Conference Programme

Day 3 – Saturday, August 6

Registration and Coffee

09:00 - 09:30

Jonathan J. Mize

University of North Texas

Video

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

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

More info: www.jonathanmizeauthor.com

9:30 - 10:00

Arthur M. Collings

(presenting joint work done with Louis H. Kauffman)

(presenting joint work done with Louis H. Kauffman)

Independent Researcher

Video

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

More info: www.researchgate.net/profile/Arthur-Collings

10:00 - 10:30

Fred Cummins

University College Dublin

Video

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

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: pworldrworld.com/fred

10:30 - 11:00

Coffee Break

11:00 - 11:30

Leon Conrad

The Traditional Tutor | The Academy of Oratory | The Next Society Institute

Video

How many sentence types are there? What does Spencer-Brown's

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

More info: www.leonconrad.com

11:30 - 12:00

Alexander Tsigkas

Postdoctoral candidate at the Department of Philosophy, University of Ioannina, Greece

Video

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

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

More info: www.linkedin.com/in/prof-dr-dr-alexander-tsigkas-b59b1019/

12:00 - 12:30

Kevin German

Karlsruhe University of Applied Sciences

Video

The presentation will demonstrate how to simulate visually and intuitively the dynamics of

Kevin German has studied Computer Engineering and Design & Future Making. Last year, he came into contact with

More info: kevingerman.de

12:30 - 13:00

Lunch Break

13:00 - 14:30

William Bricken

Unary Computers, Snohomish Wa. USA

Video

Like

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: iconicmath.com

14:30 - 15:00

Lyle Allen Anderson III

Association for Computing Machinery

Video

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

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: groups.io/g/lawsofform

15:00 - 15:30

Kate Doyle

Rutgers University-Newark

Video

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

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: acm.newark.rutgers.edu/acm_faculty/kate-doyle/

15:30 - 16:00

Stephen Watson

Associate Professor, Faculty of Education, University of Cambridge

Fellow of Wolfson College

Fellow of Wolfson College

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: https://www.educ.cam.ac.uk/people/staff/watson/

16:00 - 16:30

Coffee Break

16:30 - 17:00

INVITED KEYNOTE

Francis Jeffrey

Francis Jeffrey

Video

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:

O

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

(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 (

More info: See this and a new, mathematical theory of real information in his forthcoming publication,

17:00 - 17:40

Panel Discussion

17:40 - 18:30

Graham Ellsbury

18:30 - 18:45

Dinner

(Advance booking required)

The Pen Factory

TBA