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BIBLIOGRAPHY:
George Spencer Brown




An Observer Web Focus File




As of 2001, many of the best Websites on Spencer Brown's work have disappeared.
This Focus File is an attempt to salvage and preserve one of the most important 'missing' resources  a massive bibliography on Spencer Brown and his work.


In his 1979 book Principles of Biological Autonomy, Varela
intensively explored (and elaborated upon) the British logician George Spencer
Brown's 'calculus of indications'. Spencer Brown's Laws of Form
(1969) outlines a complete and consistent logic based on 'distinctions', which
Maturana and Varela identify as the elementary cognitive act.
In 1991, Dave Keenan set out to assemble a list of references on Spencer Brown and his Laws of Form. This was done via the Internet. Several of us from around the world contributed citations, which Dave compiled into an ASCII text file. The resultant bibliography was eventually posted on the Web, but all locations containing it have disappeared.
I have obtained the last (1995) edition of the ASCII text bibliography from Dave (Thanks, Dave!) and reformatted it for presentation as an Observer Web Focus File.
Some editing has been done on the listing (e.g., some Webaccessible items have been added).
This page has been constructed as a preservation project. It is not my intention to establish or maintain a Spencer Brown site per se.



















Prefatory Notes from the Original ASCII Text Bibliography (Dave Keenan)



Laws of Form and George SpencerBrown
Bibliography
David Keenan
16 Bowman Parade, Bardon QLD 4065, Australia
davek@peg.pegasus.oz.au
7Feb95


1 Laws of Form
Here is an update of my list of references relating to George SpencerBrown
and his book Laws of Form (1969). The first edition of this bibliography resulted from an enquiry posted to the Internet/USEnet newsgroups sci.logic and sci.math in Nov91 and the collated list was first posted to these groups on 7Dec91.
Many thanks to Dick Shoup, Tim Peters, Randall Whitaker, Kevin Sahr, William
Bricken, Cliff Joslyn, Lou Kauffman, Jorn Barger, Nancy (Whole Earth
Review), R Colin Johnson, Ralph Gillmann and the Sciences Citation Index for
supplying these references. And thanks to Jeff James for maintaining the
BibTeX version.
A new edition of Laws of Form can be ordered from BookMasters (USA). It
contains the original text plus a new preface and extraduction (see
description below).
BookMasters can be contacted at: PO Box 2039, Mansfield OH 44095, USA.
They're asking $50 + $5 shipping within the USA.
Voice: (tollfree in USA) (800) 2476553
(otherwise...) (+1) (419) 2811802
Fax: (+1) (419) 2816883
The latest address I have for George SpencerBrown (GSB) is: 18A Greville
Place, London NW6 5JH. Phone Int+441716242358. SpencerBrown was born in
Grimsby, Lincolnshire, England, on the 2nd of April 1923.
2 Other References
Apart from Laws of Form (LoF) itself, Francisco Varela's book Principles of
Biological Autonomy (1979) may be the most useful single reference below.
Author's adress: Email: fv@ccr.jussieu.fr
Lou Kauffman appears to be the most published writer on LoF related topics.
He has also written books on knot theory. His address is:
Dept Math Stats & Comp Sci
University of Illinois at Chicago (M/C 249)
PO Box 4348, Chicago, IL 60680.
Email: u10451@uicvm.uic.edu
William Bricken is also prolific on LoF related topics. His address is
Email: williamb@u.washington.edu
Some other authors' addresses appear after their first listing below.
3 Searching
If you are searching elsewhere note that citations can appear as "Brown, G.
S." or "SpenserBrown, G." (with an "s" instead of a "c") or "Keys,
J." (a pseudonym), as well as the correct "SpencerBrown, G.". For
example, in the Sciences Citation Index you should look for SPENCERBROWN,
SPENSERBROWN, BROWNGS, and KEYSJ.
If you find errors in these references, or fill in some of the unknowns, or
find references to add to this list, I would be extremely grateful for some
email or mail.
Apart from LoF, all works by SpencerBrown are out of print except possibly
by SpencerBrown & Co. (publishing), London, phone 441716242358 or
441836313122.



















The Bibliography


Here is the listing adapted from the 1995 ASCII text file.
 A few new citations have been added.
 Address / contact data for authors has been left within the listing, in case it could help you locate documents.
 Bear in mind that this listing dates back to 1995, and that the address / contact data is likely to be obsolete.



Acta Analytica (1993).

