[CG] Re: Theme One Program • Motivation

Theme One Program • Motivation 2 • https://inquiryintoinquiry.com/2024/06/04/theme-one-program-motivation-2-b/ All, A side‑effect of working on the Theme One program over the course of a decade was the measure of insight it gave me into the reasons why empiricists and rationalists have so much trouble understanding each other, even when those two styles of thinking inhabit the very same soul. The way it came about was this. The code from which the program is currently assembled initially came from two distinct programs, ones I developed in alternate years, at first only during the summers. In the “Learner” program I sought to implement a Humean empiricist style of learning algorithm for the adaptive uptake of coded sequences of occurrences in the environment, say, as codified in a formal language. I knew all the theorems from formal language theory telling how limited any such strategy must ultimately be in terms of its generative capacity, but I wanted to explore the boundaries of that capacity in concrete computational terms. In the “Modeler” program I aimed to implement a variant of Peirce's graphical syntax for propositional logic, making use of graph‑theoretic extensions I had developed over the previous decade. As I mentioned, work on those two projects proceeded in a parallel series of fits and starts through interwoven summers for a number of years, until one day it dawned on me how the “Learner”, one of whose aliases was “Index”, could be put to work helping with sundry substitution tasks the “Modeler” needed to carry out. So I began integrating the functions of the “Learner” and the “Modeler”, at first still working on the two component modules in an alternating manner, but devoting a portion of effort to amalgamating their principal data structures, bringing them into convergence with each other, and unifying them over a common basis. Another round of seasons and many changes of mind and programming style, I arrived at a unified graph‑theoretic data structure, strung like a wire through the far‑flung pearls of my programmed wit. But the pearls I polished in alternate years maintained their shine along axes of polarization whose grains remained skew in regard to each other. To put it more plainly, the strategies I imagined were the smartest tricks to pull from the standpoint of optimizing the program’s performance on the “Learning” task I found the next year were the dumbest moves to pull from the standpoint of its performance on the “Reasoning” task. I gradually came to appreciate that trade‑off as a “discovery”. Resources — Theme One Program • Overview • https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview Theme One Program • Exposition • https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Exposition Theme One Program • User Guide • https://www.academia.edu/5211369/Theme_One_Program_User_Guide Survey of Theme One Program • https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/ Regards, Jon cc: https://www.academia.edu/community/VodZxj cc: https://mathstodon.xyz/@Inquiry/112554698776574635