Book Review: The Archimedes Codex

Back in October, I first came across a news story about the Archimedes Codex. Very cool and interesting to be sure. At the time, there was mention of a book detailing the project to read the Codex.

Now that I’ve read the book based on the research performed so far in recovering and translating the text, WOW. "The Archimedes Codex" by Reviel Netz and William Noel is by far the most interesting work of non-fiction I have read in a long time. Part history, part mathematics, part imaging science, part travel diary, the work is an enjoyable, almost conversational review of the history of a medieval prayer book, its contents and the project to read it.

Despite the valid excuse of being busy with work, I did put off this review to give my impressions time to settle. I have a feeling this is a work that will improve with additional reads. While conversational in tone, it is a very dense work (but not in a hard to read way).

In full post are my thoughts on the book and Greek-style versus modern-style math.

The authors alternate chapters with one covering the history of the book and the project to read it (Mr. Noel) and another covering a history of Greek mathematics and providing context for the discoveries thus far (Dr. Netz). The context chapters led to a highly interesting discussion of how Greek science and math is different from our own.

Knowledge of this difference was critical during the chapters explaining the various propositions from The Method which led to the revelation that Archimedes had begun developing calculus two thousand years before Newton. The only part of the book I had difficulty with were these reviews, mainly because I am very much a creature of modern mathematical thought in that I prefer to think in terms of equations as opposed to raw text. When going over the math, it struck me how incredibly visual modern science & math are.

In some respects, it makes a great deal of sense that Greek scientific thought was not. A high-technology society like ours places large value on high familiarity with things like Cartesian coordinates and reading graphs as well as ease of transmission of data. For the Ancient Greeks, the opposite was true: low familiarity with mathematical concepts* and difficulty transmitting data. This means there was a real need to both retain everything inside your own head and when you are communicating to refrain from any form of symbol-system (like equations) that is dependent on a great deal of familiarity with that particular system.

This is particularly important when you realize how small and varied Archimedes audience was. One of my favorite portions of the book speaks about how alone in their genius those first discoverers must have been. Archimedes works aren’t formal papers at all but letters to competitors or like-minded individuals. And these letters were probably read by audiences less than twenty. These people were NOT all Greek but from and spread around the Mediterranean. This international scope in combination with the small audience works against having a more universal system of symbol-reference.

Modern communication of scientific and mathematical ideas is based on a universally (for the most part) agreed upon system of symbols, abbreviations and jargon. This system is so huge that it has long since subdivided based on the focus of your study (engineers speak a different dialect than astrophysicists; programmers speak a different dialect than chemists). We only developed this system in the last 200 yrs or so. This coincides with scientific study becoming less the work of the occasional polymath and instead a profession for large numbers of people. Not to mention, we do have a bit of a mania for remembering and keeping records of things. While some in the past were also focused on this (Library of Alexandria, Copying Greek Texts in the Dark Ages), it was usually the work of a small segment of the population. So we increased not just the people engaged in mathematical & scientific thought, but also we increased the numbers of people charged with recording and transmitting that thought. When you combine that with modern society's ideas about efficiency (ie - "laziness in action" or "shortcuts for a better world"), our usage of complicated symbol-systems and jargon make a good deal more sense.

At the end of the day, it’s hard to believe that there was a time when we didn't know the center-of-gravity of a triangle, the area of a parabola or the volume of a cylindrical cut. Again, I’m a creature of the modern era. The formulas for CG of a triangle and other shapes are available in any “Mechanics of Materials” textbook. Areas of parabolas are covered in any Calculus course as are volumes of complicated curvilinear objects such as cylindrical cuts. But these are the results of two millennia of effort, not the self-evident theorems and solutions they are presented as.

When you combine these thoughts with the quite excellent historical chapters discussing the long, strange trip that resulted in these works being rediscovered by the modern world, “The Archimedes Codex” makes for fascinating and thought-provoking reading.

Another wonderful aspect of “The Archimedes Codex” project is that the participants have placed a great deal of information on-line for others to share or to track the progress of the project. The raw images of the prayer book in different types of light are particularly stunning.

* I mean "low" as in a low percent of the population as a whole. Obviously, there were some individuals who had quite high familiarity with mathematical concepts.