Fractal within, fractal without

“Science cannot solve the ultimate mystery of science. And that is because, in the last analysis, we ourselves are a part of the mystery that we are trying to solve”

-          Max Plank

“I believe that scientific knowledge has fractal properties, that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex as the whole was to start with”

-          Isaac Asimov

This one might be a bit more technical and longer than usual, but there are important insights that I need to get off my chest for quite some time now and it just won’t work without a bit of physics, math, and geometry. But you may just glance over them and go on with the article. I will compensate you by adding multiple pictures.

Fractals are mathematical patterns that exhibit two interesting properties:

1. Self-similarity – they are composed of repeating shapes and motives that appear similar across the scales.

2. Recursion – each step in the fractal generation is fed back into its equation to generate the next step.

This gives fractals the ability to form very complex structures from very simple patterns and rules. That makes them very efficient.

For example, the famous Mandelbrot set has a simple equation of Zn+1 = Zn² + C, and you can see that every step Zn+1 is calculated by feeding the previous step Zn back into the equation. There are also a lot of fairly similar shapes found in the set. Note that they never repeat. The simple equation of the Mandelbrot set contains infinite complexity.

Arguably, fractals are the only way the human mind can grasp infinity and also the only way infinity can be implemented in reality – not as a thing, but as a process – a computation.

In my view, the very nature of existence is fractal and I hope that in this article, I will sell the idea to you too.

First of all, the very laws of physics themselves are self-similar. The concept of scale invariance refers to the idea that certain physical laws and phenomena remain unchanged when viewed at different scales. For example, the laws of thermodynamics, which govern the behavior of energy and matter, are thought to be scale-invariant, meaning that they apply at all scales, from the microscopic to the cosmic. Both the classical and quantum field theories also have scale invariance.

Another way in which reality and the laws of physics can be seen as having fractal nature is through the concept of the holographic principle, which suggests that the universe is like a holographic projection, in which the information that makes up the universe is encoded in the surface of a boundary, such as the cosmic event horizon or the boundary of a black hole. Consider surface encoding as an equation that defines the fractal and the world we live in as a pattern generated from it. There are suggestions that even the brain works like that.

The third way is via Schrodinger’s equation, which is basically a sine wave or layers thereof. And there is Schrodinger’s equation for (literally) everything. Hence, all of reality as far as we know it, the entirety of the standard model of physics, is based on very self-similar stacked sine waves.

It is all vibrations, man.

No wonder that the universe built on fractal laws exhibits a fractal nature.

There is a universality of fractals – whether in the omnipresence of the Fibonacci sequence, the golden ratio or spiral galaxies… or shells. It seems that fractals are indeed very efficient systems of organization. They are also projected in man-made objects like cities, the internet, or railroad systems.

And once you run the universal fractal long enough, it starts to model itself – the large scale on the small scale – that’s how self-reflective consciousness comes about from our ability to model the world around us. And given the self-similar nature of fractals, is this really any surprise?

No wonder scientists see the similarities between brains and the universe. Or neural nets for that matter. Yeah, the net is a nice metaphor here, as we shall see.

Are you familiar with Indra’s net parable?

Francis H. Cook describes Indra's net thus:

Far away in the heavenly abode of the great god Indra, there is a wonderful net which has been hung by some cunning artificer in such a manner that it stretches out infinitely in all directions. In accordance with the extravagant tastes of deities, the artificer has hung a single glittering jewel in each "eye" of the net, and since the net itself is infinite in dimension, the jewels are infinite in number. There hang the jewels, glittering "like" stars in the first magnitude, a wonderful sight to behold. If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so that there is an infinite reflecting process occurring.

-          Francis H. Cook, Hua-Yen Buddhism: The Jewel Net of Indra

The question is – how did the Buddhist monks grasp the recursive, scale-invariant, holographical fractal nature of our universe in the concept of Indra’s net without knowing any of these concepts? Or much of physics, really. How come hermetic sages knew that everything is frequency, movement, and mental vibration – as in wave function - without any knowledge of quantum mechanics?

A lucky guess? Can you really guess something like this and on multiple occasions to boot?

I guess – and wager – that it is because self-knowledge is universal knowledge. It is because “as within, so without”. Through deep introspection and meditation, you can derive truths about the universe. How could you not? The code of the universal pattern is holographically reflected within you. You are the universe. It is the very stuff you are made of. You are the very same fractal pattern that constitutes the entirety of existence.

The trick was always there. To look for the truth you have to look inside and realize, that what is doing the looking is exactly what you are looking for. And looking at, for that matter.

Reality is a living mind that is learning. For are you not reality? Are you not mind? Are you not learning?

The answer is, that there is no outside world in the strict sense. Or rather, you and the outside are one continuous thing. And as was mentioned at other places herein, the nature of reality is fractal. A recursive computation.

If you study anything within the universe hard enough, you will be able to observe the projections of the same underlying laws no matter where you look. Introspection is as valid as anything else. Maybe even more so for it gives you direct access to the first-hand experience of it.

Scientists looked into smaller and smaller components of reality until they, in a glorious, fractal, and tautological fashion found themselves looking back. Monks looked inside themselves and were astonished to find the universe. The observer and the observed are not only inseparable, but they are also one and there is nothing else.

If you look deep inside yourself you will find the universe looking back at you. If you look deep into the universe you will find yourself reflected back at you.

Nature is self-similar across scales. A fractal holographic computation.

If you know about other instances of the fractal nature of existence I’m missing here, please let me know ;)