In the codices, moreover, when the count is backward, or contrary to the
general practice, the fact is clearly indicated[95] by a special character.
This character, although attached only to the lowest term[96] of the number
which is to be counted backward, is to be interpreted as applying to all
the other terms as well, its effect extending to the number as a whole.
This "backward sign" (shown in fig. 64) is a circle drawn in red around the
lowest term of the number which it affects, and is surmounted by a knot of
the same color. An example covering the use of this sign is given in figure
64. Although the "backward sign" in this figure surrounds only the numeral
in the first place, 0, it is to be interpreted, as we have seen, as
applying to the 2 in the second place and the 6 in the third place. This
number, expressed as 6 tuns, 2 uinals, and 0 kins, reduces to 2,200 units
of the first place, and in this form may be more readily handled (first
step). Since the starting point usually precedes the number counted from it
and since in figure 64 the number is expressed by the second method, its
starting point will be found standing below it. This follows from the fact
that in numeration by position the order is from bottom to top. Therefore
the starting point from which the 2,200 recorded in figure 64 is counted
will be found to be below it, that is, the date 4 Ahau 8 Cumhu[97] (second
step). Finally, the red circle and knot surrounding the lowest (0) term of
this 2,200 indicates that this number is to be counted _backward_ from its
starting point, not forward (third step).
On the other hand, in the inscriptions no special character seems to have
been used with a number to indicate that it was to be counted backward; at
least no such sign has yet been discovered. In the inscriptions, therefore,
with the single exception[98] mentioned below, the student can only apply
the general rule given on page 136, that in the great majority of cases the
count is forward. This rule will be found to apply to at least nine out of
every ten numbers. The exception above noted, that is, where the practice
is so uniform as to render possible the formulation of an unfailing rule,
has to do with Initial Series. This rule, to which there are no known
exceptions, may be stated as follows:
_Rule 1_. In Initial Series the count is _always forward_, and, in general
throughout the inscriptions. The very few cases in which the count _is_
backward, are confined chiefly to Secondary Series, and it is in {138}
dealing with this kind of series that the student will find the greatest
number of exceptions to the general rule.
Having determined the direction of the count, whether it is forward or
backward, the next (_fourth_) step may be given.
FOURTH STEP IN SOLVING MAYA NUMBERS
To count the number from its starting point.
Public-domain text, read in full here on John Shaqi.
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