Laws of Form Bibliography

Author's address: Gary C. Berkowitz, NeuroSoft Laboratories, 7777 Fay Avenue, Suite K129, La Jolla CA 92037, USA. Also: 3284 Karok Avenue, San Diego CA 92117, USA.

``This epochal book has spawned whole disciplines, vast and surly arguments, and not a little mystical endeavor. Not bad for a rudimentary arithmetic book. In the beginning God said, `Draw a distinction.' The primordial creative act. You can take it from there.'' [publishing and availability info] [5 extracts of 2 to 4 paragraphs each from LoF]

ftp://ftp.u.washington.edu/public/VirtualReality/HITL/papers/tech-reports/bricken*.

See p.67. Mentions GSB and LoF in relation to 'time' and chaos.

Profound fiction. Does not cite GSB but is strongly related.

A thorough search by a Wright-Patterson librarian did not turn up this paper or the journal/proceedings. The Aeronautical Systems Division no longer exists. Lou Kauffman, who wrote `Imaginary Values in Mathematical Logic' when he consulted for Campbell in 1987, says he has not seen this paper either, but at the time Campbell worked for Systran Corporation, Dayton, Ohio, 45432, doing classified work for the Air Force.

Includes a rejoinder from Kauffman and Varela.

Mostly a review of Penrose, R. (1989) The Emperor's New Mind. Only cites LoF in passing: ``True, but it [the anthropic principle or Pangloss's theorem] fails to answer Spencer-Brown's fundamental question: how is it that the universe has aquired the capacity to be aware of itself?''

`The hierarchical operator, [cross], is taken from Brown's Laws of Form, and is read ``in the context of.'' For example, [X over Y-cross], means ``Y in the context of X'' and implies that whatever is asserted about Y is limited to this context.' p.24

Author's address: ``Jack'' John S. Engstrom, c/o Department of Mathematics, Maharishi International University, Fairfield, Iowa,

Author's address (also ANPA West address): 112 Blackburn Avenue, Menlo Park CA 94025. Ph: (415) 324 4235. Email: etter@boundaryinstitute.org.

Family Therapy, Taoism, Gregory Batson, and GSB.

Available on the WWW at http://www.ultratechnology.com/laws.html.

The comment ``beautifully written but content free'' is due to John Horton Conway (of `game of life' fame). It appears in a Martin Gardner column where GSB is referred to as the ``maverick British mathematician ...''. ALL of mathematics (pure mathematics!) is content free. SOME of mathematics is beautifully written. Conway's remark is a high compliment; backhanded, but high! Unfortunately, GSB took umbrage at the Conway remark, or so he often says.

A 4 valued self-referential system of logic (true, false, paradox, indeterminate) with standard references to Spencer-Brown (p.11), Gödel, and Cantor. They appear ignorant of Kauffman's mathematical treatment, but then they focus on physical interpretations as feedback circuits. Incomplete document without a bibliography.

Author's address: Mathematics Department, University of California at Davis. Also: 306 1/2 Montcalm Street, San Francisco, CA 94110, USA. Ph: (415) 641 6135.

Mathematical concept for distinction-making and complexity analysis.

Author's WWW page http://www.cs.ncl.ac.uk/people/home.php?name=chris.holt@ncl.ac.uk.

An attempt to translate LoF, the whole book, including the meta-level canons, principles and rules, into a functional language and categorical combinator system in the spirit of CAML.

Only cites LoF in passing: ``More bluntly, the way that we describe and classify events in the natural world determines the theoretical description that can be derived from it (...; Spencer-Brown, 1979; ...).''

Available on this site at http://www.lawsofform.org/collection.html.

CMP Publications, 600 Community Drive, Manhasset, NY 11030.

In German and English. The title translates to ``Logic of Distinctions. A Protologic Towards a Theory of Society.'' See http://www.tu-berlin.de/~society/Jokisch_Logik_Einleitung.htm.

An account of a seminar with the author and a group of cybernetic musicians (Herbert Brun's group) and Annetta Pedretti (the publisher), in which they explored GSB's approach to the 4-color map theorem. The book is incomplete, but the author is willing to supply copies of it plus an appendix that brings it partially up to date. Author's address: Dept Math Stats & Comp Sci, University of Illinois at Chicago (M/C 249), PO Box 4348, Chicago, IL 60680.

