week 2 \ a different mathematical sort of art \ ben marafino

Let me begin by discussing a phenomenon that may seem wholly mysterious, even after explanation – but at the same time “artistic,” if only for its mystery and aesthetic appeal. Suppose we heat the bottom of a layer of water, for example, which is much wider than it is tall, and allow the water to lose this heat through the top layer via radiation (the two layers are perfectly flat panes of glass, say). Then, the temperature of the bottom layer is gradually increased until something quite curious happens – the water sorts itself into very neatly ordered ‘convective cells,’ or Bénard cells, as they have come to specifically be called. Within these cells, a small quantity of warm fluid rises until it encounters the cooler top layer, upon which some heat is lost; the cooled fluid then descends, is heated up again, and retraces its previous journey. It is much easier to observe this effect if small (e.g. aluminium or other metal) particles are also mixed with the water, as in the picture below. You may have even observed this sort of effect yourself taking place, for example, in a bowl of hot soup or coffee that has just been mixed with milk.

What, exactly, is so (perhaps aesthetically) interesting about this phenomenon? Consider that convection typically takes place on roughly the same size scales as the liquids being heated – for instance, if you heat a pot of water, you will most likely observe one large and disorganized convective cell, if at all. More likelier still is some sort of random, turbulent pattern of convection, but the uniformity of heating does plays a big role. However, if you were to considerably flatten that pot and then gradually (and uniformly!) heat it up from room temperature, this random convection will, as explained previously, mysteriously organise itself into a series of smaller cells with themselves even more curious properties. For one, no two adjacent cells (in a straight line) have the same direction of circulation when viewed from the side – one will rotate clockwise, the next counter-clockwise, the one after that clockwise, and so on. There is an intriguing mathematical explanation for this effect (as well as for the formation of the organised cells themselves), which unfortunately falls far beyond the scope of this blog post – let’s just say it has to do with something called ‘spontaneous symmetry breaking,’ - this year’s Nobel prize for physics was awarded for its discovery.

But what truly lies behind more complex processes – say, (the atmosphere [which really ought to be included]), life, the universe, and everything, and what has this got to do with art? ‘Minimization of entropy’ or another similarly emotionless term does not exactly evoke the same romance that the process of generation of art might in us - the human creation of art is arguably just as spontaneous as these simple physical processes may be, yet art has remained, and will remain, generally resistant to the instruments of reductionism. It is for this reason – and perhaps this reason alone - that we approach art, as we do with the world that surrounds us, with some measure of awe. However, our insights into such human pursuits, along with our quantitative treatment of complex physical systems (of which the behaviour of fluids is one), fail to provide complete descriptions of the underlying processes. We can say exactly (without resorting to silly pop-evolutionary psychology claptrap) as much about why the Mona Lisa was created as we can say about, for example, what the weather will be like two weeks from now: nothing definitive. Both cases manage to evade not only explanation, but our entire system – as it stands now - of coming up with them!

One Response to “week 2 \ a different mathematical sort of art \ ben marafino”

  1. connor petty says:

    reminds me of fun with cornstarch: http://www.youtube.com/watch?v=vCHPo3EA7oE

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