Chaos Theory
for Beginners
Hub
Quantum Mechanics
Chaos Theory
Scripture Theory
Introduction
Self-similarity
Kurt Gödel
Most deceitful thing
The Mandelbrot Set
The Household Set
Agape and Gravity
The number sequence
(a 4 part supplement)
 |
Summary | Hub | Contact | Book Reviews | Copyright | Author |  |
8. Self-Similarity
- Variety Makes All the Difference -
So, how does nature do it?
|
How does nature direct molecules into snow flakes, or crystals or any other regular form? Chaos Theory has an answer: Self Similarity, a fundamental principle that allows building blocks to mimic their own shape in the building they make. Remember this one, from chapter 2? |
Hold that thought (2b)
A large number of particles will display a pattern that is near equal to the initial possibilities of a single particle.
Self-similarity is a really big deal. It occurs all over nature and many have argued that self-similarity is one of the key natural principles that shape our world the way it is. Self-similarity has been observed in all fields of research: physics but also biology and even psychology and sociology. It also happens all over Scriptures and has been studied extensively, most often referred to as type-Theology. In the Book of Exodus for instance, Moses constructs the Tabernacle according to heavenly patterns he observed (Ex 25:40, Heb 8:5), making the tabernacle a self-similarity of something that exists on a different level of complexity, namely heaven.
No wonder that it is written:
I will open My mouth in parables; I will say things hidden from the foundation of the world.
- Matt 13:35.
Hold that thought (8a)
Self-similarity is the repetition of a shape, form or behavior on different levels of complexity. Not as an identical copy, but as a variation of the same basic shape.
And how do mathematicians do it?
| An image that displays self-similarity is usually called a fractal. One of the first works of Fractal Art was made in 1904 by a Swedish mathematician named Helge von Koch, and his piece was the so-called Koch Snow Flake. He took a triangle and added a similar but smaller triangle to each of the sides of the first one. Then he added smaller triangles to the sides of the second ones, again to the sides of the third ones, and so on at infinitum. |
 |
And that is more important than it seems. The big difference between God's snow flakes and Koch's snow flakes is that God's are all different while Koch's are all the same. Koch's Snow Flake is sterile while with God's flakes, variety makes all the difference. This is why no tree is alike, no mountain is alike, no human is alike. But there's more:
Koch's tiniest triangles are identical to the big triangle, but way down the line this concoction proves to be an impossible structure. It's an un-fractal since the tiniest triangles will lose their form and fuzz up. A sleek triangle like that will only occur in the minds of Koch and perhaps Plato, but not in nature. Nature produces snow flakes that are never the same because the large-scale phenomenon doesn't mimick the shape of the small-scale phenomenon, but the behavior : unpredictability, randomness and sovereignty. And Math has no way of generating randomness.
Randomness
Generating random numbers is somewhat of a sport among mathematicians. Because how does one program randomness? There's no way! And so they cheat. They take some kind of infinite number sequence (like the number pi) and tell a computer to select decimals at certain intervals (like every fourth digit, or seventh, or whatever). Pi is a number without inner structure and its digits are random (for as far as we know now), so out comes a random number sequence. But! this is not real randomness because any other smart computer could analyze the result and blow the whistle: This is not random random, this is pi random. And as the secret is out, the rest of the pseudo-random sequence can be predicted. If the second computer divides every outcome of the first by the way it generates the pseudo-random sequence, it would spew out 1 every cycle. That violates the prime definition of randomness, and the sequence is not random. True randomness can not be divided by something other than itself.And besides that, the decimals of the number pi go on forever. That means that if we try to express the relationship between diameter and circumference of a circle in numbers we need infinite detail to stay truthful. But infinite detail does not exist, and so we must yield to the rather shocking conclusion that the before mentioned relationship can not be expressed in numbers, and that pi is not a number at all!
The same goes for that other famous 'number' e, and all so-called transcendental numbers (numbers that go on forever after the dot; in other words, numbers that represent infinite detail). And to make matters worse, transcendental numbers out-number real numbers with an infinite factor.
It may seem a bit paradoxical but since mathematics can not release its detailed accuracy, it loses connection with the real world around quantum level.
Hold that thought (8b):
Since reality is fuzzy, accuracy is approximation.
Some say that the number sequence displays true randomness in its prime-number distribution. If you would like to see that idea debunked go to a series of 4 supplements, starting with:
If you don't care much about numbers, skip ahead to a formal decapitation of all logical systems:
Summary 8: Self-Similarity.
|
