Promiscuous Problems and the 20th Century

The year 1913 seems to have had a strange effect on educational language, and as yet, I haven't figured out exactly what happened.

A few days ago, Dave Renfro, an internet associate who does more research into journals than anyone I have ever heard of, sent me a note that had an aside that said, "Also, ...,I've seen the terms "promiscuous exercises" and "promiscuous problems".

I did a little follow-up and found literally dozens of books that use the phrase "promiscuous problems". My Google Book search on the exact phrase produced 71 books and journals, mostly referring to mathematics, but not exclusively. In glancing at the dates, I noticed that almost all were before 1900. So I set the same search with a cut-off of before 1900. The result?... There were still 25, but only five of them were after 1910. Of these five, one was about sexual disorders of bulimic patients and had nothing to do with problem sets of the educational sort, one was a catalogue of antiquarian objects and was referencing a phrase in an older object, two were reproductions of very old texts. That leaves the one final object after 1910 that referred to Promiscuous exercises in regard to problem sets, with a date of 1913. For some reason, the usage to describe a set of problems or exercises seems to have disappeared after that date almost completely.

So what do they mean, "promiscuous" problems. One of the definitions leads back to the old Latin root. Here is the way they gave the etymology in the Online Etymology Dictionary:

"consisting of a disorderly mixture of people or things," from L. promiscuus "mixed, indiscriminate," from pro- "forward" + miscere "to mix" (see mix). Meaning "indiscriminate in sexual relations" first recorded 1900, from promiscuity (1849, "indiscriminate mixture;" sexual sense 1865), from Fr. promiscuité, from L. promiscuus.

So the term was essentially used for a general mixture, thus promiscuous exercises were a mixed review; but then in 1900 the phrase became associated with "indiscriminate in sexual relations" and apparently that usage became so common, that the use of promiscuous exercises was no longer classroom acceptable.

Makes me think of a story that John H Conway, told (I believe) about the word hexagon. If you search the word "sexagon" you will see that it was very common in old math texts, then during the Victorian era, it became too suggestive for classroom use, and so hexagon, which also has a long history of use, became the preferred term.

The Art of Asking Questions

It started with an old (1848) journal article by JJ Sylvester on a property of concurrent lines in a triangle. He pointed out that if you had a triangle and located a point in its plane (I begin this with students by placing the point in the interior of the triangle) then the three cevians (lines from a vertex cutting the opposite side, perhaps extended) through the point will lie on a circle. He went on with some more detail, but ended the article by saying something about it being a good classroom exercise because it raises many good questions.

It reminded me of all the quotes I have about the importance of "questioning" to being a good mathematician.

"In mathematics, the art of asking questions is more valuable than solving problems." Georg Cantor

I wonder if math teachers in general agree, and if you could tell they did by the way they run their classes?

"The scientist is not a person who gives the right answers,
he's the one who asks the right questions." Claude Levi-Strauss

So if the art of asking questions is more important, should we be spending more time getting students to ask, rather than answer questions.

"Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs. " Felix Klein

I don't think I teach them to ask quesitons very well. My kids are good at asking, "How do I do that?", but not at the kind of questions that develop and reinforce intuitive development. I think I model asking questions well... "what might happen if we changed this? What does this remind you of???", etc...but I don't have any activities that actually are designed to help them learn to ask good mathematical questions.

So do you do that? And how do you do it?

"It is better to solve one problem five different ways, than to solve five problems one way." George Polya

The Mathematics of Spontaneous Synchronization

Even the inanimate??? just watch...
Mathematician Steven Strogatz shows how flocks of creatures (like birds, fireflies and fish) manage to synchronize and act as a unit -- when no one's giving orders. The powerful tendency to synchronize even extends into the realm of inanimate objects?

Carnival 51--- back from the "near dead"

The 51^st Carinval of Mathematics is back, alive and, hopefully, well. Go by and check it out at Square CircleZ. One of the nice ones at a site I had not seen before was a Facebook for numbers example at Math Nuggets which looks like a blog I will need to explore more in the future.

I also really enjoyed Aspects of a Topic by Vlorbik, who makes a really good argument for doing arc length with parametric functions... how come I never get these kinds of good ideas????

They even had a link to my blog on Benford's Law (blush).

So swing by and check it out...