Brown, Mind and Logic (theme issue), Vol. 8, Issue 10, 1993.
Table of Contents listing abstracts for an issue apparently dedicated to analysis of Spencer Brown and his logic is available on the Web at:
http://www.unimb.si/~actaana/toc10.htm

Andrew, A. M. (1979).

A comment on Varela's "Calculus for selfreference"
(letter to the editor). International Journal of General Systems,
5:5759.

Asenjo, F. G. (1966).

A calculus of antinomies. Notre Dame Journal of Formal Logic, 7(1):103105.

Banaschewski, B. (1977).

On G. Spencer Brown's Laws of Form. Notre Dame Journal of Formal Logic, 18(3):507509.

Beer, S. (1971?).

Book review: Laws of Form. Nature.
An extract appears on the cover of some editions of LoF. A wrong
reference was supplied as Nature 215:312 (1971).

Berkowitz, G. C., Greenberg, D. R., and White, C. A. (1988).

An approach to
a mathematics of phenomena: canonical aspects of reentrant form
eigenbehavior in the extended calculus of indications. Cybernetics and Systems, 19(2):123167.
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.

Brand, S. (1981).

Review: Laws of Form. In The Next Whole Earth Catalog,
page 31. Point Foundation, California, 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]

Bricken, M. (1990a).

A calculus of creation. Technical Report HITLP913,
Human Interface Technology Laboratory of the Washington Technology
Center, University of Washington, Seattle, WA.
Meredith and William Bricken are wife and husband.

Bricken, W. (1986a).

A deductive mathematics for efficient reasoning.
Technical Report HITLR862, Human Interface Technology Laboratory of
the Washington Technology Center, University of Washington, Seattle, WA.
ftp://ftp.u.washington.edu/public/VirtualReality/HITL/papers/
techreports/bricken*.

Bricken, W. (1986b).

A simple space. In Proceedings of the Sign and Space
Conference, University of California at Santa Cruz. Also as Technical
Report HITLR863, Human Interface Technology Laboratory of the
Washington Technology Center, University of Washington.

Bricken, W. (1987a).

Boundary numbers. Technical report, Advanced Decision
Systems.

Bricken, W. (1987b).

The efficiency of boundary mathematics for deduction.
Technical Report ADS68241, Advanced Decision Systems.

Bricken, W. (1987c).

Utilizing boundary mathematics for deduction.
Technical report, Advanced Decision Systems.

Bricken, W. (1990b).

Boundary logic (boundary implementations). Technical
Report HITLP903, Human Interface Technology Laboratory of the
Washington Technology Center, University of Washington, Seattle, WA.

Bricken, W. (1990c).

Extended abstract: A formal foundation for cyberspace.
Technical Report HITLM9010, Human Interface Technology Laboratory of
the Washington Technology Center, University of Washington, Seattle, WA.

Bricken, W. (1992).

Spatial representation of elementary algebra. In
Proceedings of the 1992 IEEE Workshop on Visual Languages, pages 5662,
Seattle, Washington.

Bricken, W. et al. (1987).

Implementation of the extended program model for
the intelligent program editor. Technical Report TR104703, Advanced
Decision Systems.

Bricken, W. and Gullichsen, E. (1989).

An introduction to boundary logic
with the Losp deductive engine. Future Computing Systems, 2(4). Also as
Technical Report HITLR891, Human Interface Technology Laboratory of
the Washington Technology Center, University of Washington.

Bricken, W. and Nelson, P. C. (1986).

Pure lisp as a network of systems. In
Proceedings of the Second Kansas Conference: KnowledgeBased Software
Development, Kansas State University.

Calvino, I. (1976).

A sign in space. In Cosmicomics, pages 3139. Harcourt
Brace Jovanovich.

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

Campbell, H. (1987).

Mathematical development of the Laws of Form and
related Brownian algebraic logics. In Artificial Intelligence for
Advanced Concept Aircraft, volume II. Aeronautical Systems Division,
WrightPatterson Air Force Base.
A thorough search by a WrightPatterson 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.

Comfort, A. (1981).

Comments on Kauffman and Varela's 'Form Dynamics'.
Journal of Social and Biological Structures, 4:9196.
Includes a rejoinder from Kauffman and Varela.

Comfort, A. (1989).

A bridge to twentyfirst century science. The Lancet,
2(8678):15121513.
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 SpencerBrown's fundamental question: how is
it that the universe has aquired the capacity to be aware of itself?"

Cronen, V. E., Chen, V., and Pearce, W. B. (19??a).

Coordinated management
of meaning: A critical theory. In Theories in Intercultural
Communication, pages 6698.

Cronen, V. E., Johnson, K. M., and Lannamann, J. W. (1982).

