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pancakemath.org is back again with

pancake/ boundary / box arithmetic and algebra.

This stuff is really all the same thing: pancake math, box arithmetic, boundary mathematics.

Based on Spencer-Brown's Laws of Form, this is the future of grade-school math teaching. It affords experience with mathematical proof without numbers or left-right facility. By giving early experience in formal systems and proof, we'll rear stronger, proof-fearless majors for graduate work in math.

Because authors were unaware of each other during earlier work, and because Spencer-Brown gave no convenient overall term other than the cumbersome “calculus of indications,” this mathematics goes by several names, each motivated by heuristic considerations. Presentations differ mainly in notation used and target audience:

yyGrams™ [outlink] : Pancake (below) in puzzle guise, in the style of crossword puzzles, Sudoku™, rebuses &c.

Designed for learning in laundromat time. Nesting parentheses, middle-school and younger. Weekly and monthly periodical layouts. Another attempt to end-run the schools to reform US math education in the "grades" and high school.

pancake [here] : Nesting parentheses, the keyboard-friendly, programming-friendly notation. Middle-school and younger.

boundary [outlink] : Nesting circles (not Venn diagrams; overlapping is forbidden)—graphically avoids the erroneous impression that serial order is meaningful. Serial order is not part of this arithmetic. Computer engineering undergraduates/gymnasium, high school.

box [outlink] : Nesting rectangles also graphically avoids the serial order impression. Computer engineering undergraduates/gymnasium, high school.

Laws of Form [outlink] : “Cross” (terminated, nestable overbar) original notation for Spencer-Brown's “calculus of indications.” Devotees and math majors.

Let's Say: a Child's First Calculus [here] by David Zethmayr, HTML edition (parenthesis notation)

Sphinx Challenge: a Try-it-Torial™

Wearables and collectibles with summaries of pancake math essentials and how it does boolean better (throw away Karnaugh maps!), and formal logic including propositional and existential logic