weights increased from left to right in each row, and from top to bottom
in each column.
When Mendeleyev began his work, not all the elements were known. As
a result, there were occasional gaps in the periodic table—places where
Mendeleyev would have expected an element with a particular atomic
weight and chemical properties to be, but no such element was known to
exist. With supreme confidence, Mendeleyev predicted the future discov-
ery of three such elements, giving their approximate atomic weights and
chemical properties even before their existence could be substantiated.
His most famous prediction involved an element that Mendeleyev called
eka-silicon. Located between silicon and tin in one of his columns, Men-
deleyev predicted that it would be a metal with properties resembling
those of silicon and tin. Further, he made several quantifiable predic-
tions: its weight would be 5.5 times heavier than water, its oxide would be
4.7 times heavier than water, and so on. When eka-silicon (later called
germanium) was discovered some twenty years later, Mendeleyev’s pre-
dictions were right on the money.
While this may be the most notable success of discovering an arrange-
ment to which the real world conformed in part, and then attempting to
discover aspects of the real world that conformed to other parts of the ar-
rangement, this story has been frequently repeated in physics.
The Garden of Negative Width
One of the most famous of these examples occurred when Paul Dirac pub-
lished an equation in 1928 describing the behavior of an electron moving
in an arbitrary electromagnetic field. The solutions to Dirac’s equation oc-
curred in pairs, somewhat analogous to the way that the complex roots of
a quadratic ax^2 bxc whose discriminant b^2 4 ac is negative occur in
complex conjugate pairs, having the form uiv and uiv. Any solution in
which the particle had positive energy had a counterpart in a solution
in which the particle had negative energy—an idea almost as puzzling as
a garden whose width is negative. Dirac realized that this could corre-
spond to an electron-like particle whose charge was positive (the charge
on an electron is negative), an idea initially greeted with considerable
skepticism. The great Russian physicist Pyotr Kapitsa attended weekly
seminars with Dirac. No matter what the topic of the seminar, at its end
Kapitsa would turn to Dirac and say, “Paul, where is the antielectron?”^1
The last laugh, however, was to be Dirac’s. In 1932, the American physi-
cist Carl Anderson discovered the antielectron (which was renamed the
positron) in an experiment involving the tracks left by cosmic rays in a
Space and Time: Is That All There Is? 135