MY.STIU USE OF NUMBERS 951 One thing worthy of notice in this diag-rani (figure 41) is that one

MY.STIU

USE OF NUMBERS 951

does notappearto have bi'ought it into use as a counter. Its appear- ance, therefore,in thetime system and time countuiaybeconsidered as accidental,orat leastwithoutsignificance. Neverthelessitdoesappear occasionally in relations

where

^{its use} seems to bemystical.

From

the earliest times, the Cakchiquel. with perhaps others with

whom

they Averc related, are mentioned in their annals as

"seven

tribes"

orseven villages arranged in thirteen divisions. Their sacred daj's

were

the seventh and the thirteenth. Tradition lirings the ancestors of the

Mexicans from

seven caves; thej^

come

as seven ti-ibes, the descendants ofseven brothers.

Among

their gods

was

a deess

named

Centeocihuatl, also called Chicomecohuatl or the

"Seven

Serpents,"

who,^{it is} said,nourished theseven gods

who

survived theflood. Itis said in the Quiche legend (Popul ^{Vidi) that}

Gucumatz,

their great culture hero, ascended each seven days toheaven,

and

in seven days descendedinto Xibalba;thatfor sevendays he took the

form

ofaser- pent; seven others that ofan eagle; seven others that of a tiger, and seven others that of coagulated blood, ashas been already mentioned.

Aiuong

their mythical heroes was

Vukub-Cahix ("Seven

Aras"). and the ruler of Xibalba was

Vukub-Came ("Seven

Deaths").

The number

9, though siddom ^{referred to} in the ceremonials and

myst(M'i(^s, was not without a place therein

among

the Mexicans.

They

recognized nine

"Lords

of the Night." These are evidently referred toin theBorgian codex,as in theTonalamatl,])lates 31 to 38,

where

theyare

marked

l)yfootprints,and on plate 75, wluu'c th(>night

is svmboIiz(Ml In' the large black flgure and the nine loi-ds by nine star-like ligures. It is stated in the Kxplanation of the

Codex

Tel- leriano-Kemensisthiit he

who was

born on the day ^!• Ehecatl

would

be prosperousasamerchant,whilehe

who was

born on theday^t)Itzcuintli

would

^l)e a great magician.

The

Mexicans also recognized nine heavens. This numbei' appears also to have had

some

significance

among

^{the Quiche, as they held that in each}

^month

^{there would be}

nine

good

and ^nine bad days, and

two

indifl'erent.

Next

to20, 13

was

the

most

important numl)er in the time systems of

Mexico

and Central America.

Not

only

was

^it the numl)erof daj's in their so-called week, butit

was

that l)y which tlie days

were imm-

bered.

Although

it did not

form

one of the regular time periods, as

THOMASl

MYSTIC USE OF NUMBERS 953

the month, ahau. yeai' oi' katun, the so-called

week

not ^{bein^'} recog- nized as a regular period in theirsystems, itentered intoalmostevery time count and every time series in the codices and inscriptions. It

was one of the factors on which the so-called "sacred year" of ²⁽⁾⁰ davs

and

the cycle of tifty-two years

were

based.

Being

so importantin the time systems, it

would

bo expected to enter

more

^oi' less into the activitiesof life; nevertheless itappears to have played a comparatively unimportant role asa mysticor cere- monial number. It

was

thecustomofseveral

Mayan

tribes toarrange theirarmiesinthirteen divisions. Itappearsinthe

Votan myth among

the Tzeutal,

where

"thirteen serpents" are referred to; and

among

theCakchiquel theda}^

numbered

13

was

considered sacred.

The number

20 is the base of the numeral S3'stem of the

Mexican

and Central

American

tril)es,

and

it

may

perhaps also be correctly considered the base of their calendarsystem, although thereare other necessary factors. Nevertheless 20 does not appear to have lieen

usedas a mystic

number

in ritesand ceremonies, exceptso far asthe calendar

was made

to serve divinatory purposes.

