Sunday, January 4, 2009

everywhere a sign

Wax and clay tablets, animal skins and tree bark have been used by humankind to record data for over 4,000 years. Math symbols for addition, subtraction, and other computations have only been around for about 500 years as recorded on paper.

In medieval times p and m, with a bar or wavy line over the top, indicated plus or minus. The first textbook to use the symbols + and - was written in 1498 by Johann Widman, used to indicate business surpluses or deficits.

Robert Recorde, and English mathematician in the sixteen century, introduced the symbols to England, and thereby the rest of the English-speaking world. His mathematical works were written in English; unusual for the time, as most math books were in Latin. (More than one hundred years later, Newton wrote his works in Latin, as did many scholars after him.) Recorde's most famous work was the Whetstone of Witte of 1557. In it he introduced these newfangled signs: “There be other 2 signes in often use of which the first is made thus + and betokeneth more: the other is thus made - and betokeneth lesse”. In the same book he introduced our modern equals sign: “I will sette as I doe often in woorke use, a paire of paralleles, or Gemowe [that is, twin] lines of one length, thus: ======, bicause noe 2. thynges, can be moare equalle”.

The word whetstone in the title of Recorde’s book was a pun on the word coss, then used in English for the unknown thing in algebra (and hence the cossic art or the rule of coss for algebra). This word had come through French from the Italian cosa as a translation of the Arabic shai, “a thing”, but Recorde probably got it from German, where it was also used. The pun arises because in Latin cos means a whetstone. Recorde may have written in English, but he still expected his audience to appreciate a trilingual pun!

The ÷ sign was originally used to indicate writings that were considered dubious, corrupt or spurious. It was first used in a book by Johann Rahn, Teutsche Algebra in 1659, as a symbol for division. Until recently ÷ was used by the Danes to mean subtraction; to avoid confusion they adopted the international usage of division.

The division sign in Rahn’s time was known either as the obelus or sometimes the obelisk, from a Greek word meaning a roasting spit. The idea seems to have been that such dubious matter was thrust through, as with a spit; the word is the same as that for a tapering pillar, another object with a pointed end. Confusingly, the word obelus was later used for the printer’s character we often call a dagger, another symbol with a point.

When people began to write computer languages in the 1950's, there were no keyboard symbols for multiplication and division, so the * and / were used. The forward slash is also known as the solidus, oblique or virgule, among other names.

~ A gull by any other name...

There is math in music, but on an unrelated note, today as I was standing at the bay of Lake Mac, listening to the ice creaking and watching the flocks of gulls, all of a sudden one flock and then another flew up with a raucous cry. As I watched their sky patterns over the middle of the lake, one gull stood out as larger...darker...wait...white head and tail...hmm...always a thrill, bald eagle!


  1. Hi all. How are you?

  2. Did you know that USA and Europe blocked Wikileaks? What do you think about it?
    Hope for no silence

  3. Insects The almost whole almost mass of knowledge was pretty later collected under ea and ea and little

  4. Wnat totell you...

    Doesnt matter