Ahau 8 Cumhu

MK GOODMAN'S SYSTEM OF MAYAN CHRONOLOGY

reach 4 Ahau 8 Cumhu

Moreover, ^if the Dresden codex, which, so far as appears, follows the

same

time system that is found in the inscriptions, can have cor- rectly 19 cycles,

where

^is the evidence to be found that 17 cycles

would

necessarily be erroneous in the inscriptions^

Mr Goodman's

objection seems ^{to rest}wholly onhistheory of thechronologic system.

Thisis insufficient to justify belief insucha radical diti'crcnce between the systems of

two

records which ^{in all} other respectsare so nearly alike.

Following

Mr Goodman's

interpretation of numeral symbols, an additional fact bearing on this question,

we

^tind in certain details of the great cycle and katun symbols. According to him, the

comb-

like figure similar to those on the katun

symbol

has the value of ^0.

If itplays

any

part in

making up

the numerical value of the katun, ^it

may

reasonablybe

assumed

that itperforms a similar office in<-onnec- tion withthegreat cyclesymbol, of which ^{it is} a usualaccompaniment.

It istrue that

Mr Goodman

has furnished no proofthatthisparticular chai'acter is a numeral

symbol

denoting 20, but in accordance with histheorj' it should have the

name

value in connection with the great cycle gh'phas elsewhere.

Inthisseries

we

have the only evidence in the inscriptions of which

I

am aware

that thegreat cycles

were

numbered, 14 ))eingthe higiiest

number

given.

But

this

numbering

is just as the

numbering

of oui' thousands or millions;

we

say 10 thousand and 10 million. In the Dresden codex four of these periodsare noted in

some

four orfiv'e series. Theseare the highest counts,so far asis

known,

that the

Maya

reached, their notation seemingtohavespent itself in the sixth order of units.

We

^{conclude,therefore, that, though the dataare not suffi-}

cient to settle allthese points

by

absolute demonstration,as allthe evi- denceobtainable is against the theory of 13 cycles to the great cycle andin favor of 20, andas the only evidence as to the

numbering

of the great cycles indicates thatthey

go

above 13, it issafest to

assume

that the vigesimal system

was

followed throughout after the count rose

abovethechuenorsecondorderofunits.

Itis oftenjustifiable toadvance into thefieldof speculation in order to clear

away

^.so far as possible obstructions to advancement and to fix the limits of investigation, butthe result of speculation can not safely be u.sed as a factor in mathematical demonstration, and

Mr

Maudslay

has candidly stated the necessity for further investigation inthis respect.

We

^have noticed the

numbering

of the ahaus by the day numbers,

7y8 MAVAN CALENDAR SYSTEMS

[eth.ann.19 thus. 9, 5. 1, 1»). (5.^.

U.

7. 8. IM. S. 4. IS. !. 5. 1. otc. Si'lcctiiii,^ in a tontinuod series of days in jjrojjer order, witli the day nunihers attached,any dayAhau. forinstanc'e 1 Ahau.andconntinj^ forward^StjO days ((ioothnan's ahau period),

we

rtnd that the next ^Stio day period heL-ins witli K*

Ahau:

that the third period beo:ins witli 6; the next with ^'2\ the next with 11,

and

so on in the order given above. P>ut the

same

istrue if

we

select any other day. as 1 Aivbai in our table 1.

or begin at any point in the continued series, counting8(i() daysto each step.

As Mr Goodman

^holds that eat-h ahau begins witli the day

Ahau.

it' follows,according to this system, that the katuns,which contain just 20 ahaus,

must

begin with the

same

dav.

By

^{this it}resultsthatkatuns begin with day

numbers

running ⁱⁿ the order 11, ^it. 7, 5, 3. 1. etc.

This is apparent if

we

write out^{tht^} ahau

numbers —

^{the 9. 5. 1. 10,}

etc.

—

ⁱⁿ a contiMut)us series

and

take each twentieth one.

As

there

ar(> twenty katiuis in a cycle, the latter

must

also, according to this system, begin with the day

Ahau. Writing

the

numbers

^{11. 1*. 7, 5,}

3. 1. etc.. in a contiimous series, and taking each twentieth one, the result will Ije the series 11, 10, 9, 8, 7. ^ti. 5, ^-4. 3, 2, 1.13, 12, 11, etc.

If the correct count be. as

Mr (ioodman

asserts, 13 cycles to the greatcycle, thelatter will all begin with the

same

day and

same

day

number,

butif 20 be the correct count, th(>n the order will be 11. ^-4.

10. 3, 9, 2, 8. 1. 7. 13, 6, 12. 5, 11, 4, etc.

But

after all, this kind of tiguring is a

mere

source of

amusement

except

where

th(>

knowledge

conveyed

may

aid to

more

certain and

ra})id counting. It is as though

we were

^to take the days of our almanac in regular order as named, beginningthe tirst hundred with Sunday: the second hundred

would

begin with Tuesday, and. so on.

By

taking these and phu'ing

them

in consecutive order

we

^could pick out e\'ei-v tenth one as the begiiuiing of the thoasands. This

might amuse

us. and ^niiglit under possible circumstances be an aid to us in

counting time. l)ut it woidd be no ex[)lanation of our calendar system, and wiiuld not be a part. t)ut a result thereof.

