Conference Programme
Day 3 – Saturday, August 6
Registration and Coffee
09:00 - 09:30
Jonathan J. Mize
University of North Texas
C. S. Peirce Meets George Spencer-Brown: Seeking Semiotic Self-Evidence for Logic


Although there is ongoing debate about the mathematical influence of George Spencer-Brown's novel formalisms, one thing can hardly be denied: there is an intuitive and aesthetic simplicity to his notation which, if nothing else, deserves scholarly admiration and consideration. Of course, it is one thing to simply sit back and imbibe the simplicity of Spencer-Brown's "distinction" or "mark" and another thing entirely to meditate on what exactly makes these notions so intuitively pleasing and "amenable to common sense." I invite people to both indulge in the former and dabble in the latter, as we journey into an investigation of self-evidence as it relates to Spencer-Brown's notations and, moreover, logical notation in general. In this paper, I draw on C. S. Peirce's semiotics and philosophy of mathematics and Spencer-Brown's passion for maximally self-evident symbolism to craft a new breed of logical representation. I also highlight Hans Freudenthal's masterful "Lincos," an underappreciated language devised to be understood by any conceivable form of extraterrestrial life. In the end, I offer a style of self-evident logical notation that effectively collapses the boundary between metalanguage and object language, between definiendum and definiens.

Jonathan J. Mize is a scholar and author from Dallas, Texas. He has a BA in philosophy from the University of North Texas and has published several books and academic articles, primarily centered on logic, social philosophy and metaphysics. His most recent book is Modernity and the Rise of the Pocket God.

More info:
9:30 - 10:00
Arthur M. Collings
(presenting joint work done with Louis H. Kauffman)
Independent Researcher
The BF Calculus, Laws of Form, and Modal Logic


This paper establishes representations for modal logics within the BF Calculus, introduced by the authors at LoF50 in 2019 as a four-valued extension to Spencer-Brown's Primary Algebra.

This paper establishes three principal results:

1) Exactly 16 normal modal operators can be constructed asexpressions in BF and be expressed as combinations of four specific expressions in the Primary Algebra. These can be directly interpreted as accessibility relations within a 2-world version of Kripke's "many worlds" semantics.

2) BF operators L4 and L4* not only satisfy the axioms of the Lewis logic S4, but also satisfy all extensions to S4 (other than S5), as well as the the critical modal systems identified by Esakia and Meshki; their modal operations in BF express faithful representations of Sobocinski's system K4, known to be modeled in the form of finite 4-valued matrix. The K4 system contains all extensions to S4, Establishing that K4 is isomorphic BF's modal systems L4 and L4* is an important result regarding the relation between many-valued and modal logics.

3) Within the finite model for K4, analogous operations to both L4 and L4* are defined as M4 and M4*. By defining a bi-modal system, in which both M4 and M4* exist as modal operators, the square root of negation operation SQ(a,b) = (~b,a) can be derived and the bi-modal form of K4 can be understood to be isomorphic to the full BF Calculus.

We end by reflecting on the possible meanings of the pairs of values in BF, and suggest a new, intuitive interpretation that incorporates both coherence and correspondence concepts of Truth.

Arthur M. Collings lives in New York's Mid-Hudson Valley, where he works for the Dutchess Land Conservancy as a conservation planner and cartographer, with special interest in Geographic Information Systems. Since 2015 he has been on the Board of the American Society of Cybernetics. He has a BA in Mathematics and a Masters Degree in Conservation Planning and Design. He first encountered Laws of Form in 1977 while combing through the stacks in the public library the summer after graduating from high school in Annapolis Maryland.

More info:
10:00 - 10:30
Fred Cummins
University College Dublin
The First Distinction and the Swerve of Lucretius


I wish to think collectively around the generative potential of the first distinction, facilitating a kind of formal imagination or choreography, working with graphical, mathematical and textual figures relating to the numbers 1, 2 and 3, as they pertain to monisms, dualisms and trinities. Only trinities, I will argue, are generative and capable of accounting for coming into being, persisting, and going out of being.

John Conway's Look-and-Say sequence, which he described as the stupidest problem you could imagine leading to the most complex answer you could imagine, provides a figure of a triune generative process of perturbation arising through self-description leading to a generative form.

