[CG] Re: Differential Propositional Calculus

Differential Propositional Calculus • 33 • https://inquiryintoinquiry.com/2024/12/28/differential-propositional-calcul… Example 2. Drives and Their Vicissitudes (cont.) Expressed in the language of “drives” and “gears” our next Example may be described as the family of fourth‑gear curves through 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 order differences are equal to 0. Because 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 the orbits and show how they partition the points of E³X. It turns out there are just 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/lP14eK cc: https://www.researchgate.net/post/Differential_Propositional_Calculus