Everything in the 400 pages of Russo's "The Forgotten Revolution" is aimed at explaining and justifying his sub-title. Fortunately, the author tells us what he means by science:
- The statements are about theoretical entities, not actual objects.
- The exposition is rigorously deductive.
- To test the theory in practice, there must be correspondence rules.
Russo has achieved and exhibited an extensive survey of science in the Hellenistic world at the time after Aristotle, which is intended to show that, at the time of the founding of Alexander's empire, there was not only scientific mathematics, say in Euclid and Archimedes, but there were also the sciences of optics, geodesy, mechanics, hydrostatics, astronomy (including heliocentric), etc., and that there was extensive technology to complement it.
Russo considers that the ancients had trigonometry: the only difference that he finds is that we use the sine of an angle of a triangle and they used the chord of the circle in which the triangle is situated. But while the ancients had tables of arcs and chords, we use continuous trigonometric functions. Since Euler, analysis is dominated not only by the limit notion, but also by the notion of a function.
Another example: Russo has a section on dream theory. He finds it "fascinating to reconstruct what was thought in Hellenistic times about the analysis of the psyche" (page 214). Since none of the writings of Herophilus of Chalcedon are extant, we have no access to anything that he wrote on dreams, so that Russo must use whatever fragments we do have that refer to those writings in order to believe that Herophilus had a science of dream interpretation. What Russo has going for him is that Freud himself mentions Herophilus as an interpreter of dreams. However, even if there were ancient writings on dreams that were as 'scientific' as those of Freud, should we consider Freud himself as scientific, especially since his writings do not meet the rigorous standards that Lucio Russo demands that a science have?
Russo finds Hellenistic interpretations everywhere, and where there is no text to back him up, he speculates that such a text is lost. Nevertheless, there is great value in "The Forgotten Revolution," for there is not enough appreciation of the achievements of these Hellenistic writings.
In any case, the Hellenistic scientific enterprise became dim, and the understanding of it lost. Is our modern science also susceptible to fading? Perhaps it is chiefly a matter of numbers. There were not enough scientists to form a critical mass so that science could be counted upon to continue.
As Russo interprets the facts, science could only be re-born because enough of ancient science remained intact to make a renaissance possible. Otherwise modern science would have been delayed and off to a shakier start.
The treat in store for the reader of this book is the vast learning that Lucio Russo has acquired, which he explains with lucidity. What is hard for the readers, however, to judge is to what extent the ancient world had true science in Russo's sense. What is definitely so is that the Alexandrine world had great accomplishments to excite our wonder.
This book has two uses. On the one hand, it is useful for private study, for one's own enlightenment; on the other it will enrich every science course and every history course that involves these time periods.
It would be wonderful to read this book in connection with two others: The Mathematics of Plato's Academy (2nd Edition), by David H. Fowler (Oxford, 1999), and The Shaping of Deduction in Greek Mathematics, by Reviel Netz (Cambridge, 1999).
At the turn to the 21st century, we are fortunate to have works that suggest new ways to view, and thus review, the origins of modern mathematics and science.
Samuel S. Kutler (firstname.lastname@example.org) teaches at St. John's College in Annapolis, MD.