The Geometry of Music

One of my favorite phrases I have quoted from people's reviews of my book is from K. Flekkoy, who had this to say at amazon.com: "an imaginative and strangely 'musical' way of imagining superimposed dimensions". I was strongly reminded of that phrase today when I saw the picture at left, which was created by Dmitri Tymoczko of Princeton University. I came across the picture in an article published a few days ago by ScienceDaily.com, click here for the full story.

The article is about three music professors -- Clifton Callender at Florida State University, Ian Quinn at Yale University and Dmitri Tymoczko at Princeton University -- who (to quote from the article) "have devised a new way of analyzing and categorizing music that takes advantage of the deep, complex mathematics they see enmeshed in its very fabric."

Their system uses colors and a five-dimensional grid to analyze and portray the differences and similarities between one piece of music and another: "geometrical music theory", as they are calling this new system, provides a rich set of visualization tools that analyze elements like rhythm, melodic density, and chord structure, in a sense boiling a piece of music down to its essence and providing ways of visualizing that essence.

In this picture, the red dot at the center represents a diminished seventh chord, and the other nearby dots are some of the chords we would be most familiar with. As an analysis method, it appears their system is more suited for chordal music, and "Western" sensibilities as opposed to the music of other cultures, but within that context these professors are saying this graphing method might be able to show the differences between the composition style of Lennon versus McCartney, or how classical compositions from centuries past are related to modern-day pieces.

It's All About Connections
Persons familiar with the Imagining the Tenth Dimension project will recognize one of my central themes here: what gives a piece of music its innate power, its emotional and cultural resonances? Thinking of music as being created from interlocking sets of memes that are connected across time and space is an important key, and it appears these three researchers are now providing us with new tools to categorize those musical memes.

Another related fascination for me is the rhythm of language, and how different cultures have their own patterns of pitch, rhythm, and grouping. How does emotion translate into speech in different languages, and are there universal physicalities for communicating sorrow, happiness, fright, (and so on) that transcend language? Might such connections be able to be tracked and coded with a similar visualization tool to the one we're looking at above?

A blog entry at Cosmic Variance talks about the work of researcher Diana Deutsch, who specializes in the psychology of music. There is a real audio interview embedded into that blog entry, listen to the first four minutes or so for a fascinating example of how music and language are so easily intertwined. When we begin to see ourselves as being part of patterns that exist across time and space, this all ties in nicely.

Edit: A few days after I published this entry, Millsley (one of the regular contributors to the tenth dimension forum) posted his latest list of fascinating links that fit into the Everything Fits Together paradigm. This collection of podcasts from WNYC about music as patterns was one of those links.

Enjoy the journey,

Rob Bryanton

Other entries related to this:
Waveforms in the Ten Dimensions
Music and the Dance of Creativity
Song 19 of 26 - Positive Vibes
Song 6 of 26 - Connections
Seeing Eye to Eye

The Universe as a Song

To start off, here's a recent conversation I had with author Gevin Giorbran ("Everything Forever: Learning to See Timelessness") which relates to some of the ideas in this blog entry.


A direct link to this video is at http://ca.youtube.com/watch?v=-SI5MgGnP1g

This time, I'd like to work through more of a poetic take on this way of imagining how our reality is constructed: The Universe as a Song. My song "Big Bang to Entropy" ends with this verse:

It begins as nothing, silence at the end
Every song's the same after or before
But the parts in between, there are so very many forms
More than we could ever hope to know...

So what we're exploring in this blog entry is the idea that a particular universe can be thought of as a particular song. Lots of people have at least some ability to play a particular musical instrument, and this idea works no matter what instrument you play. But this is also an interesting part of the metaphor, because each instrument has its own limitations and its own strengths: not every song can be played on every instrument. Bagpipes have their own unique characteristics that make them very good at playing a certain subset of all possible songs, but not so good at playing four-part fugues. Since my instrument of choice is the piano, that's what I'll use for this example, but the same still holds true: not every song in the world can be played on the piano, and the piano's strengths and weaknesses are what make it more likely to be used to play one song over another.

Okay, I sit down at my piano, and at this point I am still in the unobserved realm of indeterminacy, the multiverse of all possible songs. Now I play the first note or chord: by doing so, I immediately collapse out from all possible songs only the songs that start with that particular configuration of notes. That first musical "event" still defines a seemingly infinite number of songs that could have started that way, but that first event also has become a "binary yes/no" that, by playing that first note, removes all of the other songs that don't start that way.

I've remarked here before that I'm surprised at how often the following point of view comes up: some people believe that the big bang set in motion a certain number of processes that make everything about our universe inevitable. This includes our illusion of free will: according to this worldview, each of us is acting out a pre-defined script that cannot be changed. If I were to sit down at my piano then, and strike one note or chord, and let it die to silence (a la the climactic last chord of the Beatles "A Day in the Life") this single musical event would be a song representing that "hard determinist" view of the universe. All of the textures and shifting harmonics we hear as certain parts of the sound die more quickly than others would be defined only by the physics and basic laws of the universe: how hard the chord or note was struck, what particular notes were chosen, whether the instrument had an innately long or short sustain, what resonant characteristics were specific to that instrument, how reverberant the room the instrument was in happened to be, and so on: all of this richly nuanced interplay of harmonics and texture as the sound decays would be the inevitable result from the impetus of that single music event.

