Redefining Reality - The Intellectual Implications of Modern Science

Abbott’s takes place on a two-dimensional plane. It is a
increasing diameter, then a circle of decreasing diameter, then
to convince the square of the existence of the third dimension
world into space above it.
Upon returning to Flatland, the square tries to convince his
arrested and charged with heresy by the high priest, and at his
trial, he is asked to provide evidence for the existence of the
third dimension.
The square’s argument is mathematical. If we can take a point
and move it, we get a line. If we take a line and move it parallel
to itself, we get a plane. If we take that plane and move it
parallel to itself, we get space. The priest asks for physical,
not mathematical, reasoning, but the square can provide none.
The priest then argues that there is no reason to think that this
mathematical talk is anything but trickery with no relation to
anything real.
The argument is compelling, although the reader knows it is
mathematics at the time—results that threatened to undermine
our certain basis for rationality.
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