User:Egil/Sandbox/Comparative metrology

Comparative metrology is a branch of historic metrology where conclusions about ancient systems of measures are drawn based on methods of pure numerical comparison of the actual values of various standards of measurement, or of other artifacts. Typically, no, or very little supporting evidence in form of archeological finds or historical documents are given, the evidence is almost always in form of mathemathics showing relations. The theories are often quite complex, and fail the Occam's razor test.

Interest seems to have been triggered by interest around the Great Pyramid of Giza, and later by the discoveries of standards of measurement in Mesopotamia, especially in Gulash. Resistance against the metric system also seems to have played an important role.

Origins
In 1637, professor of geometry at Gresham College, John Greaves, made his first of several studies in Egypt and Italy, making numerous measurements of buildings and monuments, including the Great Pyramid. These activities caused him to be deprived of his Gresham professorship for having neglected his duties, but it did fuel many centuries of interest in metrology of the ancient cultures by the likes of Sir Isaac Newton and the French Academy. [Shalev]

Charles Piazzi Smyth
John Taylor, in his 1859 book "The Great Pyramid: Why Was It Built? & Who Built It?", claimed that the Great Pyramid was planned and the building supervised by the biblical Noah, and that it was:
 * built to make a record of the measure of the Earth.

A paper presented to the Royal Academy on the topic, was rejected.

Taylors theories were, however, the inspiration for the deeply religious archeologist Charles Piazzi Smyth to go to Egypt to study and measure the pyramid, subsequently publishing his book Our Inheritance in the Great Pyramid (1864), claiming that the measurements he obtained from the Great Pyramid of Giza indicated a unit of length, the pyramid inch, equivalent to 1.001 British inches, that could have been the standard of measurement by the pyramid's architects. From this he extrapolated a number of other measurements, including the pyramid pint, the sacred cubit, and the pyramid scale of temperature.

Smyth claimed, and presumably believed, that the inch was a god-given measure handed down through the centuries from the time of Israel, and that the architects of the pyramid could only have have been directed by the hand of God. To support this, Smyth said that in measuring the pyramid, he found the perimeter of the base to equal the number of days in a year in inches, and found a numeric relationship between the height of the pyramid in inches to the distance from Earth to the Sun, measured in statute miles.

Smyth used this as an argument against the introduction of the metre in Britain, which he considered a product of the minds of atheistic French radicals. [Dunn]

The pendulum
The first known descrition and practical use of a physical pendulum is by Galileo Galilei. Flinders Petrie, a disciple of Smyth, is of another opinion, writing in an article in Nature, 1933:
 * If we take the natural standard of one day divided by 105, the pendulum would be 29.157 inches at lat 30 degrees. Now this is exactly the basis of Egyptian land measures, most precisely known through the diagonal of that squared, being the Egyptian double cubit. The value for this cubit is 20.617 inches, while the best examples in stone are 20.620±0.005inches.

No explanation is offered as to why no Egyptian pendulums have been found, despite the extremely rich archeological material from this culture, nor to the question as to why none of the rich historic material from Egypt mentions this.

The circumference of the Earth
From the 18th century, inspired by the statement of Aristotle that the circumference of the Earth was calculated as 400,000 stadia, it became a belief among members of the French Académie des Sciences that ancient linear measures were all derived directly from the circumference of the Earth. Archaeologist Jean Antoine Letronne, in 1822, tried to show the connection to a supposed pre-Greek measurement of the Earth.

The grand scheme
By the time measurements of Mesopotamia were discovered, by doing various exercises of mathemathics on the definitions of the major ancient measurement systems, various people (Jean-Adolphe Decourdemanche in 1909, August Oxé in 1942) came to the conclusion that the relationship between them was well planned. Livio C. Stecchini claims in his A History of Measures:
 * The relation among the units of length can be explained by the ratio 15:16:17:18 among the four fundamental feet and cubits. Before I arrived at this discovery, Decourdemanche and Oxé discovered that the cubes of those units are related according to the conventional specific gravities of oil, water, wheat and barley.

Stecchini makes claims that implies that the Egyptian measures of length, originating from at least the 3rd millennium BC, were directly derived from the circumference of the earth with an amazing accuracy. According to "Secrets of the Great Pyramid" (p. 346 ), his claim is that the Egyptian measurement was equal to 40,075,000 meters, which compared to the International Spheroid of 40,076,596 meters gives an error of 0.004%. No consideration seems to be made to the question of, on purely technical and procedural grounds, how the early Egyptians, in defining their cubit, could have achieved a degree of accuracy that to our current knowledge can only be achieved with very sophisticated equipment and techniques.

The grand foot
Building on Stecchini and Smyth, John F. Neal, in his book All Done With Mirrors (in 2000), came to the conclusion that the foot was the grand unit, and that the common system of the ancient cultures was that the definition of their respective foot is 1/360,000th part of the longitudinal meridian degree of their respective latitudes.  Even the theoretical odometer described by Vitruvius was used as evidence. The conclusion of Neals book is:
 * The English foot is the root, or number one, from which all other measures are extrapolated.

This is then used as a form of defense form the Imperial units against the metric system, and adopted by parts of the anti-metric movement.

Stonehenge
Alexander Thom, doing calculations on measurements of British stone circles like Stonehenge, came to the conclusion that there must have been a common unit of measure. By measuring crude and rough stones, he claims to have found some mathemathical common factor to a precision of micrometers, which he called a megalithic yard.

Later, these ideas has been further developed as defense for the Imperial units against the emerging metric system, and adopted by parts of the anti-metric movement.

Robin Heath, in his book Sun, Moon & Stonehenge, connects the megalithic yard (and thus Stonehenge) to the imperial foot, and manages to connect a few astronomnical phenomena, and the Egyptian Royal Cubit (and thus the Great Pyramid) into one grand equation (MY is an abbreviation for megalithic yard):
 * if the lunar year is represented by 12 MY then 1 ft corresponds precisely to the extra 10.875 days to coincide with the end of the solar or seasonal year. Furthermore, the period between the end of the solar year and 13 lunations - 18.656 days - is represented by another unit of length from antiquity, the 'Royal Cubit' of 20.63" or 1.72 ft.

This seems to bring pseudoscientific metrology to new heights, especially in view of the conclusion:
 * Hence the equally astonishing revelation that 1 MY = 1 ft + 1 RC. Assuming that the MY was the primary unit, then the derivative foot and cubit appear to have formed a logical and essential part of the astronomical and calendrical researches of our Neolithic ancestors. If, however, the foot preceded the MY in time - and here we must remember that 1/1,000th of a degree of arc around the equatorial circumference of the Earth is just 365.244 ft in length! - then knowledge of the roundness of the Earth must have predated use of the MY…i.e. well before 3,000BC. There are no other choices readily apparent!