Why

twenty days were adopted as a time period and a division of the year has asyet received no entirely satisfactory explanation, though it is generally supposed that it

was

chosen because the arithmeticalsystem of these tribes

was

vigesimal. That there is

some

connection between the

two

isquite likely, especially as this

would seem

to correspond with the probableorder of thesteps in the formation of the

two

systems. That the formation of the vigesimal system preceded ^{that of the time}sys-

tem

appears tobe an absolute requisite, but the steps in the forma- tion of the lattercan not he

assumed

with the certainty

which we may

have with regardto the former.

That the custom of groupingthe days b}'fives did not begin until 20 had

come

into use ^{is clear.}

Did

the introduction of 13 asa factor precede or follow the adoption of ^2(»?

Dr

Brinton states in his Native Calendar that he is persuaded that this period

was

posterit)r and secondary to the twenty-day period.

Although

this opinion

may

be, and probably ^is. correct, the evidence on which to base it is not so apparent as to leave no doubt. It seems probable, as

Dr

Brinton suggests, that the twenty-day period was derived

from

tine \'igesimal

number

system, but thisdoes not explain the origin of the peculiarities of the unusual time system, which seems to have reference to no natural

phenomena

save the earth's annual revolution.

There

are other peoples than those of

Mexico

and Central

America who

use the vigesimal system, but no others, so far as

known, who

^adopt

the twenty-day

month

or eighteen-month year.

The

moon's revo- lution is the factor on which the

month

in

most

of the world's time sj'stems is based, and the

name

for

month

in most, or at leastseveral

indicate an original lunar month. It is also true that the oldest inscriptionsand the

Dresden

codexreferto a 3^earof 365 days.

How-

ever,againstthis evidence

must

^])eplaced the fact.that all theinscrip- tions and codices base the time count on the twenty-daj' month, and the day

numbering

on 13, the latter alsobeing a factor in othercounts of the inscriptions and ^codices.

The

oldest evidence, therefore, to

which we

can appeal

where numbers

are used, agrees with the time systemof the 'native calendar."

That

a change

from

a lunarcountto atwenty-dayperiod couldhave been

made

otherwise thanarbitrarilyseemsimpossible;

we

can not con- ceive

how

the onecouldhave

grown

out of theother. This

must

have been ^true or the system

must

have developed with the

growth

of the

number

system; at leastno other supposition seems possibleunless

we assume

that

two

time svstems, a secular anda sacred one,

were

in use atthe

same

time,and that the latter tinallyobscuredthe former. This seems ^tohave beenthe casewith

some

tribes. Tf the suppositionthat the time system developed with the

number

system be correct, then the lunar period could never have been a factor. It is

somewhat

strangely in aci'ordancewith this supposition that the

moon,

so far as the aboriginal records and early authorities show, is almost wholly absent

from

tlie codices, and does not appear, so far asis

known,

in the inscriptions.

Notwithstanding this negative evidence, I can not ^Ix'Iieve that a time syst(>m witliout reference to the lunar periods could have devel- oped

among

^{the tribesof the region of which}

we

ar(> treating.

My

conclusion is, therefore, that the priests at an early date adopted a

method

of countinii- time for their ceremonial anddivinatory purposes whicli would ^{tit nio.st easily into their} numeral system, and that this system, in conse(iuence of the

overwhelming

intluence of the priest- hood, cau.sed the lunar count to dro]) into disuse. Moreover, theonly native records which are availa))le an^ those

made

by the priestsfor their purposes. This Avill j^robabiy account for the introduction of the twenty-day period, but does not account for the introduction of the13.

Dr

Fcirstemann sugg(\sts that at one time the

Mayas

arranged the daysof the solar yearin four groui)s of seven

weeks

each, the

week

consistingof ^l.'l davs. tlH> vear l)eing then counted ^{as :-!(;4} days

(4x18