Flinders Petrie, M.W., "Weights and Measures", Encyclopædia Britannica 1911 (6)

Petrie’s observation on the early system of measure present in the UK raises an intriguing question: Could units of measure similar to the modern metre have existed long before the French Revolution? The possibility may seem counterintuitive, but ancient cultures developed advanced systems of measurement, predating the metric system by millennia. The metre, and other divisions of the polar circumference, have a place in historical metrology.

   Petrie himself noted the striking similarity between early systems of measurement in Germany and Britain and the modern decimal metric system. He lamented that these ancient systems, once nearly compatible with the metre, were gradually replaced by the 12-inch foot and restricted by legal statutes.

  The assumption that ancient civilisations lacked precise systems of measurement overlooks significant evidence that these cultures had an advanced understanding of the Earth’s dimensions. If we find ancient units aligning closely with the metre, in systems such as those from Persia, Egypt, or Greece, it may force a re-evaluation of our narratives about both ancient science and the origin of the metric system.The raison d’être of the metre is that it represents a 40 000 000th part of the polar circumference, to within a small margin of error (modern estimates give the polar circumference around seven and a half kilometres more than 40 000). It is usually assumed that ancient civilisations had only basic systems of measure and that a precise measure of the earth’s size would have been impossible for them. Should we find ancient units, be they Persian, Egyptian or other, that align with the metre, and thus to the polar circumference, being equivalent to multiples of 6, 7 or 12 millimetres, we might be in a position to reconsider these narratives. What an analysis of ancient systems of measure may reveal is that the polar circumference was precisely measured at some point in the distant past. 

   The implications of this would be profound, and compel us to re-evaluate our understanding of ancient scientific capabilities and to recognise that what we often attribute to modern innovation may have much deeper historical roots. Ancient civilisations may have possessed a level of technological and scientific precision that we are only now beginning to appreciate.

   In this article, I explore how reading ancient measurements in terms of metres and millimetres can reveal intriguing patterns. Special attention is given to the work of French 19th century metrologist C. Mauss, whose findings offer intriguing insights into the ancient world's sophisticated understanding of measurement. I argue that ancient civilisations had a sophisticated understanding of Earth's dimensions and that measurement systems like the metre predate the Enlightenment. The values and denominations used by Mauss are the ones used here.

.

Evidence of an ancient and sophisticated system of measure

  Despite the wealth of data from accurately measured ancient sites, the generally held assumption is that the metre emerged in the 18th century, ex nihilo, and that it was the product of the first true age of science, kick-started by the Copernican revolution. It goes in tandem with the belief that the earth was only accurately measured in the 18th century, the metric system being based on a fraction of the Earth’s meridian circumference. 

   This persistent belief overlooks the fact that the English miles, foot and inch themselves imply an ancient and accurate knowledge of the Earth's dimensions. For instance, the Earth's equatorial circumference is astonishingly close to 365.242199 times 4,320,000 inches, reflecting a yuga, a unit of time from Hindu cosmology of 4 320 000 years. The dimensions of the earth, as they are described by the inch, are linked to the dimensions of the Great Pyramid, expressed in inches, and to periods of time, expressed in days. 

Figure 1: Equatorial circumference, yuga, year and inch.

Figure 2: Yuga, sidereal year, sidereal month, Great Pyramid height

Figure 3: Earth circumference, 4320, year, Great Pyramid of Giza

  Similarly, the moon’s equatorial radius, being exactly 1,080 miles, reflects extraordinary precision. The number 108 (and multiples of it) is a key number in the ancient Indian system, and elsewhere in the ancient world, and equal to 9 x 12. In the Hebrew calendar, for example, an hour is divided into 1080 parts. The sun’s radius is 432,337.6 miles (695,780 km), just over 432 000 miles, and there are 43 200 (equal to 12 x 3 600) seconds in 12 hours. The sun’s diameter would therefore be close to 864 000 miles, the number 864 being frequently associated with the sun. As John Michell explains, the mile itself may have been derived from a division of the sun’s radius in miles. In Michell’s words:

   This observation suggests that the mile, far from being a purely arbitrary unit of distance, is closely linked to ancient astronomical and symbolic studies of the sun. The number 864, with its many connections to cosmological and sacred structures, reflects a profound understanding of both the physical and metaphysical world. The Earth's mean circumference is 24 880.5964 miles (40 041.4386 km), and this can be interpreted as 24 883.2 miles, a value which aligns similarly with a system of miles and multiples of 12. Expressed mathematically, 24 883.2 miles equals 12⁵ ÷ 10, demonstrating a deliberate use of powers of 12 to structure the system of miles. The Earth’s mean radius is 3 958.7559 miles (6371.0 km) and this is very close to 12 x 33 = 3 690 miles. There are various historical references to the yojana, an ancient Indian unit, but according to the Arthashastra by Chanakya, a mile is exactly a ninth part of yojana.  The word mile comes from the latin for a thousand, and the mile as a unit of length is equivalent to exactly a thousand dhanushas, from the ancient Indian system. The so-called English or imperial mile can therefore be directly associated with the ancient Indian system of measure, as well as to a decimal system, as opposed to a purely duodecimal one. 

