Many of the earliest measurements we know about are anthropomorphic, based on the length of a stride, a foot, a nose, a forearm, and so forth.  These 'standardized' units are of course variable depending upon the body being used as the model.  Even when such measures became standardized they did not remain static for long.  Glover (1989:416-417) reports the lengths of no fewer than twelve different cubits (elbow to fingertip distance) from the ancient world, spanning a range from 18.0 to 21.8 inches.  Some early measures not based on anthropomorphic principles include the bowshot and stone's throw (both common in many areas throughout the world), and an uncounted number of idiosyncratic units including a Latvian measure of the distance from which one can hear a bull bellowing, and the Hungarian "hatchet's throw backwards from a sitting posture" (Kula 1986:7-8).  If standardized units of measurement existed in the prehistoric Southeast, and if they followed historic precedence, they would vary through time and according to region, possibly by a significant amount.  Considering the length of time between the beginning and ending of the construction of many mound sites, on what grounds could we assume that the same measure was applied throughout the site's occupation?  Or even that the same units were used in both the construction of the individual mounds and the overall layout of the site?

            The most common type of historical metrology is literally historical: the study of past units of measurement as described, defined, or employed in written records.  Scales and weights recovered archaeologically are sometimes used to calibrate the measurements named in these written records.  Less frequently does historical metrology concern itself with attempting to discover units about which there is no written record.  I propose that this sub-discipline of the field be more appropriately termed 'cryptometrology', because it attempts to derive units of measurement about which nothing is known, and which may not even exist.  The question immediately comes to mind of how to interpret the results of distance analyses: even if a particular distance stands out against the statistical background at a mound site, on what basis could we infer that it was actually a measurement of length employed by the people who built the mounds?  Patterns, cycles, and regular distances are quite common in purely natural phenomena.  The territories of birds, the scales of fish, desiccation cracks in mud and ripples from a stone thrown into a pond all exhibit a remarkable regularity that can be quantified, but these patterns are easily explained through external, natural factors.  Might similar patterns be expressed in human constructions, unrelated to standardized units of measurement? 

            For a modern example of how standardized measurements are not always directly related to a finished product, consider the overall construction of wood frame homes and many other buildings in North America.  The frames of these buildings are usually made with standard 2 x 4 pieces of lumber, '2 x 4' referring to the cross-sectional size of the wood.  A 2 x 4 piece of lumber is not actually 2 by 4 inches in cross section, however.  These dimensions refer to the nominal cross-section of the lumber as it is rough milled and do not include the kerf  (the thickness of wood removed by the blade).  The cross-section is further reduced as the wood is smoothed through planes and sanders.  A standard 2 x 4 has a cross section closer to 1 1/2 by 3 1/2 inches – but even this can vary by as much as a 1/4 inch or more depending on the lumber mill, the type and moisture state of the wood, and many other factors.  Attempting to deduce a standardized unit of inches from such cross sections would clearly be problematic.

            The lengths of pieces of lumber can be equally capricious.  Generally cut to something close to an even foot at the mill, 2 x 4s are sectioned into smaller pieces using not only inches but decimal fractions of feet – 7/10 of a foot, for example (equal to 8 2/5 of an inch – not one of the more common inch divisors).  Lengths of wood are oftentimes not even cut to any pre-existing measure, but fit individually to custom insets and windows, various slopes, bevels, bezels, and other irregularities in a structure, and the inevitable gaps and minor overlaps that occur with any major construction.  The spacing of 2 x 4 studs in building frames is generally consistent (usually between 16 to 24 inches), but can vary greatly depending on local building codes, the load an individual wall is intended to carry, the presence of doors, windows, chimneys, or other structures that must be taken into account, etc.  So we begin our construction with raw materials that are conceived, produced, bought, sold, and nailed together under a paradigm of feet and inches, but which may not reflect these dimensions in their final form.  The example is extended but the point is a simple one: there is no reason to believe a priori that standardized units of length will be expressed in the features they are used to construct. 

            Related to this is the question of scale, certainly an important issue in matters of cryptometrology, although little has been written about it in the Southeast or elsewhere.  What is the proper scale at which to address prehistoric units of length?  If a mound site were indeed engineered using multiples of a particular measurement, at what scale should we be addressing the question: centimeter to decimeters, meters to decameters, decameters to kilometers?  The answer depends on the length of the unit that was used to engineer the site to begin with.  If the base unit were only a few centimeters long, we should not expect to find it clearly expressed across distances of hundreds of meters or more.  If the unit were 50 or so meters in length, and we didn't know into what fractions it may have been divided, it would do us no good to look for expressions of the unit at the scale of a few meters.  And here we are stuck: without knowing the length of the unit to begin with, we don't know if we are applying the appropriate scale of analysis to find it, and if we don't know whether our scale of analysis is appropriate, how can we have confidence that our conclusions are?  If our mathematical locutions are not to become completely circular, we must begin with some external line of reasoning for choosing a scale of analysis to begin with; some separate bit of information to tell us, independently of the measures we measure, what and where we should measure in the first place. 

            The question of scale is tied to the question of fractionation.  'The' metric system standardizes fractionations into decimals, but this particular system is no older than the French Revolution that spawned it.  Myriads of other systems of metrics are still in use today.  Feet are fractioned into tenths and hundredths by engineers but into the duodecimal system of inches by most everyone else.  Inches are fractioned by doubling the increments with every iteration from halves to quarters to eighths to sixteenths and so on.  At the other end of the scale, measures are also extrapolated inconsistently.  Feet are commonly grouped into three to become yards, and it takes a somewhat enigmatic 1,760 yards to make a mile.  If such inconsistent fractionations and extrapolations were employed in prehistoric times, it is difficult to imagine that the base units would yield easily to mathematical analysis, even if significant target points could be determined with precision.

            Modern counter-examples come to mind where specific units of length are clearly expressed in large-scale features.  County section lines, for example, are easily recognizable on many road maps in flattish portions of the North American mid-continent, tessellating the landscape with a fairly regular one-mile grid.  The grid is obvious at this scale because the measure is so much larger than any potential margin of error in the size of the roads: an average road width of 25 feet is 0.5% of the measure the roads are demarcating.  This is much smaller than the margin of error for proposed prehistoric units of measurement in the Southeast, though, and county section roads only follow section lines in flat areas of the country which were platted using mile sections, which does not cover a great deal of the country.  There are also examples of very regular spacing at a large scale that have little to do with any unit of measurement.  In aerial photographs of modern housing developments, for example, the structures are commonly spaced at almost exact distances from one another.  In this case, the spacing reflects average house and lot size, and the locations of the houses within the lots.  Regular distances between houses are fairly uniform within individual developments, and vary from one development to the next.  In this case, the 'module' of average house-to-house distance would reflect average lot and house size (and possibly convey important information about differences between developments) without having been employed as a specific unit of measurement in the construction of the houses or layout of the development.

            At this point I can only offer a direction for theoretical discussion: how would we know whether a regularly expressed distance – even if it were very strongly expressed – represented a unit of measurement used by the builders of any particular feature or set of features?

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