Science Forum

jonhays

I defined "proto-learning" as "knowing but not knowing you know" to redefine "learning" as "knowing and knowing you know". By learning factor algebra (prime/composite numbers, least common multiple, greatest common divisor), one becomes proto-educated in 20+ fields of math via "The Barbie Doll (Multiple) Mathematics": by changing factoring labels of operations/operands as a girl changes costumes of Barbie Doll. I kenned this years ago by reading that factors of, say, 30, form a "boolean algebra". In trying to commmunicate this, I've been ostracized in the way magicians ostracize any magician publicly explaining a trick. When I was running a Workshop for High School
Mathematics Teachers under a National Science Foundation, by saying that standard sets prohibit the multiple tokenage of "nonsqare numbers" but this need not be, I became persona non grata to NSF: implicitly I'd said "The New Math does not support The Old Math". My extended sets appeared much later as "multisets". But these are ybrids: "exogenously" mapping from sets to integers. But my "o-sets" -- "o" or "order/degree" -- "indogenously" remain in set theory. (Their indicator tables -- "truth tables"-- form digital fuzzy logic.)
Mathematicians stop at what I call "t-sets" -- "t" for "type" -- to save
proof-by-contradiction. (L. E. J. Brower rejected this proof, angering D.
Hilbert. I wrote a math fable -- "The Battle of the Frog and The Mouse",
a title suggested by A. Einstein's comment on their controversy -- online
GooGle ("Fable+jonhays") -- which appeared in "The Mathematical Intelligencer", 1984, reprinted "Pi in The Sky" (1992) by John D. Barrow.) -- I've labeled this stand of mathematicians as "Ad hominem Math": spoiling math to make work easier for mathematicians.--Google("toteenmathpaj+jonhays") to see a version of lattice theory (Barbie-transformable) for preschooolers: "Pecking Order"
as in a barnyard of chicks, but same hierarchical ordering as in Military or many corporations. Chicks are colored to translate as additive theory of color for light in optics or quarks in quantum theory; Colored anti-Pecking Order translates as subtractive theory of color for dyes and inks, or anti-quarks. --I've 56 websites online (file content to 50 books of 300 pages each) for this and other subjects: Google("webring+jonhays") to click these. But no response all these years. As I said long ago in that webring, I invite comment/argument.