Since I believe that a certain amount of choice is involved in the ongoing creation of the universe and the world we live in, I'm going to continue now to the second note or chord of my song. This second event is as important as much for its placement as for what it is: as many famous musicians have remarked, the spaces between the notes have at least as much intellectual/emotional weight as the notes themselves. So, whether my second note is a few milliseconds or a few minutes after the first, that second musical event again narrows down the logical choices for what is going to follow, for what song I am likely to be playing.

Another worldview that is often advanced is that everything about our universe is random: imagining the spacetime tree of possible parallel universes that could have sprung from our big bang, that school of thought says we are on one branch of that tree right now purely because of a series of random occurrences. Those random occurrences caused matter to coalesce, life to begin, evolution to proceed, and so on. In the metaphor we're talking about here, then, if I were to sit at my piano and play a completely random set of notes of varying duration, speed, and volume, I would create a unique song, different from all other songs, and that would be the universe we live in. Since there are so many recurring patterns within our universe and our awareness, the idea of a universe that is completely randomly generated may seem unlikely to some, but even in that random song I just played there will have to be places where a certain amount of organization will seem to be evident: there will be places where more high notes than low notes happen next to each other, places where there seems to more or less density of notes, places where more soft notes happen next to each other, even places where the same note occurs several times in a row: that's the nature of randomness.

(However, since our brains are so strongly designed to crave and discover order out of a potentially overwhelming sea of incoming data, the idea of me physically playing a truly random collection of notes is most certainly impossible... but a computer program generating a truly random piano performance would still generate a "song" that had pockets of perceived order. Designing a computer program that rejects the next possible note if it is too similar to the one before would be a way to avoid these pockets of perceived order, but then the output would no longer be truly random.)

"I Can Name That Tune in Five Notes"
Name That Tune was an old game show where contestants had to guess what song was being played, and the competition was based upon how few notes a person could identify a particular song within. Continuing with our metaphor, then, we're going to move on to the third, the fourth, the tenth, the eighty-seventh note, and so on. Each succeeding note or chord defines the song we're playing more specifically, until there is no question that we are definitely playing one song and not another. Still, this is not the hard determinist song we are talking about: even if we are talking about something as rigidly structured as a Bach Two-Part Invention, there is still lots of room for interpretation in every performance of any piece of music. This also includes allowing for mistakes (randomness), and even the possibility that the performer will get bored and switch to a different piece of music half way through (free will).

In "How to Make a Universe", we worked through how quantum mechanics allows us to imagine the universe as a move from indeterminacy to a specific starting point that we look back upon now and think of as the big bang. By sitting down at a piano rather than picking up a set of bagpipes, I already defined a certain starting point for what possible song-universe I was going to select from, which corresponds to the choices for gravity and the speed of light that are part of the first few "notes" that begin to define a particular universe out of all the possible universes that could potentially exist out there within the multiverse, and that would be just as true for any other universe with different fine structure constants as it is for our own.

Let's look at our song as a recorded waveform. Before the song, we see a straight line, which represents the indeterminate state, the zero of no sound, no musical events. Then we see the waveform leap out in width to represent the very first note of our song. Now, whether we are thinking about the single event universe of hard determinsm; or the Dawkins-style universe of random notes which, through the nature of randomness, achieve a revealed order; or if we are thinking of a universe that has been created by some kind of conscious interference; in all cases these universes will share one other common feature. No matter what, that shared feature occurs at the end of the song, as the last note dies to silence, and the positive and negative parts of the waveform gradually balance each other out and we return to the same straight line of silence from which we started.

This brings us back to my song lyrics quoted at the start, and the ideas that Gevin Giorbran has described so well in his book: what happens just "before" the maximum grouping of the first yes/no that selects one possible song from all others, and what happens with the enfolded zero of maximum symmetry just beyond the end of the song (no matter what song we are talking about) are one and the same, and both are "outside the system" in the sense that Gödel speaks of with his Incompleteness Theorems.

We can think of that unobserved quantum fabric that is my way of portraying the tenth dimension, then, as being equivalent to the Zero that we start from. In our song metaphor, we can imagine that Zero as a giant ball that contains every musical event and gesture possible. We choose to start some specific place on the outside layer of the ball with the first note or chord, and move within the ball on a specific winding path as we select one musical event after another to create our song. Then, no matter how short or long the song was, and no matter how inevitable, random, or deliberately composed the song might be, as the last note of our particular song dies we end up back outside of the ball, ready to start some place else to create a completely different song.

A lot of these same ideas can also be applied to thinking of any particular person's life as being a song: this is one of the ideas I touch on in my book as well. Whether we are talking about the overall duration of the universe, or the tiny line that one person's life draws through the probability space of available choices from birth to death, the concepts are similar, and fun to imagine.

