(This article originally appeared in Gilbert!, The Magazine of G.K. Chesterton.)
Reviewed by John Peterson
This is a writer who invites extremes of criticism. David Berlinski has his fans and his foes, but no one, it seems, is lukewarm.
His foes debate whether to tear his books to pieces before throwing them into the trash compactor. Several things inflame this wrath: his prose style (“cute,” “self-indulgent,” “silly,” and “dense”), his sudden and eccentric excursions into imaginative fiction, and his insistence on using mathematical symbols in discussions and proofs. Popular books on mathematics, these commentators think, should stick to plain English prose.
His fans praise his ability to explain the most difficult mathematical and logical ideas clearly and memorably. They like his style (“playful,” “witty,” “literate,” and “humorous”). They praise him for bringing difficult ideas to life in his brief historical vignettes of mathematical pioneers, and they admire his clear explanations of how these ideas have changed history.
The mystery of David Berlinski and his critics can easily be solved if we remember that he is a classroom teacher (of mathematical logic), and if we see him as one of those highly creative, bright, and quirky professors whom undergraduates love — or loathe. Berlinski’s teaching style permeates his books. And the books are best enjoyed if the reader will imagine himself in Berlinski’s classroom. No doubt the diagrams that appear throughout his pages were first rendered in chalk on a blackboard (or marker pen on a plastic panel).
Each of the three books reviewed here takes an idea — a crucial one in the history of mathematics — and explores its discovery, its meaning, and its influence. Newton is the most biographical book of the three; but, still, its focus is on the great scientist’s ideas more than his life story. Calculus is an attempt to bring some understanding of this difficult subject to those who dodged it or failed it in school. Algorithm does the same for the math and logic that drives our computers.
Of all writers on popular mathematics, Berlinski is uniquely worthy of respect for this reason: he does not mistake mathematics for reality. He is as much aware of the limitations of mathematical laws and systems as he is in awe of their beauty and power. Newton’s quest, he admits, has ended inconclusively. In Calculus he writes with regret that
The simple melancholy fact is that outside the charmed circle of those working on the current frontiers, no one believes any longer that physics or anything like physics is apt to provide contemplative human beings with a theoretical arch sustaining enough to provide a coherent system of thought and feeling.
Berlinski has some very big doubts.
His feisty essays in Commentary have caused something of a sensation. In February of 1998, his Was There a Big Bang? exposed the flimsy evidence and questionable mathematical logic supporting current theories of cosmology. Worse, his eleven-page article of June 1996, “The Deniable Darwin,” cast stones upon the most revered and untouchable of all the dogmas of modern science:
Unable to say what evolution has accomplished, biologists now find themselves unable to say whether evolution has accomplished it. This leaves evolutionary theory in the doubly damned position of having compromised the concepts needed to make sense of life — complexity, adaptation, design — while simultaneously conceding that the theory does little to explain them.
These are not the heresies of a bible-thumper or papist. While Berlinski’s writings do not tell his readers about his own personal religious beliefs (he may have none), it is crystal clear that his opinions and proofs are not based on any sort of ideology. His exposés are based on the systems of empirical logic used by science’s own theoreticians. Their logic is such that, says Berlinski, the claims now being made for modern systems like Darwin’s theory of evolution are “extravagant and silly.”
If Berlinski has no religion or philosophy of his own to offer us, that deficiency, sad to say, makes him the more creditable foe of scientism in the eyes of scientism’s gurus. That is what has caused the furor surrounding his writings. What Berlinski offers the God-fearing believer is his unremitting, clear-eyed honesty. That should be enough of a marvel to make his books worth looking into.