The Science of Metrology
John Neal

I welcome this opportunity to broach a subject that has become a virtual obsession; those who have seen the point of what I have to offer have likened the content to the Rosetta Stone. This may be an exaggeration, but time will tell. It intimately concerns the pre-historic world and those who access these pages have been drawn here through an interest in this subject, just the sort of people whom I would wish to interest. It ain’t easy but it is very rewarding, and that’s no exaggeration.

Although I may have certain specific criticisms of the work of Graham, our host, it is impossible to deny the fact that the main thrust of his work is to propagate an interest in the ancient world, which is identical to my own. This he has done in no uncertain terms and my work will be entirely supportive of this point of view.

Many of the hypotheses forwarded for an advanced civilization in remote history concern measurements. Very few of them agree, one with another, as to the values used, causing fundamental flaws in their arguments. Once it is grasped, what I have to offer is a level place where all can stand, that never existed before. As Stecchini said:

It is a basic principle of epistemology that our ability to reject erroneous theories increases in proportion with the precision and accuracy of the measurements.

The Science of Metrology

The most important study of the ancient world is that of its metrology, for this is the medium through which its architects and artisans expressed much of their intention. All ancient civilizations have their unique and distinctive styles and personas, one has only to see objects of everyday use, examples of artistic expression or buildings to enable us to identify them and the culture to which they belong. Literally, from all over the world, there is a distinctive similarity of technique that underlies all of these seemingly disparate cultures; this is because all that was created had to conform to a canon of order in order to acceptable. The canon could be likened to music where a limited number of governing factors allow a limitless number of harmonious arrangements. These cultural similarities extend to their creation myths, functions of the gods, astronomy, counting methods and cosmologies. Although any of these linkages may be open to criticism or made to seem arbitrary, the one unifying factor, which cannot, is their metrology. Measurement is at the root of all civilizations and at the root of metrology is pure number.

It has become customary for us to label certain metrological values with a cultural appellation, such as Sumerian, Egyptian, Greek, Roman, etc. Although many bureaucracies adopted certain values for the regulation of their societies, they were not the sole or dominant modules used by that nation. All of the modules from all of the societies form an elegant structure and were concurrently used in their entirety by each ethnic group. As this measurement system was in use in its sophisticated wholeness at the very dawn of the historical period, the reasonable assumption is that it was developed in very remote antiquity. The earliest monuments from the prehistoric period overtly display the use of the system -- with the most astonishing degrees of accuracy. So exactly are the modules and their rational multiples seen to be in use at widely dispersed locations by civilizations that were no longer aware of each others existence -- one may also assume that at one time, all the nations of the world had access to a common canon of reference. The metrologist, Berriman, posed the question "Was the earth measured in remote antiquity?" The short answer is yes -- but not by any culture from the historical record.

For around two centuries, theories regarding the geodetic origins of ancient metrology have been regularly mooted. Before this, it was generally accepted that this was the case. Our ancestors were traditionally regarded as being more advanced in all of the arts and sciences. Newton sought the dimensions of the earth in ancient measures; Kepler made guarded references to his knowledge being of an Egyptian provenance. Galileo stated astronomical facts that he could not have known from observation and renaissance scholars are known to have reckoned the geographic degree of latitude to be 75 Roman miles. Classical texts are strewn with facts that the authors could not have calculated but must have been known from even more ancient records, now destroyed; mere fragments of higher learning had percolated down to the Greeks who are our premier reference. Before we elaborate on these points it is necessary to establish the general structure of the subject.

The constituent feet and their fractional integration.

Throughout history, scholars have sought to unravel the mysteries of metrology. Regarded as a whole it is a very confusing picture and when viewed in millimetres, becomes utterly impenetrable, it is fair to say that the enigmas of metrology would never have been resolved through the medium of the decimal system. One noted scholar (De Sanctis) remarked that "(Ancient) metrology is not a science, it is a nightmare." As is any branch of science -- if one is unversed in its peculiarities. Nevertheless, once the principal threads that bind the subject together are grasped, its connective links can fall into place with remarkable rapidity. It is a quote from another author (De Morgan) that hints at how the subject should be approached: "The

There runs through all these national systems a certain resemblance in the measures of length; and, if a bundle of rods were made of foot rules, one from every nation, ancient and modern, there would not be a very unreasonable difference in the lengths of the sticks.

This means that if you are going to study comparative metrology, the module of comparison should be an ancient foot measure. The English foot is just such a touchstone and when decimally expressed is the most suitable medium to represent the complexities of the subject. Secondly, all of the measures being compared should be reduced to their constituent foot value. By that, it is meant that there are many modules other than the sixteen digit or twelve-inch feet that are often called feet. Certain of them are really half cubits, some are 18 or 20 digit modules, and once identified they may be discarded for comparative purposes. Also, in all ancient cultures there was a range of variations of the modules in what are essentially the same foot measure, and when taken at their extremes, are often recorded as different feet. Thereby one may discard some of the variants, until a single example remains. Because the observed variations in the modules are the same in all cultures, one must learn to classify them and identify what is termed the Root in each one, then one can compare like with like. Once this process of reduction to the relevant modules is complete, it is apparent that there are probably only 12 basic feet used throughout the world. These are listed below at their parity with the English foot:

Table 1

Assyrian

.9ft -- When cubits achieve a length of 1.8ft such as the Assyrian cubit they are divisible by two, instead of the 1 ½ ft division normally associated with the cubit length. Variations of this measure are distinctively known as Oscan, Italic and Mycenaean measure.

Iberian

.9142857ft -- This is the foot of 1/3rd of the Spanish vara, which survived as the standard of Spain from prehistory to the present.

Roman

.96ft -- Most who are interested in metrology would consider this value to be too short as a definition of the Roman foot, but examples survive as rulers very accurately at this length.

Common Egyptian

.979592ft -- One of the better-known measures, being six sevenths of the royal Egyptian foot.

English/Greek

1ft -- The English foot is one of the variations of what are accepted as Greek measure, variously called Olympian or Geographic.

Common Greek

1.028571ft -- This was a very widely used module recorded throughout Europe, it survived in England at least until the reforms of Edward I in 1305. It is also the half sacred Jewish cubit upon which Newton pondered and Berriman referred to as cubit A.

Persian

1.05ft -- Half the Persian cubit of Darius the Great. Reported in its variations throughout the Middle East, North Africa and Europe, survived as the Hashimi foot of the Arabian league and the pied de roi of the Franks.

Belgic

1.071428ft -- Develops into the Drusian foot or foot of the Tungri. Detectable in many Megalithic monuments.

Sumerian

1.097142ft -- Perhaps the most widely dispersed module of all, recorded throughout Europe, Asia and North Africa, commonly known as the Saxon or Northern foot.

Yard and full hand

1.111111ft -- This is the foot of the 40 inch yard widely used in mediaeval England until suppressed by statute in 1439. It is the basis of Punic measure and variables are recorded in Greek statuary from Asia Minor.

Royal Egyptian

1.142857ft -- The most discussed and scrutinised historical measurement. Examples of the above length are plentiful.

Russian

1.166666ft -- One half of the Russian arshin, one sixth of the sadzhen. Variants at one and one half of these feet as a cubit would be the Arabic black cubit, also the Egyptian cubit of the Nilometer.

The number of decimal points used to express these values is sometimes criticised, but what we are actually looking at is an elaborate series of rational fractions. Exactly how these, which have been previously regarded as separate measures, fractionally integrate into a single organisation is shown in the table below.

Table 2