Michael Mislove wrote:
This thread reminds me of John Rhodes' review of the classic, "The Algebraic Theory of Semigroups, Vol. I" by Clifford and Preston. This exceptional account of the state of semigroup theory in the early 60s contained more than copious citations, to authors for published works, to colleagues for ideas, and even to the extent that solutions to problems were cited. Rhodes, his acerbic wit at hand, commented on this incredible documentation of where even the simplest ideas had originated, was led to comment, "it's surprising that the authors didn't cite Gutenberg for the type."
i agree, it is easy to exaggerate with citations, and with many other things, in all kinds of ways. one could cite gutenberg out of a scholarly zeal, or just to emphasize that they only use the shoulders of giants. but such generalities aside, we had a much smaller issue here: there is this very interesting research in self-similarity, and it is based on the theorem that [0,1] is a final coalgebra. on the other hand, vaughan and i had written some papers promoting the idea that the reals form a final coalgebra, and felt that we were a bit closer to the topic than gutenberg to semigroups. but enough of that. it is interesting that mandelbrot is talking about the real interval in coalgebraic terms. there are many such examples. continued fractions are also a familiar instance of a coalgebraic expansion. i don't think that we are really discovering the coalgebraic nature of self-similar and analytic objects; just giving it a categorical formulation. but math analysis consists of lots of coalgebraic constructions, often just thinly disguised. -- dusko 30-Nov-2004 08:03:55 -0400,2441;000000000000-00000000