Monday, September 14, 2009

Bach Mobius Canon

Dear Musicians,

I just want to point out this rather lovely mathematical purity:
Bach's Canon from Musical Offering with Mobius strip computer graphics.

And while I'm admiring how well the Mobius strip works for this purpose, I have a confession of either great genius or great whackiness.

About two years ago, I had an epiphany about the Mobius strip, and how easily it might be overlooked in mathematics and quantum theory, because it is just too darn simple.

Additionally as it only has "one side, one face" it is capable of great complexity, but perhaps, somehow [1 x 1] shapes are geometrically too simple to cause much of a stir. As we all know, when you multiply anything in math by the number 1, you hardly notice the result.

Yes, that made me laugh indeed.
Invisible due to its one-ness. hahhahaa.

But the mobius strip's physical attributes of one side and one face, may just make it one of the most flexible shapes in the universe.

Imagine the mobius strip as a possible description of the motion of an electron around a nucleus. Imagine that a mobius formula could describe solar system's recycling of energy. What if the mobius formula is a possible definition of Pi? Afterall, even Pi when written out as 3.14......has that endless quality, doesn't it?

And with the mobius strip, its great flexibility allows you to create any and all possible shapes out of single construct. Try making a paper one, just to cut it apart and see all the permutations.

Or if you want to confound yourself just with office supplies, simply wrap a thick rubber band around a cylinder, like a pencil, and have a look for yourself at all the shapes that are possible:

Notice how the mobius configurations look different from every side at once (one side of the pencil has two wraps crossed with a third one on the diagonal, in the above pink pencil example, while the other side of the pencil has three parallel wraps).

It was after toying with a paper mobius strip and cutting it apart, just as we show children to do, that I realized that at the same time it can look like multiple loops, when compressed, and yet when elongated, it can look like a single strand.

Perhaps we need only improve our microscopes to fully understand the double helix of DNA or the single strand RNA, with their incredible power to remain unchanged as they stretch during cellular division and then shrink back to their original size.

That made me think of string theory vs. particle theory (yes I've watched a ton of documentaries on these topics) and that made me think that it's just possible (not likely, but at least a tiny bit possible) that the universal mathematical mystery that Stephen Hawking (yes, the Stephen Hawking) needed to spend more thinking time on, was indeed the Mobius strip.

So... ha ha....I'm so bold that ...ha ha....I emailed Mr. Hawking the theory.
I couldn't quite put my finger IN the theory, but I waved my hand in that direction, anyway.

Oh sure...laugh.

I did laugh. I assure you; everyone I tell has a wee chuckle.

And I did receive a very polite automatically generated email from his lab student saying: "Thank you for your email. Mr. Hawking is far too busy to read most email. Reminder: Kindly do not send mathematical theories".

Sigh. Well so much for that.
I'm at one with it (ho ho oh ho!)

But I want to at least put this confession of my own radical self-confidence in the Mobius strip down in history with a blog date on it.
Just in case it turns out to be useful.
I bet the entire Universe is in the shape of the Mobius, and that's why we find it so confusing to study.

And, of course, the Bach canon above only makes it more fun to contemplate.

Best, (and please don't send any more crazy mathematical theories. hahahhaha!)

Back to practising Opera Arias (arranged for two flutes and piano by moi for upcoming comedy-flute show.)
Comments (1)
Blogger jen said...

2016 - July 25th:
Hey readers!! :>) Jen here 7 years later.
Guess what?
Turns out my MOBIUS theory was exactly right. I was right. gosh!
Can't believe it. Read science article at this link.
Seriously. I'm stunned.


Best, Jen

Monday, July 25, 2016 10:42:00 PM


Post a Comment