Paradoxes,
double binds, and reflexive loops: An alternative theoretical
perspective. Family Process, 20:91112.

Cronen, V. E. and Pearce, W. B. (1981).

Logical force in interpersonal
communication. Communication, 6:567.
'The hierarchical operator, [cross], is taken from Brown's Laws of Form,
and is read "in the context of." For example, [X over Ycross], means
"Y in the context of X" and implies that whatever is asserted about Y
is limited to this context.' p. 24

Cronen, V. E., Pearce, W. B., and Harris, L. M. (19??b).

The coordinated
management of meaning: A theory of communication. In Human
Communication Theory, pages 6189.

Cull, P. and Frank, W. (1979).

Flaws of form. International Journal of General Systems, 5(4):201211.

Doyle, B., Friedman, M., and York, B. (1987).

An introduction to forms and
logic. Technical Report BUCS87008, Boston University.

Edmonds, Jr, J. D. (1978).

Hypercomplex number approach to Laws of Form and
logic. Speculations in Science and Technology, 1(3):245251.

Engstrom, J. S. (1994).

Natural numbers and finite sets derived from G.
SpencerBrown's Laws of Form. Thesis, Master of Science in Mathematics,
Maharishi International University, Fairfield, IA.
Author's address: "Jack" John S. Engstrom, c/o Department of
Mathematics, Maharishi International University, 1000 N 4th Street,
Fairfield IA 525570129, USA. Ph: (515) 472 5031 ext 2222 rm 4, Fax:
(515) 472 1123, Email: grads@math.miu.edu. Also: 2725 Carmel Street,
Oakland CA 946023406, USA. Ph: (510) 531 6427

Etter, T. (1991).

Are the Laws of Form nonboolean? ANPA West (Journal of
the Western Chapter of the Alternative Natural Philosophy Association),
2(3):1943.
Author's address (also ANPA West address): 112 Blackburn Avenue, Menlo
Park CA 94025. Ph: (415) 324 4235. Email: 72134.3066@compuserve.com.

Flemons, D.

Completing Distinctions: Interweaving the ideas of Gregory Bateson and Taoism into a unique approach to therapy, Boston / London: Shambhala, 1991.
An interesting book in which Flemons heavily invokes Spencer Brown's calculus of indications within a context laced with von Foerster, Varela, Bateson, and Eastern thought.

Fry, R. (1994a).

Neural processing of information. In Proceedings of the
IEEE International Symposium on Information Theory.
Author's Email address: robert_fry@aplmail.jhuapl.edu.

Fry, R. (1994b).

Observerparticipant models of neural processing. IEEE
Transactions on Neural Networks.

Gardner, M. (197?).

Review. Scientific American. Date and pages unknown.
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.

Glanville, R. (1979).

Beyond the boundaries. In Ericson, R., editor,
Improving the Human Condition: Quality and Stability in Social Systems.
Springer, London.

Glanville, R. (1990).

The self and the other: The purpose of distinction, in Trappl, R. (ed.) Cybernetics and Systems '90. Singapore: World Scientific, 1990.
The nature of distinction drawing (Spencer Brown) is examined with special reference to the distinction between the self and the other. Glanville's critique of Spencer Brown and his calculus of indications.
http://www.univie.ac.at/constructivism/papers/glanville/glanville90selfother.pdf

Glanville, R. (1995).

The cybernetics of value and the value of cybernetics. The art of invariance and the invariance of art, in Glanville, R. & de Zeeuw, G. (eds.) Problems of Values and (In)variants, Amsterdam: Thesis Publishers, 1995.
Abstract
In this paper, Spencer Brown's Logic of Distinctions is considered in the light of various amendments proposed by the author. These considerations, concerning (in the main) the notion of the separation of the mark and the value of the distinction, are examined in terms of value (meaning) and invariance (remaining, being) in art Objects. The contradiction between an older view of meaning as inherent in Objects and the more recent view of meanings being with the observer is elaborated; and the way that these attitudes can be seen as complementary is related to attitudes to and experiences of such art Objects.
http://www.univie.ac.at/constructivism/papers/glanville/glanville95value.pdf

Glanville, R. and Varela, F. J. (1980).

Your inside is out and your outside
is in. In Lasker, G., editor, Applied Systems and Cybernetics,
volume II. Pergamon, Oxford.

Goguen, J. A. and Varela, F. J. (1979).

Systems and distinctions; duality
and complementary. International Journal of General Systems, 5:3143.

Goldman, J. and Kauffman, L. H. (1993).

Knots, tangles and electrical
networks. Advances in Applied Mathematics, 14:267306.

