There are many different ways of showing this fact (in fact, when I give exams in
a first-year course in topology, I ask students to show this in at least two ways).
One way to show that the unit interval cannot be mapped continuously onto a
solid square one unit on a side is to take one point out of the middle of each. Do-
ing so separates the unit interval into two distinct pieces; in the language of to-
pology, it is disconnected. However, removing a point from the middle of the
solid unit square still leaves an object that is connected; you can walk from any
point to another with your path still in the square without the point, like avoid-
ing a gopher hole in your back yard.
R. Dawkins, The Blind Watchmaker (New York: W. W. Norton, 1986). This is a
great book, but it touches on ideas that make some people nervous. Dawkins has
since become one of the leading spokesmen for atheism. Of course, that’s his
point—that evolution can occur without the direction of a creator. I think every-
one should read this book, as it will make you think, no matter what your point
of view.
