Differential Propositional Calculus • 35
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https://inquiryintoinquiry.com/2023/12/29/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 of 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/Vj44Wl