This is going to be as deep as it can get; at the borderline of philosophy and mathematics. Let’s start by laying the ground work. Watch this AMAZING lecture by Jordan Peterson esp. from 16:00 on in which he explains the concept of Yin and Yang, “Chaos” vs. “Order” as understood in Taoism.
Jordan Peterson: Reality and the Sacred
56 min, 2013
Now. Peterson explains that at the border between order and chaos the INTERESTING thing happens, which generally means, turning chaos into order or destroying order and making chaos. The latter process is usually the inevitable increase of entropy via the 2nd law of Thermodynamics a.k.a. the dying of the universe.
Peterson is a psychologist, sociologist, philosopher, and as such he uses a slightly different terminology than mathematicians, signal processing experts and computer scientists. So let me redefine using CHAOS in the sense that mathematics, or, the sub discipline CHAOS THEORY uses it.
In this definition: ORDER is static, nothing UNEXPECTED happens, things are orderly. Think of it as stasis, a crystalline form. Things that do happen here are PERIODIC and PREDICTABLE. Like a sine wave oscillation or a motor humming along with desired constant RPM. Periodic processes have a MEMORY, a STATE: an oscillation is a function that translates a state into a follow-up state in predictable ways, after n steps a cycle is complete, the state machines are big cycles of states. Every period is like the one before.
The opposite is NOISE: The Taoists call it Chaos but we use the technical term noise here. Noise is memoryless, unpredictable, constant in its statistic properties (in other words, we can average many samples and get repeatable predictable results, but we cannot predict one sample ahead.) Noise is created everywhere all the time by Brownian motion of particles – or at least that’s what we know currently.
The border between ORDER and NOISE is CHAOS as used in Chaos Theory definition. A chaotic process is a quasi-periodic process; it can look like a perfectly periodic predictable oscillation for a while yet somehow you never quite get the prediction right and the further into the future you try to predict the worse your prediction gets: The error of your prediction to the chaotic process you try to predict grows exponentially over time. After a while the chaotic process can completely change its behaviour – switching into a different ergodic orbit, suddenly having different statistic properties.
These chaotic processes require several preconditions:
- they must have a memory, like the clean ORDERly oscillations.
- they must have an internal amplification of the state variables, so tiny deviations get systematically amplified over time. (Lorenz, the father of chaos theory, used the metaphor of the wings of a butterfly in China leading to a Hurricane on the other side of the world within two weeks)
- they must be nonlinear. This is necessary to be able to shift energy from one part of the spectrum to other parts – from low to high frequencies and vice versa. Linear systems cannot do this (A sine wave oscillator would be a linear system for instance.)
- The difference between a linear and a nonlinear system with memory is very well demonstrated by electric guitars; the non-distorted guitar as used in the 1950ies and 60ies is the linear system with a pure and very sinoid waveform; the distorted guitar used since the 60ies adds nonlinearity. This shifts energy to higher frequencies, into the overtones. The string of the guitar in itself is an oscillator with a memory and feedback; now add a fuzzbox distorter and a guitar amplifier and have the guitarist use the sound from the amplifier to feed back into the string and you get the preconditions for a chaotic system. The result could be sounds like Jimi Hendrix made popular.
So we can say that Jimi Hendrix operated on the border between ORDER and NOISE: He used a CHAOTIC system to produce an amazingly rich texture of sound.
He also uses a Wha-Wha here; a resonant band pass filter which is another memory process.
And that’s where the action is: the CREATION process is using CHAOTIC systems to turn NOISE into ORDER; and we are far less impressed by ORDER itself than by watching the creation process in action. We are creation engines; the engineers of creation. Is it a coincidence that we have a consciousness then? No. It is the precondition for engineering creation.
This means that CREATION follows from CONSCIOUSNESS, not the other way round.
Closing for now, a flythrough through the Mandelbrot set – the most famous chaotic equation. Notice the complexity of the border between the BLACK NOTHINGNESS of the inner set and the outer area: the blackness is perfect ORDER or stasis.