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BIBLIOGRAPHY: George Spencer Brown

An Observer Web  Focus File

Prefatory Notes from the original ASCII text listing (Dave Keenan) The Bibliography ... on Spencer Brown and/or his Work 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 Web-accessible 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 Spencer-Brown Bibliography David Keenan 16 Bowman Parade, Bardon QLD 4065, Australia davek@peg.pegasus.oz.au 7-Feb-95

1 Laws of Form Here is an update of my list of references relating to George Spencer-Brown 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 Nov-91 and the collated list was first posted to these groups on 7-Dec-91. 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: (toll-free in USA) (800) 247-6553 (otherwise...) (+1) (419) 281-1802 Fax: (+1) (419) 281-6883 The latest address I have for George Spencer-Brown (GSB) is: 18A Greville Place, London NW6 5JH. Phone Int+44-171-624-2358. Spencer-Brown 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 "Spenser-Brown, G." (with an "s" instead of a "c") or "Keys, J." (a pseudonym), as well as the correct "Spencer-Brown, G.". For example, in the Sciences Citation Index you should look for SPENCERBROWN, SPENSERBROWN, BROWN-GS, and KEYS-J. 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 Spencer-Brown are out of print except possibly by Spencer-Brown & Co. (publishing), London, phone 44-171-624-2358 or 44-1836-313122.

