Category Archives: Differential Calculus

History, Its Arc, Its Tangents • 2

Posted on December 25, 2019 by Jon Awbrey

Re: Renaissance Mathematicus • Both Sides of History Are there watersheds in the history of science?  A continental divide between basins of right and wrong ideas?  I was pondering these questions when one of my favorite passages from Leibniz came … Continue reading →

Posted in Differential Calculus, History of Science, Hologrammautomaton, Leibniz, Thony Christie | Tagged , , , , | Leave a comment

Differential Logic and Dynamic Systems • Overview

Posted on September 10, 2019 by Jon Awbrey

In modeling intelligent systems, whether we are trying to understand a natural system or engineer an artificial system, there has long been a tension or trade‑off between dynamic paradigms and symbolic paradigms.  Dynamic models take their cue from physics, using … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Abductive Inference, Concept Formation, Hypothesis Formation • 1

Posted on April 26, 2019 by Jon Awbrey

In pragmatic semiotics, concept formation like hypothesis formation falls under the heading of abductive inference.  A lot has been said and there’s a lot more to say about that, but things are too much in flux right now to allow … Continue reading →

Posted in Abduction, C.S. Peirce, Complexity, Concept Formation, Differential Calculus, Differential Logic, Dyadic Relations, Dynamical Systems, Dynamics, Geometry, Hypothesis Formation, Inference, Logic, Logic of Relatives, Mathematics, Peirce's Categories, Physics, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 8

Posted on December 24, 2018 by Jon Awbrey

Re: Systems Science • Len Troncale It’s been a while since I started this thread, with many sidetrips and tangents, so let me go back to the top and expand on the motivations I expressed there, addressing a few issues … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 7

Posted on December 20, 2018 by Jon Awbrey

Re: Systems Science • JS Let’s stand back from the picture and see how the dimensions of syntax, semantics, and pragmatics look from a pragmatic semiotic or sign relational perspective. is an object domain, a set of elements under view … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 6

Posted on December 19, 2018 by Jon Awbrey

Re: Systems Science • JS A few of my readers are racing well ahead of me, exploring a range of different roads, but I’ll be making a dogged effort to stick to my math-bio-graphical narrative this time around, and try … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 5

Posted on December 18, 2018 by Jon Awbrey

Re: Systems Science • JS Yes, all these strands are strongly entangled. I had already spent a full decade wrestling with the works of Charles Sanders Peirce and George Spencer Brown before my need to figure out what they were … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 4

Posted on December 17, 2018 by Jon Awbrey

Re: Systems Science • LT To clarify my previous remark about General Systems Theory, I wasn’t trying to define a whole field but merely to describe my experience in forums like these, where it took me a while to realize … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 3

Posted on December 12, 2018 by Jon Awbrey

Re: Systems Science • (1) • (2) • (3) Various discussions in various places bring back to mind this thread from early this fall, prompting me to make a try at continuing it.  Here’s a series of blog posts where … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 2

Posted on October 5, 2018 by Jon Awbrey

Re: Cybernetic Communications • SU One thing that interests me here is the relation between narratives and navigation.  Navigation has to do with how we move through actual state spaces while narratives are the tales we tell about past adventures … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 11 Comments