On 2/22/2014 1:09 AM, Robert Hansen wrote: > On Feb 22, 2014, at 1:29 AM, Louis Talman <email@example.com> wrote: > >> The two of you need to understand that you are arguing about the formalizations---not about the underlying concepts. The programmers' function is an implementation of the mathematician's function---and neither of them is likely to think much about the formalization. (Kemeny makes this point, too, at least for mathematicians.) > > Interesting tidbits from the Kemeny paper? > > ?The first thing that we can all do is to give the students a good book to read. An able high school student is old enough to read books. There are many books on the market that can be given to a student. SMSG is undertaking a major effort to turn out special pamphlets and monographs for just this type of use in high school, and other groups are doing the same.? > > Kind of makes you sad. > > Also? > > ?I saw a list compiled recently (by Mu Alpha Theta, Box 1155, University of Oklahoma, Norman, Oklahoma) that tried to prove that for $180 you can build up a superb high school mathematics collection.? > > $180 in 1961? The average salary in 1961 was $5,315 or $102 a week. That must have been one hell of a collection of books, or, the relative price of books then was more than now. > > I know the price of academic articles wasn?t more then. This cost me $15. Damn JSTOR. > > Bob Hansen > > Possibly off-topic, but I once came upon the statement to the effect that you can understand a process by studying it; or better yet by explaining it to someone else - or even better yet by explaining it to a machine via programming.