Michele Dondi said:
Probably not; the evidence seems to be leaning the other way. It's very
hard to say and perhaps will always lie, with most cosmology, in the
realm of faith. I certainly prefer discrete models.
This is among the earliest philosophical questions to be raised.
Democritus and Leucippus advocated a theory of indivisible /atoma/; the
discovery of subatomic particles has done nothing to upset this
position. Plato and Aristotle argued for infinite divisibility of the
universe: a continuum. Well, Aristotle also argued for heavier objects
falling faster.
My mother was a combinatorialist, so blame her if you like for my atomic
orientation. I'd venture that programmers in general side with atomists;
our tools are digital so we tend to believe in quanta. Perhaps if analog
computers had turned out to be cheap, compact, and reliable, we would
lean to a continuum.
The general public today seems to stand in the camp of the atomists. My
students often demand to know the "real", true value of pi; they are
unsatisfied with all explanations. It is said that the irrationality of
the diagonal of a unit square was a scandal and a guarded secret of the
Pythagoreans.
When I was young, I was such a stubborn atomist that I remarked to an
engineer my senior that I had no interest in electronics outside of
digital logic. Our project was an early CCD camera -- which, despite
such things being called "digital cameras" today, demand quite a bit of
analog TLC. I swaggered with a belly full of boolean truth. The senior
man said, "You'd better branch out. It's an analog world." It took me
years to believe him but I did eventually delve into transistor and
op-amp theory. Now, I'm one of a dwindling number of San Jose residents
who are willing to do small analog projects for clients.
I say all this to show that I see both sides of the issue. I think any
given problem may be best approached with a flexible blend of views. I
don't believe that any fixed rule or orientation makes for the best
solution.
We've all heard the story of the IBM interview question: "Why are
manhole covers round?" I first heard it from my father, who failed to
land the job. When I ask it -- as I often do -- of my students, I'm
often surprised by how many just can't wrap their brains around the
basic requirement: to come up with a large number of inventive, perhaps
conflicting explanations. They fixate on the need -- expressly
disclaimed -- to discover the one "right" answer.