This folder contains links to papers related to Recursive Distinctioning. Recursive Distinctioning means just what it says. A pattern of distinctions is given in a space based on a graphical structure (such as a line of print or a planar lattice or given graph). Each node of the graph is occupied by a letter from some arbitrary alphabet. A specialized alphabet is given that can indicate distinctions about neighbors of a given node. The neighbors of a node are all nodes that are connected to the given node by edges in the graph. The letters in the specialized alphabet (call it SA) are used to describe the states of the letters in the given graph and at each stage in the recursion, letters in SA are written at all nodes in the graph, describing its previous state. The recursive structure that results from the iteration of descriptions is called Recursive Distinctioning. Here is an example. We use a line graph and represent it just as a finite row of letters. The Special Alphabet is SA = { =, [, ], O} where "=" means that the letters to the left and to the right are equal to the letter in the middle. Thus if we had AAA in the line then the middle A would be replaced by =. The symbol "[" means that the letter to the LEFT is different. Thus in ABB the middle letter would be replaced by [. The symbol "]" means that the letter to the right is different. And finally the symbol "O" means that the letters both to the left and to the right are different. SA is a tiny language of elementary letter-distinctions. Here is an example of this RD in operation where we use the proverbial three dots to indicate a long string of letters in the same pattern. For example,

... AAAAAAAAAABAAAAAAAAAA ... is replaced by
... =========]O[========= ... is replaced by
... ========]OOO[======== ... is replaced by 
... =======]O[=]O[======= ... .
Note that the element ]O[ appears and it has replicated itself in a kind of mitosis. To see this in more detail, here is a link to a page from a mathematica program written by LK that uses a 'blank' or 'unmarked state' instead of the '=" sign. Program and Output. Elementary RD patterns are fundamental and will be found in many structures at all levels. To see an cellular automaton example of this phenomenon, look at the next link. Here we see a replicator in 'HighLife' a modification of John Horton Conway's automaton 'Life'. The Highlife Replicator follows the same pattern as our RD Replicator! We can begin to understand how the RD Replicator works. This gives a foundation for understanding how the more complex HighLife Replicator behaves in its context. HighLife Replicator. Finally, here is an excerpt from a paper by LK about replication in biology and the role of RD. Excerpt.

Recursive Distinctioning (RD) is the study of those systems that use symbolic alphabetic language that can describe the neighborhood of a locus (in a network) occupied by a given icon or letter or element of language. An icon representing the distinctions between the original icon and its neighbors is formed and replaces the original icon. This process continues recursively.

RD processes encompass a very wide class of recursive processes in this context of language, geometry and logic. These elements are fundamental to cybernetics and cross the boundaries between what is traditionally called first and second order cybernetics. This is particularly the case when the observer of the RD system is taken to be a serious aspect of that system. Then the elementary and automatic distinctions within the system are integrated with the higher order discriminations of the observer. The very simplest RD processes have dialectical properties, exhibit counting and they exhibit patterns of self-replication. Thus one has in the first RD a microcosm of cybernetics and perhaps, a microcosm of the world.

See SpecialIssueJSP. This is a Special Issue of JSP, Vol. 5, No. 1, Spring 2016, devoted to Recursive Distinctioning.

Dr. Louis H. Kauffman Professor of Mathematics, University of Illinois at Chicago, presented the following briefing Recursive Distinctioning. via Zoom at the International Space Development Conference - 2016 in San Juan Puerto Rico on May 22, 2016. It will be in the archives maintained by the National Space Society (NSS) and is also here available on Research Gate. "This presentation, and the formal paper titled "RECURSIVE DISTINCTIONING," co-authored by Louis H. Kauffman and Joel D. Isaacson, published in The Journal of Space Philosophy, Spring 2016, create a major milestone in the Information Sciences, Cybernetics, Cellular Automata and Astro Physics." Bob Krone, Ph.D., President of Kepler Space Institute (KSI) and Editor-in-Chief of the Journal of Space Philosophy.

