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> Is it possible that even our concept of numbers is similarly inspired.
>
> And so Number theory is as much a Physical theory as Euclidean
> geometry.
>
In a certain sense, I think you're right.
Counting physical objects seems very artificial, since no two objects can
ever be identical. Now, numbers can be identical, and you can easily say
that 1 = 7-6 = 10-9, etc etc, and that these separate things are if fact
identical because it can be proven - but all of this is abstract, and we
only use these numerals to signify something in our minds.
If you wanted 7 bananas, I'm not sure that you can ever have such a thing.
You need a fuzzy definition of "banana" in order to count individual
bananas, and I dont know if it is possible to create such a definition.
Say you want to count the population of humans on Earth. You need a
definition of "human". It's almost impossible to make such a definition.
Ape's and humans DNA is 95% identical !! Is a dwarf a human ? An embryo ? A
baby deformed by Thalidomide ? Is all of mankind a single organism, or a
collection of individuals ? It is quite possible that all living things are
just a single physical organism, seemingly separated, but only to be
rejoined later somewhere in the big family tree or elsewhere in the carbon
cycle as if it were a massive system of intertwined roots.Your definition,
in terms of words being used, it might start to get very long, and might
even be infinitely long. There may be an infinite number of things to take
into account when creating a fuzzy definition of a physical object, if so, a
complete definition might be impossible.
Or, you could look at it this way.
Consider 2 rocks, rock A and rock B. The most absolute and complete
definition of rock A is known as the "truth" about this object, and this
truth is obviously infinitely vast and cannot be known. Same goes for rock
B. Can you really consider the intersection of these two "truths" if they
are both infinitely vast quantities of information ? I think the question is
quite fascinating. You cant know the absolute truth about rock A, nor the
absolute truth about rock B, and so the intersection of these truths is also
beyond your reach.
This is quite different than adding numbers which are abstract and well
defined such as 1+1+1+1+1+1......
No two physical objects are identical, certainly not the way that numbers
are. But number theory is an excellent "model" of the physical world.
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