6.4: The Swallow’s Tail
Monday morning being ‘Latin’, Lottie is quite pleased to be able to distract her tutor Hipparchus with her errand. She arrives at his study, an area in the back corner of the Potting Shed that he as somehow marked off, against all commune guidelines and etiquette, as his alone, with bookshelves. She is carrying two rolled up posters which have mysteriously arrived in the den she shares with pTravis and Masongill.
“Do you know what these are?” she asks. Her tutor spreads out both posters and looks them over.
“Lovely. Not really my aesthetic but I can see that they are rather interesting. These are both pictures by Salvador Dalí from his ‘catastrophe series’. I think both may be called ‘Swallow’s Tail’ and this one is ‘Swallow’s Tail with cellos’. I am not sure of the exact names. But they were among the last pictures he painted. Indeed, this one was his last picture.”
Lottie has a strong temptation to gather them up and use answering the question with which she was charged to try to wriggle out of her Latin lesson. But curiosity intervenes. She asks, with her usual neutrality:
“That sounds stupid. What’s it all about?”
“Well Dalí became obsessed with the French mathematician René Thom and his catastrophe theory: a mathematical account of how apparently well behaved systems can yield sudden discontinuities for slight variations of input variables. The shape of Dalí’s Swallow’s Tail is taken directly from Thom’s four-dimensional graph of the same title, combined with a second catastrophe graph, the s-curve that Thom dubbed, ‘the cusp’. Thom’s model is presented alongside the elegant curves of a cello and the instrument’s f-holes, which, especially as they lack the small pointed side-cuts of a traditional f-hole, equally suggest the mathematical symbol for an integral in calculus: ∫.”
Sometimes it sounds as though Hipparchus is quoting someone else’s work!
“Catastrophe theory?” Lottie repeats. “Is that like chaos theory?”
“Yes, in a sense, although the underlying mathematics are very different. Both catastrophe theory and chaos theory study nonlinear systems. But the key difference is that catastrophe theory focuses on sudden, large-scale changes in a system occurring at specific ‘tipping points’ due to relatively small changes in parameters, while chaos theory examines systems where even tiny variations in initial conditions can lead to wildly unpredictable and seemingly random behaviour over time, despite following deterministic rules.”
“I see” says Lottie, although she probably does not. But we do, don’t we?
“Do you mean that a catastrophic system might have sudden changes even though nothing very different from normal seems to be happening to it, but only sometimes, depending on the circs.?”
“Yes.”
“Then what are these doing in our den? Who is trying to tell us what?”