osculating curve and osculant and osculum and anastomosis and anastomose

I began the previous essay by talking about osculant (kissing), but I got myself tied up in the Roman calendar and ended up explaining intercalary and bissextile. I need to climb back to kissing, but will do so via a sentence in the OED under the word bissextile. From 1696: "The Julian Calendar...intercalates the Bissextile Day immediately after the Terminalia." Terminalia? What is that? As this web site tells us, the Terminalia (February 23) was the last day of the sacral year--the annual cycle of religious holidays. On that day people recognized the boundary stone--border between properties (why would this have been done on the Terminalia?) and did other rituals relating to renewal of life. The new year began March 1--which actually was the way things were in this country until the 1750s.

Trying to Return to Osculant (Kissing)

I think I wandered because I was looking at synonyms for osculant, and I learned that intercalate, intergrading and inosculant were listed. The image created by the word osculant then, is twofold. It is either something that touches something else (and this will be its mathematical definition, see below) or it is a connection between two families or genera (biological usage). This "in between-ness" of osculant is also stressed by the word inosculant. The OED actually has the verb inosculate, which is defines as follows: "Of blood-vessels, etc.: To open into each other, to unite or join by running together; to have connextion terminally; to anastomose." I love the image created by these words, for we see a union occurring between two separate things which join together in the middle. "The arteries...at last end in small capillaries that inosculate with the veins." This stresses the mutually interpenetrative characteristics of two things. "The harbor was intersected by innumerable inosculating channels."

But I have to follow briefly only one more word before I can safely return to kissing. I promise--only one. Notice that in the definition of inoscuate we have the word "to anastomose." Coming from the Greek word meaning to furnish with a mouth (stoma) or outlet, anastomosis has come to mean an interconnection between things, a sort of merging or coming together. The word anastomosis originally referred to an "apertion" or opening of two blood vessels into another (1615 quotation), but it soon took on the figurative meaning of interconnection. From Thomas May's 1630 translation of Lucan's Pharsalia we have: "As they through each other glide/ Make many knots, as if they tooke a pride/ In these strange foldings, and themselves did please/ In those admired Anastomoses." But science quickly regained control of the word, so that it now, when it is used at all, refers primarily to cross connections in the sap-vessels of plants or between rivers or their branches, and "to cross connexions between the separate lines of any branching system, as the branches of trees, the veins of leaves, or the wings of insects." Thus anastomosis stresses connnections.

Just as we were ready to give the term back to the scientists, Nabokov again rescues us. In a long and beautiful sentence from Speak, Memory, he says:

"the distant meadows opening fanwise, the near trees sweeping up on invisible swings toward the track, a parallel rail line all at once committing suicide by anastomosis, a bank of nictitating grass rising, rising, rising, until the little witness of mixed velocities was made to discharge his portion of omelette aux confitures de fraises."

Listen to the phrase: "a parallel rail line all at once committing suicide by anastomosis." He is looking backwards, out the window of the train and seeing the parallel tracks merge into one. They unite and become a sort of Lake Tanganyika of the prairie--for Tanganyika, as 19th century Arabist Richard Burton says: "signifies an anastomosis, or a meeting place." They "commit suicide" because they are giving up their individual lives by joining to one another. Truly, a great writer.

Actually Returning to Osculant

The mathematical meaning of osculant deserves brief mention. The Century definition of osculant in this regard is impenetrable, and so I won't even pleasure you with it. But the word means something in geometry. According to the OED, to osculate means: "Of a curve or surface: to touch (another curve or surface) so as to have a common tangent at the point of contact." The term is first attested in English in Chambers' 1728 Cyclopedia, s.v., where he defines Osculum as follows:

"A Circle described on the Point C, as a Centre..with the Radius of the Evolute M C, is said to osculate, kiss, the Curve described by Evolution in M; which Point M is call'd by the Inventor Huygens, the Osculum of the Curve."

More modern encyclopedias speak of a plane or circle as osculating a curve when it has three coincident points in common with the curve. From an 1885 textbook on the Elements of Projective Geometry, we have "Three of the four points of intersection of the conics lie indefinitely near to one another, and may be said to coincide in the point A; and the conics are said to osculate at the point A."

Thus an osculum or to osculate is not precisely the same thing as to be tangent with something. Something touches once, and it is tangent. But if it touches again and again (three times in geometry) it is said to osculate the curve. Indeed, what a wonderful word--osculate. It kisses the curve and not simply touches it once. We can even hear, in the music of the spheres, the expression of love.

1805