Gould, W. E. (1977).

Review: Laws of Form. Journal of Symbolic Logic,
42:317318.

GrattanGuinness, I. (1982).

Psychology in the foundations of logic and
mathematics: the cases of Boole, Cantor and Brouwer. History and
Philosophy of Logic, 3(1):3353.

Gunji, Y. (1990a).

The algebraic properties of finite cellular automata.
Physica D, 41:282294.

Gunji, Y. (1990b).

Pigment color patterns of mollusks as an autonomous
process generated by asynchronous automata. Biosystems, 23(4):317334.

Gunji, Y. and Nakamura, T. (1991).

Time reverse automata patterns generated
by SpencerBrown modulator  invertibility based on autopoiesis.
Biosystems, 25(3):151177.

Gunji, Y. and Norio, K. (1991).

Artificial life with autonomously emerging
boundaries. Applied Mathematics and Computation, 43(3):271298.

Haddawy, P., Bricken, W., and Fung, R. (1987).

The problem of robustness:
A multivalued logic approach. Technical Report TR592801, Advanced
Decision Systems, Mountain View, CA.

Handler, I., Kauffman, L. H., and Sandin, D. (1989).

On crossing the boundary of the Mandelbrot set. In Computers in geometry and topology, number 114 in Lecture Notes in Pure and Applied Mathematics, pages
151177.

Harris, L. M. and Cronen, V. E. (1979).

A rulesbased model for the analysis and evaluation of organizational communication. Communication Quarterly, 27:1228.

Hellerstein, N. S. (1984).

Diamond: A Fourvalued approach to the problem
of paradox. PhD thesis, University of California, Berkeley.
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.

Hellerstein, N. S. (1985).

Diamond: A logic of paradox. Cybernetic, 1(1):101114. Selfpublished.

Hellerstein, N. S. (1994a).

Contra Cantor. Unpublished.

Hellerstein, N. S. (1994b).

Nfold logic  or  paradox island.
Unpublished.

Heylighen, F. (1989).

Causality as distinction conservation: a theory of
predictability, reversibility and time order. Cybernetics and Systems,
20:361384.

Heylighen, F. (1990a).

Classical and nonclassical representations in
physics I. Cybernetics and Systems, 21:423444.

Heylighen, F. (1990b).

Classical and nonclassical representations in
physics II: Quantum mechanics. Cybernetics and Systems, 21:477502.

Heylighen, F. (1990c).

Relational closure. In Trappl, R., editor,
Cybernetics and Systems '90, volume 21, pages 335342. World Science.
Mathematical concept for distinctionmaking and complexity analysis.

Heylighen, F. (1990d).

Representation and Change. A Metarepresentational
Framework for the Foundations of Physical and Cognitive Science,
Communication and Cognition. PhD thesis, Gent, Belgium.

Heylighen, F. (1992).

Nonrational cognitive processes as changes of
distinctions. In van de Vijver, G., editor, New Perspectives on
Cybernetics. SelfOrganization, Autonomy and Connectionism, Synthese
Library v.220, pages 77220. Kluwer Academic, Dordrecht.

Holt, C. M. (1994).

An algebra of lines and boxes. In Proceedings of the
1994 IEEE Symposium on Visual Languages.
Author's Email address: chris.holt@newcastle.ac.uk.

Hopkins, M. (1994).

Laws of Form as a functional calculus. Posted to the
USEnet newsgroup sci.math Mar 13, 1994 and updated to sci.logic Apr 21.
An attempt to translate LoF, the whole book, including the metalevel
canons, principles and rules, into a functional language and categorical
combinator system in the spirit of CAML. Author's Email address:
mark@omnifest.uwm.edu.

Howe, R. and von Foerster, H. (1975).

Introductory comments to Francisco
Varela's calculus for selfreference. International Journal of General Systems, 2:13.

Jacobs, W. J., Blackburn, J. R., Buttrick, M., and Harpur, T. J. (1988).

Observations. Psychobiology, 16(1):319.
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 (...; SpencerBrown, 1979;...)."

James, J. M. (1993).

A calculus of number based on spatial forms. Thesis,
Master of Science in Engineering, University of Washington.
http://www.hitl.washington.edu/publications/JamesThesis.ps. Author's
Email address: jjames@acm.org.

James, J. M. and Bricken, W. (1992).

A boundary notation for visual
mathematics. In Proceedings of the 1992 IEEE Workshop on Visual
Languages, pages 267269, Seattle, Washington.

Johnson, R. C. (1994a).

