Certain philosophers of ancient Greece—Democritus for one—were
fascinated by the question: _what is matter?_ You can imagine one of the
philosophers saying to his pupils:
“Gentlemen, let us consider a piece of cheese. With a knife we can cut
it in two, thus obtaining smaller pieces. We can then cut one of these
smaller pieces in two, obtaining still smaller pieces. We can _think_
about repeating this process over and over to get smaller and smaller
pieces of cheese. Now can this process be continued without limit, or
will a time come when we arrive at the smallest possible piece of
cheese? In other words, is there a piece so small that we must have at
least that much or none, with no choice in between?”
It is probable that most people who thought about this question at all
during the next two thousand years answered the last question in the
negative. The prevailing notion was that matter was continuous, with no
theoretical limit as to how small a piece of cheese, or anything else,
might be.
This concept was humorously expressed by the British mathematician
Augustus De Morgan (1806-1871) in these lines:
_Great fleas have little fleas upon their backs to bite ’em,
And little fleas have lesser fleas, and so, ad infinitum._