That theseahaus or3H0-day counts always began, as

Mr Goodman

as.serts. with a day

Ahau,

^is not pi-oved; moreover, there is no reason forbelieving the assumption to be correct, but there ari> on the con-

trai'v,

good

reasons forbelieving it tobeincori('<-t. It

may

be true,as will

seem

to be thecasefi-oni what follows, that

Ahau

was

more

usually selected as an initial date than any other day. is. in fact, the initial

day

in most oftheinsci'iptionsand ^{is also} prominent ⁱⁿtheDresdencod(>x, t)ecause. periiaps.

some

gi'eat event took ])lace orwas supposed tohave taken placeonadayAhau. But it can l)edemonstrated thatthe initial

dayof

some

ofthe series in the 1)|-es(len codex where the 3(!0-dayperiod

is one of thecounters ^is Kaii. which, in th(>se. is necessarily the i)egin-

ning of the ahau count, it is true. liowcNcr. that the ahau or3()0-day period must, if the >uccession be continucius and luibroken. begin on

THOM.ss]

Goodman's

syistem ^'

799

•

the .same day. a fact to \vhi<-h I hav(^ heretofore called attention (see

The Maya

Year, pag-es -iT and 53). But the series

may

be arl)i- trary: that ^is. the eno-raver or painter

may

^{have chosen to begin t)ne}

series with one dayand another with another day. This, however, goesto the very root of the subject, as Mi-

Goodman's

systxmi al)so- lutely requires that the ahaus or?)6i>-day counts shall all begin with the

same

day, and as

worked

out l)y hini with a day Ahau.

Dr

Seler. impressed by the result of

Dr

Forstemann's investigations, has been led to l)elieve that

most

of the series of the Dresden codex have 4

Ahau

^N

C'umhu

astheir initial date, orthe day to which they refer.

^Vhile I athnit that this ^is undoul)tedly the day which seemsto be most prominent in tiiis codex,

my

investigations do not lead

me

^to

indorse his conclusion.

Now.

^{it is} true that the serieson plates -iB-.oO of theDresden codex, of which there are in reality Hit sectional, or 3 complete, have

Ahau

as the initial day, but the initial days of the three series are notall

360days or an even multiple of 3t;o days apart, as they should be if

Mr Goodman's

theorybecorrect.

But

the seriesareallexact multiples of 260,

showing

that they are l)ased on a 260-day period.

The

long series on plat(\s .51-58 does not

commence

with the day

Ahau.

whetlier

we

consider the upper ^line or lower line of days the properone to count l)ack from. It is also apparentthat in thiscase the series is based primarily on the 260-day period.

As

the least

common

nudtiple of 260and 360 is 4,680, ^itdoes notappear possible to bring those series based on the 260-day period into

harmony

with the

Goodman

theory except

where

the total nimiber of days ^is a multiple of 4,68n. uidess

we

^{suppose that there are}

^two

^{series of} non- coincidentfactors running through them. It is true that

we may

use the

week

of tmr calendar ⁱⁿ counting lOO-day periods l)y allowing for the supplementary days, asis undoubtedly done in

some

of the series of the codices and inscriptions: but the theory that the ahausaretime periods which can not overlap (thus indicating

two

starting points not consistent with the idea of uniform unbroken succe.ssion) is the point aimed at in the above ^{references to} the series of the Dresden codex.

Another

pointⁱⁿ connectionwith the serieson plates 51-58 dithcult to account for on this theory is that the first day of the cliuens (suppos- ing the

munbers

in the lower orderof units to represent the day of the chuen) is Muliic throughout. It is true that the

number

in the lower order of units

may commence anywhere

in the chuen. l)ut if

these are fixed time pei'iods and the chuens (but not tru(> months) as well as the ahaus conmience with

Ahau

^it seems that such important series as this one

would

reveal this fact

somewhere

ⁱⁿ the reckoning.

In the inscription at the end there are

two

sj-mbols of the usual type, one indicating 1 katun, the other 13 ahaus

=

ll,880 days, while the

sum

of the series is 11.960, or 80 days more.

The

^series on plates 71-73 has, if

we may

judge by the number.^

SOO MAYAN CALHNDAR SYSTEMS

[f,th.ann.19 in tlic lower order of ^unit.--. Hen as tiic tirst day of the ehiien-. and 5 Kl) as tiie tirst day of the series.

While

these examples do not

fiirnisli j)ositi\e proof in reoard to the cpiestion at issue, they at least, in connection with

what

has been presented concerning the

))laii and ^oliject of these reci<onings, do indicate that the so-called time ])eriods are merely ordei's of units and not chronologic periods always

coming

in regular ordei-

from

a fixed jjoint in time.' Ni'ver- theless, it

must

be admitted that

most

of the initial series in tiie

inscriptions, as will clearly aj)p(>ar

when

their reckoningispresented, begin with Aliau, which fai't

must

receive a satisfactory explanation b(>fore this question can be considered settled.

Another fact to be borne in

mind

^{is that} according to

Mr ^Good-

man's idea, if a katun begins with

Ahau,

all the chuens or ^2(i-da}' periods

must commence

with the

same

day,^though not the

same

day

number,

and this

would

continue indefinitely. Th(>

same

thing,

how-

ever, would be true in this

scheme

were any other day selected as the initial date; all that will apjjly in any respect to

Ahau

^will, until the year <()unt

comes

into play, a])ply in every particular to any other day. a statement which admits of positive demonstration.

The

only reason for preferring

Ahau,

if there be any, is historic, or rathi>r mythologic, as tnany of the series cover too great lapsesof time to be historic.

If the two ahau sym]x)ls in the inscription inthe

Temple

of Inscrip tionsof Paleiupie, referred to above on page ^77-1:, be counters in the time series with wliich they are connected, they certaiidy occujiv the katun j)lacc.

As

they present the true ahau form, it

may

be possible that they bear

some

relation to the

name

of the period for which they stand. This, however, ^is at Ijest but a

mere

guess, and the

names

are of but minor importance in the discussion.