Breaking the laws of logic. Electronic Engineering
Times, pages 1,31,34,35. Part 1 of 4.
CMP Publications, 600 Community Drive, Manhasset, NY 11030. Author's
Email address: rcjohnson@aol.com.

Johnson, R. C. (1994b).

Laws of Form are gaining support. Electronic Engineering Times, pages 3133. Part 2 of 4.

Johnson, R. C. (1994c).

Building the laws of form. Electronic Engineering Times, pages 4362. Part 3 of 4.

Johnson, R. C. (1994d).

Laws of form exceed bounds. Electronic Engineering Times, pages 3739. Part 4 of 4.

Jokisch, Rodrigo

SUMMARIES OF CHAPTERS I. TO V. from:
Logic of Distinctions A Protologic for a Theory of Society.
English translation of: Kapitelzusammenfassungen I. bis V. (3246), from: Logik der Distinktionen. Zur Protologik einer Theorie der Gesellschaft, Opladen:Westdeutscher Verlag, 1996.
Summary overview of sections of a German thesis. Contains some interesting remarks about Spencer Brown in the context of distinctions and differentiations as applied to the social.
http://www.geocities.com/Athens/Thebes/4211/jokischlog_i_v.html

Kampis, G. (199?)

Computability, selfreference, and selfamendment, Communication and
Cognition  Artificial Intelligence, Vol. 12, Nos.12, Special Issue on
SelfReference in Biological and Cognitive Systems, pp. 91109.
Available via WWW at:
http://www.c3.lanl.gov/~rocha/kampis.html

Kauffman, L. H. (1977).

Review #4892: Laws of Form. Mathematical Reviews,
54:701702.

Kauffman, L. H. (1978a).

DeMorgan algebras  completeness and recursion. In
Proceedings of the Eighth International Symposium on MultipleValued
Logic, pages 8286. IEEE Computer Society Press.

Kauffman, L. H. (1978b).

Network synthesis and Varela's calculus.
International Journal of General Systems, 4:179187.

Kauffman, L. H. (1980).

Complex numbers and algebraic logic. In Proceedings
of the 10th International Symposium on MultipleValued Logic, pages
209213. IEEE Computer Society Press.

Kauffman, L. H. (1983).

Multiple viewpointa review essay. Journal of Social and Biological Structures, 6:265271.

Kauffman, L. H. (1984).

On the form of selfreference. In Proceedings of
the 1984 General Systems Society Meeting, Los Angeles.

Kauffman, L. H. (1985a).

Sign and space. In Religious Experience and
Scientific Paradigms, Proceedings of the IASWR Conference, pages
118164, Stony Brook, NY. Institute for Advanced Study of World
Religions.

Kauffman, L. H. (1985b).

Transformations in special relativity.
International Journal of Theoretical Physics, 24:223236.

Kauffman, L. H. (1986).

Map Reformulation. Princelet Edition #30, 25
Princelet Street, London, U.K.
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 4color 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. Author's Email address:
u10451@uicvm.uic.edu.

Kauffman, L. H. (1986,90,92a).

Arithmetic in the form. Technical report,
University of Illinois at Chicago, Dept Math Stats & Comp Sci.

Kauffman, L. H. (1986,90,92b).

String arithmetic. Technical report,
University of Illinois at Chicago, Dept Math Stats & Comp Sci.

Kauffman, L. H. (1987a).

Imaginary values in mathematical logic. In
Proceedings of the 17th International Symposium on MultipleValued
Logic, pages 282289, Boston, MA. IEEE Computer Society Press.

Kauffman, L. H. (1987b).

On Knots. Princeton University Press.
See chapter VI, sections 4, 5, 8.

Kauffman, L. H. (1987c).

Selfreference and recursive forms. Journal of Social and Biological Structures, 10:5372.

Kauffman, L. H. (1987d).

Sign and space  an introduction. Handwritten
notes toward a book of the same title. 68 pages.

Kauffman, L. H. (1988a).

The form of arithmetic. In Proceedings of the 18th
International Symposium on MultipleValued Logic. IEEE Computer Society
Press.

Kauffman, L. H. (1988b).

Notes on the arrow. Technical report, University
of Illinois at Chicago, Dept Math Stats & Comp Sci.

Kauffman, L. H. (1988c).

Special relativity and a calculus of distinctions.
Technical report, University of Illinois at Chicago, Dept Math Stats &
Comp Sci.

Kauffman, L. H. (1989).

FormCreation. 30 pages. Poetry regarding 0, 1, 2
and 3 dimensions, boundaries, knots and selfreference.

Kauffman, L. H. (1990a).