See chapter VI, sections 4, 5, 8.

This paper is a condensed version of Kauffman (1993) `Circuit Automata'.

Shows how Peirce (1839-1914) discovered the notation of LoF in 1886, and later developed his existential graphs, which can now be seen as a clear anticipation of the primary algebra of LoF.

Contains an introduction to quantum topology by L. H. Kauffman that is an example of the interaction of formal mathematics with physics and topology.

Special Issue: Peirce and Spencer-Brown: History and Synergies in Cybersemiotics. "In this issue of Cybernetics and Human Knowing we have a collection of papers devoted to the cybernetics and mathematics of Charles Sanders Peirce with a special focus on its synergies with Spencer Brown’s thinking." See http://www.imprint.co.uk/C&HK/vol8/v8-1ind.html.

A response to Cull and Frank (1979) and Kohout and Pinkava (1980).

Available at the author's WWW page http://users.bigpond.net.au/d.keenan/.

Poetry. ``James Keys'' is a pseudonym of George Spencer-Brown.

Love poetry plus scientific mysticism.

First US edition.

He refers to Brown, G. Spencer on pages 31, 40-44 in the context of a discussion of distinction which refers to Buddhist dialectics, Kant, Heidegger, Derrida, etc. I wouldn't say he deals directly with LoF but rather that he uses quotes from LoF as a springboard for his philosophical discussion of distinction (which is insightful and interesting).

A boundary arithmetic system based on prime factors. Address: Prime Arithmetics, 3410 Geary Street, Suite 311, San Francisco, CA 94118, USA.

Only contains, as a preface, a quote from LoF pp109-110 ``Discoveries... furtively.'', without comment.

``...a lengthy study of notation and of Ultra-Structure''

An essay exploring the philosophical significance of distinction and its essential role in the process of creation, sprinkled with suggestive quotes from mystics.

According to the author, this publication contains many errors. Contact him at philip.meguire@canterbury.ac.nz for a corrected PDF version, or just read the following.

In a note (p.153) he says ``I cannot overestimate the influence of Spencer-Brown's `Laws of Form' on this book.''

The index has 14 entries under Spencer-Brown and several for Varela, Maturana, and Kauffman. The author's real passion is for C. S. Peirce.

D. J. Spencer-Brown is G. Spencer-Brown's brother who died in 1976.

Chapter 4, entitled ``Mathematics and Models for Autopoiesis,'' examines LoF and Varela's extension. It concludes, ``Mathematically we have seen attempts to model self-reference by using the laws of form, but it is not really clear at this point how valid or usefuul this has been.''

Here Nicod marries the Sheffer stroke (NAND, dually NOR) to Principia Mathematica (PM), a marriage the second edition of PM cited warmly and took on board. Nicod’s notation curiously anticipates LoF. Nicod denotes negation by the overbar, and material implication by connecting the overbar to the Sheffer stroke, which effectively results in the LoF "mark". Let concatenation express the Sheffer stroke and (p) the negation of p; Nicod then writes "if p then q" by p(q) and sometimes even by (q)p. The latter notation is, in effect, the LoF "mark". Nicod’s article would have been readily available in any British research library during the 1960s. Appendix 1 of LoF demonstrates that Sheffer's (1913) postulates are primary algebra consequences. -- Philip Meguire

Author's address: Department of Physics, Stanford University, Stanford CA 94305-2196, USA.

Largely a correction and extension of Oshins (1990). Oshins describes this work as ``an alternative to LoF in which the transposition axiom is violated thereby giving a nondistributive lattice for linguistic (like Epimenedes) and psychological propositions, similar to von Neumann's formulation of quantum logic for physical propositions.''

Not related in any way to LoF but contains a foreword by GSB as the publisher. Each tune is identified by a string of U, D, R, representing movement Up, Down, or Repeat from the last note. Amazingly, this works pretty well in 15 and often fewer notes. The book is divided into two parts, classical themes and popular melodies.

