Is there randomness and chaos in our world at a fundamental level, or is it still just the degree of our ignorance?

 From a birds’ eye point of view, which is the view from a mathematical - philosophical - point of view, chaos is absolutely deterministic while at lower level points of view, or physical point of view, chaos appears haphazard.

The above shows a point that has “escaped” from the Mandelbrot set.

The position of the point gives the appearance of escape although it deterministically occurred at iteration number 1019. This can be described as a deterministic escape.

We do have mathematical theories on chaos that can describe chaos as a deterministic phenomenon. The study is called dynamical system. The equations of dynamical systems are non-linear and many are impossible to solve. What this means is that the domain of manifestations will appear haphazard.

Here’s a simple exercise: Play the pinball machine. Are the motions of a pinball machine deterministic?

https://plays.org/game/pinball/

More about that here:

https://www.researchgate.net/publication/267386121_THE_PINBALL_MACHINE_AS_HYBRID_SYSTEMS_CONTROL_PROBLEM

From a philosophical -mathematical - point of view, chaos is absolutely deterministic. This is because the laws of nature conforms to the mathematics of dynamical systems.

It’s physical manifestations however is a different story. The effects of initial conditions on a system can appear unpredictable.

A system is chaotic if its trajectory through state space is sensitively dependent on the initial conditions, that is, if unobservably small causes can produce large effects. Some people call it the butterfly effect.

Resonance play a big role in natural phenomena. Wind, waves, earthquakes and population growth.conform to mathematical power laws in nature as does the configuration of galaxies, whirlpools, flowers, and trees, the former to exponential laws and the latter to logarithmic laws.

Exponents and logarithms are two sides of the same coin. However, they face opposite to each other. An understanding of this aspect of nature is of utmost importance. A face is two dimensional in nature.

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