Cutting it Short

It is generally true that algebra in its development in individual countries passed successively through three stages: the rhetorical, the syncopated, and the symbolic. - Tobias Dantzig

The first time I remember hearing the word "syncopated" was in Ken Burn's documentary on Jazz. It seems to have a specialized meaning in music, which is to modify rhythm by stressing or accenting a weak beat. In Burn's movie, Wynton Marsalis uses it in his running commentary to describe the musical flights of various great jazz artist.

So when I came across the word in Tobias Dantzig's book Number, I was intrigued that the word seemed to have a more fundamental meaning with broader implications for abstraction and meaning -- and therefore possibly for writing and art.

In his book, which traces the origins and evolution of numbers and mathematics, Dantzig demonstrates a progression from oral mathematics that uses only words (such as "the sum is independent of the order of the terms") to symbolic algebra in which graphical symbols represent concepts previously conveyed by the words (a + b = b + a).

Syncopation is the process of abbreviation by which the words become symbols. Certain words that are used regularly are gradually shortened until they have no obvious connection with the original word.

Webster's tells us that the word syncope dates to 1550, and comes from the Greek synkopē, which literally means cutting short from synkoptein to cut short. It is the loss of one or more sounds or letters in the interior of a word.

Dantzig offers the history of the symbols + and - as examples of words become algebraic signs.

In medieval Europe the latter was long denoted by the full word minus, then by the first letter m duly superscribed. Eventually the letter itself was dropped, leaving the superscript only. The sign plus passed through a similar metamorphosis.

Here seems to be the key trait of syncope: abbreviation. It is the process by which a sign for something becomes abbreviated.

In this way, it seems to be subclass of metonymy, which Webster's tells us "is a figure of speech consisting of the use of the name of one thing for that of another of which it is an attribute or with which it is associated."

This certainly seems to hold in the broadest sense that metonymy consists of using a derivative sign to represent an original object or concept. The "sails crossed the ocean," being a classic example of this kind of derivation (i.e., the sails are derived from the ship.)

When we see a sign on the side of the road with a simple graphic of ship on it and find a marina at the next exit, its the end result of the process of syncopation.