Differential Propositional Calculus • 24

Posted on December 16, 2023 by Jon Awbrey


Urge and urge and urge,
Always the procreant urge of the world.

— Walt Whitman • Leaves of Grass

Example 1. A Square Rigging

Returning to the universe of discourse based on a single feature A, suppose we are given the initial condition A = \mathrm{d}A and the second order differential law \mathrm{d}^2 A = \texttt{(} A \texttt{)}.  Since the equation A = \mathrm{d}A is logically equivalent to the disjunction A ~ \mathrm{d}A \lor \texttt{(} A \texttt{)(} \mathrm{d}A \texttt{)} we may infer two possible trajectories, as shown in the following Table.

\text{A Pair of Commodious Trajectories}
Commodious Trajectories

In either case the state A ~ \texttt{(} \mathrm{d}A \texttt{)(} \mathrm{d}^2 A \texttt{)} is a stable attractor or terminal condition for both starting points.

Resources

cc: FB | Differential Logic • Laws of Form • Mathstodon • Academia.edu
cc: Conceptual Graphs (1) (2) • Cybernetics • Structural Modeling • Systems Science

This entry was 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 and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

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