Hello,
I've been trying to extract things from Penrose's book, "The Road To
Reality". One passage that got to me was "Yet we may still ask whether
the real-number system is really 'correct' for the description of
physical reality at its deepest levels."
In my own naive way I thought in the past that real numbers had to
be part of reality because, for example, if you stretched a string
out across the hypotenuse of an isoceles right triangle, it would come,
as near as could be measured to be the square root of 2 times the
length of one of the sides, and I remembered from calculus 101 way
back when how, a step function could not be smoothed out. The function
x=y, if graphed out would look like the hypotenus of an isoceles right
triangle, and have a length that was the square root of 2 times x (or
y), but if it was a step function, even using very tiny steps so that
it 'looked' like it was a straight line, it would still have a length
of 2 * x (or 2 * y). So, it seemed to me that if the universe, even if
it was at a very miniscule level, was 'grainy', you would encounter this
step function kind of problem that would reveal itself. Apparently it's
still an open question.
One possibility that occurred to me after reading some of Penrose, is that
one could have 'right triangles' that were very close to being isoceles
right triangles in that two sides were very nearly equal, but not quite,
off just enough to form whole number sided triangles, the 3-4-5 right
triangle after all has two sides different by only '1'. I write a little
program to look for other examples, and got, for instance, a
10205-10212-14437 triangle. Penrose went on to mention various attempts,
including one he made many years ago, to come up with 'discrete' theories,
and I wondered if this would have been part of such theories.
Am I expressing myself in a way that's getting through? Does anybody out
there care to respond to this question about how the universe could be
discrete yet approach irrational values in every testable way?
Regards,
Carl Weidling
--
Alexander Pope wrote what oft was thought but ne'er so well express'd.
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