Tuesday, 3 May 2022

Victorian Political Correctness, Math Terminology, and Urban Legends

 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 catalog 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 1911, John Henry Diebel's  Arithmetic by Analysis. 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 earliest use of Sexagon in English , according to the OED, was by A. Rathborne in Surveyor, written in 1616. The term in English probably came from the use of Latin as the language of choice in science.  Sex was the prefix for six ans still remains in words like sextant, sexagenarian, and sextet.  Its demise may have been due to the hybrid nature of the word, sex from Latin and gon from the Greek for knee.  Hexagon was a union of two 

After I wrote this I got a comment:
r.r. vlorbik said...

i've heard, though never verified, that Victorian prudery also caused certain teachers to begin referring to the "arms" rather than the "legs" of a right triangle (the non-hypotenuse sides).
this is to say nothing of "parent function".i've *always* thought of the higher node
of a link in a tree as the "parent' of the lower... so this terminology (in discussion of
function transformations; x^2 is the "parent" for 3(x-2)^2 +1... you know the drill...) seems perfectly natural to me.

but somebody with some public-school experience told me,what may even be true, that up to a point,
one had called these things *mother* functions. which had to be made to stop.... latus rectum. (wrecked 'em, hell... it killed 'em).

So I was off on another search:

I have a pretty extensive collection of old textbooks, including many British texts, and I didn't remember ever seeing anyone use "arms" in that fashion, so my first thought was that, if it were true, it was only a very minor usage. Since the good lady Victoria, ruled from 1819 to 1901, I thought I would search before and after her reign.

I pulled out my 1804 edition of Playfair's "Elements of Geometry", published in Edinburgh. He referred to the right triangles sides as..."sides"... His Book VI, prop. XXXI reads exactly like the Thomas Heath Translation. No help there, so I skipped forward 99 years to the other end of the Victorian period, 1903 and looked in "A Junior Geometry" by Noel S Lyndon, published in London, only to find he also used only the terms hypotenuse and "other two sides" in his statement of the Pythagorean Thm.

Perhaps neither term was common in the Victorian period, and these stories were a bit of urban legend. I went on to Google Books to see if I could find any examples of geometric usage such as Vlorbik had described..... I entered a search for "arms 'right triangle' geometry"

....Yikes", there they were. The first listing was "Plane Geometry" by Arthur Schultze, Frank Louis Sevenoak, Limond C. Stone, from 1901. It contained, "The sum of the squares of the arms of a right triangle is equal to ..." along with 388 other listings, some dated as late as 2008. "In a right triangle whose arms have lengths a and 6, find the length of the .." appears on page 451 of the fourth edition of Schaum's Outline of Geometry from that year.

 Ok, but that still did not mean it was the influence of the dreaded Victorian stuffed-shirts... I switched the cut-off to 1850... and there were NO results prior to that year... only one last check. Would there be examples with the use of "legs" prior to that year? There were indeed, including several by the famous American Mathematician, Benjamin Pierce. Another from 1734 was from the British Benjamin Martin.

So it appears that there was some pressure to use "arms of a right triangle" suggested by these dates; but there is still no smoking gun. One observation that suggests that if such a suppression existed, it may have been much more influential in the US than in England. One is that the OED gives no reference to the use of arm as a mathematical or geometrical term.  The other is that most of the books  found using "arm" seemed to be of US origin. Does anyone out there know of a document or statement of any kind in the math education literature that makes a clear suggestion to teachers? If you know of such a document, please share whatever level of information you have and I will pursue it.

Functions, Parents, and Parent Functions

From what I have been able to discover in a short period of research, the use of terms like "parent function" seems to have worked its way into mathematics from statistics, which seems to have gotten it from the anthropologists/sociologists.

Across America and Asia: Notes of a Five Years' Journey Around the World ...‎ - Page 250 by Raphael Pumpelly - Voyages around the world - 1870
"if it should bear the same relation to the parent population that.."

Prior to 1900 there are almost no listings of "parent function" in a mathematical usage. Around the end of the 19th century, statisticians began to talk about the distribution from which a sample was taken as the "parent distribution" of the sampling distribution (population of all samples of some size n). Some of these may be related to the study of eugenics in which the study was about the relations of some characteristic of the offspring to the actual parents, but the usage grew.

Data reduction and error analysis for the physical sciences , by Philip R. Bevington - 1969 10-2 the F TEST As discussed in the previous section, the x^2(chi square) test is somewhat ambiguous unless the form of the parent function is known because the statistic
x^2 (chi-sq)... "

Occasionally I find the term "parent function" applied in this way when the distribution of the original sample was a normal distribution.
The Annals of mathematical statistics‎ - Page 179
by American Statistical Association, Institute of Mathematical Statistics, JSTOR (Organization) - 1948
" Usually the parent function is the Type A or normal curve, as discussed by Gram "

There are also some early uses of the "parent function" in association with the use of inverses and derivatives in calculus and analysis texts back to about 1925. By 1970 the term had become commonly understood, but not abundantly used.

The teaching of secondary mathematics‎ - Page 521
by Charles Henry Butler, Frank Lynwood Wren - Education - 1965 - 613 pages

".. of an inverse function and its relation to the parent function or else in failure to attach clear meanings to the terminology and notation employed. ..."

It was the 1980's and the introduction of computers and graphing calculators into modern classrooms that seemed to make the term "parent function" ubiquitous. Any function that appeared on the calculator was a parent function, and the translations, rotations, shears, etc became the "children".
I think this use also led to the introduction of "mother function" rather than the other way around. I can only find a few examples of "mother function" and there does not seem to be any pattern to the frequency as one might expect if a term had arisen to replace this one as an "off-color" predecessor. In fact, it seems "mother function" is more commonly used by continental writers, often in conjunction with "daughter functions"; but admittedly the sample size I have to draw on was small. Perhaps these were early pioneers for language equality.

If you are one of those people with access to old journals, or a collection of old texts, I would appreciate any references to the use of any of these terms and a source earlier than 1900; and if you have a way to make a digital copy and send it by email, I will have my students name their children after you.  

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