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.uni-mb.si/~actaana/toc10.htm Andrew, A. M. (1979). A comment on Varela's "Calculus for self-reference" (letter to the editor). International Journal of General Systems, 5:57-59. Asenjo, F. G. (1966). A calculus of antinomies. Notre Dame Journal of Formal Logic, 7(1):103-105. Banaschewski, B. (1977). On G. Spencer Brown's Laws of Form. Notre Dame Journal of Formal Logic, 18(3):507-509. 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):123-167. 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 HITL-P-91-3, 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 HITL-R-86-2, Human Interface Technology Laboratory of the Washington Technology Center, University of Washington, Seattle, WA. ftp://ftp.u.washington.edu/public/VirtualReality/HITL/papers/ tech-reports/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 HITL-R-86-3, 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 ADS-6824-1, 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 HITL-P-90-3, 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 HITL-M-90-10, 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 56-62, Seattle, Washington. Bricken, W. et al. (1987). Implementation of the extended program model for the intelligent program editor. Technical Report TR-1047-03, 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 HITL-R-89-1, 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: Knowledge-Based Software Development, Kansas State University. Calvino, I. (1976). A sign in space. In Cosmicomics, pages 31-39. 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, Wright-Patterson Air Force Base. 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. Comfort, A. (1981). Comments on Kauffman and Varela's 'Form Dynamics'. Journal of Social and Biological Structures, 4:91-96. Includes a rejoinder from Kauffman and Varela. Comfort, A. (1989). A bridge to twenty-first century science. The Lancet, 2(8678):1512-1513. 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?" Cronen, V. E., Chen, V., and Pearce, W. B. (19??a). Coordinated management of meaning: A critical theory. In Theories in Intercultural Communication, pages 66-98. Cronen, V. E., Johnson, K. M., and Lannamann, J. W. (1982). Paradoxes, double binds, and reflexive loops: An alternative theoretical perspective. Family Process, 20:91-112. Cronen, V. E. and Pearce, W. B. (1981). Logical force in interpersonal communication. Communication, 6:5-67. '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 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 61-89. Cull, P. and Frank, W. (1979). Flaws of form. International Journal of General Systems, 5(4):201-211. Doyle, B., Friedman, M., and York, B. (1987). An introduction to forms and logic. Technical Report BUCS-87-008, Boston University. Edmonds, Jr, J. D. (1978). Hypercomplex number approach to Laws of Form and logic. Speculations in Science and Technology, 1(3):245-251. Engstrom, J. S. (1994). Natural numbers and finite sets derived from G. Spencer-Brown'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 52557-0129, USA. Ph: (515) 472 5031 ext 2222 rm 4, Fax: (515) 472 1123, Email: grads@math.miu.edu. Also: 2725 Carmel Street, Oakland CA 94602-3406, USA. Ph: (510) 531 6427 Etter, T. (1991). Are the Laws of Form non-boolean? ANPA West (Journal of the Western Chapter of the Alternative Natural Philosophy Association), 2(3):19-43. 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). Observer-participant 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/glanville90-selfother.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/glanville95-value.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, 5:31-43. Goldman, J. and Kauffman, L. H. (1993). Knots, tangles and electrical networks. Advances in Applied Mathematics, 14:267-306. Gould, W. E. (1977). Review: Laws of Form. Journal of Symbolic Logic, 42:317-318. Grattan-Guinness, I. (1982). Psychology in the foundations of logic and mathematics: the cases of Boole, Cantor and Brouwer. History and Philosophy of Logic, 3(1):33-53. Gunji, Y. (1990a). The algebraic properties of finite cellular automata. Physica D, 41:282-294. Gunji, Y. (1990b). Pigment color patterns of mollusks as an autonomous process generated by asynchronous automata. Biosystems, 23(4):317-334. Gunji, Y. and Nakamura, T. (1991). Time reverse automata patterns generated by Spencer-Brown modulator - invertibility based on autopoiesis. Biosystems, 25(3):151-177. Gunji, Y. and Norio, K. (1991). Artificial life with autonomously emerging boundaries. Applied Mathematics and Computation, 43(3):271-298. Haddawy, P., Bricken, W., and Fung, R. (1987). The problem of robustness: A multi-valued logic approach. Technical Report TR-5928-01, 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 151-177. Harris, L. M. and Cronen, V. E. (1979). A rules-based model for the analysis and evaluation of organizational communication. Communication Quarterly, 27:12-28. Hellerstein, N. S. (1984). Diamond: A Four-valued 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):101-114. Self-published. Hellerstein, N. S. (1994a). Contra Cantor. Unpublished. Hellerstein, N. S. (1994b). N-fold logic - or - paradox island. Unpublished. Heylighen, F. (1989). Causality as distinction conservation: a theory of predictability, reversibility and time order. Cybernetics and Systems, 20:361-384. Heylighen, F. (1990a). Classical and non-classical representations in physics I. Cybernetics and Systems, 21:423-444. Heylighen, F. (1990b). Classical and non-classical representations in physics II: Quantum mechanics. Cybernetics and Systems, 21:477-502. Heylighen, F. (1990c). Relational closure. In Trappl, R., editor, Cybernetics and Systems '90, volume 21, pages 335-342. World Science. Mathematical concept for distinction-making 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). Non-rational cognitive processes as changes of distinctions. In van de Vijver, G., editor, New Perspectives on Cybernetics. Self-Organization, Autonomy and Connectionism, Synthese Library v.220, pages 77-220. 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 meta-level 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 self-reference. International Journal of General Systems, 2:1-3. Jacobs, W. J., Blackburn, J. R., Buttrick, M., and Harpur, T. J. (1988). Observations. Psychobiology, 16(1):3-19. 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;...)." 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/James-Thesis.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 267-269, 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 31-33. Part 2 of 4. Johnson, R. C. (1994c). Building the laws of form. Electronic Engineering Times, pages 43-62. Part 3 of 4. Johnson, R. C. (1994d). Laws of form exceed bounds. Electronic Engineering Times, pages 37-39. 