Specification of a Non-deterministic Turing Machine Solving the Reciprocity Problem

By relying on the Laws of Form (Laws of Form by George Spencer-Brown) cross operator, and precisely redefining the underlying terminology, this article illustrates the contributions of terminological precision brought by the concept of Distinction outlined in Laws of Form to clarify the boundary between Deterministic and Non-deterministic Turing Machines.

Laws of Context

How do nothing and one connect? How do we count when both 0 and 1 are to be included in our scale of number? The mathematical questions led Spencer-Brown to consider the structure of Laws of Form to be about distinction. In a world of becoming, the process of something asserting itself from nothing is equivalent to what is distinguished. This creates a strange logic between 0 and 1, that if 1 is its own assertion, then for 1 to act on 1, undoes this assertion and turns into a negation. For to change the assertion means it can only undo 1 and turn it into the opposite of 0. This means that if you apply identity to itself, then one undoes existence back into emptiness. While if existence is placed alongside another existence, then one can not go further than the process of becoming. The Laws of Context argue this from the process that erases a boundary. If 0 Is its own negation, the for 0 to act on 0, undoes this negation and turn into an assertion. For to change the negation means it can only undo 0 and turn it into an assertion as a spontaneous appearance of 1. If you apply negation to itself the one undoes emptiness back into the existence that proves itself. The mathematics is obviously symmetrical in existence and emptiness. 0 alongside 0 can not add anything to negation. Turning 0 and 1 from being a separation into a relation, is a characteristic that applies equally well to the erasure of identity into a limitation of context as a distinction of form as structure of existence. Such spontaneous process of appearance is found in myths where the chaotic combination of gods, heroes and events transforms non-existence into creation. But it is also necessary in physics as the spontaneous materialisation entering as jumps punctuating the unfolding form of existence. The action of context having its own laws separates it from the distinction of matter, allowing the choice of negation and assertion to weigh the relationship of 0 and 1 in spontaneous appearance.

After a mathematics degree from Oxford University, Philip Franses has followed a career in intelligent software, Senior Lecturer in Holistic Science, co-founding the Flow Partnership and writing Time, Light and the Dice of Creation (2015) and co-authoring The Language of Water (2024)

Phenomenology in the Flotation Tank: Renewing John C. Lilly’s Phenomenology Experimental Research Center (PERC) with Thinking the Float Tank

In an effort to create an environment conducive to a first-person science of consciousness, neuroscientist John C. Lilly invented the sensory deprivation chamber, or flotation tank. Lilly’s research paradigm, which included a central place for phenomenology, led to the development of his float tank laboratories in Big Sur, California, called the Phenomenology Experimental Research Center (PERC). The phenomenological reduction, whether transcendental or eidetic or otherwise, is a meditative performance that brings about the state of cognition necessary for rigorous scientific philosophy. While it is unclear how much Lilly relied upon Husserl’s methods, it is evident that the anaesthetic environment of the float tank provides a tool for phenomenological experimentation. In the early days of PERC, Lilly was experimenting with the use of a mathematical text called Laws of Form as an approach to inner space. Lilly’s move from experimental psychology to a cosmology of inner space relied on that text’s central mathematical operation called the first distinction. This primordial act of distinction is, for Lilly, the crossing of the boundary common to all phenomena. As Dermot Moran has recently suggested, this “primary distinction” is perhaps closest to Husserl’s mature (1907 onwards) concept of the transcendental ego’s ability to take a stance on itself, which Husserl calls ego-splitting (Dermot Moran, The Nature of Self-Experience, Husserl’s Sphere of Ownness and the Experience of the Flotation Tank, at Thinking the Float Tank). In 1973 Lilly and Alan Watts invited the book’s author, the mathematician George Spencer-Brown, to lead a week-long seminar called the American University of Masters (AUM) conference. Since the days of PERC and the AUM conference, the scientific and philosophical landscape has changed significantly. This presentation reviews the past, initiates updates in certain areas of the science and philosophy relevant to Lilly’s program, and finally proposes a new framework based on Lilly’s work. At the contemporary art museum West Den Haag in The Hague in the summer of 2023, the interdisciplinary conference Thinking the Float Tank marked the fiftieth anniversary of the AUM conference. Thinking the Float Tank aimed at bringing the attention of Husserlian phenomenologists, psychologists, and psychical researchers to Lilly’s “void method” of inner space travel through “Spencer-Brown’s doorway”—novel ways through the mind to essential structures. Such practices call for synthesis with phenomenological psychology, eidetic and ontological phenomenology, and new approaches to the field of immanence. Thinking the Float Tank reconstructed Lilly’s phenomenological research and also focused on bringing that work into conversation with contemporary work in Husserlian phenomenology. In this presentation, the tour through flotation science will culminate in a new ontology and phenomenology based on Laws of Form and specially designed for the float tank experience.

