Ontological Wallop

The structure of the world is shot through with a sublimity so sublime that it simply had to exist. …

The sublimity that had to burst into existence is not one that particularly concerns itself with us. Such a human-centered goodness would not pack the ontological wallop required to bring forth existence. (Plato at the Googleplex, pages 385-389.)

I like that phrase “the ontological wallop required to bring forth existence.” I’ll return to it in a moment. First, let’s look at a pretty picture.

Mandelbrot Satellite Bug

The area colored black is the Mandelbrot set, a set of numbers whose graph is infinitely intricate, meaning that you can zoom in to any depth and it never smooths out. (As a bonus, the “bug” shape keeps recurring, with variations, at every scale.)

Amazingly, the Mandelbrot set is generated by a very simple mathematical formula applied over and over. The details are here, but for this post the important points are these:

  • Humans did not invent the Mandelbrot set; they discovered it. The set has always existed, just as much as the number pi always existed before people figured it out. (Take a moment to decide whether you agree with this. It’s important for what follows.)
  • A very simple formula with an iterative procedure generates the set.

You could state the formula for the Mandelbrot set, or you could list all the numbers in set itself, and you would be saying the same thing. To state the formula is just a compact way of stating the set.

Although the Mandelbrot formula is not a machine, we say that it “generates” the Mandelbrot set. However, the formula only goes so far. It generates the set of numbers, but not a graph of the numbers. The graph requires someone to draw it and the Mandelbrot formula does not “generate” that person, let alone the graph. It does not have that much ontological wallop.

Nevertheless, the set and its formula have always existed. We have discovered them, but nobody created them. It’s like the number pi. Pi has always existed, as has the fact that pi can be generated by dividing a circle’s circumference by its diameter, or by this formula:

Taylor Series for Pi

Now let’s shift gears.

We have discovered that the universe is, as far as we know, completely describable in math. The laws of physics, therefore chemistry, therefore biology, could have been based on something else (justice?) but they are not. They are math.

In fact, the more we learn, the more we suspect that all laws of nature are just facets of a single law: a mathematical formula that is a Theory of Everything.

We said that the Mandelbrot formula and the Mandelbrot set were two ways of referring to the same thing. Would the formula for the Theory of Everything and the universe it “generates” be likewise identical?

In other words, would the formula be just as real as the results, and vice versa?

That is not as outlandish as it sounds. As reported in Science News, “Today some experts believe that the quantum formula describing atomic phenomena is not simply a mathematical tool, but is just as real as atoms are. That formula is known as … the wave function (*).” It describes in a very precise and mathematical way how each particle of the universe behaves over time.

The quantum wave function is so utterly complete that scientists are left asking, “What else is there?” Maybe this formula is all there is. Maybe what we call particles are just convenient ways of talking about the results of this formula.

The quantum wave function is like a Mandelbrot function that also generates someone to draw the graph, then the graph itself, then people looking at the graph, then someone writing about people looking at the graph, and finally someone (you) reading about it.

If the Mandelbrot function has the power to bring forth the infinitely complex Mandelbrot set, why can’t we say that the quantum wave function has the power to bring forth its set of results … which just happen to be the entire universe?

And if the quantum wave function has always existed (which it has, just as much as the Mandelbrot or any other function), do we need any other explanation for the origin of the universe?

And if there are other functions with that much ontological wallop, would they generate very different universes of their own?

I don’t know, but it’s fun to think about.

(*) – The quantum wave function is probably not be the final answer, the Theory of Everything, but it is tantalizingly close.

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