Foreign Policy Recommendations for a Brighter Linguistics Future--M. Hadrian Thumpsem et al. SpecGram Vol CXLVIII, No 2 Contents Phonological Theory and Language Acquisition--Notker Balbulus

How Many is Umpteen?

A Linguistic and Mathematical Exploration and Explanation

brought to you by Ura Hogg
of Skaroo University 1

and the Letter U.
We have all heard various people use the quasi-numerical expression umpteen to refer to a largish number of items, as in (1) below:
(1) I have umpteen things to do before I can leave.2
What I plan to do in this brief paper is to determine how many umpteen is. First I feel I must in part justify the claim that umpteen can in fact refer to an exact numerical quantity despite its varying use.3 Though we often use vague number expressions such as in (2) and (3) below, we nearly as often use exact, though large, expressions, such as a million, in the same way (as in (4)).
(2) I have many things to do before I can leave.
(3) I have a few things to do before I can leave.
(4) I have a million things to do before I can leave.
I will show that umpteen, likewise, is a large number, and thereby explain its inexact usage.

Our first and only assumption has already been made,4 but for clarity we will spell it out explicitly now: umpteen is an exact number, with a definite, though perhaps now lost, history and a logical, mathematical origin.5 We can reconstruct much of this lost history, at least in general outline.6 Now, on with the show.

For those not familiar with such things, let me introduce the concept of letters as numbers. The ancient Romans and Greeks7 used their letters for numbers, and a similar8 modern group, computer programmers, does likewise. When dealing, as they often do, in hexadecimal9 they typically use the letters A-F to represent the numbers 10-15, as in (5) below.

(5) 1A3E16 = 671810
These numbers are often referred to by non-letter names, such as alpha for A and charlie for C, etc.

Let us suppose that a similar system is at the root of umpteen's origin. There are two possible cases we must deal with. The first is that we are dealing with a system in which ump is the non-letter name for U when used as a numeral. Also, by analogy with fourteen, sixteen, seventeen, etc., the numbers such as 1A, 1C, and 1U are alphateen,10 charlieteen,11 and our focus: umpteen. The minimum base for such a system, to require the use of U, is base 31.12 In this case, the value of umpteen would be 1U31 = 6110.13

Our second possible case to consider is more complicated and gives a larger value for umpteen. In this scenario, the base used is so large that it is necessary to go beyond the alphabet for numerals to combinations of letters. In this case, umpteen would actually be more correctly written as UMPteen or 1(UMP) in a base yet to be calculated. If we are using a system in which all alpha-numerals have three letters, then UMP is the 14,550th alpha-numeral. If we first must exhaust the single and double letter alpha-numerals, then UMP is 15,252nd. Thus we have as a minimum possible base either 14,551 or 15,253.14 In these cases UMPteen would be either 1(UMP)14,551 = 29,10110 or 1(UMP)15,253 = 30,50510.15

Thus we see that umpteen (which we may want to distinguish from UMPteen) is in fact in all likelihood the remnant of a large and powerful mathematical system that is now lost in the mists of time. It comes as no surprise that such a euphonious term as umpteen, with such a grand, almost so-large-as-to-be-holy number meaning, would be the last remnant of this surely majestic number system.

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Notes:
1 I would like to thank Professor U. R. Stoop, ID and Ann Abolic at Skaroo U.
2 This is not only an example sentence. It is also a true statement. Sigh.
3 My therapist claims this has to do with my unresolved self-doubt stemming from my parents' poor choice of names for me.a
4 And I bet you missed it, too!
5 Which, of course, is one of the basic assumptions that Linguistics makes about all words.b
6 Which, of course, is another basic assumption that Linguistics makes about all words.
7 And, it has recently been proposed, perhaps Cro-Magnons as well.c
8 i.e., those who are often thought by the ignorant to be primitive, nearly stone-age barbarians, but who are in fact highly cultured, socially adept and mathematically advanced people.
9 Base 16.
10 Alas, this form is unattested in the geek dialects I have been able to study.
11 This form, too, is unattested, though it may survive in a slightly altered form as Charlie Sheen, though the investigation of such a possibility is beyond the scope of this paper.
12 This is where our calculations become a little unsure. It is possible that a higher base was used, perhaps 32 (since powers of twod are so popular among geeks).
13 In the hypothetical base 32, umpteen would be 1U32 = 6210
14 Of course, larger bases are again possible. In the geek-based power of two system, a likely candidate for a base would be 16,384e or perhaps 32,768f.
15 In the hypothetical geek-based system UMPteen might be:

if UMP = 14,550
      1(UMP)16,384 = 30,93410 or 1(UMP)32,768 = 47,31810 or
if UMP = 15,252
      1(UMP)16,384 = 31,63610 or 1(UMP)32,768 = 48,02010.

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Notes on the Notes:
a And my sister, Ima.
b Except, of course, the mathematical part.
c Though only the most recent ones.
d 32=25
e 16,384=214
f 32,768=215, a perhaps more aesthetically pleasing choice.

Foreign Policy Recommendations for a Brighter Linguistics Future--M. Hadrian Thumpsem et al.
Phonological Theory and Language Acquisition--Notker Balbulus
SpecGram Vol CXLVIII, No 2 Contents