ARE NUMBERS REAL?

The emphasis is on “real” in the latest by the prolific British science writer, who questions the extent to which mathematics truly reflects the workings of nature.

Clegg (Ten Billion Tomorrows: How Science Fiction Technology Became Reality and Shapes the Future, 2015, etc.) has a degree in physics from Cambridge, and he uses that knowledge to discourse on the relationship between math and science. Math builds its own universe based on given (i.e., not proven) axioms and rules of operation to derive facts (theorems) that are true in that system. Science, on the other hand, builds theories based on observations and experiments, and the theories become conventional wisdom until questioned by new observations and data. Nevertheless, over time, there has been an eerie congruence between abstruse developments in math—e.g., non-Euclidean geometry—and the equations that govern Einstein’s theory of general relativity. Clegg suggests that math increasingly has come to rule the roost in physics. Nobody has ever seen a black hole he notes; the objects are “more the product of mathematics than of science,” the evidence for their existence being indirect. Likewise the Higgs boson and superstring theory. The author urges caution and a step back rather than obedience to a questionable math authority. Before reaching this conclusion, Clegg treats readers to an orderly history of math. He begins with counting on fingers or marks on sticks to match the amount of a physical object, leading to symbols for numbers. These numbers are really real, he says, because they are based on matches with objects in nature. But as math evolved, that connection blurred. By the 19th century, with set theory and concepts of orders of infinity, and 20th-century proofs on the incompleteness of mathematical systems and other logical conundrums, the relation to reality has faded—as will some readers’ attention, because this is not easy stuff.

Solid as a straightforward chronology of how mathematics has developed over time, and the author adds a provocative note urging scientists to keep it in its place.