which is the study of human social behavior. His treatise, Plan of Scien-
tific Studies Necessary for the Reorganization of Society, outlined his phi-
losophy of positivism. Part of this philosophy can be expressed in terms
of the relation between theory and observation—as Comte put it, “If it is
true that every theory must be based upon observed facts, it is equally
true that facts can not be observed without the guidance of some theory.
Without such guidance, our facts would be desultory and fruitless; we
could not retain them: for the most part we could not even perceive
them.”^1
Simon Newcomb made significant contributions to astronomy and
mathematics. He was a computer—in the days when this described a job
occupation rather than an electronic device—and oversaw a program that
revised the calculation of the positions of the astronomical bodies. He
helped Albert Michelson calculate the speed of light, and also helped re-
fine the calculation of the amusingly named Chandler wobble, the change
of spin of Earth around its axis. Newcomb did not confine himself to the
physical sciences; his Principles of Political Economy (1885) was praised by
the famed economist John Maynard Keynes as “one of those original
works which a fresh scientific mind, not perverted by having read too
much of the orthodox stuff, is able to produce from time to time in a half-
formed subject like economics.”^2 High praise, indeed, from one of the
leading economists of the twentieth century. To cap a distinguished ca-
reer, Newcomb was buried in Arlington National Cemetery, and Presi-
dent Taft attended the funeral.
Obviously, both these individuals were among the leading intellectuals
of their times—but they are both known for making predictions that
would make the all-time Top 100 list under the heading of “Predictions
You Wish You Hadn’t Made—At Least, Quite So Publicly.” Comte wrote a
philosophical treatise examining things that would never be known, in-
cluding in his list the chemical composition of the stars. Several years
later, Robert Bunsen and Gustav Kirchhoff discovered spectroscopy, and
the analysis of the spectrum of light emitted by stars permitted their
chemical composition to be deduced. Newcomb was interested in powered
f light, but did calculations—later shown to be erroneous—that convinced
him that such was impossible without the development of new methods of
propulsion and much stronger materials. A few years later, Orville and
Wilbur Wright achieved powered f light with not much more than a
wooden frame, wires for control, and an internal-combustion engine.
As Niels Bohr so wryly observed, “Prediction is difficult—especially of
the future.”^3 Predicting what can or cannot be known in the area of math-
ematics is also difficult, but since most such predictions involve fairly ar-
30 How Math Explains the World