whatever holds for one set must also hold for the other. Magicians are apt
to assign magic properties to many of the words and symbols which they are
in the habit of using, and scientists are constantly confusing objective
things with the subjective formulas for them. After the physicist has set
up correspondences between physical facts and mathematical formulas, the
"interpretation" of these formulas is his most important and difficult
task.




*3.* In mathematics, effort is constantly being made to set up one-to-one
correspondences between simple notions and more complicated ones, or
between the well-explored fields of research and fields less known. Thus,
by means of the mechanism employed in analytic geometry, algebraic
theorems are made to yield geometric ones, and vice versa. In geometry we
get at the properties of the conic sections by means of the properties of
the straight line, and cubic surfaces are studied by means of the plane.




[Figure 1]

FIG. 1


[Figure 2]

FIG. 2