[Aztlan] Maya mensuration/metrology

[Falken Forshaw]

Greetings:  I would like to add comment to the thread involving 
possible Mayan and other Mesoamerican use of units of length 
measurement (i.e. metrology):

Discussion so far seems to refer to use of a unit close to that of a 
meter, which itself is close to, though different from, a pace (vara). 
It is possibly also an extended arm span, nose to finger tips.  There 
is additional support for this unit in the design of Teotihuacan's 
urban block grid, though the reference is not handy;  the less-accepted 
work of Hugh Harleston, also proposes a unit (the "hunaab") very 
similar in length.  Also, Andrjew Wiercinski proposed in the 
mid-seventies (in INSTITUTUM CANARIUM, 1977) the design use of a unit 
of 2.72 feet at each course perimeter of the Pyramid of the Sun at 
Teotihuacan.  Readers might recognize this as the unit proposed by 
Alexander Thom, in his work on British stone circles (MEGALITHIC SITES 
IN BRITAIN.) There is also the matter of the Pyramid of the Sun, and 
another structure near it, being designed with the same footprint/base 
plan as the Great Pyramid in Egypt, discussed by Peter Thompkins in 
MYSTERIES OF THE MEXICAN PYRAMIDS (which also features Harleston's 
work).  This would involve discussion of the  use of feet, cubits, and 
megalithic yards at the same time, an ongoing one in pyramidology.

We can expect the survival of pre-Spanish Mesoamerican units in certain 
Colonial building projects, as the Spanish employed indigenous workers 
still using their traditional techniques, as well as their pre-Conquest 
urban spaces.  This has been referred to by Logan Wagner (dissertation: 
"Open Space as a Tool of Conversion: The Syncretism of Sacred Courts 
and Plazas in Post-Conquest Mexico," UT, Austin, 1996), and Margarita 
Martinez del Sobral, in her work on Mesoamerican design geometry, 
GEOMETRIA MESOAMERICANA (Fondo del Cultura Economica, Mexico, 2000).  
She is gained this insight through restorations of Colonial convents.  
This reference was contributed here earlier by Dr. Clifford Brown, 
referencing a question about the Golden Proportion.

The mention of fields being sized in squares with a side of 20 paces 
reminds one of the number 400 (20 squared, the number of Little Boys 
mentioned in the Popol Vuh, a possible Quincunx reference through 
"five-eighties".)  One is similarly reminded of the number 8000 (cacao 
beans in a sack).  This would be twenty cubed, a volumetric 
measurement, so we must accept that there are many aspects to how and 
what the Maya counted, and what units they used in constructing art 
objects, buildings, and site/landscape design.

In my own research, I have encountered length values very close to the 
meter in use in some unexpected pre-Colonial contexts, in wall 
thicknesses, for instance.  While I have not conducted systematic 
studies that might reveal culture-wide intentional use of dimensional 
units, I think there is no doubt that systematic use of a range of 
units would be of practical necessity to builders and two-dimensional 
artists.  Glyph block composition alone requires such design intent.  
So does repeated, modular pattern on buildings, such as the median band 
on the Temple of the Three Lintels at Chichen Itza, or even building 
proportion itself. I currently prefer to geometrically determine 
proportional and alignment design intent in the built environment than 
first use published measurements; when design rules can be seen to have 
been used systematically, then the units with which they were applied 
can be easily determined with accurate dimensioning. Published 
measurements are not universally dependable data.  A project to match 
this regularity with accurately measured dimensions is planned for the 
coming year.

By range of values, I mean that there could have been at least two 
different lengths in use by indigenous Mesoamerican peoples, using both 
the width and diagonal of a square, for instance, as in traditional 
Japan and Egypt.  There is ample evidence too of other geometric 
relationships in units being used: those of a circle and its diameter 
(pecked crosses, cacao vessels, buildings); the diagonal of a 
half-square (1:square root 5), exhibited in a grafitto within the 
Caracol at Chichen Itza (vis Karl Ruppert's Caracol archaeology report, 
CIW Publication #454, 1935); and the proportion 1x3, which has a 
diagonal, for practical purposes, of pi (square root ten=3.162).  The 
latter shape is also depicted in the grafitto, as is an equilateral 
triangle.  This is discussed to some extent in my dissertation, 
COSMOGRAPHY AT THE CARACOL, Chichen Itza, Yucatan, Mexico (UO, Eugene, 
1984.) The proportion 1x3 can be found rather precisely in the 
ground-level footprint of the playing alley at the Great Ballcourt, and 
at the entrance doorways/facade at the Temple of the Owls, at Chichen 
Itza.  Using accurate drawings I have found Mayan use of intended 
geometry to be precise enough to require the use T-Square and 
triangles, and sharp pencils.  A design synopsis of the Caracol's 
platforms can be found at my website, www.studiofalken.com.  The 
Caracol's Tower and its other two buildings await the writing of a 
similar design synopsis.

It seems a simple matter to determine the intended metrology standards 
of the ancient Maya through study of how they made two- and 
three-dimensional objects, especially large and modular ones that 
display regular geometry.  I look forward to comments, especially from 
those who are conducting similar studies.

A Happy Shortest Day Holiday to one and all.

Thank you,

Falken Forshaw, PhD
Studiofalken
NWWL 503
3131 Western Avenue
Seattle, WA 98121

falken at studiofalken.com
www.studiofalken.com
cell: 425.343.4754