Differential Propositional Calculus • 35
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https://inquiryintoinquiry.com/2024/12/29/differential-propositional-calcul…
Example 2. Drives and Their Vicissitudes (concl.)
Applied to the example of 4‑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
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https://inquiryintoinquiry.files.wordpress.com/2023/12/differential-logic-e…
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 2⁴ = 16. In that
way the temporal succession of states can be reckoned by a
“parallel round‑up rule”. Namely, if (dₖ, dₖ₊₁) is any pair
of adjacent digits in the state index r then the value of dₖ
in the next state is dₖ′ = dₖ + dₖ₊₁.
Resources —
Differential Logic and Dynamic Systems
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https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part…
Differential Logic • Drives and Their Vicissitudes
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https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part…
Regards,
Jon
cc:
https://www.academia.edu/community/V96Dbj
cc:
https://www.researchgate.net/post/Differential_Propositional_Calculus