It bears consideration alongside the notion of the swerve, introduced by Lucretius in De Rerum Naturae. French philosopher Michel Serres has explicitly linked Lucretius' swerve to contemporary dynamical models and to the metaphysics of Leibniz.
Both perturbation and swerve may be placed alongside George Spencer-Brown's first distinction, providing us with a larger set of prototypes which may help overcome conceptual barriers we inevitably encounter when we acknowledge plurality in realities or universes that come into being through distinction.

This approach to distinction may be elaborated within a biological register through Maturana's concept of autopoiesis, to inform a participatory ontology/epistemology for embodied being.

The rich debate about monisms and dualisms in Vedanta and the iconography and embodied world of Shaivism are both potentially instructive. The experience of thinking together with these figures will feedback into their further elaboration in future work.

Cognitive scientist with empirical focus on joint speech (chant), theoretical interests in embodiment and enaction, and syncretic philosophical leanings.

More info:
10:30 - 11:00
Coffee Break
11:00 - 11:30
Leon Conrad
The Traditional Tutor | The Academy of Oratory | The Next Society Institute
The Sense of Sentences


How many sentence types are there? What does Spencer-Brown's Laws of Form offer in terms of helping us reach an answer? This paper focuses on the intentions which give rise to different sentence types in British English. These intentions are mapped to the simple expressions outlined by Spencer-Brown. The paper concludes that the approach reveals hitherto unappreciated subtleties at the very ground of language and puts forward suggestions for further work in the application of Spencer-Brown's work to the study of language.

Leon Conrad has run training courses in voice-centred communication skills for business for over 20 years. He is a writer, poet, storyteller and educator. He is passionate about reviving the integrated approach to teaching the liberal arts, in particular the Trivium of logic, grammar and rhetoric. He has an undergraduate degree in Music, an MA in the History of Design and Material Culture of the Renaissance.
In 2013, George Spencer-Brown began mentoring Leon through the process of engaging with Laws of Form on a weekly basis, following which the engagement continued through the last 3 years of Spencer-Brown's life, and resulted in a meaningful friendship. Leon has gone on to successfully apply Spencer-Brown's methodology to the practice of logic, and – most recently, in his book, Story and Structure: A complete guide – to the analysis of story structures, looking at the close link between story structures and different types of problems. As founder of The Traditional Tutor (, Leon works with gifted and talented youngsters, and with professionals as a communication consultant through The Academy of Oratory ( and is Orator in Residence at the Next Society Institute.

More info:
11:30 - 12:00
Alexander Tsigkas
Postdoctoral candidate at the Department of Philosophy, University of Ioannina, Greece
The in-between as potentiality in Architecture


The work (not restricted to this paper) has the ambition to reveal ways of how design ideas in architecture may be formalised and systematised through the promotion of the in-between as condition of possibility to achieve forms of dwelling that are better in-formed, i.e., balanced using the Calculus of Indication in George Spencer-Brown's Laws of Form.

Alexander Tsigkas is a retired professor at Democritus University of Thrace, Greece. His research concentrates on cybernetics and performativity, especially on the intelligence of natural-artificial-economic systems. His current research, focuses on the philosophy of artificial intelligence and architecture using George Spencer-Brown's Laws of Form.

More info:
12:00 - 12:30
Kevin German
Karlsruhe University of Applied Sciences
Cellular Laws of Form


The presentation will demonstrate how to simulate visually and intuitively the dynamics of Laws of Form using a cellular automaton. It is less about the philosophical implications, but rather to simplify the access to Laws of Form for beginners. Among other things, it will be shown how one can intuitively simulate a full adder and parts of the reentry in this cellular automaton.

Kevin German has studied Computer Engineering and Design & Future Making. Last year, he came into contact with Laws of Form through his personal interest in radical constructivism. Currently, he is doing research on natural language processing and artificial intelligence for chatbots at Karlsruhe University of Applied Sciences.

More info:
12:30 - 13:00
Lunch Break
13:00 - 14:30
William Bricken
Unary Computers, Snohomish Wa. USA
The Postsymbolic Arithmetic of James Algebra


Like Laws of Form, iconic arithmetic is void-based (no 0!), unitary (yes 1!), containment-based (numbers with an inside and an outside), postsymbolic (spatial, not strings of characters), algebraic (substitution supported by axioms), formal (rigorous provable transformations), physical (realizable in concrete form), minimal (as few concepts as possible) and elegant (unifying and explanatory concepts). I'll show how the standard objects and operations of arithmetic (+, –, x, ÷, ^, √, log, sin, π, e, i, ∞) can be represented in a Laws of Form-based language with two boundary types and three simple substitution rules covering almost all computation. New mathematical creatures appear: spatial dialects, a generic inverse, base-free exponents, quantized trigonometry, non-numeric forms, and a new additive imaginary number.