See Report. This is the Isaacson-Kauffman report on RD, summarized in a letter-to-the-editor of JSP, Vol. 4, No. 1, Spring 2015.

See RDLetter. This is the Isaacson-Kauffman report on RD, summarized in a letter-to-the-editor of JSP, Vol. 4, No. 1, Spring 2015, directly accessed on this server.

See Patent. This is Joel Isaacson's patent document for RD.

See Israel Patent. This is the Israeli version of the patent document for RD. Some aspects are more accurate in this document.

See Patent. This is Joel Isaacson's patent document for RD as a searchable Google document.

See Dialectical Machines. This is a report written in the late 1980's by Joel Isaacson.

See Stegano. This is an article by Joel Isaacson, pointing out RD relations with particle physics.

See Biological Replication. This is a related paper by Kauffman.

There are many relationships among recursive distinctioning, mathematics, logic and cybernetics. Below are other references that are related to RD.

See Box Algebra Exercise. This exercise is an introduction to the mathematics of G. Spencer-Brown and Charles Sanders Peirce.

See Recursive Forms. Hand-drawn notes by LK on forms and fractals, circa 1984.

  • SELFREF Self Reference and Recursive Forms.
  • LUHMANN Talk dedicated to Nicolas Luhmann by Heinz von Foerster, Translated by LHK and DBS.
  • REL Special Relativity and a Calculus of Distinctions.
  • ARITH Arithmetic in the Form.
  • Autopoeisis Classical paper on autopoesis by Maturana, Uribe and Varela.(FV).
  • Design Counters Notes on circuit design.
  • Balance GameA supplement to the Network Synthesis paper showing how to structure circuit design as a game of balance and transition on the circuit graphs.
  • Form Dynamics LK and FV paper - Spatial and Temporal Dynamics of Forms.
  • ROBBINS LK paper on the Robbins problem from Proceedings of 20th Intenational Symposium on Multiple Valued Logic (1990).
  • Simplified solution to the Robbins Problem using Box Algebra RobbinsSolution
  • Simplified solution to the Robbins Problem using Box Algebra RobbinsSolutionDetails
  • KNOT AUTOMATA LK Paper on knot automata and problems about asychronous circuit design from Proceedings of 24th Intenational Symposium on Multiple Valued Logic (1994)..
  • EigenForm Slides for a talk given in Vienna in November 2006 -- the "Heinz von Foerster Lecture on Cybernetics".
  • EigenForm LK paper on Eigenform.
  • Reflexivity LK paper on Eigenform and Reflexivity.
  • ReflexivityPhysics LK paper on Eigenform, Reflexivity and Physics.
  • Peirce LK paper on the Mathematics of Charles Sanders Peirce.
  • Bios Paper on Bios with Hector Sabelli.
  • MathematicalBios A second paper on Bios with Hector Sabelli.
  • "KnotLogic" Paper by LK on foundations of mathematics and logic in relation to knots. Discusses knot set theory, lambda calculus, magmas, braids, tangles, electricity, pregeometry and more. This paper is published in the book "Knots and Applications" edited by LK and published by World Scientific Press.
  • "Protein Folding Topology" Paper by LK and Yuri Magarshak on topological invariants of protein folding. This paper is published in the book "Knots and Applications" edited by LK and published by World Scientific Press.
  • Iconic Slides for a talk given in Brussels, December 2008 at Trends in Logic VI and for the talk I gave at the Short Course in Quantum Compputing at the AMS Meeting in Washington D.C. on January 4, 2009. Shows how the Fibonacci model, universal for topological quantum computation is constructed from the "logical particle" implicit in C. S. Peirce's Sign of Illation and in the Mark of G. Spencer-Brown, and the relationship of this logical particle to the Jones polynomial and the Temperley-Lieb recoupling theory. This structure leads to quantum algorithms for computing colored Jones polynomials and Witten-Reshetikhin-Turavev invariatns at roots of unity.
  • BioLogic -- What is the relationship of Logic and Biology? Slides for a talk given at the Wollic Conference in Rio de Janeiro in July 2007.