A seminal advance that allowed for the development of the modern world seems never to be consciously noted by most persons. That advance was when people began to identify groups of objects with the abstract idea of numbers. The concept that 1, 2, 3, 4 and so on could be mapped with a one-to-one correspondence to a group of skins or fruit or whatever, took a considerable amount of abstraction, and can be counted as one of the great conceptualizations humans embraced.
Francis Galton (1822-1911) is reported to have made this observation about a tribe in Southwest Africa:
When inquiries are made about how many days’ journey off a place may be, their ignorance of all numerical ideas is very annoying. In practice, whatever they may possess in their language, they certainly use no numeral greater than three. When they wish to express four, they take to their fingers, which are to them as formidable instruments of calculation as a sliderule to an English schoolboy. They puzzle much after five, because no spare hand remains to grasp and secure the fingers that are required for units. Yet they seldom lose oxen; the way in which they discover the loss of one is not by the number of the herd being diminished, but by the absence of a face they knew.
I don’t know if Galton felt sanctimonious about this lack of numeracy, but if he was, it was not particularly justified. Isaac Asimov (1920-1992) was the person who led me to this realization. In his book Fact and Fancy he states:
It was 1300 A.D. before the word “million” was invented. Until then, the largest number word was “myriad,” which was Greek for 10,000. Even Archimedes, in calculating the number of poppy seeds in the entire Universe as he knew it, used expressions meaning “myriads of myriads of myriads. …
It was only seven centuries ago that a word to describe 1 000 000 was created, which is equivalent to the modern metric prefix Mega—and adopted only in 1960.
In 1871, Fredrick A.P. Barnard (1809-1889) gave a speech which was expanded into a book called The Metric System of Weights and Measures. Barnard had done his best to make the metric system the exclusive system of measure in the US, but Charles Davies managed to derail this initiative. In his book Barnard presents this table:
The largest metric prefix used with a meter is a myriametre. The myriad apparently continued to remain an upper value limit for the everyday person. This is true even though the word million existed at that time, and Friedrich Bessel (1784-1846) determined in 1831 that the star 61 Cygni was about 98 Petameters from Earth, or 9 800 000 000 000 myriametres. The early metric system was provincial and still mired with numerical magnitudes from the time of Archimedes. It would not be until 1960 when a prefix larger than myria would be adopted, which is of course Mega. The prefixes Giga and Tera were also adopted that year. The use of myria as a prefix, despite its ancient origin, seems to have been eschewed without much difficulty, and the better by 1000 approach began. The seldom used prefix cluster around unity has proven much more difficult to eradicate.
While the numerical value for the word million was agreed upon after 1300 A.D., a fork occurred when English words were chosen for larger numbers. The word billion is used for Giga in the short scale; in the long scale, the word milliard is used. The word billion is used for Tera in the long scale, but it is called trillion in the short scale. The history of the changing values of words used to describe large numbers is considerable and meanders. This prefix table provides succinct documentation of the differences between short and long scale words:
Douglas Adams’ The Hitchicker’s Guide to The Galaxy has a computer called the Milliard Gargantubrain, which shows that long scale usage is still with us. The use of the short and long scales has allowed for very poor literary numerical expression, which was long ago forbidden in the metric system, but is ignored when long and short scale words are combined with metric prefixes. The statement that a celestial object is one million Kilometers from Earth does not meet with objection, but if it is a KiloMegameter away, that would be laughable. The proper term Gigameters would probably also cause heartburn for the provincial literary crowd who are proudly literate and willfully innumerate, but it is the most succinct prose expression, and does not contain any numerical ambiguity. If we have a billion meters, it could be a Gigameter or Terameter. Carl Sagan (1934-1996) used the term billions and billions. But which billion? Alternatively he could have said milliards and milliards, which would have been unambiguous by comparison—even if it is a metaphor.
The long or short scale words are not prefixes, they are improper prefixes which at worst have dyadic values (i.e. two different values for billion and billionth) and at best are redundant. Long and short scale words should not be combined with metric prefixes to present a numerical value. They only promote innumeracy. Does a milliardth of a nanometer improve one’s understanding of magnitude? Attometer is shorter and clearly and unambiguously defined and has a metric context. When I see a headline like: 35 years and 18 billion kilometers later, NASA’s Voyager approaches exit from solar system, I can only do a face-palm. Is this 18 Terameters or 18 Petameters? 18 000 Gigameters is probably more meaningful. Until we are able to reform our prose, and make them all metric, we have little justification to believe that we are clearly more numerically advanced than the Southwest African tribe described by Dalton in the 19th Century.