Wednesday 5 October 2022

# 9 Billion and Chaos...History and Etymology of Math Terms


Billion,Centilion, Decillion,  Billion seems to have been a French creation, and was originally bi-million. The term originally meant 10^12 or one million millions, and still has this meaning in many countries today. In the US and some other countries it is used for 10^9 or one thousand million. The table below compares the names as used in the US and in Germany:
Value -----German name--------US name
10^6 ----- Million ---------- Million
10^9 ------ Millard------------Billion
10^12 ----- Billion -----------Trillion
10^15------ Billiarde -------- Quadrillion

Cajori attributes the first publication of the words above million to Nicholas Chuquet (1445-1488). Here is a quote from his A History of Elementary Mathematics with Hints on Methods of Teaching:

Their origin dates back almost to the time when the word million was first used. So far as known, they first occur in a manuscript work on arithmetic by that gifted French physician of Lyons, Nicolas Chuquet (1445- He employs the words byllion, tryllion, quadrillion, quyllion, sixlion, septyllion, octyllion, nonyllion, "et ainsi des aultres se plus oultre on voulait proceder" to denote the second, third, etc. powers of a million, i.e. (1,000,000)2, (1,000,OO0)3, etc. Evidently Chuquet had solved the difficult question of numeration. The new words used by him appear in 1520 in the printed work of La Roche. Thus the great honor of having simplified numeration of large numbers appears to belong to the French. In England and Germany the new nomenclature was not introduced until about a century and a half later. In England the words billion, trillion, etc., were new when Locke wrote, about 1687. In Germany these new terms appear for the first time in 1681 in a work by Heckenberg of Hanover, but they did not come into general use before the eighteenth century. About the middle of the seventeenth century it became the custom in France to divide numbers into periods of three digits, instead of six, and to assign to the word billion, in place of the old meaning, (1000,000)2 or 1012, the new meaning of 109

In The Book of Numbers by John Conway and Richard Guy (pp. 14-15) they write

These arithmeticians [Chuquet and de la Roche] used "illion" after the prefixes
b, tr, quadr, quint, sext, sept, oct and non to denote the
2nd, 3rd, 4th, 5th, 6th, 7th, 8th and 9th powers of a million. But around the middle of the 17th century, some other French arithmeticians used them instead for the
3rd, 4th, 5th, 6th, 7th, 8th, 9th and 10th powers of a thousand. Although condemned by the greatest lexicographers as "erroneous" (Litr'e) and "an entire perversion of the original nomenclature of Chuquet and de la Roche" (Murray), the newer usage is now standard in the U.S., although the older one survives in Britain and is still standard in the continental countries (but the French spelling is nowadays "llon" rather than "llion".
Because of continued conflict with England for the first fifty years of the new United States existence, it was much more willing to base the foundation for its numeration system on the method of the French, who had supported them in their revolution. In spite of this, "In many textbooks prior to the War of 1812 (eg. those by Consider and John Stery 1790, John Vinall 1792, and Johann Ritter 1807) if any numbers higher than 999,999,999 were discussed, the British system was used." [for example 1,000,000,000 was one-thousand million rather than one-billion ] {from Karen D. Michalowicz and Arthur C Howard in "Pedagogy in Text", from the NCTM's A History of School Mathemaitics}  

Million first appeared in a printed work in the Treviso arithmetic of 1478. Thereafter it found place in the works of most of the important popular Italian writers, such as Borghi (1484), Pellos (1492), and Pacioli (1494), but outside of Italy and France it was for a long time used only sparingly. Thus, Gemma Frisius (1540) used "thousand thousand" in his Latin editions, which were published in the North, while in the Italian translation (1567) the word millioni appears. Similarly, Clavius carried his German ideas along with him when he went to Rome, and when (1583) he wished to speak of a thousand thousand he almost apologized for using "million," referring to it as an Italian form which needed some explanation. 

