Genus, Species, Pie Charts, Radio Buttons • Discussion 1

Re: Genus, Species, Pie Charts, Radio Buttons • 1
Re: Laws of FormWilliam Bricken

Here’s an analysis of “Boolean” structure.  It’s actually a classification of the structure of distinctions containing 2 and 3 variables.  The work was originally done within the context of optimization of combinational silicon circuits, so I used “boolean” for that community, but we all know that “boolean” is just one interpretation of Laws of Form distinction structure.

  • Bricken, W. (1997/2002), “Symmetry in Boolean Functions
    with Examples for Two and Three Variables” (pdf).

And here’s some different visualizations of distinction structures in general.  Section 4 is relevant to us, the rest is just too many words for an academic community.

  • Bricken, W. (n.d.), “Syntactic Variety in Boundary Logic” (pdf).

Dear William,

Thanks for the readings.

Here’s a few resources on the angle I’ve been taking, greatly impacted from the beginning by reading Peirce and Spencer Brown in parallel and by implementing their forms as list and pointer data structures, first in Lisp and later in Pascal.

One thing my computational work taught me early on is that planar representations are an efficiency death trap on numerous grounds.  For one thing we don’t want to be computing on bitmap images and for another the representations of logical equality and exclusive disjunction, whether they require two occurrences of each variable or whether they introduce a new symbol like “=” requiring separate handling, lead to combinatorially explosive branching.  A decade of wrangling with that and other issues eventually led me to generalize trees to cacti, and this had the serendipitous benefit of leading to differential logic.

Not too coincidentally, differential logic is one of the very tools I needed to analyze and model Inquiry Driven Systems.

cc: CyberneticsOntolog ForumStructural ModelingSystems Science
cc: FB | Minimal Negation OperatorsLaws of Form • Peirce List (1) (2) (3)

This entry was posted in Amphecks, Animata, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Functional Logic, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Venn Diagrams, Visualization and tagged , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

2 Responses to Genus, Species, Pie Charts, Radio Buttons • Discussion 1

  1. Pingback: Survey of Animated Logical Graphs • 4 | Inquiry Into Inquiry

  2. Pingback: Survey of Animated Logical Graphs • 5 | Inquiry Into Inquiry

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