# nines

Gregory {Greg} Downing downingg at is2.nyu.edu
Wed May 21 16:21:50 UTC 1997

```At 04:36 PM 5/21/97 BST, you (Patricia M. Greer) wrote:
>It seems to me that the 9 is closely related to the 0,
>since it in effect acts as a zero when added to any other
>number -- eg.  7 + 9= 16 = 1+6 = 7.

Right -- I see why these multiples all add down ultimately to nine now:
mutliples of nine are of course just additions of nine, and in a base-ten
system any addition of nine decreases the "ones"-place by one and increases
the "tens"-place by one (thus, 18 + 9 = 27, 27 + 9 = 36), two things which
cancel one another out when one goes to add the digits together. This leaves
all the multiples of nine as numbers that ultimately come to nine as well if
one keeps adding digits together. This is true because nine is one less than
the key-number ten of a base-ten system. The same would apply to the number
one below the base-number in any base-system. Thus, in a base-six system,
any multiple of five would "add down" to five: e.g., in base-six, 10 is
written as 14, which adds down to 5 (etc.). So there's nothing magic there,
it's simply a function of our base-number. If we had eight fingers and eight
toes (and the resultant sense of eight as the "round" number), we'd be
making the same point about seven.

Still, logic aside, what number-lore ancient people believed is another
issue. Nine as the proportion between menstrual/lunar cycles and the typical
human gestation period (another accident [?] of human anatomy or product of
evolution), and nine as three threes, are likely to have made the number
stand out in general, in addition to more local associations in particular
cultures.

Greg Downing/NYU
greg.downing at nyu.edu
or
downingg at is2.nyu.edu

```