On 12 Dec 2012, at 17:00, Jason Resch wrote:


One of the questions in mathematics is where does mathematical truth come from, if it exists platonically, how does it manifest physically (e.g. as the utterances of mathematicians).

I could explain, but it can be long, that it is impossible to explain where the natural numbers come from, or where the Fortran programs come from, of were the GoL comes from.

Now if you assume the natural numbers, and the + and x laws, then I can prove the existence of the Fortran programs, and of GoL, etc.

if you assume GoL, I can prove the existence of the numbers, etc.

So the numbers, or anything Turing equivalent are mysterious. It is the least that we have to assume to get anything capable of supporting a computer, or a brain.

But once we assume the numbers, then we can explain why they will eventually develop a mathematics (and physics) much richer than the numbers (including many infinities).

Above arithmetic, the mathematics (and physics) are just number mind tools to simplify their lives when the relation with other (universal) numbers get too much complex, a bit like the complex Riemann Zeta function is a tool for making simpler the relation between the prime numbers and the study of their distribution.

I had a thought inspired by one of Roger's posts regarding cause and effect extending outside of spacetime. I thought, there is nothing preventing the goings on in this universe from having causal implications outside our universe. Consider that an advanced civilization might choose to simulate our universe and inspect it. Then when they observe what happens in our universe the observations generate causal effects in their own universe. The same applies to our universe, we might choose to observe another universe through simulation, and our discoveries or observations of that other universe change us. Thus, the various universes that can exist out there are more interconnected than we might suppose. Our universe is an open book to those universes possessing sufficient computational power to simulate it. Likewise, how simple universes like certain small instances of the game of life are open books to us. The possibilities of gliders in the GoL has led to many discussions about GoL gliders, their existence in the GoL universe has led to the manifestation of physical changes in our own universe.

I think the entrance of mathematical truth to our own universe is no different. Mathematicians have used their minds to simulate objects and structures that exist in other universes, in a sense they observe them, and then those mathematicians report their observations and discoveries concerning those objects, just as an advanced civilization might report discoveries about our universe, or we might report discoveries about the GoL universe. Thus the structures and objects which exist in other universes have directly changed the course of the evolution of our own.

This explanation seems to assume universe(s) and observers, but with the CTM, we know we don't need to assume them, nor can we really use them to relate consciousness and matter. This should follow form the uda reasoning, normally. Apart from this, mathematics looks indeed like exploration of mathematical realities, but the physical reality is not one mathematical structure among others, it is a mathematical structure summing all the other mathematical structure, in some way, and in arithmetic.



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