[Edu-sig] news and views from Rams Head (PDX)
kirby.urner at gmail.com
Wed Jan 14 00:42:24 CET 2009
Ian is promoting my Chicago talk, lots of details, feel free to link
to this page if sharing with others, in addition to whatever official
I did some good work with the XO today, working for 4D Studios:
I've got Midhat Gazale's 'Number' out from Multnomah Library again,
wanting to get his "cardination" versus "ordination" distinction more
clearly, been relying on memory.
Cardination: establishment of one-to-one correspondence, or matching,
"consists of pairing objects or groups of objects". "Nomen est numen"
says the Latin adage (pg 11), meaning that to name is to know. Link
to "right brain" for heuristical purposes.
Ordination: i.e. counting, requires a notion of succession or
sequence, Latin root "computare" (compter, conter). "According to
studies conducted by Charles J. Brainerd and others, the faculty of
ordination (establishing an asymmetrical relation of transitivity
between three balls of increasing weight, or three sticks of
increasing length **) is more fundamental than that of cardination or
Page 14: Says Tobias Dantzig, "Correspondence and succession, the two
principles permeate all mathematics -- nay, all realms of exact
thought -- are woven into the very fabric of number system."2 For all
we know, and that does not amount to much, they are perhaps woven into
the very fabric of our brain hemispheres...
philosophically, "ordination" relates to "ranking" i.e. better versus
worse, as in "the fall" into good versus evil (knowlege of).
Cardination is "beyond good and evil" (more primitive than) in the
sense of "noticing differences without judgment" e.g. in Python we
have the integer type, string type, fraction type, but don't have to
say "which we like better" (give some better examples?).
All moral judgments aside, there's also the obvious hierarchy of
"containership" as in "what contains what". We say Q > Z (rationals >
integers) because the set of all rationals *contains* the set of all
integers. This takes us to the ancient greek concept of "atoms" i.e.
"that which everything contains" (relates to later talk of bosons,
Another obvious source of sequencing or ordination (left brain in
Midhat's analogy) is temporal, what happens *after* or *before* what
else in some given scenario. N < W < Z < Q < R < C is likewise
temporal, especially if we use Roman Numerals to illustrate N, add
zero from Baghdad (Algebra City) via Fibonacci of Pisa, to get W, then
My thanks to Juaquin, Ram's Head (McMenamins), for a fantastic lunch,
complete with Bloody Mary. I'm on chauffeur duty for Quakers, one of
my several routine gigs.
** a nod to Gattegno, also Egyptian
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