To describe these things in detail would make a long story; it took l) R.
Allen and Professor Schindler-Bellamy and their helpers many years of hard work
to puzzle out the Tiahuanaco system of notation and its symbology, and to make
the necessary calculations (before the age of computers). The result was a book
of over 400 pages,
The Calendar of Tishuanaco,published in 1956.
Thorough analysis of the Sun (Sate sculpture revealed the astonishing fact
that the calendar is not a mere list of days for the "man in the street" of the
Tiahuanaco of that time, telling him the dates of market days or holy days; it
is actually, and pre-eminently a unique depository of astronomical,
mathematical, and scientific data- the quintessence of the knowledge of the
bearers of Tiahuanacan culture.
The enormous amount of information the calendar has been made to contain-and
to impart to anyone ready and able to read it is communicated in a way that is,
once the system of notation has been grasped, singularly lucid and intelligible,
"counting by units of pictorial or abstract form.
The different forms of those units attribute special, very definite and
important additional meanings to them, and make them do double or multiple duty.
By means of that method "any number" can be expressed without employing definite
"numerals" whose meaning might be difficult, if not impossible, to establish.
"It is only necessary to recognize the units and consider theirforms, and
find their groupings, count them out, and render the result inour own numerical
notation.
Some of the results seem to be so unbelievable that superficial critics have
rejected them as mere arrant nonsense. But they are too well dove-tailed and
geared into the greater system (and in some cases supported by peculiar
repetitions and cross-references) to be discarded in disgust; one has to accept
them as correct.
Whoever rejects them, however, also accepts the onus of offering a better
explanation, and Professor Schindler-Bellamy has the "advantage of doubt,"
at any rate.
The "solar year" of the calendar's time had very practically the same length
as our own, but, as shown symbolically by the sculpture, the earth revolved more
quickly then, making the Tiahuanacan year only 290 days, divided into 12
"twelfths" of 94 days each, plus 2 intercalary days.
Tilese groupings (290, 24, 12, 2) are clearly and unmistakably shown in the
sculpture. The explanation of 290 versus 3651/4 days cannot be discussed here.
At the time Tiahuanaco flourished the present moon was not yet the companion
ol our earth but was still an independent exterior planet.
There was another satellite moving around our earth then, rather close-5.9
terrestrial radii, center to center; our present moon being at 60 radii. Because
of its closeness it moved around the earth more quickly than our planet rotated.
Therefore it rose in the west and set in the east (like Mars' satellite
Phobos), and so caused a great number of solar eclipses, 37 in one "twelfth," or
447 in one "solar year " of course it caused an equal number of satellite
eclipses. These groupings (37, 447) are shown in the sculpture, with many
Corroborating cross-references. Different symbols show when these solar
eclipses, which were of some duration, occurred: at sunrise, at noon, at sunset.
These are only a small sample of the exact astronomical information the
calendar gives. It also gives the beginning of the year, the days of the
equinoxes and solstices, the incidence of the two intercalary days, information
on the obliquity of the eliptic (then about 16.5 degrees; now 23.5) and on
Tiahuanaco's latitude (then about 10 degrees; now 16.27), and many other
astronomical and geographical references from which interesting and important
data may be calculated or inferred by us.
Tiahuanacan scientists certainly knew, for instance, that the earth was a
globe which rotated on its axis (not that the sun moved over a flat earth),
because they calculated exactly the times of eclipses not visible at Tiahuanaco
but visible in the opposite hemisphere (One wonders whether they were
actually able to travel around the world, and speculate in what sort of
vessel ! )
A few more facts revealed in the calendar are both interesting and surprising
As indicated by an arrangement of "geometrical" elements we can ascertain that
the Tiahuanacans divided the circle factually astronomically, but certainly
mathematically} into 264 degrees (rather than 360).
Also, they determined-ages before Archimedes and the Egyptians the ratio of
pi, the most important ratio between the circumference of the circle and its
diameter, as 22/7, or, in our notation, 3.14+. They could calculate squares (and
hence, square roots).
They knew trigonometry and the measuring of angles (30, 60, 90 degrees) and
their functions- They could calculate and indicate fractions, but do not seem to
have known the decimal system nor did they apparently ever employ the duodecimal
system though they were aware of it.
(For a still unknown reason, however, the number 11 and its multiples occur
often.) They were able to draw absolutely straight lines and exact right angles,
but no mathematical instruments have yet been found.
We must take notice of the evident parallels with the markings of the Nasca
Plain. We do not know the excellent tools they must have used for working the
glass-hard andesite stone of their monuments, cutting, polishing, and incising.
They must have employed block and tackle for lifting and transporting great
loads (up to 200 tons) over considerable distances and even over expanses of
water from the quarries to the constructionsites.