In the above video conversation with Gevin Giorbran, I tell him that his book caused me to rewrite the chorus of my song Big Bang to Entropy. The idea that our universe is destined to end in a meaningless heat death of maximum entropy is what many scientists still propose. The idea that the end of the universe is a return to the enfolded timelessness of maximum symmetry and absolute zero is, I believe, a much more satisfying answer and the one that will eventually be accepted by mainstream science. As I say to Gevin, the chorus for this song used to be just the phrase "Big bang to entropy" repeated three times, but that is no longer the case: now the chorus is "Big bang to entropy/Big bang to symmetry/Big bang to everything". So, to finish off, here is a new video for the revised lyrics version of my song "Big Bang to Entropy", as performed by Ron Scott.


A link to this video can be found at http://www.youtube.com/watch?v=lIeOd-TlzEo

Enjoy the journey,

Rob Bryanton

Waveforms in the Ten Dimensions

The simultaneous wave/particle nature of reality means that many things that appear to us as particles are waves just being observed in a certain state. By the time we have arrived at the tenth dimension as the enfolded timeless whole (as explained so well by Gevin Giorbran), we have finally reached what some people think of as God, or a state of enlightenment (as referred to in Tom Huston's article about this project in the current issue of What Is Enlightenment?, or the ultimate theory of everything.

In Imagining the Tenth Dimension, I spend a lot of time talking about triads, insisting that all dualities have a third option, which can be both, neither, or no choice. Our physical world interacts with a world of memes and spirit, and the third option that results can be life as we know it, or it can be just the timeless whole that represents every possibility contained within the multiverse. But the dualities of one order pushing against another as we move along our line of time (a line that is actually created by a series of slices, here we go again with that simultaneous wave/particle stuff) allow us to see that this instant in time is a slice of a waveform, and that waveform is reflected in the beautiful and complex universe that we see around us.

Waveforms are interesting, because one waveform can incorporate many different frequencies simultaneously. So, a simple single line drawn from the big bang to the end of the universe can be overlaid with the many different waveforms representing the many possible expressions of reality, and the organizing dynamics that push against each other to create the preference for one kind of reality over another in different parts of the multiverse.

One of the reviewers for my book on Amazon.com has this to say:

"The present exposition is an imaginative and strangely "musical" way of imaging superimposed dimensions--not surprising perhaps, since the author among his achievements also is a musician. Still, the treatise has relevance for physicists. It is also pleasurable to read."

(thanks for the kind words!).

I suppose, since I spend a lot of my work day staring at waveforms, thinking of reality as being a complex waveform precipitated from potentials contained within the higher dimensions doesn't seem like much of a leap to me. Once you arrive at this idea, you have a way of explaining entrainment (how like attracts like, how attitude affects outcome, how eating live veggies imparts healthful vibrations, how charismatic or depressed personalities can immediately impart their "vibe" to a room full of people, how "Sync" as described by Steven Strogatz can cause order to arise out of chaos, how thoughts become things, and so on).

Thinking of our reality as a waveform also shows how there are always certain sets of "you can't get there from here" points in our physical reality (both past and future), but how a reality of memes and spirit can move more freely across time and space. This week in the blog dedicated to lucid dreaming, "Dreaming Life" , host Ben Q. published an interview with me where we discuss some of those ideas. I encourage you to check out this fascinating blog on a regular basis.

One of the most unusual and convincing examples of how reality could be constructed from waveforms, and the possiblity that the mind can be used to change our reality came to me a few months ago from Deena Zalkind Spear, whose lovely book "Ears of the Angels" tells a story most of us would have thought unbelievable, had it not been collaborated by so many intelligent and sensitive classical musicians. Told with a self-deprecating sense of humor, Deena's book is a pleasure to read, and I recommend it highly if you're looking for something that will challenge your limited worldview of physical reality.

Finally, while we're talking about vibrations and waveforms, we have now posted my song "Everything Fits Together" to a site called "JamGlue", which allows you to remix all of the instrumental and vocal parts to the song in whatever way that pleases you (click on the Remix button to see the song as six sets of waveforms, and you may want to work through the tutorials on the site to see what the possibilities are). These "stems" (as we call them in the audio industry) can also be downloaded from Amie Street, so if you have an audio sequencer of your own, I invite you to cut and paste this material to your heart's content. And please, email me mp3s of any of your mashups of this song you think are worth listening to (rob at tenthdimension dot com), and I will post them at a future date. These songs are released under a Creative Commons license, basically this says you are free to play with and re-edit this material as long as you give me credit as the original composer, and do not sell your remixes.

Enjoy the journey,

Rob

PS: The blog in which I originally published the lyrics to this song can be found here. And three videos of "Everything Fits Together" are below, just for fun:



A link to this video can be found at http://www.youtube.com/watch?v=6nAS2trDuck





A link to this video can be found at http://www.youtube.com/watch?v=KcdjX72VcKI