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Posted by on Nov 1, 2013 in Off Topic | 0 comments

A Theory of Everything

Hey, shouldn’t everyone have one?

I’ve suggested many times on this blog that number is at the heart of all things. Here’s one article: Pythagoras’ Epiphany. I think the beauty of music, especially harmony, is similar to the beauty of math, but happening in real time. It slightly parts the veil, deepening the view of what is most basic and true about our universe. I believe that this connection with the deeper reality gives us a sensation of beauty. Here are a few more articles that go into detail, with examples and illustrations.

Saturn’s Rings

Beauty Is Truth

Prime Numbers and the Big Bang

If the Big Bang actually happened, then our universe blossomed outward from a point of infinite density, a singularity. What existed before that?

I assert that it was number. The Big Bang was a mathematical event.

What space did it occur in?

One of the gnarliest problems in physics is the issue of reconciling gravity with the rest of the basic forces. There are four: gravity, electromagnetism, and the strong and weak nuclear forces. Gravity is the odd one. It is far weaker than the others. It appears to operate in a continuum, a smooth field, while the others seem to be quantized — that is, they come in little discrete packets. Even space and time themselves may be quantized.

Math is like gravity, in that it works in a continuum. In the world of mathematics, there is no smallest anything. You can zoom in forever.

Here’s an example. If I measure the circumference and diameter of a circle very accurately, and divide one by the other, I always get the same number, pi, about 3.14. If I measure more and more accurately, I can get the value of pi to quite a few decimal places, but even with the best equipment imaginable, I will eventually run into the sizes of atoms themselves, and the calculation can’t get any finer.

But in the ideal world of math itself, pi goes out to as many digits as you please. There is no point where it runs into the grainy nature of reality.

It’s as though in the real world, there are pixels, and when you blow things up enough they start to show, but math itself has no such trouble. Things are infinitely divisible.

———————–

Einstein’s relativity and quantum mechanics are famously incompatible. Each describes the universe beautifully within our ability to measure so far. But it’s really hard to come up with a theory of reality that allows both to be true. Part of the problem is that relativity assumes a smooth continuum, and quantum mechanics assumes that on a tiny, tiny scale, everything happens in jumps, rather than smoothly. A theory of everything would have to explain how both relativity and quantum mechanics can be so true.

So how about this for a TOE:

The deepest reality, the substrate, upon which our universe is based, is simply the world of number.

The universe we live in, with its stars and planets and galaxies and people, is a mathematical object, like the Mandelbrot Set or a cellular automaton, that grew from this substrate.

Here’s a tiny, tiny piece of the Mandelbrot Set. Click to enlarge for full glory! This is a mathematical object, at least as big as our universe, and if our universe is one too, then maybe the beauty of this object is related once again to the beauty of music, or of Keats’ Grecian Urn — it shows us, a little bit, the nature of Creation.

Mandelbrot_Set-12-DOUBLE_SPIRAL-large

If the deep reality is a continuum, and the immediate reality of stars and planets sprang from this continuum, then maybe gravity is different from the other three forces because it is a feature of the deep reality. It is a manifestation of the shape of space-time. It is working in the substrate.

Relativity and gravity are happening in the basic reality, the continuum, the world of number.

Quantum mechanics, electromagnetism, light, nuclear forces, matter and energy are all happening in the particular reality that came about when the singularity happened.

Relativity and quantum mechanics can’t be reconciled because they actually operate in different realities — gravity in the basic reality, and the other forces in the immediate universe.

If this is true, it may offer insight into the nature of dark matter.

Dark matter has not been observed directly within our quantized universe. Its existence has been deduced, or conjectured, because galaxies move and rotate as though there is a lot of mass there that we cannot see. The idea is that dark matter interacts with “our” universe only through gravity, and not through the other forces. That is why we can’t see it, because seeing requires light.

What if dark matter is something that exists in the basic reality, rather than in our particular Big-Bang-generated one? The only link between the realities would be gravity.

There is no reason why our particular singularity should be the only one.

Perhaps what we call dark matter is just the gravitational shadow of other universes.

Here’s a scenario:

  1. Ours is one of many universes, each one starting with a different set of “seed” values.
  2. Ours is of course perfectly designed for us to exist, and the other universes are also “coincidentally” perfect for whatever exists in them.
  3. The universes all exist in a space-time continuum, in which gravity is the only “force,” being actually a distortion of space-time as Einstein described.
  4. The universes can attract each other through gravity, and so they tend to clump in the same places.

The ratio of dark matter to ordinary matter (about 5:1) may turn out to be an important number. Maybe “nearby” universes (those with similar seed values) attract each other more strongly than more “distant” ones (those with more different seed values), and the 5:1 ratio is the result of an infinite sum — the total pull of all those other universes, fading off into the “distance.”

