Dmitri A. Borgmann, Naming the Numbers, 1968
Following is the article Naming the Numbers from pages 28-31 of Word Ways: The Journal of Recreational Linguistics, (1968) vol. 1, #1.
This article refers to:
W. D. Henkle (here called "Prof. Henkle"), Names of the Periods in Numeration, 1860.
Edward Brooks, The Philosophy of Arithmetic, 1876 (as reprinted in 1904).
This article is referenced by Rudolf Ondrejka, Renaming the Numbers, 1968.
Naming the Numbers
The field of recreational linguistics is full of unsolved problems. The purpose of this article is to acquaint readers with one such problem, in the hope that someone will be inspired to work out a solution to it.
Large numbers have names. A "1" followed by three zeroes is called a "thousand"; followed by six zeroes, it is called a "million"; and so on. If we consult the dictionary, we find the following set of number names in existence:
Further the dictionary saith not.
Aside from the spicy character of some of the names (SEXtillion, SEXdecillion), the list raises two obvious questions:
(1) What are the names of the numbers between the "vigintillion" and the "centillion"?
(2) What are the names of numbers larger than the "centillion"?
Since no dictionary chooses to enlighten us on this score, we have ransacked mathematical literature in search of the missing number names. The only material on the subject to turn up has been in The Philosophy of Arithmetic by Edward Brooks, published in 1904. In the appendix to that book, there is quoted a list of number names formulated by a Professor Henkle. Up to and including the "duodecillion," Henkle's names coincide with those in the list given above. Henkle's continuation, at variance with the foregoing list, follows;
In the preceding table, word elements ending in "O" represent numbers to be added, while those ending in "I" represent multipliers. When two word elements end in "I", the sum of the numbers indicated is to be taken as the multiplier. In each, the last word element indicates the number to be increased or multiplied. The names of the intermediate numbers, omitted from the previous table, are to be formed by analogy to those names in the table.
Much as we would like to accept the list of number names as authoritative, we cannot do so, for it does not live up to the standards to which one expects it to adhere. Neither, for that matter, does the dictionary list given first.
With one exception, all of the number names end with the suffix -ILLION. The name "thousand" does not. Exceptions are intolerable. The name could be changed to something like "thusillion."
An examination of the further reaches of these lists makes it painfully clear that 1,000 should be called "million," 1,000,000 should be called "billion," etc. Only by shifting all of the number names backward one space can we avoid the ridiculous "3" with which the numbers of digits in the major numbers named end.
Allegedly, the names of the numbers are derived from the Latin names for small numbers. However, the derivation of the successive names from Latin is full of inconsistencies, beginning with "million" itself. If the names are derived from the Latin cardinals, they should start out as follows: UNILLION, DUILLION, TRILLION, QUATTILLION, QUINQUILLION, SEXILLION, etc. If the derivation is from the Latin ordinals, the names should begin: PRIMILLION, SECUNDILLION, TERTILLION, QUARTILLION, QUINTILLION, SEXTILLION, etc. The existing number names are a hodgepodge without any consistency. This makes it impossible to extend the system of names in an entirely consistent fashion.
Latin itself is inconsistent. Thus, the word for "eighteen" is either OCTODECIM or DUODEVIGINTI, and the word for "nineteen" is either NOVENDECIM or UNDEVIGINTI. In each case, the second word was the one more commonly used, and many Latin textbooks don't even list the first word. Which set of names shall we use for constructing a system of number names?
At points, Henkle introduces the name clement SEMELI, derived from the Latin "semel," meaning "once." The word is neither a cardinal nor an ordinal. In spirit, it belongs to a third category of Latin number names, the distributives, although the regular distributive term for "once" is SINGULI, not SEMEL, What are we going to do about that?
Latin for 7 is SEPTEM, for 17 is SEPTENDECIM, How do we achieve uniformity: by always using SEPTEM, or by always using SEPTEN, or by trying to make some distinction, sometimes using one, sometimes the other?
Anyone who attempts to fill in the intermediate names omitted from Henkle's table will soon run into difficulties. One difficulty is that some of the intermediate names are so long as to be unwieldy. The only way of overcoming that difficulty is to introduce additional sets of prefixes into the nomenclature. For instance, the word MILLILLION is difficult to pronounce. It could be replaced by the easier and shorter word MEGILLION, using a Greek prefix. By introducing the Latin distributives, and Greek and Sanskrit prefixes, the intermediate number names could be streamlined.
A related difficulty is trying to avoid ambiguity. If we try to eliminate the defects in Henkle's nomenclature, it is very easy to run into situations where the same word appears in two different places, with two different meanings. Thus, we could discover that SEXCENTILLION is a name both for the number that uses 321 zeroes, and for the number that uses 1,803 zeroes. Avoiding such ambiguities is a difficult problem, not always foreseeable.
Henkle's number names are full of hyphens. Esthetically, a hyphen is a mar in the verbal landscape. Can't most or all of the hyphens be eliminated?
The name for "1803," SEXCENTILLION, is inconsistent with the names preceding and following it. Should it not be changed to SEXINGENTILLION?
This has been a sampling of the problems encountered by anyone who attempts to formulate a wholly rational system of number names. So far, no one has succeeded. The challenge remains....
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