[CG] Re: Differential Propositional Calculus

Differential Propositional Calculus • 33 • https://inquiryintoinquiry.com/2023/12/27/differential-propositional-calcul… Example 2. Drives and Their Vicissitudes (cont.) Expressed in terms of “drives” and “gears” our next Example may be described as the family of 4‑th‑gear curves in the fourth extension E⁴X = ⟨A, dA, d²A, d³A, d⁴A⟩. Those are the trajectories generated subject to the dynamic law d⁴A = 1, where it's understood all higher differences are equal to 0. Since d⁴A and all higher differences dⁿA are fixed, the state vectors vary only with respect to their projections as points of E³X = ⟨A, dA, d²A, d³A⟩. Thus there is just enough space in a planar venn diagram to plot all the orbits and to show how they partition the points of E³X. It turns out there are exactly two possible orbits, of eight points each, as shown in the following Figure. Example 2. Fourth Gear Orbits • https://inquiryintoinquiry.files.wordpress.com/2023/12/differential-logic-e… Resources — Differential Logic and Dynamic Systems • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Differential Logic • Drives and Their Vicissitudes • https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Regards, Jon cc: https://www.academia.edu/community/VXAx1L