IATROGENIC MATH

IATROGENIC MATHEMATICS
(Mathematical Problems Created by the Teaching of Math, Etc.)

Karl Menger: "The language of calculus is so atrocious that it makes the profound look trivial and the trivial look profound!" ["Gee! You mean that òxdx = òudu = òvdv? What theorem's that?" No! This is Logical replacement, not analysis. Or, "Sure, I know that (dy/dx)(dx/dt) = dy/dt. I learned that in fractions!" Wrong! This implied theorem looks properly profound when viewed in Leibnizian notation: (D_xy)(D_tx) = D_ty.]

The primary operations of "calculus of one variable" are differentiation and antidifferentiation [not "integration", which is a functional, not a function-function mapping; "indefinite and definite integrals" confuses]
Bertrand Russell: "The thing about a variable is that it doesn't vary." [can say functand, since it's the map of a function, just as we speak of operator and operand].

Some students detect what seems to be cheating in the quasi-axiomatic presentation of arithmetic in our schools ["You say you can subtract 5 from 3 unless you put a funny sign in front of it!" "You say you can't divide 12 by 5 without remainder unless you put a funny sign between 12 and 5!"]

Sloppily, we say "add a topic", not "adjoin a topic", confounding arithmetic and rhetoric! No wonder kids get confused with math!

"Less" is analogic -- "fewer" is digital [even "language maven" W. Safire stutters over this],

The buzziest of buzz-words ["average" means "set-representor": mode(s), median, arithmetic mean, geometric mean, harmonic mean, logarithmic mean, etc. are all averages]. The word "average" derives from Latin "havaria" for "share" [in a primitive form of Mediterranean merchant's theft-or-other-loss insurance].

Say "negative one", not "minus one": don't confuse subtraction with ordering in the number system [replacing medial signs by superscript signs helps: -5, not -5; +3, not +3; etc,]

Not Aristotle but Chrysippus the Stoic instituted bivalency in logic! [please see E. W. Beth, The Foundations of Mathematics, 1959]

Quantity! Quality! Quibble! Quack! ["qualitative": typological & ordinal measurement scales; "quantitative": interval & ratio scales; so quantitative is qualitative & a little more, i.e., less general]

The "Challenger Disaster Report" [killing astronauts and a school teacher] shows that good engineering measurements were wasted and bypassed by vague administrative decision language. [An engineer was ordered to "take off your engineering hat and put on your administrative hat and vote with us for take-off!"]