Thursday, September 19, 2013

Mathematical Impressions: Making Music With a Möbius Strip

What fascinates me about this article and video is the relationship of music and chords to the mobius strip (an abstraction of the surface of a torus) and music notes to the torus. I'm not the hottest in math (I have to work at - perhaps because I had so few good teachers in it) but it reminds of the relationship in Calculus of the derivative to the integral. I've had many discussions with GW Hardin about relationship of tones to the Rodin coil, Solfeggio frequencies and the apparent musical nature of the structure of the universe.  This seems to also support that insight as the surface he is showing is a torus.  I don't know if you see what I see in this but I think you will enjoy the video either way.  CLICK ON THE IMAGE TO PLAY BELOW... -Bill

Mathematical Impressions: Making Music With a Möbius Strip

The connections between mathematics and music are many. For example, the differential equations of vibrating strings and surfaces help us understand harmonics and tuning systems, rhythm analysis tells us the ways a measure can be divided into beats, and the study of symmetry relates to the translations in time and pitch that occur in a fugue or canon.
This video explores a less well-known connection. It turns out that musical chords naturally inhabit various topological spaces, which show all the possible paths that a composer can use to move between chords. Surprisingly, the space of two-note chords is a Möbius strip, and the space of three-note chords is a kind of twisted triangular torus.
For a thorough presentation of the ideas introduced here, suitable for both mathematicians and musicians, see “A Geometry of Music” by Dmitri Tymoczko.
The “Umbilic Torus” sculpture shown at the end of the video was created by Helaman Ferguson.

A Jewel at the Heart of Quantum Physics

Artist’s rendering of the amplituhedron, a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated — the probabilities of outcomes of particle interactions. Illustration by Andy Gilmore


A Jewel at the Heart of Quantum Physics

By: Natalie Wolchover
September 17, 2013

Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.

“This is completely new and very much simpler than anything that has been done before,” said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work.

The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like “amplituhedron,” which yields an equivalent one-term expression.

“The degree of efficiency is mind-boggling,” said Jacob Bourjaily, a theoretical physicist at Harvard University and one of the researchers who developed the new idea. “You can easily do, on paper, computations that were infeasible even with a computer before.”

The new geometric version of quantum field theory could also facilitate the search for a theory of quantum gravity that would seamlessly connect the large- and small-scale pictures of the universe. Attempts thus far to incorporate gravity into the laws of physics at the quantum scale have run up against nonsensical infinities and deep paradoxes. The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity.

“Both are hard-wired in the usual way we think about things,” said Nima Arkani-Hamed, a professor of physics at the Institute for Advanced Study in Princeton, N.J., and the lead author of the new work, which he is presenting in talks and in a forthcoming paper. “Both are suspect.”

The Birthing

You are ready for this.  We are partners in this next dance, with all sorts of accompanying music!  Let’s listen to some of it…

A conversation with “Cosmic Awareness” as interpreted by Will Berlinghof, from Rainbow-Phoenix.

A conversation between Inelia Benz, Lucia Rene and Victoria More, co-founders of A.W.A.K.E.N. Academy.

And finally, a song:

“Happy” is oozing through the air today.  This is new, and not because of any external event in this 3D life being lived, quite the contrary. There are people whom I love desperately, who are choosing to leave/exit/pass over now.  This body is still the same as it was 9 months ago, no magic age-eraser or healing has occurred.  Our bank account is pretty much as it has been for quite some time, living paycheck to paycheck.  Everything looks pretty much the same as it has all year. What is it then?

It is oneness. It has been reflected and this time, the image was captured.  I had help, most certainly, yet there it is.  Nothing and everything about it is simple, all at once. 

Any one of the links here refers to the universal.  What we are doing is shifting.  Which point of view you adopt determines your perception.  It is okay to disagree, with everyone; your life is yours, as ONE.

It doesn’t make sense, yet it is absolute truth.  Light and Dark are the same.  The struggle to overtake one for the other has been just part of the game.  We are all here for the experience, for the living, for the life.

No right, no wrong, no judgment, just love.  It is all okay.  It’s good.  It’s all good.  You’re good.  In fact, you are perfection.

All choices are perfect choices.  All lives are well lived.  All intentions are unknown except by the intender and therefore opinions don’t matter.  It has always been up to you.  Would you like Door #1, 2 or 3?  Choose now. You’ve made the perfect choice. It’s all happening at once.

Happy is a by-product of freedom; freedom to choose, to be, to do.  Go for whatever lights you up, it will work out just precisely as you believe it will. Trust.

You are the one you’ve been waiting for.  I love you madly.

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