 In Spain the word cuento was early used for 10^6, the word million being reserved for 10^12. When the latter word was adopted by mathematicians, it was slow in coming into general use.

France early took the word "million" from Italy, as when Chuquet (1484) used it, being followed by De la Roche (1520), after which it became fairly common.

England adopted the Italian word more readily than the other countries, probably owing to the influence of Recorde (c. 1542). It is interesting to see that Poland was also among the first to recognize its value, the word appearing in the arithmetic of Klos in 1538.

The French use of milliard, for 109, with billion as an alternative, is relatively late. The word appears at least as early as the beginning of the 16th century as the equivalent both of 109 and of 1012, the latter being the billion of England today. By the 17th century, however, it was used in Holland to mean 109, and no doubt it was about this time that the usage began to change in France. 

As to the American usage, taking a billion to mean a thousand million and running the subsequent names by thousands, it should be said that this is due in part to French influence after the Revolutionary War, although our earliest native American arithmetic, the Greenwood book of 1729, gave the billion as 109, the trillion as 1012, and so on. Names for large numbers were the fashion in early days, Pike’s well-known arithmetic (1788), for example, proceeding to duodecillions before taking up addition.

Decillion occurs in English in 1847.

Centillionen is found in German in 1740 in Biblischer Geographus by Johann J. Schmidt: “Was wirds nun helfen, die Zahlen so zu häufen, daß man sie mit Centillionen aussprechen könnte; wer wird denn einen Verstand hergeben, der sie begreift?”

Centilion (spelled this way) is found in English in 1754 in The Gentleman’s Magazine.

 Centillion is found in English in 1863 in The Normal: or, Methods of Teaching the Common Branches, Orthoepy, Orthography, Grammar, Geography, Arithmetic and Elocution by Alfred Holbrook
In Many South Asian numbering system, 10^9 is known as 100 crore or 1 arab.  in Japanese 10,000 is a common base, and above this they normally use 
10,000: ichi-man 「1万」
100,000: juu-man 「10万」
1,000,000: hyaku-man (one million) 「100万」
10,000,000: issen-man 「1000万」.

*(Wikipedia, Jeff Miller, PB notes)

Chaos Although the ideas of chaos theory as we know it today have been actively studied at some level for most of the 20th century, the word as a mathematical term dates only from an article in American Mathematical Monthly in 1975, "Period Three Implies Chaos". The Greek root khaox was for an empty space. This meaning still persists in archaic usage where it refers to a canyon or abyss. The evolution of the word to mean disorder seems to come from reference to the time before God created the universe. The empty space was with out order and the creation filled the emptiness and created order.

more common form of the word exists today, but few people are aware of the connection. At the start of the 17th century, a Flemish scientist named Jan Baptist van Helmont was studying the bubbles that rise when fruit juice was allowed to stand. These strange vapors, without shape or form, reminded him of the Greek idea of Chaos, so he called them by the Germanic (Flemish is a dialect of German) spelling of chaos, gas.

The physical objects formed out of the void were called the cosmos, the Greeks word for orderly or well formed. Today we often hear people refer to the Universe as the cosmos. When Robert Milliken, the American physicist, sought a term for the radiation that seemed to be coming from everywhere in the universe (the cosmos) he suggested the name Cosmic Rays . Today the word cosmos also remains as the root of words like cosmopolitan and cosmetics.

cosmopolitan (adj.)

1815, "free from local, provincial, or national prejudices and attachments," from cosmopolite "citizen of the world" (q.v.) on model of metropolitan. From 1833 as "belonging to all parts of the world, limited to no place or society." Meaning "composed of people of all nations, multi-ethnic" is from 1840. The U.S. women's magazine of the same name was first published in 1886.

As a noun, "one who is at home all over the world, a cosmopolite," 1640s. As the name of a vodka-based cocktail popular in 1990s (due to "Sex and the City" TV program) from late 1980s (the drink itself seems to date to the 1970s).

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