Laterally related topic: Abraham Seidenberg.
The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews, published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet.
Angell, Ian O. Megalithic mathematics, ancient almanacs or neolithic nonsense. Bull. Inst. Math. Appl. 14 (1978), no. 10, 253--258. (Reviewer: C. R. Fletcher.) SC: 01A10, MR: 80f:01002.
Discusses different explanations for the shapes of megalithic stone rings. The author briefly discusses some of the theories of Alexander Thom, which involve an astronomical calendar and an effort to make the circumference equal to 3 times the "diameter" rather than the irrational pi. He then discusses two new theories of his own. One explains the shapes of the stone rings as extensions of the ellipse, generated with three or four pegs and a string rather than with just the usual two. The other explains the shapes as an effort to store shadow lengths. Neither theory may be given entirely in earnest. A theme of the paper is how theories may start as intellectual games, go out of control, and be changed into pseudo-science. Closely related topics: The Stone Builders, Astronomy, The Calendar, The Ellipse, and Pseudoscience.
Atkinson, R. J. C. Obituary: Alexander Thom. J. Hist. Astronom. 17 (1986), no. 1, 73--75. SC: 01A70 (01A10), MR: 87h:01062.
As the author explains, some of the work of Alexander Thom remains controversial. However, Thom is to be credited with the invention of the subject of archaeoastronomy and with a number of interesting observations and theories. One of his interesting observations is the repeated occurrence of certain types of non-circular arrangements of stones. An interesting theory is his notion of a megalithic yard and rod, supposedly fairly consistent in Britain and Brittany. His theories of apparent alignments with solar and lunar events have been among the most influential, though are not always necessarily correct in all detail. Closely related topics: The Stone Builders, The Measurement of Distance, The Circle, and Astronomy.
Knorr, W. R. The geometer and the archaeoastronomers: on the prehistoric origins of mathematics. Review of: Geometry and algebra in ancient civilizations [Springer, Berlin, 1983; MR: 85b:01001] by B. L. van der Waerden. British J. Hist. Sci. 18 (1985), no. 59, part 2, 197--212. SC: 01A10, MR: 87k:01003.
The reviewer discusses van der Waerden's book Geometry and Algebra in Ancient Civilizations. Although the reviewer clearly admires van der Waerden for his work in algebra and in the history of mathematics in general, he is highly critical of the conclusions reached in van der Waerden's book. A basic theme of the book is that there is a pre-Babylonian ancestor to mathematics in Babylonia, ancient Egypt, Greece, China and India; thus the book can therefore be thought of in part as a further development of Abraham Seidenberg's theories on the ritual origins of ancient mathematics. The reviewer takes issue with several facts cited in the book, and in addition with three assumptions that he sees van der Waerden using explicitly or implicitly in the book: "(1) independent discovery is so rare that it may effectively be discounted as a working hypothesis for relating technical traditions; (2) derivative traditions are inferior to their source traditions; (3) borrowing from one tradition to another is not selective, but entails the adoption of whole bodies of technique." (The phrase "inferior to" in (2) could just as well be replaced by "degraded in".) The reviewer suggests in addition that van der Waerden has not been sufficiently critical in accepting claims by Alexander Thom and others about advanced mathematics in megalithic monuments, and sees these claims as forming "the veritable linchpin of van der Waerden's thesis". The author briefly discusses some of Thom's work in megalithic mathematics, and concludes that he finds no real evidence of the Pythagorean theorem, the ellipse, or a standard unit of distance in neolithic times. The review concludes with the statement "I fear even more the regrettable impact on credulous nonspecialists who may not know to distinguish between the general enterprise of scientific research and the reckless notions of some scientists." Closely related topics: Sumerians and Babylonians, Ancient Egypt, Greece, China, India, The Stone Builders, and Pythagorean Triangles and Triples.