An integral heuristic. International Journal of Modern Physics A, 5(7):13631367.

Kauffman, L. H. (1990b).

Map coloring and the vector cross product. Journal of Combinatorial Theory, Series B, 48(2):145154.

Kauffman, L. H. (1990c).

Robbins algebra. In Proceedings of the 20th International Symposium on MultipleValued Logic, pages 5460, Charlotte, NC. IEEE Computer Society Press.

Kauffman, L. H. (1990d).

Schrodinger's cat and the cheshire cat: Quantum
mechanics and Laws of Form. ANPA West (Journal of the Western Chapter of
the Alternative Natural Philosophy Association), 2(2):933.
ANPA West address: 112 Blackburn Avenue, Menlo Park CA 94025. Ph:
(415) 324 4235. Email: 72134.3066@compuserve.com.

Kauffman, L. H. (1991a).

Knots and Physics. World Scientific, Teaneck, NJ.

Kauffman, L. H. (1991b).

The primary algebra of SpencerBrown is nonboolean. ANPA West (Journal of the Western Chapter of the Alternative Natural Philosophy Association), 2(3):518.

Kauffman, L. H. (1992a).

Link polynomials and a graphical calculus. Journal of Knot Theory and its Ramifications, 1(1):59104.

Kauffman, L. H. (1992?b).

Reflections on reflexivity  the form of selfreference. Possibly an update of Kauffman, L. H. (1984) 'On the Form of SelfReference.'.

Kauffman, L. H. (1993).

Circuit automata. Unpublished.

Kauffman, L. H. (1994a).

Knot automata. In The TwentyFourth International Symposium on Multiple Valued Logic, pages 328333, Boston, MA. IEEE Computer Society.
This paper is a condensed version of Kauffman (1993) 'Circuit Automata'.

Kauffman, L. H. (1994b).

Knot logic. In Kauffman, L. H., editor, Knots and Applications. World Scientific Press. In press.

Kauffman, L. H. (1994c).

Ways of the game  play and position play. In Brier, S., editor, Cybernetics and Human Knowing. The Royal School of Librarianship, Aalborg Branch, Langagervej 4, DK9220 Aalborg 0st, Denmark.

Kauffman, L. H. and Baadhio, R., editors (1993).

Quantum Topology. Knots and Everything. World Scientific.
It contains an introduction to quantum topology by L. H. Kauffman that
is an example of the interaction of formal mathematics with physics and
topology.

Kauffman, L. H. and Solzman, D. M. (1981).

Letter to the editor.
International Journal of General Systems, 7:253256.
A response to Cull and Frank (1979) and Kohout and Pinkava (1980).

Kauffman, L. H. and Varela, F. J. (1980).

Form dynamics. Journal of Social and Biological Structures, 3:171206.

Keenan, D. C. (1991).

To dissect a mockingbird  a graphical notation for
the lambda calculus with animated reduction. Unpublished.
Author's address: 116 Bowman Parade, Bardon QLD 4065, Australia. Email:
davek@peg.pegasus.oz.au.

Keenan, D. C. (1992).

Learning logic functions explicitly by backpropagation in nornets. In Proceedings of the International Workshop on Emerging Technologies and Factory Automation, pages 435440, Melbourne, Australia.

Keys, J. (1970).

Twentythree Degrees of Paradise. Cat Books, 17 Halifax Rd, Cambridge, UK.
Poetry. "James Keys" is a pseudonym of George SpencerBrown.

Keys, J. (1971).

Only Two Can Play This Game. Cat Books, 17 Halifax Rd, Cambridge, UK.
Love poetry plus scientific mysticism.

Keys, J. (1972).

Only Two Can Play This Game. Julian Press, New York.
First US edition.

Keys, J. (1974).

Only Two Can Play This Game. Bantam (Ballantine?), New
York.

Kohout, L. J. and Pinkava, V. (1980).

The algebraic structure of the Spencer Brown and Varela calculi. International Journal of General Systems, 6:155171.

Laycock, S. W. (1994).

Mind as Mirror and the Mirroring of Mind: Buddhist Reflections on Western Phenomenology. State University of New York (SUNY) Press.
He refers to Brown, G. Spencer on pages 31, 4044 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).

LeTourneau, J. (1993).

Prime arithmetics. Overhead projector slides which accompanied a lecture.
A boundary arithmetic system based on prime factors. Address: Prime
Arithmetics, 3410 Geary Street, Suite 311, San Francisco, CA 94118, USA.

Lilly, J. C. (1972).

