True Origins Of Calculus Obscured By Prayer Book

Can we agree, at the threhshold of this post, that calculus is an immensely significant area of knowledge? It enables us to build bridges, send astronauts into space, and generate electricity by splitting atoms. I don't pretend to understand calculus in depth but I certainly respect its intellectual power and both you and I owe the mode of communication by which this blog is published to technology making use of it.

It has been taken as an article of great interest by historians, scientists, and mathematicians that a major controversy erupted in the early eighteenth century between Isaac Newton and Gottfried von Liebniz as to which one of them invented what we today call "calculus" first. The consensus seems to be that Liebniz published before Newton, but Newton advanced a substantial claim to have invented it first and refined his version of "fluxions" prior to publication.

Well, it turns out that Archimedes beat them to it by nearly two millenia. At least, certain portions of the concept. Archimedes did not use Leibniz' concepts of integrals and differentials, at least not in the same way that we do now, but he did tackle the basic problem that led both Newton and Liebniz to reach the solution -- computing the area under a curve in what we today call a Cartesian measurement system. ("Cartesian," in turn, refers to Rene Descartes; this attribution, too, appears to have been created by Archimedes rather than the pre-Enlightenment scholars whom we celebrate today.)

How do we know this? It seems that in the 1300's, a monk in France was assigned to copy a prayer book. So he did what was customary for the day -- he found an old book that it didn't seem anyone else was using, scraped off the ink on the vellum (that is, sheepskin) pages, and set to work copying devotionals. He chose what appears to be the only copy of an essay by Archimedes titled The Method, describing how to (among other things) measure the area under a parabolic curve. Only through very modern methods of analyzing the book can we now peer through the top layer of medieval Latin to see the priceless knowledge to be found underneath.

The monk clearly did not understand, or did not care about, the scientific significance of what he was obliterating. His job was to make copies of prayers, and that's what he did. He is not to be blamed personally for setting back western science by hundreds of years -- it's quite likely no one had been using the book. What is to blame is the scholastic school of thought that prevailed in "educated" circles of European Christians at the time. Everything worth knowing was already known, no knowledge was useful or valid without determining its relationship to Jehovah first, and all knowledge was only important insofar as it glorified Jehovah and/or Jesus, and brought man closer to the Godhead. The job of a scholar under this world view was to preserve, memorize, and explain the knowledge so as to help other people reconcile their souls in preparation for the afterlife.

So of what use towards that goal would be computing the area encompassed by a parabola? Of what moment the distinction between the "actual infinite" and the "potential infinite" which so vexed Isaac Newton? Even if a) the monk in question had been able to read Greek (more than a few words related to Scripture, that is), and b) the monk understood mathematics, and c) the monk knew that this was a copy of one of history's greatest geniuses, the monk still would have probably been within the realm of reason to believe that other copies of the work existed somewhere else. So he just did his job.

I would like to say that this is a profound metaphor for religion eschewing science, discounting its importance. Certainly if I were to do so I would have to aim that fire at religion in general, not just Christianity, because all of the major world religions have at least gone through phases of history in which worldly knowledge was sneered at for its insignificance compared to reconciliation with the (ficticious) divine. But that would be unfair to religious people, many of whom (I am confident) share my horror at the prospect of this knowledge having been lost forever and who see no problem reconciling their faith with science. Instead, I will point out that this sort of reconciliatory attitude is relatively modern and recent; the bulk of history indicates that a rational, rather than scholastic, approach to knowledge and learning has prevailed only during the middle to late Classical eras and the age of Modernity.

Hat tip to dana at Edge of the American West for this really fascinating piece of history news.