   The inch and the foot are key units in interpreting ancient monuments in relation to units of time, with an inch or a foot being often found to represent a day. The moon’s equatorial radius of 1,080 miles (or 120 yojanas of 9 miles) showcases an astonishing precision in ancient measurements, one that aligns with key numerological concepts in Indian and other ancient cultures. This suggests that far from rudimentary, the measurements of celestial bodies were rooted in a sophisticated system of cosmological knowledge. 

Figure 4: Sun, moon, earth, miles, and 12

   These and other clues suggest that early civilisations measured the Earth, the Moon, the sun, and time cycles, with a precision we tend to attribute solely to modern science, and that a system of measure was designed, based on values derived from the earth, the moon, other natural bodies and phenomena, and key numbers such as 9, 12, 108 and 4320 (among others). The values displayed in the relationship between the Earth, Moon, and Sun reveal an underlying mathematical structure that points to an advanced and purposeful system of measurement. These harmonious values suggest that the use of miles in ancient times had a specific cosmological significance, particularly in the way they aligned celestial and terrestrial dimensions through multiples of 12. These values also suggest the presence of a decimal system, as we see these key numbers being multiplied or divided by 10, 100, 1000 etc. As the system of measurement that existed at some point in ancient times was highly sophisticated, we might expect to find units derived from an accurate value for the polar circumference, possibly linked to the same numbers, 9, 12, 108, 4320 etc, as well as 10. 

A cubit of length equal to that of our metre  

It is not a new observation that the metre is not new. Writing in 1892, French metrologist C. Mauss compiled an account of many historical units of measure and classified them into various series. Not only was he able to make many parallels between geographical locations through this study, but he was able to show that many units could be shown to be part of a system based on a multiples of 3, 4, 6, 7, or 9 millimetres.

   Mauss observed that "the ancients knew a cubit of three feet, of which the length corresponds to our metre", referring to a cubit found at Susa, of 583.33333 mm. Mauss shows that this workers’ cubit from Susa (7 / 12 of a metre exactly), is linked to the Egyptian royal cubit of 525 mm, if it is multiplied by 9 / 10. As a result both these cubits can be simply but precisely linked to the metre, the Susa workers’ cubit being 7 /12 m and the Egyptian royal cubit being 63 / 120 m. Mauss also links these units to the Mathematical foot of China which is very close to a third of a metre, with Mauss giving it a value of 333.257 mm, and to a Berlin unit of 666.8 mm. Mauss reflects: 

    If we look at Mauss’s detailed study of ancient units, we can see that reading these units in metres helps us to grasp them as part of a system, aligned with the polar circumference of the earth. Mauss's detailed study of ancient units reveals a striking pattern: cubits from diverse regions and periods align with modern metric values, suggesting that these ancient units were not arbitrary but part of a coherent system grounded in the Earth's dimensions. For example, the workers' cubit from Susa, at exactly 7/12 of a metre, closely matches the Egyptian royal cubit, revealing that these units could be systematically linked to the Earth's polar circumference. 

Figure 5: A page from Mauss’s “L’Eglise de Saint Jérémie a Abou-Gosch, Observations sur plusieurs mesures de l’Antiquité (Suite)” Revue Archéologique, vol. 20, 1892, pp. 80–130. JSTOR, http://www.jstor.org/stable/41747027. 

Aristotle wrote:

   Aristotle says that mathematicians of his day estimated the Earth's circumference to be 400,000 stades. There are several types of historical stade, and perhaps they are not all known. Aristotle does not specify which type of stade the mathematicians used. It’s possible that those mathematicians had arrived at a good estimate of the earth’s size. If we divide the modern polar circumference of the Earth, 40,008 km, by this estimate of 400,000 stades, conveyed by Aristotle, each of these stades would be about 100 metres long. It seems likely however that such a stade would be derived from a good estimate for the polar circumference in the first place, presumably by an earlier generation of mathematicians, rather than having been used to measure it for the first time. 

   It is possible that the particular stade used by the mathematicians in Aristotle’s time to (re) calculate the earth’s size was 100 cubits of 1 metre in length, or close to this value. In view of the fact that the Chinese mathematical foot is estimated by Mauss to be close to a third of a metre (333.257 mm), the Berlin foot close to two thirds of a metre (666.8 mm), and the workers’ cubit from Susa 7 / 12 of a metre (583.333 mm), and one of the values for the Egyptian royal cubit being 63 / 120 metres (525 mm), a stade of 100 metres is not without context. Another interpretation of the Egyptian royal cubit is π × Phi² = 0.523559 metres, a reading that relies on pi (π), the ratio of a circle's circumference to its diameter, and Phi², a significant mathematical constant often associated with harmony and proportion. This idea is inspired by the work of R.A. Schwaller de Lubicz, who argued that ancient Egyptians incorporated these constants into their measurements and architecture. Another interpretation of the Royal Egyptian cubit is Phi² × 2 / 10 = 0.5236, a relationship that similarly depends on Phi² but emerges from different calculations based on the metre. There are clear connections between the Egyptian royal cubit and the metre, which serve to further support the idea that the metre was part of an ancient system of measurement.