Dr. Bricken has spent over 40 years developing the tools and techniques of boundary mathematics, with computational applications to user interface, artificial intelligence, graphic programming language, virtual reality, silicon architecture, semiconductor optimization, and most recently iconic arithmetic. He has taught Social Psychology at State College of Victoria, Education at Univ. of Hawaii, Software Engineering at Seattle Univ., and currently Mathematics at Lake Washington Institute of Technology. In industry he contributed as a Principle Scientist at Advanced Decision Systems, Distinguished Fellow at Autodesk, Software Designer at Interval Research, and CTO of two start-up companies. Stanford University, M.S., Statistics and Ph.D., Mathematical Methods of Research.

More info:
14:30 - 15:00
Lyle Allen Anderson III
Association for Computing Machinery
Laws of Form and Burkhard Heim's Theory of Everything


Both George Spencer-Brown and Burkhard Heim had visions of our understanding of reality, including our place in it, being something that could be grasped as a Unified Theory of Everything. We have seen how Laws of Form, starting from the concept of a distinction, could produce demonstrations, step-by-step procedures for the construction of scalar arithmetic and algebra, including real and imaginary numbers and logic. With his additional work on the 4-color map theorem, George Spencer-Brown opened the door to developing topography, graph and group theory, and algebras with vector, matrix, tensor, and related algebras of compound entities. Burkhard Heim built his Theory of Everything on his Extended Quantum Field Theory which is based on Four Axioms, each of which can be traced to Laws of Form. The most significant of these Axioms is that the universe is quantized with respect to areas, that is to say, each pair of dimensions, real, imaginary, or mixed, is made up of itty bitty areas that he called a metron. These are the source of the Plank length, and Plank time in Standard Quantum Physics. This paper will attempt to show the connection between the two bodies of work, and to point to areas where further work can be done to fill in any gaps.

Lyle Anderson was born in 1946 in Kalamazoo, Michigan, USA and raised just outside of Philadelphia, Pennsylvania in Jeffersonville, PA. He attended Kalamazoo College from 1963 through 1967 receiving a BA in Mathematics and Physics. He attended Iowa State University at Ames studying Solid State Physics until joining the Navy as an enlisted man in 1968. He graduated Electrician's Mate A school in 1969, and was half way through Nuclear Power School when he was picked up for Officer Candidates School. After receiving his commission in 1970, and while awaiting Naval Nuclear Power School at Submarine Development Group Two in Groton, CT, he developed "a methodology and a computer program for the real time application of sonar information" that was "a major contribution to solving the complex anti-submarine fired control problem." That work lead to a nearly 40-year civilian career in combat and intelligence systems development work. Since retiring in 2014, he has gone back to the investigation of mathematics and physics that was interrupted in the summer of 1968.

More info:
15:00 - 15:30
Kate Doyle
Rutgers University-Newark
On Paradox, Inaudible Music, and Laws of Form in Experimental Art


We have trouble with the interpretation of absence. We struggle to turn our attention to absence even though it facilitates presence, functions in conversation with presence, and allows presence to have meaning. The Conceptual artist Sol LeWitt worked to address this problem in 1967 when he said that paradox is the meaning of art. He was attempting to shift a definition of art from one rooted in the aesthetics of form to one centered in the space of ideas. Formal aesthetics can distract from idea, in LeWitt's concept; thus, challenges to morphological parameters, including the construction of paradox, allow art ideas to be made clear.
In this paper, I experiment with George Spencer Brown's Laws of Form as a tool to work with absence and paradox in art and and an alternative to linguistic approaches typically used in art discourse. To do so, I draw upon a paradoxical construction built long LeWitt made his 1967 statement: the second movement ("Hastig") of Robert Schumann's 1839 Humoreske for piano solo, a radical interruption to the logic of musical form. I then juxtapose this composition with Conceptual art work (produced around the publication of Laws of Form), a collection of examples that exemplifies the challenge to art objects-as-usual.

