Differential Propositional Calculus • 35

Posted on December 29, 2024 by Jon Awbrey

Example 2. Drives and Their Vicissitudes (concl.)

Applied to the example of 4^\text{th}‑gear curves, the indexing scheme results in the data of the next two Tables, showing one period for each orbit.

Fourth Gear Orbits 1 and 2

The states in each orbit are listed as ordered pairs (p_i, q_j), where p_i may be read as a temporal parameter indicating the present time of the state and where j is the decimal equivalent of the binary numeral s.

Grasped more intuitively, the Tables show each state q_s with a subscript s equal to the numerator of its rational index, taking for granted the constant denominator 2^4 = 16.  In that way the temporal succession of states can be reckoned by a parallel round‑up rule.  Namely, if (d_k, d_{k+1}) is any pair of adjacent digits in the state index r then the value of d_k in the next state is {d_k}^\prime = d_k + d_{k+1}.

Resources

cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate

This entry was posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Topology, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

4 Responses to Differential Propositional Calculus • 35

  1. Pingback: Survey of Differential Logic • 7 | Inquiry Into Inquiry

  2. Pingback: Survey of Differential Logic • 7 | Inquiry Into Inquiry

  3. Pingback: Survey of Differential Logic • 8 | Inquiry Into Inquiry

  4. Pingback: Survey of Differential Logic • 8 | Systems Community of Inquiry

Leave a comment

This site uses Akismet to reduce spam. Learn how your comment data is processed.