On 12/12/2012 3:37 PM, Jason Resch wrote:



On Wed, Dec 12, 2012 at 4:45 PM, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:

    On 12/12/2012 8:00 AM, Jason Resch wrote:

        All,

        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 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.


    Except the simulation of the other universe is in this universe and the 
existence of
    that 'other universe' being simulated is just an assumption.


Even the existence of our own universe, we must admit, is an assumption.

     So it boils down to assumptions made in this universe can have 
consequences in this
    universe.


I see your point, someone in this universe at least needs to have the idea about a possible other universe out there, before building a simulation of it, but we could just as well iterate over all the natural numbers, and map each number to a string of letters, and any such strings of letters which describe how to setup a simulation could be run, so it doesn't really take any creativity at all, like the UD, it can be entirely automated. Thus in just starting from 0 .. infinity, we can iterate over all possible digital simulations, and spend eternity exploring them and learning things about them.

I would also add, the existence of glider guns (and even Turing machines) in the GoL universe is not immediately clear from the assumptions of the rules that define the GoL universe. When they were discovered, is it more appropriate to say "they were discovered in our starting assumptions" or "they were discovered a GoL universe"?


    Simulating other universes which are anything like ours is impossible 
anyway because
    it is impossible to gather the necessary information to initialize the 
simulation.
     There are events out beyond our past light cone that we cannot know about 
now, but
    which will affect us in the future.


Well once you have identified the volume and length of time you wish to run the simulation for, you can fill out the X number of light years beyond that volume just so you don't get any surprises.

Then you *will* get a surprise when a gamma ray burster hits from that volume you assumed empty. :-)

E.g., to simulate our solar system over the next 5 years, simulate 5 light years around our solar system.

But the orbits are chaotic so you need arbitrarily high precision (or a quantum theory of gravity) to simulate arbitrarily long periods.

Or if our universes is folded in on itself, it has a non-infinite volume, which could serve as a boundary for the simulation.

Yeah, but what's on that boundary?  And how could anyone find out?

Brent

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