Food For Thought. 😉 Stephen Wolfram, a computer scientist, physicist, and entre

Food For Thought. 😉

Stephen Wolfram, a computer scientist, physicist, and entrepreneur, uses the terms “mathematical reducibility” and “computational irreducibility” in the context of his work on cellular automata and his broader philosophical framework known as “A New Kind of Science”.

Mathematical Reducibility: In the context of Wolfram’s work, mathematical reducibility refers to the idea that certain systems or patterns can be simplified or reduced using mathematical equations or formulas. For example, in classical physics, the motion of a pendulum can be described by a simple mathematical equation. This means that we can predict the future state of the system without having to observe every intermediate state.

Mathematical Formula: ( … )

Computational Algorithm ( … )

Computational Discoverability ( … )
One algorithm

Computational Adversarial Simulation ( … )
Competing algorithms

Causal Density and Externality: ( … )

Computational Reducibility ( vs Mathematical Reducibility). ( … )

Computational Irreducibility: This is a concept that Wolfram introduced to describe systems that cannot be simplified in the way that mathematically reducible systems can. In a computationally irreducible system, the only way to determine the future state of the system is to essentially simulate each step. There’s no “shortcut” in the form of a simple mathematical equation. Many of the systems that Wolfram studies, such as cellular automata, exhibit this property of computational irreducibility.

Wolfram’s idea of computational irreducibility is closely related to the concept of undecidability in computer science and the halting problem described by Alan Turing. It has profound implications for our understanding of complex systems, including physical systems, biological systems, and even the universe itself, according to Wolfram’s theories