is really no need to think so much, and create all that fancy maths. All the pure maths I’ve learnt was a marvellous intellectual exercise, wonderful for building up the brain, but ultimately useless for practical applications. - 7-8

No human investigation can be called real science if it cannot be demonstrated mathematically.

Leonardo Da Vinci (attributed)

Wikiquote has a few dozen other amusing (and often profound) reasons on why math. But the point I wanted to make, in response to sieteocho’s recent post, is that higher mathematics is not useless. Far from it, it is absolutely critical to just about any field of advanced study. In fact, from a cynical (and economic) point of view, if you study anything hard enough (and long enough), you’ll eventually wake up one day realizing that you’re no longer studying quantitative finance or theoretical physics or intercultural sociology or clinical biochemistry, but applied mathematics. (Why an economic point of view? Because once you attain this level of study, you become interoperable, i.e. applied math becomes one of your most valuable transferable skills. Many of the most successful quants on Wall Street have backgrounds in theoretical physics and chemistry.)

As far as physics and chemistry are concerned, I can speak (with some authority) on the utility of mathematical methods above and beyond the basics of linear algebra and multivariable calculus. Half of science and engineering, by the way, seems intimately connected with computing eigenvalues of eigenproblems of various sorts. (Non-theorists can skip this paragraph.) To just rattle off a few applications: group theory dictates the qualitative features of molecular spectra (like what kind of vibrations you can or cannot see with Raman spectroscopy), real (and complex!) analysis dictates the onset and measurability of phase transitions (e.g. the boiling of water, using a renormalization group approach to detect the onset of nonanalyticity in order parameters). Each of the previous list has its own long laundry list of addenda. For example, in semiclassical theory, a form of asymptotic analysis, establishing the connection between classical and quantum mechanics requires detailed Fourier analysis and various incarnations of Lie algebras (along with the associated baggage of Lie groups, Pontryagin dualities, differentiable manifolds and cohomologies). Statistical mechanics has a particularly beautiful example of a connection between number theory and spectral theory in the form of Riemannium, a hypothetical material with a spectrum described by the zeroes of the Riemann zeta function. And how about many-body perturbation theory in quantum electrodynamics, with summations over graphs best enumerated by combinatorial irreps?

Not forgetting, of course, the numerical and computational aspects of science: ofsolving differential and integral equations, so vital to all sorts of modeling, and the numerical analysis issues with regard to solution stability and computability. Think the study of vector spaces and functional-matrix (l² vs. L²) duality is useless? The proof of their equivalence is fundamental to finite-element methods for solving integrodifferential equations, for guaranteeing that months of computer time isn’t an exercise in GIGO (garbage in, garbage out). And don’t forget the myriad approximation schemes built with the aid of singular expansions and (duh) approximation theory. (Some famous examples: Taylor-Mclaurin series, Padé approximants, random phases, stationary phases…) And don’t even get me started on the applications of statistics in experimental design, curve fitting, and stochastic methods like Monte Carlo and martingales.

Assuming that you agree that high finance/computational modeling/etc. are worthy fields of study, this (woefully incomplete!) list simply begs the question of why does mathematics work so well in advanced studies? Two famous essays by Eugene Wigner (theoretical physicist) and Richard Hamming (information theorist) are particularly poignant in this context.

Then have a look-over at this Op/Ed by a Singaporean freshman in Princeton. It really doesn’t say much beyond the hifalutin’ words, which is a shame, because had the author actually tried to make a coherent statement, it would have been so, so much better.

Of course, it’s easy to be the old cynical bastard here, but is there really anything being said here apart from "Look at me I’m hot shit because I got admitted to PRRRRINCETON!"? I do agree that societies like Singapore still suffer from the stigmata of post-colonialism, in that we are still trying to ape the British while they themselves have moved on into wanton alcoholism and bitchfests. But I don’t quite appreciate the superciliousness, the holier-than-thouness, the "haha! i can see through the lenses of my upbringing, yet remain blissfully ignorant of the larger box i live in"-ness.

