Re: The Mathematical Universe
Perhaps the excitement surrounding Cellular Automata as being physically motivated is still a kind of grounded excitement. It may be reasonable in a final assessment, but for an entirely different reason than the reasons beaten to death in this 8-page discussion. Maybe Dave_O has discovered chaos theory in cellular automata. That's good progress, I would say.
There does exist the deep topic of platonism in mathematics. It's a topic worthy of book-length expository.
There does exist the topic of determinism in quantum mechanics. Another topic deep enough for book-length expository.
The topic of in-computability in math. Also could fill a whole book. No doubt.
There are (variously) topics of Mathematical Universe Hypothesis, the Simulation Hypothesis, and even Schmidhuber with his metaphysical idea that the universe we inhabit is computable. (The "computable universe hypothesis"?)
Perhaps what Dave_O is discovering about the world is not "World is math" but maybe he has, in his later years, stumbled upon what the rest of us have been calling Chaos Theory. Decades ago, the idea that the world around us operates on Chaos Theory was laughed away as crackpottery. (see the biography of Benoit Mandelbrot). But today, Chaos Theory is now universally understood to be a very accurate depiction of how our universe operates.
Completely deterministic, simple, local rules can give rise to extremely complex dynamics and very intricate temporal and spatial patterns. This happens when there is feedback among them coupled with sensitivity to initial conditions.
We have this idea that the intricacy and complexity of the forest floor ecosystem derives from the inherent noisiness of the real world. This can be countered with chaos theory :: that intricacy and noise could, in principle, arise from deterministic rules that are shockingly simple. So while from the level of macroscopic human scientists and their energy-limited measuring sticks, there could be an apparent randomness. And that apparent randomness could, in principle, be created by deterministic simple processes.
I thought that someone on this forum needed to say this. The principle idea is not bankrupt. Someone should have extended that much to Dave_O. No one yet has.
There is an entirely separate issue regarding determinism in quantum mechanics. The die-hards have been given free reign in this thread to shout that argument down everyone's throats. (forum regulars were variously insulted, told to "look up Bell's Inequalities" , deemed "research-impaired", told that they "don't understand probability" and other social misgraces).
But at the end of the day , quantum mechanics is severely limited in metaphysical scope. QM provides no coherent narrative about the world. The Interpretations of QM run the board. The Formalism of QM is barely more than a calculating device. The universe we inhabit follows the results of that calculating device with extreme precision. Nobody really knows why. Nobel prize winner in physics, Eugene Wigner didn't understand it either. The way in which the fundamental particles obey math , Wigner wrote "..borders on the mystical..." (end-quote). If you believe some guy on this forum understands this topic better than Eugene Wigner, I recommend you to turn the volume up on your skepticism.
But yes, Chaos Theory is a particular branch of mathematics. It should not be used as a synonym for "math" itself. Chaotic systems can give rise to noise that passes all statistical tests of randomness, even when the creator of the algorithm knows it is purely deterministic. One example would be block ciphers in cryptography. They must be deterministic because they must be reversed (decrypted) eventually. But the resulting ciphertext is unreadable noise.