This book bears an important message for any historians of mathematics who have ever attempted to read one of the late David Pingree’s brilliant and well-written scholarly articles on pre-modern science and found themselves unable to make head or tail of it: It’s not just you. Philip Davis, a colleague and friend of Pingree’s at Brown University for more than thirty years, offers a rambling, illuminating and thoroughly enjoyable bio/autobiographical and historical sketch setting Pingree’s immense erudition in its professional and intellectual context. Besides a string of amusing and intriguing anecdotes plentifully sprinkled with photos and sketches, this small volume supplies a valuable reminder of how complex, surprising and just plain strange the history of the exact sciences can be.
The “ancient loons” of the title are various historical figures that Davis learned about from Pingree in conversations and letters — most of them connected in some way with mathematics, astronomy or their sister disciplines of astrology, divination, magic and theology, and almost all of them peculiar, licentious, or outright reprehensible. Among the characters sketched in Davis’s short non-technical chapters are the ancient philosopher Pythagoras, whose rules for his sect of mathematician-mystics included not walking through bean fields if the plants were blossoming; the third-century Roman emperor Elagabalus, who in the intervals of his teenage libertinism apparently invented the party raffle; the anti-Catholic theologian John Napier, who devised a system of logarithms and wrote apocalyptic “End Times” literature about the Book of Revelation; the medieval Muslim astronomer and ethnographer al-Bīrūnī, the seventeenth-century astrologer Elias Ashmole, and St. Christopher the Dog-Faced. Intertwined through the vignettes of their exploits and misfortunes are anecdotes about present-day colleagues and others encountered in Davis’s investigations of the “loons” under Pingree’s sporadic jesting guidance.
These anecdotes often recount professorial quirks that may come across almost like Hollywood stereotypes of erudite dottiness. Book-lined offices so crammed with piled leather-bound Latin tomes and heaps of crumbling manuscripts that it’s difficult to walk through them and impossible to sit down in them (and yes, David Pingree’s offices were really like that). Bizarre collegial nicknames, both affectionate (“The Elephant” for the renowned Otto Neugebauer, founder of the Brown History of Mathematics Department; “The Owl” for his Assyriologist colleague Abraham Sachs) and disparaging (“Koppernickel” for Copernicus, whose scientific achievements Neugebauer considered overrated). Such eccentricities were not affectations but natural outgrowths of a shared delight in scholarship in all its profound and peculiar forms.
Nonetheless, readers who not unnaturally feel that they’ve got along fine so far without knowing anything about the seventeenth-century forged love letters of Cleopatra or early modern medical horoscopes may be initially somewhat put off by the unabashed loopiness of much of the subject matter. With so many of Euler’s mathematical papers still waiting to be translated, do we really need to devote precious time — or encourage our students and colleagues to devote theirs — to reading about Simon Forman’s astrological codes and the College of the Magi in Babylon? Davis and Pingree would both argue that such seeming trivia are not only fun in themselves but rewarding for the study of the history of mathematical sciences, and I think they have a point.
The American academic world, especially its science side, has long been gripped by profound tension about the idea of rationality vs. irrationality (in their non-mathematical sense). A couple of decades ago, a spate of books and articles bemoaned a wave of popular irrationalism that to many appeared to herald a new “Dark Ages”, in which pseudoscience and religious fundamentalism united in rejecting science, critical thinking, and civic secular empiricism. More recently, such forebodings have been overtaken by a newly fashionable militant and triumphalist anti-theistic “skepticism,” resentfully endured by American fundamentalists for the sake of its hostility to foreign fundamentalists. All these developments have deepened the modern scientific distrust of any worldview that seems insufficiently respectful of empiricism and rationality. Indifference to and ignorance of astrology, alchemy, theology and all other speculative models built on empirically barren premises are displayed with pride as badges of intellectual seriousness and hard-headed realism.
David Pingree remained quietly but firmly opposed to this comfortable puritanism as a willful and complacent distortion of history. As Davis remarks [p.29],
As a sideline to his interpretation of ancient texts, David made a deep study of human folly. He reveled in it. He knew of hundreds of oddballs in the bygone world, men whose lives had a component of folly… You and I — all of us — enjoy reading about such follies because you and I are, of course, quite sure of our own sanity and of the correctness of our ideas.
Pingree’s refusal to gloss over the importance of folly in the evolution of knowledge was part and parcel of his devotion to investigating primary sources. Reading the texts that scholars actually wrote makes it necessary to come to terms with how they actually thought, a task too easily avoided in the sanitized narratives provided by “encyclopedia or Internet write-ups” [p. 30].
It may be rather dismaying to acknowledge, for instance, that “in the 17th century, there was hardly any distinction between mathematics, physics, alchemy, astronomy, astrology, numerology, magic, theurgy, or Kabala” [p. 44]. But historically speaking, we can’t have Pythagorean number theory without Pythagorean mysticism, Ptolemy’s trigonometry without Ptolemy’s astrology, Newton’s mechanics without Newton’s alchemy, or even Euler’s calculus without Euler’s Calvinism. It’s questionable whether nurturing an aggressive disdain for irrational beliefs makes us more rational, but in any case it certainly will not make us better historians or better able to understand the history of our discipline. In his playful reminiscences, Davis makes a powerful case for seeking out and enjoying the “weirdoes” and “oddballs” who pop up everywhere in history, sometimes even in the persons of our most admired predecessors.
Kim Plofker is Assistant Professor of Mathematics at Union College in Schenectady, NY, and the author of Mathematics in India.