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.

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.

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.

Posted by on Dec 4, 2012 in The Notes | 0 comments

## The Minor Seventh

The farther we get from the center, the less consonant the notes are, when played against the tonic. Consonance is a whole subject. It’s generally spoken of as though it could be plotted on a scale, from consonance to dissonance. I think this is a big mistake. Consonance has more than one dimension. Trying to force these independent dimensions of consonance onto a one-dimensional scale leads to unnecessary confusion.

Anywayy … The minor seventh is a pretty dissonant note in all dimensions. It’s three moves away from the tonic, down a third and up two fifths:

The ratio is 9/5.

This is some beautiful, exotic harmony.

Here’s a progression that shows off the flavor of the b7, in just intonation:

Hey, that’s beautiful! I worked it out as an illustration, with the idea of showcasing the minor seventh, and it turned out to be really nice music.

See why I’m in love with the lattice? It’s a beauty engine.

Posted by on Nov 10, 2012 in Just Intonation | 0 comments

## The Chord of Nature

When I first learned to play guitar, I would sit on the couch late at night and pluck the low E string, again and again, and just listen to the beauty of the sound as it died away.

That low E note is not just a simple vibration. The full length of the string is vibrating at about 82 Hz. But a pure 82 Hz note doesn’t sound like a guitar string at all. It sounds like this:

82 sine

The guitar sound is much more complex:

guitar low e

The difference comes from the fact that a string doesn’t just vibrate along its whole length — it also vibrates at twice the frequency, three times, four, and so on — all at the same time!

Maybe you did this as a kid. I did. When you get a jump rope going, you are essentially vibrating a big string. It has a characteristic frequency, maybe two cycles per second, set by the length of the rope and the amount of tension, just like a guitar string. This frequency, the natural vibration speed of the whole string, is called the fundamental.

But if one person holds their end still, and the person on the other end moves the rope twice as fast as usual, a funny thing happens. The rope divides in two, and the center point stays still, while each half does its own circle. Again, the length and tension determine the natural speed. Go three times as fast, and three sections will appear. These higher-mode vibrations are called harmonics.

Here are a couple of guys in lab coats to demonstrate:

Video

This only works when you hit the right frequencies. Spin the rope at, say, 2 1/2 times the natural frequency and everything falls apart. The stable frequencies are the fundamental, 2x, 3x, 4x, 5x and so on. This video shows a string getting stable at 6x, 5x, 3x, and the chaos that happens in between.

Video2

When you pluck a real string, it will vibrate in all these modes, generating a complex sound. The particular recipe of added harmonics creates the timbre, or tone, of the note.

Here’s that same pure 82 Hz tone, with the harmonics 2x, 3x, 4x and 5x added successively:

Chord of Nature 2

This is the Chord of Nature. It is a sonic manifestation of number, and of the laws of the universe, and it’s very simple. If the fundamental frequency is 1, then the frequencies of the harmonics are 2, 3, 4, 5, 6 and so on. And somehow, our perception of sound is designed so that this sounds beautiful.

Here, in contrast, is the same demonstration but with the harmonics detuned randomly by less than two percent:

Chord from Hell 2

Yipe! Now go back and listen to the first one as a palate cleanser.

There is something deep inside us that recognizes the series of harmonics, and, for most of us, labels it “beautiful.” There is some connection between those small, whole numbers and musical beauty.

Next: Notes As Ratios

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

## Beauty is Truth

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

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