Reflective Interpretive Frameworks • Incident 1

Re: William Waites • The Agent That Doesn’t 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

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Riffs and Rotes • Happy New Year 2026

\text{Let} ~ p_n = \text{the} ~ n^\text{th} ~ \text{prime}.

\begin{array}{llcl}  \text{Then} & 2026 & = & 2 \cdot 1013  \\  && = & p_1 p_{170}  \\  && = & p_1 p_{2 \cdot 5 \cdot 17}  \\  && = & p_1 p_{p_1 p_3 p_7}  \\  && = & p_1 p_{p_1 p_{p_2} p_{p_4}}  \\  && = & p_1 p_{p_1 p_{p_{p_1}} p_{p_{{p_1}^{p_1}}}}  \end{array}

No information is lost by dropping the terminal 1s.  Thus we may write the following form.

2026 = p p_{p p_{p_p} p_{p_{p^p}}}

The article linked below tells how forms of that order correspond to a family of digraphs called riffs and a family of graphs called rotes.  The riff and rote for 2026 are shown in the next two Figures.

Riff 2026

Riff 2026

Rote 2026

Rote 2026

Reference

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#algebra, #arithmetic, #combinatorics, #computation, #graph-theory, #group-theory, #logic, #mathematics, #number-theory, #recursion, #representation, #riffs-and-rotes, #semiotics, #visualization