On Fri, 01 Mar 2013 08:43:47 -0700, GS Chandy <email@example.com> wrote:
> I personally believe that the 'quantitative techniques' (and > tools/processes) are not really relevant or appropriate to apply to > human beings and their problem-solving or learning processes.
Here I must disagree. Mathematics has been, is, and will remain, central to human endeavor; it is one of only two effective tools we have for manipulating ideas.
In his little monograph, "Liberal Education," Mark van Doren distinguishes three families of arts. There are the Useful Arts, with which we manipulate objects and there are the Fine Arts, with which we create. In between these two are the Liberal Arts, with which we manipulate ideas. According to van Doren, there are but two liberal arts (though he follows the ancients in dividing them into seven disciplines divided into two categories named the Trivium and the Quadrivium). They are language and mathematics. Of these two, he says:
"'Language and mathematics are the mother tongues of our rational selves'---that is, of the human race---and no student should be permitted to be speechless in either tongue, whatever value he sets upon his special gifts, and however sure he may be at sixteen or eighteen that he knows the uses to which his mind will eventually be put. This would be like amputating his left hand because he did not seem to be ambidextrous. The languages of art and science are of twin importance. It is crippling to be illiterate in either, and the natural curriculum does not choose between them. They are two ways in which the student will have to express himself; they are two ways in which the truth gets known."
In the paragraph just above, van Doren places the first sentence in quotation marks, so he is quoting someone. He doesn't give a source, and I've never been able to find the original. I think it was probably Scott Buchanan, but I can't support that statement with anything more than a gut feeling.