Differential Propositional Calculus • 35

Posted on December 29, 2023 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 of 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: FB | Differential Logic • Laws of Form • Mathstodon • Academia.edu
cc: Conceptual Graphs (1) (2) • Cybernetics • Structural Modeling • Systems Science

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