A fingerpost is a directional sign, shaped like a finger, pointing the direction to go. To Francis Bacon, a fingerpost was a piece of evidence that excludes all but one possibility.
An Instance of the Fingerpost is a murder mystery, set in Oxford in the 1660's, shortly after the death of Cromwell and the restoration of the Monarchy. It is written in four sections, each in the first person, and each from the point of view of a different character. The first two characters are fictional, Marco da Cola and Jack Prescott, but the last two are actual historical figures, John Wallis and Anthony Wood. The book is of particular interest to mathematicians because of the central role of mathematician and cryptographer John Wallis.
The real, historical John Wallis, you may recall, barely missed discovering Calculus. He was adept at manipulating infinite products and infinite sums, and could calculate areas algebraically. Several of Isaac Newton's great insights came to him when he was studying the works of Wallis. Wallis was also an expert cryptographer, and the author exploits this aspect of Wallis' talents to its fullest in building an intriguing work of historical fiction.
At one point in Wallis' narrative, he mentions Newton's statement "If I have seen farther than others, it is because I have stood on the shoulders of giants." The real Wallis had died when Newton wrote this, but the fictional Wallis, regarding Newton as an immature upstart, grumps that "a dwarf standing on the shoulders of a giant may see farther than a giant himself." What arrogance to call Newton a mathematical dwarf!
The author gives us a fascinating representation of academic life in the late 1600's, the time when Calculus was being discovered. Universities were not so much places of learning as places of politics, where people vied for juicy lifetime appointments to positions that required little or no work. Nevertheless, great science was being done, and the work of Boyle with his vacuum pump plays an important role in the plot of this novel. The characters are entirely oblivious to the flagrant prejudices they display, prejudices of religion, of science and of philosophy. It is simply beyond the scope of scholarly discourse of the time to discuss those prejudices. It makes a modern reader wonder how our beliefs will be viewed in three hundred years. Some readers will find the accurate representation of those prejudices to be the best feature of the book.
For example, one of the key events in the novel is the invention of blood transfusion. Everyone involved believes that a blood transfusion transfers some kind of vital spirit from the donor to the recipient and that if the donor dies then the vitality of that spirit will be destroyed and the recipient will die at the same instant. It is a logical consequence of the science of the day, and everyone accepts it as true.
As a murder mystery, An Instance of the Fingerpost is pretty good. In good murder mystery form, it is a surprise who the killer is, yet, in retrospect, it was almost obvious all along. The clues are like fingerposts. On the other hand, the author gives an exciting description of academic life at the time Calculus was being discovered. It gives the University at the time of restoration a vitality and a reality that the non-fictional narratives lack.
If you are interested in the times in which Calculus was invented, or if you like fairly long historical murder mysteries, then you are likely to enjoy this book. I did.
Ed Sandifer ( firstname.lastname@example.org) is a professor of mathematics at Western Connecticut State University, Contributed Papers Coordinator for the Northeastern Section of the MAA and an avid runner.