The Babylonian Theorem: The Mathematical Journey To Pythagoras And Euclid, by Peter S. Rudman
Very few people, likely only those who are particularly interested in both geometric algebra as well as ancient history, are likely to find a book such as this one of interest. Yet this book has vastly more than meets the eye to reveal to the suitably critical reader, especially when that reader notes that this book contains sample problems of the sort that would appear in a Common Core classroom  and that it manages to show a particularly harsh and mistaken view of the Sabbath as springing from mistaken Babylonian beliefs about the unluckiness of the number seven (60) (which appears to have motivated the Romans as well, although that is not discussed in this book), harsh views of Ptolemy because of the way that his calculations served Catholic dogma (116), and the author’s praise of the metric system and subsequent denigration of the English method with its measurement system based on tangible and even human measurements as opposed to mere decimal calculations (31). The book is published by the radical humanist Prometheus Press, which suggests that the author and publisher have more than merely mathematics, but also dubious politics, in mind, and the knowledge of the corrupt source and grossly incorrect reading of the biblical text suggest that the author’s inventive conclusions are nevertheless not to be trusted. Even where the discussion is light and entertaining, and the geometric algebra reasonable, the author’s known bias and clearly misguided worldview make every statement or interpretation of the author suspect.
The contents of this book are rather straightforward, even if the author’s continual hostility to religion, despite his obvious debt to heathen religion and the book’s forthright praise of the mathematical skill of Babylonian mathematicians, who were just as religiously oriented as their Egyptian and Greek equivalents, is tiresome to the reader. The book begins with introductory discussion on figures and mathematical symbols before progressing to number system basics, Egyptian numbers and arithmetic, and Babylonian numbers and arithmetic, of which it can be said that Egyptians used a base ten and Babylonians used what we consider base 60, which was really sequential systems of base six and base ten repeated. The author then discusses Old Babylonian problem texts related to quadratic algebra in the mind of their translator, Babylonian mathematics on Pythagorean triples, square root calculations, pi, similar triangles, sequences and series, simultaneous linear equations (where the author argues that ancient Babylonians were only comfortable solving two simultaneous equations), pyramid volume, and the path from Babylonian scribes to Pythagoras and Plato, and a final chapter on Euclid. After this there are appendices that show the answers to the author’s “fun” questions, a derivation of one of the book’s many equations, and an elegant proof by contradiction that the square root of two is an irrational number, contrary to the religious dogma of the early Pythagorean mystery cult.
If the reader is able to avoid irritation at the author’s strident tone, there is much that can be enjoyed in the author’s obvious intellectual curiosity and in his sensible opinion that such intellectual curiosity was shared by mathematicians in the ancient world. That said, perhaps the chief value of a work like this one is that it demonstrates clearly that even a field as rigorous as mathematics cannot be seen apart from larger religious and moral worldviews. The author clearly desires a rigorous mathematics, and obviously values intellectual achievement, yet the author simultaneously denigrates any sort of creation or design story, relegating the biblical story of creation not to a creation ex nihilo (see, for example, John 1:1), but rather to the classic pagan conception of creation that brings order to a preexisting chaos. In so doing the author seeks to remove the logical contradictions of praising his own intellect and reason and denying the existence of intellect and reason in the creation and design of the universe, committing the fallacy of equivocation by moving the goal posts and relying on his complicated language and superfluous equations and graphics and the assumption that the reader will share certain anti-religious biases to cover for his dodgy and illegitimate rhetoric. If fields as arcane and technical as mathematics, even simple geometric algebra, cannot be discussed without relating to larger questions of religious worldview, then truly any kind of discussion about rational matters is impossible without addressing the reality of God and the importance of the rational order and design of the universe, which has immense implications far outside the obscure but intriguing mathematical subject matter discussed here. Even the author’s folly in suppressing truth has at least some purpose for the shrewd and critical reader.
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