Mathematicians don’t need to attach to art to suggest that what we do is inherent in nature. Unlike art and music, what mathematicians do is inherent in nature. The best maths always feels like discovery, not invention.

Mathematicians attach to art and music because they’re often interesting. And mathematicians are geeks first; we can’t let a technically interesting topic drop.

I’m not aware of any art with a representation of a Moebius strip, but I suspect that’s just because I don’t know enough art. Either way that says nothing about the validity – mathematical or artistic – of Moebius strips.

The single greatest word of praise a mathematician uses for work in pure maths is not “clever” or “useful”. It is “elegant”.

(Like most concepts of beauty, it’s very hard to describe to anyone else what constitutes an elegant theorem. But we know it when we see it.)

Since the moebius gradually turns the staff upside down, it might be cool if the music played this way, the notes smushing together where the strip goes flat, and then inverting high and low notes when the staff is upside down.

Yes, yes it should be, but I figured the spello didn’t need it’s own corrective reply. Sorry for any misunderstanding. I didn’t mean one should pair up the 3rd measure with the measure was most opposed to the next-to-last, I did mean that one should pair the 3rd with the one that is last but two.

Shame that his genious wasn’t realized until after his death. Although, really, the idea of musical fame or a “start” is relatively new (starting around Beethoven).

Bach worked as a conduit of (what her perceived as) God and devine inspiration.

He also kinda when nuts towards the end and tried to make a piece using his name as the harmonic structure (In his time “B” was seen as B-flat and “H” was seen as B natural).

H. C. Absj would be happy with it.

I love it! It’s magic!

While listening to Wendy Carlos. Looped. Backwards.

I really wished I understood the genius of this, and I do appreciate the geekiness and coolness of the exercise, and at the same time its so far beyond me. I think I first realized this when I had to google Moebius strip.

I understand perfectly well what a Moebius strip is, and I still don’t get it. It just sounds like some kid plinking randomly away on a harpsichord to me, with alternating vague trends up and down the keyboard.

It’s possible that you need an IQ of at least 160 to ‘get’ Bach.

To make this more embarrassing, the Escher is behind me on a poster on my wardrobe. Within touching distance as I wrote.

@Takuan: As always, you have said what I meant, but with greater elegance.

Apparently not – his name’s only been mentioned 50 times in this thread :-)

http://images.google.com/images?q=escher+moebius

Also, for the Gödel, Escher, Bach fans out there I highly recommend a more recent book also by Douglas Hofstadter – “I Am a Strange Loop”. It’s basically a more direct explanation of the central theme of GEB, written because Hofstadter felt that so many people missed that point. I was one of those that missed it, and I found the later book very provocative, fascinating and enlightening.

We had to do this in counterpoint class as a basic exercise (good enough for Bach, damn well good enough for us). We also had to write them so that the second voice worked out when played backwards and upside down. Ugh.

Telemann wrote quite a few wind “duets” in this manner: they were meant to be played from a single sheet of paper on a table between the two performers (standing opposite each other). So each plays the upside-down inverse of the other.

It was pretty mind-blowing the first time I played an oboe duet this way. (“You mean we can play a duet from the single sheet? Even though my part is upside-down? And backwards?”)