Being a human activity, calculation has a history, even if its operations yield “facts” apparently true in any context. One plus one might always be two, but the methods to arrive at such results, not to mention what they might mean, are another matter. Recent histories involving calculation on this blog include Staffan Müller-Wille and Giuditta Parolini, “Punnett Squares and Hybrid Crosses: How Mendelians Learned Their Trade by the Book”; D. Senthil Babu, “Handbooks of the Mind into Ready Reckoners in Print: The Story of the ‘Encuvati’ in the Nineteenth Century”; and Karine Chemla, “Reading and (Re-)Classifying Canonical Instructions of the Past: Commentaries on ‘The Nine Chapters on Mathematical Procedures’…”
The earliest extant Chinese mathematical writings include two types of components of particular interest for our discussion on manuals and handbooks. On the one hand, there are mathematical problems that often evoke tasks carried out by officials working in the imperial bureaucracy. On the other hand, there are mathematical “procedures,” or “algorithms” in today’s parlance, to solve such problems. This description fits most of the mathematical books composed in China until the seventh century.
The Effects of Nuclear Weapons was by far the most popular handbook of nuclear defense during the Cold War. Adapted from an original publication of the Los Alamos Scientific Laboratory (1950),1 the handbook was amended and made commercially available for popular use (1957),2 revised (1962),3 reprinted (1964),4 expanded (1977),5 and even illicitly translated into Russian for use in the Soviet Union (1960).6 Edited by Samuel Glasstone, a prolific author of science textbooks, The Effects of Nuclear Weapons was described as a “comprehensive summary of current knowledge on the effects of nuclear weapons” and commended by the Federal Civil Defense Administration as “the definitive source of information on the effects of nuclear weapons.”7
Selling insurance against possibly harmful future events became popular among Americans in the late eighteenth century. Among the reasons that more and more people in the former British colonies were drawn to conduct this kind of business was that acting as an insurer required neither formal training nor special equipment. Basically, anyone who was literate and had access to pen and paper could write up a contract that promised some sort of financial compensation for losses or damages to someone, if that person feared a certain event could disrupt his or her comfort and in exchange made a regular payment. Thus, a man named Ephraim Tucker decided in 1793 to issue insurance for “the elegant full-blooded horse Clericus” during its transfer between stables.1 Philadelphia merchants routinely agreed to insure each other against the so-called dangers of the sea. Churches in New England raised funds to insure the lives of their clergy and the clergymen’s widows and children. Neighbors issued contracts to insure each other’s homes against destruction by fire. Firemen, too, clubbed together to provide financial means for any event that caused one of them to suffer physical harm. The practice of taking on other people’s risks, this shows, was often performed by nonexperts.
The Encuvati was the quintessential Tamil multiplication table book, used in precolonial South Indian schools. Nowadays they are available as palm leaf manuscripts, collected from different geographical locations of the Tamil-speaking region of South India and stored in various manuscript libraries there as well as in other collections inside and outside the country. But why is something as innocuous as a multiplication table book important for us? Their contents look nothing like modern tables, with lines and columns, but the numbers are arranged the same way. Their importance emerges from the simple fact that countless children participated in their making from about the seventeenth century, if not earlier.
In 1901, Erich von Tschermak (1871–1962) produced a critical edition of Gregor Mendel’s (1822–1884) paper on “Versuche über Pflanzenhybriden”; and in the same year, William Bateson (1861–1926) submitted an English translation entitled “Experiments in Plant Hybridization” to the readers of the Journal of the Royal Horticultural Society. Tschermak’s edition appeared as volume 121 of the renowned series Ostwalds Klassiker der exakten Naturwissenschaften (Ostwald’s Classic Texts in the Exact Sciences). Historians have rarely noted the paradox that lies in the fact that a paper, which scientists like von Tschermak and Bateson had lifted from obscurity just a year earlier, was almost instantaneously included in the Pantheon of classical contributions to the “exact” sciences. The discipline that Mendel supposedly founded, namely genetics, did not yet exist in 1901, and his alleged “discovery” of laws of inheritance would remain highly contested for at least another decade, even involving accusations of scientific misconduct.