Here’s a terrific article on dark matter from April 2013 if you’d like to explore further.

Next: A Harmonic Journey: ET and JI Compared

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Posted by on Nov 5, 2012 in Background, Just Intonation | 0 comments

Beauty is Truth

It’s probably Keats’ most famous pair of lines:

‘Beauty is truth, truth beauty,—that is all
Ye know on earth, and all ye need to know.’

I believe he’s right on the money. I think that when we experience beauty, it’s because we have seen a little deeper into the nature of things.

This seems especially true of mathematical beauty. I had a college friend who found math exquisitely beautiful. He bought a blackboard for his room, and stayed up until all hours, glorying in the work. Elegance, simplicity (but not too much!),  and beauty are important guidelines to the rightness of a solution or direction of research. A sense of beauty guides the scientist as well as the artist. I’m really familiar with this from my engineering career.

So there is the nugget of my own epiphany:

The beauty of music is the beauty of mathematics, perceived in real time.

We see this in its visual manifestations all the time. The curve of the cables of the Golden Gate Bridge, the pattern of seeds in the sunflower, the rings of Saturn — all clear manifestations of the way the universe works, that can be described by math, and that we find beautiful.

Music presents a pure, distilled form of this: beauty created by small, whole numbers and their relationships to each other.

Next: Notes and Intervals

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Posted by on Nov 4, 2012 in Background, Just Intonation | 0 comments

Pythagoras’ Epiphany

Pythagoras was a Greek philosopher who lived about a century before Athens’ golden age. Some time before 530 BC, he had an epiphany. He had been investigating vibrating strings, and found that when you cut the length of the string in half, the note it makes is an octave higher.

Sound is vibration. When one sound is vibrating twice as fast as another, it still sounds the same in some crucial way. The pitch is higher, or lower, but somehow we perceive it as having the same essential character. A C note, multiplied or divided by two as many times as you like, still sounds like a C.

Here are all eight C’s on the piano. They are different in pitch, but all have the same character. Eight Cs

Pythagoras also found that when you shorten the string to a third of its original length, it vibrates three times as fast. The note this creates is different in character from the C. Today it is called a perfect fifth. If you’re in the key of C (that is, if the full string sounds a C), this note will be a G.

This observation led him to what must have been a terrific epiphany — math, particularly number, is at the heart of all things. I sometimes envy those early Greek thinkers — what joy, to come across something basic for the first time!

But you know, everyone, everywhere, has lived in modern times. A thousand years after Pythagoras, Galileo was the first to find out that the Milky Way is made of stars. Can you imagine how he felt? And we are still on the cutting edge — civilization is in its infancy. Future generations will envy us our discoveries while smiling at their primitiveness. “A keyboard, how quaint!”

Pythagoras’ epiphany still has merit. Cosmologists have imagined many alternate universes, with different basic physical constants and laws, curved space, more dimensions — but it’s pretty tough to imagine a universe without number. I believe the integers — 1, 2, 3 and so on, are the most basic things we know about for sure.

Pythagoras actually founded a religion based on this insight. The inner circle were called the mathematikoi, and they lived a monastic life of study. The order had many rules, including a ban on eating beans. Perhaps they worked in close quarters. They also had a rule against picking something up when you dropped it. Cluttered, close quarters! But they found out a lot about math.

Next: Beauty is Truth

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Posted by on Nov 2, 2012 in Background | 0 comments

Back Story

Music is the thread that stitches my life together. I was born singing, as are we all. My parents loved to sing and they both had beautiful voices. They met in a musical play in college.

I remember our house as being filled with music, especially jazz and harmony vocals. Stan Kenton, the Mills Brothers, Sons of the Pioneers, and all the big bands. Sing Sing Sing at Carnegie Hall. Cool Water. All from the Curtis Mathes stereo, literally a piece of furniture, as big as a couple of dressers. I loved that sound, LPs coming out of that big resonant wood cabinet.

With my sister, we had four good voices, and singing harmony in the car was a highlight of growing up. My sister and I started writing songs together when we were kids.

I troubadoured randomly around the country with a guitar and the clothes on my back (hey kid, can you play that thing? hop in!), formed a rock’n’roll band, sang Christmas carols professionally, did singing telegrams in a chicken suit, and continued to write and record. I spent most of my “serious” career designing electronics for the remarkable L.R. Baggs Corporation in California. They make beautiful, innovative equipment for amplifying acoustic instruments.

I’ve become increasingly focused on music over the past five years or so. About two years ago, I began working full time on music and almost nothing else. Soon after, I had a huge epiphany, the best intellectual and spiritual experience I’ve ever had.

Next: Pythagoras’ Epiphany

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