NUMBERS are everywhere. Youâve probably described two equally appealing
choices as âsix of one, half a dozen of the otherâ, or prayed for a seven on the
dice, or celebrated a landmark age like 30 or 50.
These integers, the natural counting numbers, may seem unimpressive when
stacked up against the awe-inspiring quantities that span the Universe. A number
like 3 is tiny compared with, say, 15 billionâthe number of light years to
the farthest cosmic objects. But it is huge compared with the number of metres
it takes to span a proton, about 1 Ă 10-15. The counting numbers also lack the
semi-mystical aura of quantities such as the irrational number &pgr;(3.14159âŠ)
with its infinite string of non-repeating digits, or the enigmatic imaginary
number i, the square root of â1.
Although the integers that lace human culture are not very large, very small
or very mysterious, they are significant. They can carry religious, social,
political or psychological meaning, as in the Holy Trinity, the Gang of Four,
the twelve-step treatment for alcoholism, and the adage âtwoâs company but
threeâs a crowdâ. Numbers can be linked to good or bad fortune, as in lucky 7
and unlucky 13. And numbers are embedded in enduring human artefacts, such as
the 50 five-pointed stars on the American flag, and the eight candles of a
Hanukkah menorah.
Advertisement
Such culturally loaded numbers have appeared in human societies across
centuries and continents, and are more pervasive than our other great stockpiles
of symbolsâletters, words and images. Even simple statistical facts about
a languageâfor instance, that the most common word in English is âtheâ and
the most common letters are âeâ, âtâ and âaââdonât hold for other tongues.
Pictures, too, are far from universalâthe conventions of perspective
drawing donât automatically work in every culture.
One for all
By contrast, the meaning of any specific number seems fixed and unambiguous
across languages and cultures. Thatâs why I decided to determine the most
popular numbers that people use. After all, if I could find their representative
value, it would be the nearest thing we have to a universal symbol.
The parallel analysis of letters and words requires poring over compendiums
such as the Oxford English Dictionary. While we donât seem to have an
equivalently massive and definitive Oxford Numerical Dictionary, there are at
least two existing sources of number lore. The first is Three-Toed Sloths
& Seven-League Boots: A dictionary of numerical expressions by Laurence
Urdang, editor of the Random House Dictionary of the English Language.
This collection of phrases involving numbers has some 3500 entries, including
fractions and &pgr;. They are arranged in increasing numerical order from â273
(absolute zero on the Celsius scale) to a googolplexâwhich is 10 raised to
the power of a googol (10100)âand then âinfinityâ.
The second book, Name the Seven Dwarfs and Other Numbered Diversions
by Diane Giddis, challenges the reader to list all the dwarfs in Walt Disneyâs
1937 classic Snow White and the Seven Dwarfs, to name the 12 signs of
the zodiac, and so on. Along the way, it provides more than 200 expressions and
cultural references that contain the numbers 1 to 14. Between them, Urdang and
Giddis give nearly 2800 entries for these particular integers, which I analysed
by simply counting up how many entries there were for each number.
By a wide margin, 2 has the greatest number of entries. We live in a world
full of duality. We have paired contrasts, like black and white, or good and
evil, and paired complements, like yin and yang, or ham and eggs, or the 0 and 1
of binary arithmetic. Then there is the fundamental pairing of man and woman, an
expression of our biological destiny as a species with two sexes. Possibly
creatures such as the amoeba, which reproduce asexually, would vote for 1 rather
than 2 as their most popular number, but in my survey 2 appeared three times as
often as 1.
After 2, the count of entries for each integer drops steadily as we move up
towards 14, but with some notable blips. The number 7 is seen twice as often as
its neighbours 6 and 8, reflecting its special cultural meaning. It appears in
the titles of both books I mentioned and has a long and widespread history. For
example, the seven wonders of the ancient world, the seven chakrasâpsychic
energy centres of the bodyâprominent in some Eastern religions,
Shakespeareâs Seven Ages of Man and the Chicago Seven of the late 1960s.
However, the power of 7 does not carry over to its multiple, 14, which is not
especially common.
As you might expect, 10 also appears a great deal. Perhaps thatâs an
expression of biological reality, since our base-10 numerical system could well
have arisen from counting on our fingers. But biology canât explain easily why
12 is also widely used, which probably depends instead on a practical arithmetic
fact. The number 12 is a handy integer that can be evenly divided by 2, 3, 4 and
6 whereas 10 has only 2 and 5 as divisors (each number, of course, can also be
divided by itself and 1). This may be why the ancient Babylonians were partial
to multiples of 12 in measurements of time. Vestiges of this linger on in our
24-hour day, 60-minute hour and so on.
By this reasoning, the prime numbers among these integersâthose
divisible only by themselves and 1âshould be relatively uncommon. Thatâs
not true for 2, 3 and 7, all widely used, but may account for the dismal showing
of 11, the number nobody loves. The number 13 is also a prime but carries
powerful connotations of bad luck and Witchâs Sabbaths and is far more
common.
Which number among this variety best qualifies as our universal symbol? One
way to decide would be to use the average of the numbers 1 to 14, weighting each
integer by the number of entries that allude to it, which gives a value of 5.29.
That is no integer, itâs true, but the decimal point lends it a certain
scientific heft. Itâs clearly the number to use in all sweeping statements that
require exactitude. Try authoritatively asserting that there are 5.29 million
habitable planets in our Galaxy and youâll see that it rolls nicely off the
tongue.
An alternative candidate is 2, the number that appears most frequently. Plug
it in as an all-purpose ever-suitable integer, and you create new truths such as
âtwoâs company but twoâs a crowdâ, an apparently contradictory statement that
may yet conceal deep meaning. Hard to choose between them isnât it? I guess you
could call it 5.29 of one and a sixth of a dozen of the other.