Here’s one I take particular offense at: Johann is clearly implying that third-world engineering students can’t be well-read sophisticates at the same time. Why should knowledge of Hegel and Maxwell take up mutually exclusive parts of the brain? Like seriously, he needs to broaden his social circle. I really hope he doesn’t belong to the "I can be smart yet remain blissfully and woefully ignorant of regression statistics, quantum mechanics and clinical biochemistry" sect of pseudo-intellectuals. The world already has far too many of such people, as evidenced by recent Congressional hearings.

This might be a good place to add (while I’m at it) that Singaporeans should wake up and smell the international currents. Singapore is already several years behind the crest of transnational trends, and the list of things for which it is falling behind just keeps growing. If you don’t believe me, just look at Micron and PSA-Maersk.

On the other hand, if you are a regular reader of the Young Republic, then you’d probably be in ecstasies reading this essay. Or, depending on your stand, apoplectic.

Let’s see if this vehement denouncement of apeing antequated European colonialist trappings will become enthusiastic embracing of apeing antequated American ideologies of life, liberty and the pursuit of happiness.

My radio is currently playing The Best of All Possible Worlds from Candide. Paragraph Two, Axiom Seven is so apropos. Amo! Amas! Highly recommended if you have yet to listen to it, by the way.

P.S. It’s not every day you spot a comic strip which, at least peripherally, appears to espouse some form of molecular orbital theory.

Since it’s been nearly a week since my last post, I’m putting all my cards out on this tableau. If my life were a newsroom, this is probably how the latest bulletins would come out as:

From the Counterintuitive Democracy department: the latest Student Senate elections are out, and of the three items on the referendum, it was the cheapest measure that failed. Huh? I thought people in capitalist societies valued cash-in-the-pocket more than words.

From the Art Snob department: I just came back from a performance by the Vienna Philharmonic. Riccardo Muti is some hot shit. Voluminous hairdo, flying coattails, wide swathing strokes with the conductor’s wand, he could well contend for a living rendition of the stereotypical conductor. But oh, the dynamic range is to die for. He put the issimo in fortessimo and pianissimo. And the encore piece tonight, a waltz from John Strauss, was absolutely, mind-blowingly divine. Wow. Oh, and by the way, the notion of the Vienna Phils being the world’s best orchestra was driven home. With. Every. Single. Note.

And by the way, I caught a patron eating (of all things) a fish sandwich, during Schubert’s Symphony No. 9. Yes, it’s one of the longest symphonies on the repertoire, but seriously.

From the I wannabe a Scientist department:a link to IM interviews with a principal investigator and other people in various other stages on the way there.

From the Weird and Wonderful Science department: The biggest science news story this week is undoubtedly the discovery of liquid water on Enceladus, one of Saturn’s moons. The mass media is abuzz with speculation on whether the discovery of extraterrestrial life will follow in short order. Which is of course grossly oversimplifying the phenomenon of life (think of it as a necessary but hardly sufficient condition), but hey, it’s an interesting speculation.

From the America, What Were You Thinking? department: I thought Krispy Kremes were one of the most evil inventions of the American marketplace, with one of the highest combined fat and sugar densities of any food in the world. Than, I was introduced to the 1,000-calorie donut burger native to Sauget, Illinois. « Grrlscientist, Living the Scientific Life

One thing’s for sure: American’s aren’t ashamed of outdoing themselves at any activity, including making things that, when eaten, are guaranteed to put you one step closer to cardiac oblivion.

From the Who said campus is boring? department: the campus is putting up a triple serving of community outreaching its simultaneous launching of Engineering Open House, ExplorACES and the Illinois State Geological Survey Centennial Open House. I went to EOH and saw a magnetic induction cannon launch aluminum rings across a room, and got my name engraved by laser on a poker chip. Way cool! I’ll try my luck tomorrow to see if I can get tickets to the Beckman CAVE. Too bad the fistulated cow won’t be there this weekend, but at least she’s going to be on display at next month’s Veterinary Sciences Open House.

EOH Poker Chip, originally uploaded by Elia Diodati.