Randolph Dible is a lecturer in philosophy at St. Joseph's University, New York, and a philosophy doctoral student at The New School for Social Research. He has recently published the chapter "First Philosophy and the First Distinction: Ontology and Phenomenology of Laws of Form," in Laws of Form—A Fiftieth Anniversary (2022), and he has forthcoming publications in Analecta Husserliana, including "Ontopoiesis, Autopoiesis, and a Calculus Intended for Self-Reference." Recent publications can also be found in Natur und Kosmos (2020) and The Further Shores of Knowing (2021). He has published on mysticism in the Journal of Consciousness Exploration and Research (2010), and his Masters thesis is entitled Phenomenology of the Spheres: from the Ancient Spherics to Philosophical Cosmology (2018). Randolph Dible's current research focuses on the historical hypothesis of an infinite sphere and its relevance to the interpretation of formation in the cosmologies of George Spencer-Brown and Hedwig Conrad-Martius. Associated with this thesis is a general theory of extension and dimensionality. Randolph Dible is the Secretary and the Director of the Webinar for the Society for the Phenomenology of Religious Experience (SOPHERE), the Communications Director for the North American Society for Early Phenomenology (NASEP), and Assistant to the Editor for the journal Phenomenological Investigations.

More info: http://randolphdible.com/

Letting Go. The Form of Mourning.

Threnos in antiquity was understood as the activity of mourning. S. Freud dichotomised mourning with melancholia, entangling both in libido. A. and M. Mitscherlich took this up in the 1960s for the German people post Holocaust as their “inability to mourn”. J. Ruesen tried “Trauer” in this context again in the 1990s as “mourning humaneness”, bloating its abstraction. While M. Rothberg introduced the notion of “implicated subject” to the field/s of historical violence and injustices to modify R. Hilberg’s perpetrator-victim-bystander triad in 2019, the German “Historikerstreit 2.0” was raging, but not about Rothberg’s “implication”, yet about his 2009 concept of “multidirectional memory”, wherewith he demonstrated how the Holocaust had enabled the articulation of other histories of victimisation at the same time that it had been declared "unique" among human-perpetrated horrors, while uncovering the more surprising fact that public memory of the Holocaust emerged in part thanks to postwar events that seemingly had little to do with it. A particular [German] insistence on the uniqueness of the Holocaust seems to function as local, differentiation-hostile veneer and global delayer of fruitful, actually teachable distinctions, instead presenting an inability of letting go all over again, by not re-entering the form of mourning, therefore continually confusing memory with threnody. This contribution aims to decline “Trauer” (mourning) within the Form.

U.S.-Austrian lecturer, researcher, facilitator, filmmaker; with particular interest in epistemological implications and practical consequences of what has been called “representational perception”.

Engstrom Critiques LoF Appendix 2 p 119 'all a are b' And Its Use in Barbara, etc.

Supplementary PDF

1a. Preface: Wittgenstein emphasized the importance of distinguishing different "language games" … In Laws of Form’s Appendix 2, George Spencer-Brown conflates (?successfully) several distinct languages, each having its own “universe” of syntax and semantics, including: unquantified.propositional-formulas; and quantified-class.logic (involving non-proposition terms, e.g. the three nonproposition-terms in the syllogism Barbara). 1b. On p119 of Laws of Form (1969-94) in Appendix 2, Spencer-Brown represents 'all a are b' as the Laws of Form-expression 'a-cross b’, and then uses it and variants to express a “mandala” of 24 universal- and existential-syllogisms. 2. I, Engstrom, translates 'all a are b' as ‘set.A is a subset of set.B’, i.e. ‘set.A–B is necessarily empty, but A.intersection.B possibly-has some member(existence)’. I represent these two conditions by a modification of ‘LoF.C6 interpreted as: bifurcating.set.A by set.B’. These modifications are designed to perspicaciously-account for each-component of the “logical.matter” in a collection of modally-quantified-class-relationships that are sometimes hypothesized and other times asserted, e.g. Barbara as: If ‘A is a subset of B’, then ‘necessarily A–B is empty’ i.e. ‘A= A.intersection.B’: therefore if some.existence‘a’ is in A, then ‘a is also in B’. And if ‘necessarily B–C is empty’, then ‘a is in A.intersection.B.intersection.C’, therefore ‘a is also in C’. Q.E.D.

Jack Engstrom bio (2024):
• b. 1951;
• 1972 B.A. chemistry U.California Santa Cruz;
• seeking and finding 1.&2.: 1. deep-connections bridging/integrating math&science-knowledge with consciousness(“inside”), and 2. (re)generative ontology and epistemology;
• since 1973 doing Transcendental Meditation;
• since 1976 Arthur M. Young’s ‘Institute for the Study of Consciousness’, now president (“theory of process” and ‘Geometry of Meaning’, arthuryoung.com/organizations/institute-for-the-study-of-consciousness)
• 1994 math M.S. Maharishi International University Fairfield IA: thesis on 'numbers from Laws.of.Form'.

The Pervasive Illusions of LoF

Spencer Brown’s Law of Crossing equates the form of a double boundary with the absence of form. This void-equivalence profoundly empowers both representation and computation. In particular a void-equivalent form has the same status as the space underlying all recorded forms. Crossing asserts that the double boundary is anywhere, everywhere and nowhere, all at the same time, all at the discretion of the reader. Void has no properties; forms that are “confused with” nothing can have no meaning and no impact. Each of Bricken’s three axioms for the algebra of iconic forms asserts a variety of void-equivalence, making the forms of Spencer Brown’s primary algebra both pervasive and illusory. Laws of Form, rather than being disabled, becomes a ground for pure, principled formal creativity. The presentation shares newly emerging computational technique and newly forming understanding of deductive logic.

>40 years developing iconic mathematics, with applications to user interface, programming languages, AI, VR, silicon architecture, numeric arithmetic and logic. Stanford University, Ph.D., Mathematical Methods of Research.

More info: iconicmath.com