Kate Doyle is an Assistant Professor of Music in the Department of Arts, Culture & Media at Rutgers University-Newark. Her writing and engaged scholarship explores the performance and ideas of music in conceptual and experimental art practice, particularly through cybernetic frameworks. She work actively within the American Society for Cybernetics and has been an invited speaker or collaborator at The Library of Congress, The University of the Arts Chelsea College, the Dia Art Foundation, and the Festival of Original Theater.

More info:
15:30 - 16:00
Stephen Watson
Associate Professor, Faculty of Education, University of Cambridge
Fellow of Wolfson College
Mathematics education as a social system: a Laws of Form perspective

In this presentation I will describe my research into mathematics education that draws on Laws of Form in two ways. Firstly by considering mathematics education as a social system as informed by the systems theory approach of Niklas Luhmann, which in turn draws on George Spencer Brown's approach to distinction or 'difference in unity' and recursion/ self-referentiality but in the context of educational social systems. Secondly, by considering mathematics and mathematics education, philosophically, from a historical sociological perspective, and from a critical consideration that employs Spencer Brown's Laws of Form, I argue provides a new and alternative perspective on mathematics education – a general theory of mathematics education based on a general theory of difference and recursion. A self-referential and recursive general theory of mathematics education meets the condition of being a general theory as I will show, as it presents itself as a theory of itself, but not as a grand representational theory but as one that considers how meaning is made in the context of mathematics and mathematics education.

My overall aim is to articulate a non-normative theory of education and society drawing on the traditions of sociocybernetics and social systems theory.

More info:
16:00 - 16:30
Coffee Break
16:30 - 17:00
Francis Jeffrey
The Phenomenology of Zero Bits


Warren S. McCulloch asked, "What's in the brain that ink may character?"
John C. Lilly proposed the mammalian brain as a modeling space for simulations of internal and external realities. I include Penrose & Hameroff's latest version within my broader paradigm of 'quantum neurophysiology'; in line with Schrödinger's view of capacity for experience and action inhering in the actual and intrinsic integration of all the 'scales of nature'. As we define and discern such, it all must somehow sum to Zero, or our equations will be tweaked, so also, "...time must have a stop."
A non-distinction of indeterminate and determinate must replace 'first causes' and 'mechanisms of action.'
This is satisfied by Zero, which has an Onomatopoetic, glyphic, pictographic, ideographic sign:


GSB's intrinsically two-dimensional mark can be most easily expressed in lineal writing/typing, as,


and in my 'Boole_notes' format to draw equal attention to the inside and outside,


If and when you take sides, it's fine to nest on the chosen side only:

⟨| ⟨⟨⟨⟩⟩⟩ ⟩

C. E. Shannon defined his now-ubiquitous 'Bit' as equal to 1 full unit of information when the probabilities of two sides are equal.
Context and communion must each strike a similar balance for one binary bit of information transmission 'bandwidth' or information storage capacity to potentially maximize up to One bit of real information, in any communication that is about something and is between minds; and conversely, how it must approach Zero when the three metrical dimensions and their maxima do not align.
The resulting bit-per-bit ratio distinguishes conflicted dual realities from non-conflicted dual realities; War from Peace.

Neurophysiologist Dr. Francis Jeffrey worked for the University of California, NASA, and DARPA, and created enterprises and laboratories, including the Phenomenology Experimental Research Center (PERC). In studies with John C. Lilly and George Spencer-Brown, he pioneered the application of Spencer-Brown's calculus to neuropsychology in the flotation tank, and to vast-scale systems for human and interspecies communication technology. After the historic AUM Conference, his studies with G. Spencer-Brown led him to at least three practical applications of the math from Laws of Form, in:
(1) rapid, optimized design of digital circuits;
(2) communications research with dolphins;
(3) new software-building & network methods, including in U.S. Patent 6,085,233 (et seq.), that drew a bid from Steve Jobs of Apple (inter alios) as a foundation for everything after 1999 including vast-scale systems for human, interplanetary & interspecies communication. Working with the Math in the optimal conditions of anechoic chambers & sensory isolation tanks led to easy reliving of the 'higher samadhis' as these are outlined in the classical literature of Buddhist & Hindu Yogic practice.

More info: See this and a new, mathematical theory of real information in his forthcoming publication, Communication is between MindsTM ©
17:00 - 17:40
Panel Discussion
17:40 - 18:30
Graham Ellsbury
Closing the Conference
18:30 - 18:45
(Advance booking required)
The Pen Factory

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