Shimura Curves

Monday, January 22, 2018

A Straight Line

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Lead Vocals and Countdown: Lisa Payne
Harmony Vocals: Kate St.Claire
Bellzouki: Ed Lynch-Bell 
Electric Guitar, Programming and Everything Else: Kate St.Claire

"In Non-Euclidean geometry
The shortest path between A and B
Is not necessarily
A straight line"

Now that's a rhyme I'm quite proud of. I had been reading about multi-dimensional geometry on account of, well, being in a band called Shimura Curves, I thought I better have some general understanding of what the Taniyama-Shimura Conjecture (now called the Modularity Theorem) actually was. I was aware it was something linking number theory, in the form of Fermat's Last Theorem, to the strange and wondrous multi-dimensional mathematical shapes that also included Calabi-Yau Spaces (once linked to the idea that all the extra dimensions that needed to be added to String Theory to make Grand Unification work mathematically might be bundled up in very small spaces indeed - I haven't kept up with the theory over the past ten years, so this is probably all terribly out of date)...

The band arrived for rehearsal at Anna's house one day, to find that someone had erected a representation of the 3-dimensional shadow of a 4-Dimensional Hypercube (at which I gasped, "Ah, yes! The Tesseract!") using toothpicks and blueberries, on the living room table, so multi-dimensionality was very much in my mind. It was my favourite joke, back when I used to drink, that when I started lurching about and staggering, I would insist "I'm not drunk. I'm just being affected by gravitational masses beyond the visible dimensions, so in the fourth dimension, I'm walking a perfectly straight line!"

The central metaphor was the idea that the courses of airplanes around the globe were generally plotted around Great Circles, which are the shortest possible path between any two points on a curved surface such as a globe, but which look dramatically curved when viewed on a standard 2-Dimensional map affected by the usual distortions of map projections. A similar kind of phenomenon affects cosmological horizons, where an event happening very far away cannot be viewed in certain quadrants because light, travelling through straight lines in four-dimensional spacetime, cannot reach it in time.

Of course this was all a heavy-handed way of expressing that progress in one's own life isn't necessarily linear, there are all kinds of set-back and detours, but only with hindsight from a different perspective, can the "great circle" of the curved and circuitous path be ascertained. Or something.

The introduction, especially the slow, stately guitar rhythm and the little piano riff, is of course shamelessly nicked from Time by La Düsseldorf. (It's amazing to me, how no one ever called us on our shameless lifts, as if people didn't actually listen to the record before going "ah, sounds like The P*p*ttes.") The countdown was originally purely accidentally. The song was so long and so linear (and deliberately "Lang-Gerade", as Klaus Dinger used to call his motorik beat) that Lisa used to have to count the bars to know when the next verse was due to begin. When someone pointed out that Spiritualized had already used this trick in 200 Bars, we turned it around, counting down, calm and steady, like the countdown to a rocket launch. This proved so effective it became a regular feature of the song. (Around 2.30 the bassline shifts to a quite deliberate homage to Mr. William B. Carruthers' famous bassline - like I said, shameless! Absolutely shameless!)


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