Reflective Interpretive Frameworks • Incident

[Jon Awbrey]

Reflective Interpretive Frameworks • Incident 1
• https://inquiryintoinquiry.com/2026/03/26/reflective-interpretive-frameworks-incident-1/

Re: William Waites • The Agent That Doesn't Know Itself
• https://johncarlosbaez.wordpress.com/2026/03/20/the-agent-that-doesnt-know-itself/

WW: ❝Why Has Nobody Done This?❞

People who study C.S. Peirce would say reflective reasoning requires
triadic relations at core and there is work being done on that.

One of the challenges is clarifying the role of triadic relations
in category theory and raising them into higher relief as fundamental
operations.

Note. I was looking for a word to describe a random encounter with
something that jogs one's memory of a recurring theme — “incident”
plays into the “reflection” theme and looked worth trying for now.

Resources —

Inquiry Driven Systems • Inquiry Into Inquiry
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview

Reflective Interpretive Frameworks
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_10#Reflective_Interpretive_Frameworks

The Phenomenology of Reflection
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_11#The_Phenomenology_of_Reflection

Higher Order Sign Relations
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_12#Higher_Order_Sign_Relations

Notes On Categories
• https://inquiryintoinquiry.com/2013/02/22/notes-on-categories-1/
• https://inquiryintoinquiry.com/2021/07/31/notes-on-categories-2/

Regards,

Jon

cc: https://www.academia.edu/community/lJbE8E
cc: https://mathstodon.xyz/@Inquiry/116301214597527620

[Jon Awbrey]

Reflective Interpretive Frameworks • Incident 2
• https://inquiryintoinquiry.com/2026/08/27/reflective-interpretive-frameworks-incident-2/

Re: Terence Tao • Modular Arithmetic Challenge
• https://terrytao.wordpress.com/2026/06/08/modular-arithmetic-challenge/
• https://competition.sair.foundation/competitions/modular-arithmetic-challenge/overview

The Modular Arithmetic Challenge asks a simple question:

• Can a neural network learn to do modular multiplication efficiently?

Incidental Reflection 1 —

There are alternative models of neural networks which do not
depend on threshold neurons and endlessly fiddling with weights.

Incidental Reflection 2 —

The series of three blog posts linked below present a case study
comparing two ways of handling a classic example from the Parallel
Distributed Processing paradigm, namely, the “Jets and Sharks” database
problem, first taking up the original treatment by McClelland and Rumelhart
and then proceeding according to a program I developed for propositional
logic modeling. The latter method makes use of ideas from Grossberg's
competition‑cooperation and winner‑take‑all dynamics, but is purely
propositional‑logic based, involving no extraneous weights.

Theme One Program • Jets and Sharks
(1) https://inquiryintoinquiry.com/2024/06/20/theme-one-program-jets-and-sharks-1-a/
(2) https://inquiryintoinquiry.com/2024/06/22/theme-one-program-jets-and-sharks-2-a/
(3) https://inquiryintoinquiry.com/2024/06/23/theme-one-program-jets-and-sharks-3-a/

Resources —

Survey of Theme One Program
• https://inquiryintoinquiry.com/2025/05/06/survey-of-theme-one-program-7/

Differential Analytic Turing Automata
• https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_Overview

cc: https://www.academia.edu/community/VBRMg3
cc: https://mathstodon.xyz/@Inquiry/116301214597527620
cc: https://www.researchgate.net/post/Reflective_Interpretive_Frameworks_Incidents

Regards,

Jon