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.
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.
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:
- Ours is one of many universes, each one starting with a different set of “seed” values.
- Ours is of course perfectly designed for us to exist, and the other universes are also “coincidentally” perfect for whatever exists in them.
- 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.
- 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.Read More