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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