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.

The article presents a system for extending the "Chuquet" number-names, comparable to but less authoritative than the later system of Conway and Wechsler.

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:

Zeroes Number Zeroes Number
3 thousand 36 undecillion
6 million 39 duodecillion
9 billion 42 tredecillion
12 trillion 45 quattuordecillion
15 quadrillion 48 quindecillion
18 quintillion 51 sexdecillion
21 sextillion 54 septendecillion
24 septillion 57 octodecillion
27 octillion 60 novemdecillion
30 nonillion 63 vigintillion
33 decillion 303 centillion

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;

Zeroes Number Zeroes Number
42 tertio-decillion 2703 nongentillion
45 quarto-decillion 3003 millillion
48 quinto-decillion 3303 centesimo-millillion
51 sexto-decillion 3603 ducentesimo-millillion
54 septimo-decillion 3903 trecentesimo-millillion
57 octo-decillion 4203 quadringentesimo-millillion
60 nono-decillion 4503 quingentesimo-millillion
63 vigillion 4803 sexcentesimo-millillion
66 primo-vigillion 5103 septingentesimo-millillion
69 secundo-vigillion 5403 octingentesimo-millillion
72 tertio-vigillion 5703 nongentesimo-milllillion
75 quarto-vigillion 6003 bi-millillion
78 quinto-vigillion 9003 tri-millillion
81 sexto-vigillion 12,003 quadri-millillion
84 septo-vigillion 15,003 quinqui-millillion
87 octo-vigillion 18,003 sexi-millillion
90 nono-vigillion 21,003 septi-millillion
93 trigillion 24,003 octi-millillion
123 quadragillion 27,003 novi-millillion
153 quinquagillion 30,003 deci-millillion
183 sexagillion 33,003 undeci-millillion
213 septuagillion 36,003 duodeci-millillion
243 octogillion 39,003 tredeci-millillion
273 nonagillion 42,003 quatuordeci-millillion
303 centillion 45,003 quindeci-millillion
306 primo-centillion 48,003 sexdeci-millillion
333 decimo-centillion 51,003 septi-deci-millillion
336 undecimo-centillion 54,003 octi-deci-millillion
339 duodecimo-centillion 57,003 novi-deci-millillion
342 tertio-decimo-centillion 60,003 vici-millillion
345 quarto-decimo-centillion 63,003 semeli-vici-millillion
363 vigesimo-centillion 66,003 bi-vici-millillion
366 primo-vigesimo-centillion 69,003 tri-vici-millillion
393 trigesimo-centillion 72,003 quadri-vici-millillion
423 quadragesimo-centillion 75,003 quinqui-vici-millillion
453 quinquagesimo-centillion 78,003 sexi-vici-millillion
483 sexagesimo-centillion 81,003 septi-vici-millillion
513 septuagesimo-centillion 84,003 octi-vici-millillion
543 octogesimo-centillion 87,003 novi-vici-millillion
573 nonagesimo-centillion 90,003 trici-millillion
603 ducentillion 120,003 quadragi-millillion
903 trecentillion 150,003 quinquagi-millillion
1203 quadringentillion 180,003 sexaggi-millillion
1503 quingentillion 210,003 septuagi-millillion
1803 sexcentillion 240,003 octogi-millillion
2103 septingentillion 270,003 nonagi-millillion
2403 octingentillion 300,003 centi-millillion

Zeroes Number Zeroes Number
303,003 semeli-centi-millillion 1,800,003 sexcenti-millillion
306,003 bi-centi-millillion 2,100,003 septingenti-millillion
600,003 ducenti-millillion 2,400,003 octingenti-millillion
900,003 trccenti-millillion 2,700,003 nongenti-millillion
1,200,003 quadringenti-millillion 3,000,003 milli-millillion
1,500,003 quingenti-millillion

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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