Date: Nov 27, 1997 3:41 AM
Author: Bill Dubuque
Subject: most famous codiscoverer gets credit (Matthew Effect) [was: This Week's Finds in Mathematical Physics (Week 112)]



baez@math.ucr.edu (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 ...

Also keep in mind the Matthew Effect, which says that attribution
tends towards the most famous of codiscoverers, cf. my message
below from the math-history-list archive at
http://forum.swarthmore.edu/epigone/math-history-list/

-Bill Dubuque

>Subject: symmetry; simultaneous discoveries [was: Art: ornaments & music]
Author: Bill Dubuque <wgd@martigny.ai.mit.edu>
>Date: Sat, 26 Apr 1997 16:26:51 -0400

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).

-Bill Dubuque