email@example.com (John Baez) writes: | | I can't believe I forgot my own law, Baez's Law, which says: | | "Any effect, constant, theorem or equation named after | Professor X was first discovered by Professor Y, for | some value of Y not equal to X." | | I'm sure I'm not the first to have noticed this ...
Following are some pointers to the history of symmetry groups in ornamental art, soon segued into discussion of simultaneous discoveries and confluence of ideas in mathematics.
First, regarding the history of symmetry groups in ornamental art, the following recent work of Jablan may be of interest:
Jablan, Slavik V. Theory of symmetry and ornament. Posebna Izdanja [Special Editions], 17. Matemati\v cki Institut u Beogradu, Belgrade, 1995. iv+331 pp. ISBN: 86-80593-17-6 MR 96e:20078 (Reviewer: Igor Rivin) 20H15 (00A69 51F25 52C20)
Jablan, Slavik. Geometry in the pre-scientific period, 1--32, MR 91i:01004 01A10 Ornament today, 33--65, MR 92g:01008 01A10 Geometry in the pre-scientific period; ornament today. Hist. Math. Mech. Sci., 3, Math. Inst., Belgrade, 1989. ii+66 pp. ISBN 86-80593-03-6 MR 90m:01001 01-06
Here is an excerpt from Igor Rivin's MR (Math Review) of the first book:
While the book is not particularly good as an introduction to discrete groups of motions of Euclidean and hyperbolic planes, it seems to be a considerably better art history text. The reviewer was fascinated to learn that most of the groups discussed were already known in paleolithic times, and fortunately, the book is lavishly illustrated ...
Beware that there is some controversy around the history of such matters, e.g. see the following article where Grunbaum is critical of Weyl and Speiser, and the comments by Hilton and Pedersen. Be sure not to miss Coxeter's remarks in his Math Review of this paper.
Grunbaum, Branko. The emperor's new clothes: full regalia, G-string, or nothing? With comments by Peter Hilton and Jean Pedersen. Math. Intelligencer 6 (1984), no. 4, 47--56. MR 86d:01004 (Reviewer: H. S. M. Coxeter) 01A15 (01A60 05B45 20F32 52A45)
Related historical remarks may be found in Schwarzenberger's textbook N-dimensional Crystallography, where he partly debunks the myth of the remarkable simultaneous independent discovery of the 230 3-dimensional space groups by Barlow, Fedorov and Schoenflies -- a myth fostered by Fedorov who in 1892 wrote
an extremely surprising circumstance has come to light, viz a coincidence in the work of two researchers such as, perhaps, never been observed in the history of science
Further details and bibliographic pointers may be found in the four page appendix to Schwarzenberger's book.
Speaking of simultaneous discoveries in math, does anyone know any historical works that explicitly study the reasons for such remarkable confluences? E.g.
o calculus (Newton and Leibnitz) o geometric representation of complex numbers (Argand, Buee, Gauss, Mourey, Warren, Wessel) o non-Euclidean geometry (Bolyai, Gauss, Lobatchevsky) o Hilbert's 10th problem (Chudnovsky, Matiyasevich) o Kolmogorov complexity (Solomonoff, Kolmogorov, Chaitin)
Smorynski (Logical Number Theory I pp. 193-196) discusses related issues around the priority dispute between Chudnovsky and Matiyasevich, and mentions in passing that simultaneous discovery is discussed in a slim volume by Raymond Wilder: Mathematics as a Cultural System.
Interestingly most all of these discoveries obey the "Matthew Effect" (the result ends up being attributed to the most famous co-discoverer, regardless of priority), so-named in light of the Gospel according to Matthew, 25:29-30 (cf. Li and Vitanyi, Kolmogorov Complexity, p. 84)
For to every one who has more will be given, and he will have in abundance; but from him who has not, even what he has will be taken away. And cast the worthless servant into the outer darkness; there men will weep and gnash their teeth.
I was going to close by quoting W. Bolyai's remark such that when the time is ripe for certain ideas they blossom like violets in spring, but I couldn't easily find the quote in the beautiful form that I vaguely remember. Does anyone have the precise quote? (surprisingly it was not quickly found by an Altavista search -- surely this is a glaring omission from all the online mathematical quote collections).