These notes were written sometime in the late 1980's, and therefore now dated. I've updated where I could quickly, omissions and regrets noted. -- john

G. Spencer-Brown, The Laws of Form (LoF)

First saw LoF in the Whole Earth Catalog.

I got the hardbound edition of LOF and didn't know quite what to do with it! Heard that it was best to study the appendices and notes. OK, but did not apply myself to using and learning it. Got the '79 edition, saw the note on Map Theorem. Wrote to Dutton to be put on list to get proof as soon as published. No book..

Had Chuck Epton from Clark College (Vancouver, Washington 98663) come to Lewis & Clark to demonstrate how he uses the Laws of Form in his Philosophy classes as an alternative to Boolean algebra and propositional calculus. (This was prior to 1882).


References in The Dyadic Cyclone by John C. Lilly...

I wrote Martin Gardner, he replied 30-Nov-79:

I once planned a column about Spencer-Brown, but Donald Knuth talked me out of it on the grounds that it would give valuable publicity to a charlatan! But I have some paragraphs about Brown and his flawed four-color proof, and his Laws of Form, coming up in my Feb column. Conway once described the book as beautifully written but "content free." I describe it as a "construction of the propositional calculus in eccentric notation." But it has a big cult following, and even a periodical devoted to it.

The newsletter he mentioned flourished at one time... Logical Form, Daniel Rohrlich / 260 Page Street #5 / SF 94102. I have no idea whether it is alive, or Rohrlich can be reached.

The February 1980 Mathematical Games column was devoted to the Four-Color Map Theorem. Gardner described Spencer-Brown as a maverick mathemetician. People at Stanford invited him to present his proof. He did, and went home convinced that his proof was correct. Three months later all (?) agreed his proof was laced with holes.

Knuth, Volume 1, 2.3.3. Other Representations of trees, all diagrams (3) to (8) resemble the Form notation. Several sentences in this section sound Spencer-Brownian.

I also have seen a book explaining how Lewis Carroll constructed his logical puzzles. He used nested boxes, which look like the Karnaugh map reduction used in minimizing boolean functions. (will try to recover the reference someday.)

I have also seen a paper OBJECT/EVENT-ANALYSIS in ACM Sigsoft Engineering Notes Vol.10 No.1 page 52, which has diagrams similar to the diagram on page 67 of the Laws of Form.

I would be interested in any bibliobraphy of references to the Form. (I have not searched for bibliographic references.) Books in Print show no new US or British books by Brown or James Keys (The pen name GSB used for Only Two Can Play This Game.)

A UNI-OPS-sponsored conference scheduled for October 1985 was postponed indefinitely prior to the event by "mutual agreement". (Promotional literature referred to an unidentified topologist who thinks that a proof will soon appear for the Four-Color Map Theorem, to a computer program Simplifier, to a special "Lifestyles" lecture, and to...? The hotel reservation form talked about the Japanese accomodations, suggested refraining from caffiene after 10 am, and eating nothing but lean meat!) See original text. Organized by

Walter Zintz, Executive Director
Post Office Box 27097
Concord CA 94527

The simplifier program (described in Dr. Dobb's Journal, Spring, 1985) was written by Steve Heuman in BASIC.

William Bricken

Yet another implemetation of the predicate and propositional calculus has been done by William Bricken, Advanced Information Decision Systems, Suite 286 / 201 San Antonio Circle / Mt. View CA 94040-1270. (Probably no longer there, see below --jm). I requested information from him (12-1-85) and received his paper A DEDUCTIVE MATHEMATICS FOR EFFICIENT REASONING. {insert abstract}

Excerpts from his hand-written letter:

"Simplifier" was written by...? the crux is that propositional calculus is a toy domain. Any serious system must address predicate calculus.

I'm in touch with about two dozen people also tracking S-B. No one that I know of is actually applying Laws of Form.

  1. forget the map theorem.
  2. Italo Calvino's Cosmicomics is a fictional account of the first sign.
  3. The topologist (referred to above) is Lou Kauffman at U of Chicago. His work is the best I know of.

He also sent his bibliography containing 28 references to works based on or critical of the Form. I will get those here soon, perhaps with his permission. :^)

More recently, I spotted Bricken at the University of Washington, where is is doing VR research.

A biblio of him appears at Beilfeld.

Wherein they say:

Dr. Bricken is an internationally recognized expert in architectures for virtual environments and is the inventor of Boundary Mathematics, a formalism which uses void-based and spatial techniques to simplify computation.

Just search for his name using your favorite search engine.

My own thoughts