The Centre of the Cyclone. Granada Publishing Limited.
Published in Great Britain in 1973 by Paladin Frogmore, St Albans, Herts
AL2 2NF. Reprinted 1973,74,77.
Only contains, as a preface, a quote from LoF pp109110 "Discoveries...
furtively.", without comment.

Matherne, Bobby (1999)

Brown, G. Spencer: Laws of Form Evolution of Consciousness, Book Notes by Bobby Matherne, 1999. Excerpted from A READER'S TREASURY, published by Julian Press/NY in 1972. Provides a summary sketch of Spencer Brown's ideas.
http://home.earthlink.net/~jeauxy/lofmart.htm

Merrell, F. (1982).

Semiotic Foundations: Steps toward an Epistemology of Written Texts. Indiana University Press, Bloomington, IN.
In a note (p. 153) he says "I cannot overestimate the influence of SpencerBrown's 'Laws of Form' on this book."

Miller, J. (199?)

G. SpencerBrown, The Laws of Form (essay available as a Webpage).
John provides his collection of notes on Spencer Brown's work, comments received about it, etc. Contains some interesting notes and gossip  tidbits I'd never run across before.
http://sun.lclark.edu/~miller/spencerbrown.html

Miller, J. C. P. and SpencerBrown, D. J. (1966).

An algorithm for evaluation of remote terms in a linear recurrence sequence. The Computer Journal, 9:188190.
D. J. SpencerBrown is G. SpencerBrown's brother who died in 1976.

Odegard, S. L. (1989).

Chapter 4a: The extension. Posted to Usenet newsgroup sci.math 29Nov89, reply to n8243274@unicorn.wwu.edu.

Olson, A. T. and Sawada, D. (1988).

Computer, quantized time and human duration. Cybernetica, 31(2):6576.

Orchard, R. A. (197?).

Title unknown. PhD thesis, College of Staten Island?

Orchard, R. A. (1975).

On the Laws of Form. International Journal of General Systems, 2:99106.

Oshins, E. (1990).

Why Brown's 'Laws of Form' and Pribram's "Hologram Hypothesis" are "...just what is not relevant in a 'quantum context' ". In Young, F., editor, Causal Structure and the Quantum, Instant Proceedings of the 6th Annual Meeting of ANPA West, Stanford University. Alternative Natural Philosophy Association.
Author's address: Department of Physics, Stanford University, Stanford
CA 943052196, USA.

Oshins, E. (1991).

About models and muddles, part I: Why Brown's 'Laws of Form' and Pribram's "Hologram Hypothesis" are not relevant to quantum physics and quantum psychology. In Manthey, M., editor, Alternatives in Physics and Biology, Proceedings of the XII Annual International Meeting of the Alternative Natural Philosophy Association (ANPA), Cambridge, UK.
Largely a correction and extension of Oshins (1990).

Parsons, D. (1975).

The Directory of Tunes and Musical Themes. SpencerBrown & Co., Cambridge, England.
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
uniquely in 15, often fewer, notes. The book is divided into two parts,
classical themes and popular melodies.

Pearce, W. B. and Cronen, V. E. (1980).

Communication, Action, and Meaning: The Creation of Social Realities. Praeger, New York.

Peat, F. D. (1987).

Synchronicity: The Bridge Between Matter and Mind. Bantam Books.
See pp.198206. A fairly basic description plagued by the all too common
typos where blanks, and in this case their preceding equals signs, get
lost.

Pedretti, A. (1980).

Epistemology, semantics, and selfreference. Journal of Cybernetics, 10(4):313339.

Peirce, C. S. (1931).

Collected Papers of Charles Sanders Peirce. Harvard University Press, Cambridge.
In the view of Fritz Lehmann, Email Address: fritz@rodin.wustl.edu, almost everything in LoF is in the "Entitative Graphs" developed earlier by Charles S. Peirce on his way towards developing his Existential Graphs. The notation is almost identical. Clearly GSB knew of Peirce's work because a citation to his Collected Papers appears in LoF for another purpose. GSB also cites Peirce's brilliant student Christine LaddFranklin. As an alternative to the above ref see Roberts (1973) or (1992).

Pountain, D. (1982).

Namer of the nameless. Australian Personal Computer, 3(10).
A nontechnical review of LoF. It probably appeared in Byte magazine at
about this time also.

Roberts, D. D. (1973).

The Existential Graphs of Charles S. Peirce. Mouton, The Hague.

Roberts, D. D. (1992).

The existential graphs. In Lehmann, F., editor, Semantic Networks in Artificial Intelligence. Pergamon Press. Also in Computers and Math. with Applications, 23(29).

