In 1972 the American meteorologist Edward Lorenz was to give a talk at the 139th meeting of the American Association for the Advancement of Science. As Lorenz had failed to provide a title for his talk, one of the organisers of the meeting concocted this attention grabbing headline:

Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?

The central theme of the talk was that some physical systems, including the weather, are inherently unpredictable in the long run because imperceptibly small differences in conditions now can build up to much larger differences as time goes on. The tiny effect of a butterfly flapping its wings could, theoretically, trigger a raging tornado thousands of kilometres away. This branch of mathematics is known as chaos theory and the increasing unpredictability over time is called “the butterfly effect”.

Was it a butterfly’s wing beat that prompted Crotchety Man to don his metaphorical mortar board and indulge in some academic research on Cherry Ghost this week? That seems unlikely. It was, in fact, their delightful song, Mathematics, picked at random from my Spotify collection that persuaded me it was time to familiarise myself with the band’s material. Any butterfly effect would have been extremely indirect.

Cherry Ghost was a band put together by the British singer/songwriter Simon Aldred to perform and record his songs. They put out ten singles and three albums between 2007 and 2014 before apparently fizzling out in 2016. Their first album, Thirst for Romance, reached number 7 on the UK album chart and the three singles from that album all entered the lower reaches of the singles chart. Their other two albums, Beneath This Burning Shoreline (2010) and Herd Runners (2014), were a little less successful, just getting into the top 40.

The Crotchety research project got underway with a visit to Cherry Ghost‘s first album, to see which way the wind blows, as it were. The scientific instruments gave a reading of about 80% pleasant indie rock, 20% insipid, gutless pop. Sadly, the promise of an exciting Mathematics tornado never quite materialised and the project was cut short. Perhaps the butterfly didn’t flap its wings hard enough. Still, this one track remains as delightful as any of the butterfly species and thoroughly deserves its track-of-the-week status.

Mathematics can be fun in all sorts of ways. Only a mathematician could have invented the 4-dimensional, one sided solid figure called a Klein Bottle. It can only be approximated in our 3 ordinary spacial dimensions but this model gives some idea of what it’s like.

3D model of a Klein Bottle

Imagine you are not yet a butterfly. You are a caterpillar and you crawl into the bottle through the opening on the right. You travel down the inside of the yellow tube and, without turning left or right, you follow the surface into the wider blue section. You are now going back the way you came. When you get to the right-hand end you continue to follow the surface, which turns you round again. Now you find yourself on the outside of the yellow tube. Except that there is neither inside nor outside of this bottle. Weird, huh?

A mathematician named Klein
Thought the Möbius band was divine.
     Said he: “If you glue
     The edges of two,
You’ll get a weird bottle like mine.”