stucki@wheaton.UUCP (David J Stucki) (03/10/87)
Thanks to all who have responded to my inquiry. Since some of you have
asked to here back as to what I learn and I don't know how to mail direct, I
will post here a collection of some of the results. It appears that as a
whole GSB is regarded as a crank and although his book may be interesting it
is not included by many in the field of mathematics. I found it personally
to be a good mental exercise to read it but there doesn't seem to be any
more to it than just that. So with out further rambling on my part here is
a partial listing of responses:
*********************************************************************
I finally figured out everything he talked about after reading the book
about 8 times over about 8 years. He gave no detail supporting his four
color map theorem claims so I can't comment on that. The basic systems
are perfectly valid...the biggest controversy seems to be over whether
there's any sense in having symbol/no-symbol versus symbol1/symbol2.
I don't think there's any difference myself, but I favor the latter
traditional approach for reasons of legibility. His second order form,
the calculus, is quite interesting in its ability to handle what amounts
to recursion for things that, in other systems, are difficult paradoxes.
I have not investigated the consistency nor completeness of his calculus,
which would be the number one priority for formal study, but leaving
such questions pending, his systems work and represent new work. It is
especially interesting in that, even if it proves inconsistent, it might
not make it uninteresting, unlike every other mathematical system I ever
heard of.
There is a piece of software called LOF or LOSP or something (Laws of Form
in Lisp was the full name) being sold commercial, which implements his
first order form. (Announced around Oct 1985 in Electronics).
*********************************************************************
G S-B is a crank.
*********************************************************************
My Ph.D. is from University of Waterloo in Combinatorics and
Optimization and my thesis was on map coloring. I also have
met Martin Gardner (of Scientific American) several times.
He told me (in 1977 or 78) that he was thinking of doing a piece on Spensser
Brown's Book, "Laws of Form", but that a respected
mathematician mentioned that (1) yes, the book is mostly
nonsense, and (2) the author is a crank. I has previously bought
the book (I was a student then) because the mention
of the Four Color Problem intrigued me, but when I read the
book, I saw that there was not much there at all. Still,
the book has a beautiful blue-green cover and looks good on
my bookshelf. I think this is it's main value.
*********************************************************************
I heard a talk on this alleged proof from Louis Kaufmann (approximate
name and spelling) of the U of Illinois, Circle Campus about five
years ago. It seemed that he had just reduced it to an equally hard
equivalent problem. Hope this lead helps. My own opinion of Laws of
Form is that it is interesting as metaphysics but not as mathematics.
*********************************************************************
I also have a copy of this book and was somewhat baffled by it. I came across
a review by William E. Gould in *The Journal of Symbolic Logic* (I don't have
the citation, sorry). After reading the review and re-examining the book I
came to the conclusion that G Spenser-Brown's work is much ado about nothing.
*********************************************************************
If this is the book that I remember, it is an amateurish treatment of
some very elementary parts of propositional calculus. The book is
chiefly notable for its unusual notation: boxes within boxes.
The author seems to have rediscovered the "Sheffer [sp?] stroke"
which is defined something like
x | y = NOT ( x OR y).
All the other Boolean functions can be built up from this.
Spenser-Brown's rediscovery of this mildly interesting fact is OK as
far as it goes. Unfortunately, he makes grandiose claims for the
importance and originality of his work. As for his alleged
contribution to the four-color theorem, I would dismiss it with the
rest of his self-hype.
*********************************************************************
Well, a math prof of mine, who teaches phil of math, once said
"It's not mathematics. It's fun, but it's not mathematics." I
personally reread it once a year or so, just to see what else I'll
find inside.
*********************************************************************
I seem to recall owning a copy of _Laws of Form_ in about 1970.
(I still have it, but it's at home, so I can't check the publication date.)
He must have put out a revised edition.
As for the edition I had, I read some of it, scratched my head a great
deal, then asked one of our mathematical logic professors about it.
He replied that he thought it was pretty silly himself, but that, "A student
came to me one day and told me that the book had changed his life, and it's
pretty hard to argue with that."
*********************************************************************
--
~=~+~=~+~=~+~=~+~=~+~=~+~=~+~=~+~=~+~=~+~=~+~=~+~=~+~=~+~=~+~=~+~=~+~=~+~=~+~
David J Stucki I didn't expect the SPANISH INQUISITION !!
Wheaton College C.P.O. 2507
Wheaton, IL 60187 USA ihnp4!wheaton!stucki