Rolt, C. E. (1920).

Dionysius the Areopagite on the Divine Names and the Mystical Theology.
GSB appears to have been influenced by this book based on a translation
from 5th century Greek.

Russell, B. (1967).

The Autobiography of Bertrand Russell 19441967, volume III. George Allen and Unwin Ltd, London.
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.

Schwartz, D. G. (1981).

Isomorphisms of Spencer Brown's Laws of Form and Varela's calculus for selfreference. International Journal of General Systems, 6:239255.
An analysis which purports to equate Varela's calculus with Kleene's 'total recursive undecidability'.

Shoup, R. G. (1993).

A complex logic for computation with simple interpretations for physics. In PhysComp '92, Workshop on Physics and Computation. IEEE Press.
Author's Email address: shoup@interval.com.

SotoAndrade, J. and Varela, F. J. (1984).

Selfreference and fixed pointsa discussion and extension of Lawvere's theorem. Acta Applicandae Mathematicae, 2:119.

SpencerBrown, G. (1957).

Probability and Scientific Inference. Longmans, London.

SpencerBrown, G. (1961).

An algebra for the natural numbers. Unpublished.

SpencerBrown, G. (1965).

British patent specifications 1006018 Lift Control System and 1006019 Lift Control Circuit Arrangement.

SpencerBrown, G. (1969).

Laws of Form. Allen and Unwin, London.

SpencerBrown, G. (1972).

Laws of Form. Julian Press, New York, 2nd
edition.
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.

SpencerBrown, G. (1979).

Laws of Form. E. P. Dutton, New York, 3rd
edition.
A third preface was added relating to the four colour map theorem. 2
pages.

SpencerBrown, G. (1982).

The Falkland papers.

SpencerBrown, G. (1994a).

Laws of Form. Cognizer Connection, Portland, OR.
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.

SpencerBrown, G. (1994b).

A Lion's Teeth. Bohmeier Verlag, Soltendieck, Germany.
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, D29594 Soltendieck, Germany Voice: +49 5874 801, Fax: +49 5874 1682.

Stewart, I. (1993).

A partly true story; fuzzy logic; includes related article; Mathematical recreations. Scientific American, 268(2):110.
Humorous. Paradoxes as dynamic systems. Does not cite GSB but is
related.

Swiggart, P. (1974).

Selfreference in formal languages. Notre Dame Journal of Formal Logic, 15(4).

Turney, P. (1986).

Laws of Form and finite automata. International Journal of General Systems, 12(4):307318.

Unknown (1958?).

Book review: Probability and scientific inference. Scientific American. Month and pages unknown.

Varela, F. J. (1975).

A calculus for selfreference. International Journal of General Systems, 2:524.

Varela, F. J. (1979a).

??? International Journal of General Systems, 5(1):3143.

Varela, F. J. (1979b).

The extended calculus of indications interpreted as a threevalued logic. Notre Dame Journal of Formal Logic, 20(1):141146.

Varela, F. J. (1979c).

Principles of Biological Autonomy. Elsevier / North Holland, New York.
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).

Varela, F. J. and Goguen, J. A. (1978a).

The arithmetic of closure. Journal of Cybernetics, 8:4864.

Varela, F. J. and Goguen, J. A. (1978b).

The arithmetic of closure. Progress in Cybernetics and Systems Research, 3:3864.

von Foerster, H. (1972).

Review: Laws of Form. In The Whole Earth Catalog. Random House, New York.
An extract appears on the cover of some editions of LoF.

von Meier, K., editor (1973).

SpencerBrown Transcript, Art 269. Unpublished transcript of discussions with GSB at the Aum conference at Esalen Institute, Big Sur, CA (March 1920, 1973).
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.

Vuillemin, J. (1993).

On circuits and numbers. Research Report 25, Digital PRL.
Author's address: Digital Equipment Corporation Paris Research
Laboratory, 85 Av. Victor Hugo, 92563 RueilMalmaison, Cedex France.
Does not cite Laws of Form but is strongly related to the reentrant form
dynamics thread, particularly Berkowitz et al (1988).

Waldo, I. (1978).

Nagarjuna and analytic philosophy, II. Philosophy East and West, 28(3):287298.

Walgate, R. (1977).

A colourful character. New Scientist, 6Jan:6.
A biographical and nontechnical mention of claimed fourcolor proof.

Watts, A. (1975).

Tao: The Watercourse Way. Penguin, London.
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."

Whyte, L. L. (1972).

Review: Laws of Form. British Journal of Philosophy
of Science, 23:291292.

















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