In Pursuit of the Gene

40 ¨ REVERSION TO THE MEAN
scale along the top, born to parents of the deviation, indicated along the
side (see the diagram). 40
As he sat waiting for the train, Galton noticed that numbers of the
same value formed a set of ellipses, all sharing the same center, and all of
the same basic shape. He described the moment in Memories: “The cases
were too few for certainty, but my eye, being accustomed to such things,
satisfied me that I was approaching the solution. More careful drawing
strongly corroborated the first impression.” 41 In addition to the hidden pattern
of nested ellipses, he picked out two critical lines—the lines he labeled
“locus of horizontal tangential points” and “locus of vertical tangential
points” on the diagram. The geometry of the picture made it clear to him
that the first of these lines was the by-then familiar regression of the adult
child on mid-parent height. It seemed to be a nearly miraculous confirmation
of more than a decade’s work. When he returned home, he made a
more careful graph and confirmed his first impression.
The entire afternoon must have had a strange déjà vu quality about it.
The last time he’d given serious attention to conic sections (ellipses) was
during the fall of his freshman year at Cambridge in 1839. At that time, he
had written home to his father and sister that he had never worked as hard.
However, conic sections had been difficult for him even then. He had not
managed to solve a single one of the practice problems provided by his
math tutor. 42
Forty-six years later, he went to the library of the Royal Institute in
London and ferreted out a book on analytic geometry. While struggling
with the equations for the conic sections, he was overcome by a familiar
sense of despair. As luck would have it, James Dewar, a Scottish chemist,
happened to be working in the library that day. “Why do you bother over
this?” Dewar asked upon learning of the Galton’s difficulties. “My brotherin-law,
J. Hamilton Dickson of Peterhouse, loves problems and wants new
ones. Send it to him.” 43 Dewar’s timely intervention seemed to release
Galton from his self-inflicted torture. He took up Dewar’s suggestion and
presented his data on stature to Dickson as an abstract problem in probability
theory. Dickson promptly returned a solution, including the exact formulas
of the nested ellipses and their tangent lines. Although Galton him-