Wondering if this is mathematically feasible.
Human/animal emotions, the ability to think, free will, etc
Not sure if there's anything else.
Can't emotions be deconstructed into biological functions of the brain, though -- a set of atoms and their intrinsic properties?
If we got all of the atoms and other particles in your body, all particles have the exact same spin and other properties as you have, and we put them all together in the same shape as your body, the same blood pressure etc... gave it the right amount of electric shock,... you think that person would come to life?
I think not. I think there is something else - and I believe it is consciousness (but I might technically be wrong if I have misunderstood what consciousness is).
I don't want to turn this into a philosophy discussion, since consciousness can still be modeled as a physical function of the brain.
I'm just wondering if there is any physical component of reality that can't just be modeled as a function of atoms. Can quantum randomness be modeled as such?
I would rather ask if there is anything non-trivial, which may be modelled as set (it means: not going beyond set theory).
If you insist, that 'model as a set' may be supplemented by other theories, then, of course, you may model flight to the Moon, as a 'set of one rocket' carrying a 'set of three men', following other theories such, that finally N.Armstrong could made a one element set consinsting of a 'one small step'.
No, randomness and stuff uses the normal (Gaussian) distribution from stats.
The maths behind quantum mechanics is vast, and hundreds of maths books have been written for it.
Basically, to answer your question, maths has a huge number of topics, and there are hundreds, if not thousands of important results and theorems which are far more generalised than what we see around us in the world today. From experience, there is nothing that can't be explained by maths.
However, there is no fundemental theory in physics, and we are always finding out new things in maths - i.e. math's is not "complete" (and it never will be) and so we are unable to properly assess whether or not everything in the universe can be explained by mathematical theorems.
I think accurate modeling is mostly limited to proofs. We can get close with theories, but if the model is 100% accurate, the the theory it is based on becomes a proof. Maybe a different question is, What can we model correctly? and how good is good enough?
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