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. (32-46), 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, self-reference, and self-amendment, Communication and Cognition - Artificial Intelligence, Vol. 12, Nos.1-2, Special Issue on Self-Reference in Biological and Cognitive Systems, pp. 91-109. Available via WWW at: http://www.c3.lanl.gov/~rocha/kampis.html Kauffman, L. H. (1977). Review #4892: Laws of Form. Mathematical Reviews, 54:701-702. Kauffman, L. H. (1978a). DeMorgan algebras - completeness and recursion. In Proceedings of the Eighth International Symposium on Multiple-Valued Logic, pages 82-86. IEEE Computer Society Press. Kauffman, L. H. (1978b). Network synthesis and Varela's calculus. International Journal of General Systems, 4:179-187. Kauffman, L. H. (1980). Complex numbers and algebraic logic. In Proceedings of the 10th International Symposium on Multiple-Valued Logic, pages 209-213. IEEE Computer Society Press. Kauffman, L. H. (1983). Multiple viewpoint-a review essay. Journal of Social and Biological Structures, 6:265-271. Kauffman, L. H. (1984). On the form of self-reference. 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 118-164, Stony Brook, NY. Institute for Advanced Study of World Religions. Kauffman, L. H. (1985b). Transformations in special relativity. International Journal of Theoretical Physics, 24:223-236. 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 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. 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 Multiple-Valued Logic, pages 282-289, 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). Self-reference and recursive forms. Journal of Social and Biological Structures, 10:53-72. 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 Multiple-Valued 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 self-reference. Kauffman, L. H. (1990a). An integral heuristic. International Journal of Modern Physics A, 5(7):1363-1367. Kauffman, L. H. (1990b). Map coloring and the vector cross product. Journal of Combinatorial Theory, Series B, 48(2):145-154. Kauffman, L. H. (1990c). Robbins algebra. In Proceedings of the 20th International Symposium on Multiple-Valued Logic, pages 54-60, 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):9-33. 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 Spencer-Brown is non-boolean. ANPA West (Journal of the Western Chapter of the Alternative Natural Philosophy Association), 2(3):5-18. Kauffman, L. H. (1992a). Link polynomials and a graphical calculus. Journal of Knot Theory and its Ramifications, 1(1):59-104. Kauffman, L. H. (1992?b). Reflections on reflexivity - the form of self-reference. Possibly an update of Kauffman, L. H. (1984) 'On the Form of Self-Reference.'. Kauffman, L. H. (1993). Circuit automata. Unpublished. Kauffman, L. H. (1994a). Knot automata. In The Twenty-Fourth International Symposium on Multiple Valued Logic, pages 328-333, 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, DK-9220 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, 7:253-256. 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, 3:171-206. 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 back-propagation in nor-nets. In Proceedings of the International Workshop on Emerging Technologies and Factory Automation, pages 435-440, Melbourne, Australia. Keys, J. (1970). Twenty-three Degrees of Paradise. Cat Books, 17 Halifax Rd, Cambridge, UK. Poetry. "James Keys" is a pseudonym of George Spencer-Brown. 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, 6:155-171. 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, 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). 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 pp109-110 "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 Spencer-Brown's 'Laws of Form' on this book." Miller, J. (199?) G. Spencer-Brown, 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/spencer-brown.html Miller, J. C. P. and Spencer-Brown, D. J. (1966). An algorithm for evaluation of remote terms in a linear recurrence sequence. The Computer Journal, 9:188-190. D. J. Spencer-Brown is G. Spencer-Brown's brother who died in 1976. Odegard, S. L. (1989). Chapter 4a: The extension. Posted to Usenet newsgroup sci.math 29-Nov-89, reply to n8243274@unicorn.wwu.edu. Olson, A. T. and Sawada, D. (1988). Computer, quantized time and human duration. Cybernetica, 31(2):65-76. 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, 2:99-106. 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 94305-2196, 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. Spencer-Brown & 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.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. Pedretti, A. (1980). Epistemology, semantics, and self-reference. Journal of Cybernetics, 10(4):313-339. 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 Ladd-Franklin. 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 non-technical 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(2-9). 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 1944-1967, 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 self-reference. International Journal of General Systems, 6:239-255. 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. Soto-Andrade, J. and Varela, F. J. (1984). Self-reference and fixed points-a discussion and extension of Lawvere's theorem. Acta Applicandae Mathematicae, 2:1-19. Spencer-Brown, G. (1957). Probability and Scientific Inference. Longmans, London. Spencer-Brown, G. (1961). An algebra for the natural numbers. Unpublished. Spencer-Brown, G. (1965). British patent specifications 1006018 Lift Control System and 1006019 Lift Control Circuit Arrangement. Spencer-Brown, G. (1969). Laws of Form. Allen and Unwin, London. Spencer-Brown, 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. Spencer-Brown, 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. Spencer-Brown, G. (1982). The Falkland papers. Spencer-Brown, 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. Spencer-Brown, 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, D-29594 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). Self-reference 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):307-318. Unknown (1958?). Book review: Probability and scientific inference. Scientific American. Month and pages unknown. Varela, F. J. (1975). A calculus for self-reference. International Journal of General Systems, 2:5-24. Varela, F. J. (1979a). ??? International Journal of General Systems, 5(1):31-43. Varela, F. J. (1979b). The extended calculus of indications interpreted as a three-valued logic. Notre Dame Journal of Formal Logic, 20(1):141-146. 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, 8:48-64. Varela, F. J. and Goguen, J. A. (1978b). The arithmetic of closure. Progress in Cybernetics and Systems Research, 3:38-64. 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). Spencer-Brown Transcript, Art 269. Unpublished transcript of discussions with GSB at the Aum conference at Esalen Institute, Big Sur, CA (March 19-20, 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 Rueil-Malmaison, 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):287-298. Walgate, R. (1977). A colourful character. New Scientist, 6-Jan:6. A biographical and non-technical mention of claimed four-color 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, 23:291-292.

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