Re:Constraints on the Universe as a Numerical Simulation (2012)
by aswanson on Saturday October 15, 2016 @01:00AM
(#12712787)
Suppose a "reality" where every observation of "addition" yielded unpredictable results. Would your confidence still be warranted?
Re:Constraints on the Universe as a Numerical Simulation (2012)
by dasil003 on Saturday October 15, 2016 @02:41AM
(#12713000)
There's no direct observation of addition, it's just a symbolic construct to model something we observe. I suppose a reality where such a model never made sense is possible, but it would be a very foreign environment that is completely outside the scope of our intuitive understanding. If it made sense only for a subset of the cases it does in our current understanding, then that would be the context in which it was discovered/understood.
Re:Constraints on the Universe as a Numerical Simulation (2012)
by baq on Saturday October 15, 2016 @09:44AM
(#12713890)
Addition is defined in such a way that the universe it's performed in doesn't matter (in fact, no universe is required at all), which is true for most if not all of formal mathematics. See set theory 101 for the very beginning on how's that possible.
I do not believe that to be true. While physics is heavily dependent on math, the reverse is not true.
> I can make 2 + 2 = 5 in a simulation.
No, I am fairly confident that you absolutely can not. You can make a simulation where putting 2 oranges in a box and adding two more oranges results in 5 oranges in the box (rather like putting together certain nucleons together into a nucleus results in a mass different than the sum of their individual masses). But in that simulation it would be a peculiar property of oranges, not a property of mathematics -- just as we don't claim addition is invalidated by the behavior of nucleon masses.