See p.198-206. A fairly basic description plagued by the all too common typos where blanks, and in this case their preceding equals signs, get lost.

"The semantics and proof procedure of Charles S. Peirce's graphical logic, to which he devoted much effort over the period 1895-1910, in some ways resemble those of LoF's primary algebra. However all work to which GSB would have had ready access in the 1960s UK dismissed that graphical logic as hopelessly eccentric (Meguire 2003). Peirce fully anticipated LoF's 'mark' in two papers written in 1886, but not published until 1993 (Kauffman 2001). But the primary arithmetic, the self-duality of the primary algebra, and LoF's metatheory all find no echo in Peirce." -- Philip Meguire

A very rare instance of scholarly work of the first rank citing LoF, and favorably at that.

A non-technical review of LoF. It probably appeared in Byte magazine at about this time also.

One of two books (the other being Shin, 2002) on C. S. Peirce's graphical logic, a logic quite similar in spirit to the primary algebra of LoF.

GSB appears to have been influenced by this book based on a translation from 5th century Greek.

In one paragraph on page 166, Russell describes the time in 1965 that GSB had him go over GSB's work. This passage is quoted on the cover of some editions of LoF.

An analysis which purports to equate Varela's calculus with Kleene's `total recursive undecidability'.

Rehashes LoF with a proof of soundness and a comparison to propositional logic

First American edition. A second preface was added relating to ordinary imaginary numbers and the elimination of the Whitehead Russell Theory of Types. 4 pages.

A third preface was added relating to the four colour map theorem. 2 pages.

A fourth preface was added in which he talks about ``triunions'' or ``triple identities'' such as of reality, appearance and awareness, or imaginability, possibility and actuality, or what a thing is, what it isn't and the boundary between them. He claims/acknowledges that Sakyamuni (the Buddha) is ``the only other author who evidently discovered these laws.'' He invites the reader to join a siblinghood and help found a school of his methods for intuitively feeling and naturally acting upon the consequences of there being nothing. He calls the method and the siblinghood ``tarati.'' 4 pages. An extraduction was also added in which he claims to be, since before he could talk, a liberated being with unlimited thinking, superior to Bach, Mozart, Newton and Gauss, and asks for money and volunteers to help him found schools for superintelligent children such as he was. 5 pages. May be available from Bookmasters (800) 247-6553.

This book is announced at the end of the 1994 Limited Edition of LoF. It is to contain ``The most fantastic tales ever told.'' Publication is stated to occur in August/September 1994. Inquiries should be directed to: Bohmeier Verlag, Im Grund 1, D-29594 Soltendieck, Germany Voice: +49 5874 801, Fax: +49 5874 1682.

Humorous. Paradoxes as dynamic systems. Does not cite GSB but is related.

See p.114. Mentions GSB lectures at Esalen in discussion of Varela.

See First Chapter.

In case you can't get hold of LoF, chapter 11 and appendix B of this book are the next best thing. Chapters 12 and 13 extend GSB's work. This book includes material from the following papers: Varela (1975), Varela and Goguen (1978), Varela (1979b), Kauffman and Varela (1980).

An extract appears on the cover of some editions of LoF.

122 pages. Other participants: John Lilly (Chairperson), Kurt von Meier, Alan Watts, Douglas Kelley, Heinz von Foerster, Gregory Bateson, Walter Barney, Karl Pribram, Lu Ann King, Ram Dass, Brendan O'Regan.

Does not cite Laws of Form but is strongly related to the reentrant form dynamics thread, particularly Berkowitz et al (1988).

A biographical and non-technical mention of claimed four-color proof.

Only cites LoF in passing on page 45: ``The `chaos' of hsu:an is the nature of the world before any distinctions have been marked out and named, the wiggly Rorschach blot of nature. But as soon as even one distinction has been made, as between yin and yang or 0 and 1, all that we call the laws or principles of mathematics, physics and biology follow of necessity, as has recently been demonstrated in the calculus system of G. Spencer Brown.''

See p.66-91. A collection of transcribed talks by Allan Watts. The piece called ``Intellectual Yoga'' compared pure math to yoga and brings in disscussions of Wittgenstein and ``Tractatus'', and GSB and LoF.