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04 February 2013

Folding Space-Time

Another brilliant video from Vihart which will bend (fold?) you mind...

Published on Feb 3, 2013

I needed some help to understand this a little better, so I went searching on the web...

First, I investigated Möbius Strips:
"The Möbius strip or Möbius band (UK /ˈmɜrbiəs/ or US /ˈmbiəs/German: [ˈmøːbi̯ʊs]), also Mobius or Moebius, is a surface with only one side and only oneboundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.[1][2][3]" Read much more on the Wikipedia page.

Wolfram Alpha describes Möbius Strips like this:
"The Möbius strip, also called the twisted cylinder (Henle 1994, p. 110), is a one-sided nonorientable surface obtained by cutting a closed band into a single strip, giving one of the two ends thus produced a half twist, and then reattaching the two ends (right figure; Gray 1997, pp. 322-323). The strip bearing his name was invented by Möbius in 1858, although it was independently discovered by Listing, who published it, while Möbius did not (Derbyshire 2004, p. 381). Like the cylinder, it is not a true surface, but rather a surface with boundary (Henle 1994, p. 110).
"The Möbius strip has Euler characteristic (Dodson and Parker 1997, p. 125).
According to Madachy (1979), the B. F. Goodrich Company patented a conveyor belt in the form of a Möbius strip which lasts twice as long as conventional belts. M. C. Escher was fond of portraying Möbius strips, and they appear in his woodcuts "Möbius Strip I" and "Möbius Strip II (Red Ants)" (Bool et al. 1982, p. 324; Forty 2003, Plate 70)."

Next, I had to look at space-time.  Space-time is "the four-dimensional coordinate system (3 dimensions
of space and 1 of time) in which physical events are located." (link) This NASA video explains more.

Uploaded on May 12, 2011

After this, I couldn't help thinking about palindromes (words or phrases that read the same in both directions).  Some examples:
Too bad – I hid a boot
Some men interpret nine memos
Lisa Bonet ate no basil

I was wondering if the music in the VIhart video would be a tonal palindrome.  In music, for example, Béla Bartók (5th String Quartet), Alban Berg (Act 3 of Lulu), Guillaume de Machaut, Paul Hindemith (Ludus tonalis), Igor Stravinsky (The Owl and the Pussy Cat) and Anton Webern (2nd movement, Opus 21 Symphony) incorporated palindromes in their compositions.

I leave you with Guillaume de Machaut's "Ma fin est mon commencement" (can you hear the palindrome?):