The unit which Petrie referred to, quoted in the introduction, was the most common foot used in buildings in England, called the Belgic foot, and according to Petrie measured 13.22 inches. 

   Three such feet of 13.22 inches would indeed be very close to a metre, being 39.66 inches, and the metre today being 39.3700787402 inches. This foot is also close to the Chinese mathematical foot, as Mauss calls it, of 333.257 mm (13.120354 inches). A foot of approximately 13.2 or 13.3 inches was found elsewhere too, according to Petrie:

   Metrologist John Neal believes that there is no need to call this ancient unit a metre, even though it is approximately equal to the modern metre, suggesting instead we call it a Belgic yard. He explains:

   This is perfectly true, and the modern system that has been built around the metre is far from as subtle and sophisticated as the ancient one. Nevertheless, whether we call it a Belgic yard, a stade, or anything else, it is also true that a unit close in length to the modern metre long preceded the 18th century French metre that is the basis of so many or our units of measure today. Revolutions are about the turn of a wheel.

   The consistency across historical and modern measurements suggests that ancient mathematicians were working with knowledge that parallels modern scientific precision. As I explore further with Mauss's work, other units such as the Susa worker's cubit (exactly 7/12 of a metre) illustrate how many historical units can be connected to the polar circumference of the earth, and so harmonise with the metric system, whilst fitting into a broader framework of astronomical and terrestrial alignment.

 Reading ancient units of measure in metres

    Many other historical units can be meaningfully read in metres. Mauss firstly points out that many of the measures found in Syria, Italy, and Spain are linked to the "Grande Hachémique", the Persian royal cubit, a unit to which he gives a measure of 658.285 mm. This can be expressed as 4 608 / 7, or 658.2857142 mm. When converting this into inches using Mauss's preferred conversion (1 metre = 39.375 inches), we get a length of 25.92 inches, which corresponds to 6⁴ x 2 / 100. This number is significant not only in terms of spatial measurement but also in its relation to time: the value 25,920 years corresponds to the precession of the equinoxes. The modern metre relates to the 39.375 inch measure as 39.375 x 8 000 / 8 001 = 39.3700787402 inches. It might seem, at first, more sensible to consider this unit in inches. This is true of many units, as the inch is often connected to time measurements expressed in space. However, understanding them in metres offers new insights. For example, by interpreting the Persian royal cubit in metres, we can more easily relate it to the Earth's polar circumference and other units within the metrological system. This cubit is just one of many units that align with the polar circumference. 

    Mauss writes in the article:

    Another unit which is discussed is the foot of the apadana of Susa, of 350 mm, which is 7 / 20 of a metre. One observation we can make from the outset is that while the length of 1 metre is implied, a purely decimal system is not. On the contrary we see the use of multiples of 2, 7 and 12. This is consistent with the values of many of the other units studied by Mauss which are multiples of or divisions by 7, 3 or 4. 

Other units of measure discussed by Mauss can also be simply connected to a metre. The Babylonian foot given by Mauss as 350 mm is 7 x 9 / 200 of a metre. The Persian foot of 350 mm is 7 / 20 of a metre. The Egyptian royal cubit as 525 mm is 7 x 3 / 40 of a metre. The Cairo Coptic cubit of 577.5 mm is 7 x 33 / 400 of a metre. The Babylon cubit of 630 mm is 9 x 7 / 100 of a metre. The Vara of Madrid / Jaen / Ciudad Real / Canaries of 840 mm is 9 x 7 x 4 / 300 of a metre. The Philitarian / Alexandrian stade (600 feet of 360 mm) is 216 m, which are 6³ metres, and the Armenian mile, of 7 Attic feet (derived from the Parthenon) of 308.571 mm is 2 160 m, which are 10 x 6³ metres.

   The Persian royal cubit, or Grande hachémique, given 658.2857 mm, is the equivalent of 144 / 7 x 32 mm, or 32 digits of 20.57142857 mm. Each of these digits is the equivalent of 9 x 4² / 7000 metres, or 12² / 7 = 20.57142857 mm, or 9² / 100 = 0.81 inches (using a conversion to inches of 39.375 inches to the metre). The "Petite Hachémique" of 596.571 mm is linked to many units of measure across Europe, and is three digits less than the grande hachémique (32 - 3 = 29) and was possibly the basis of the Roman foot. Mauss writes:

   Whether read in inches or millimetres, these values given by Mauss seem to be part of a system, in millimetres based on the numbers 7 and 12, and in inches based on the number 9. The presence of important, symbolic numbers such as 7, 9 and 12 suggests a sophisticated approach to designing a system of measure.

   A digit of 0.81 inches relates to an Egyptian digit of 0.729 inches as 10 / 9. We can interpret the imperial yard of 36 inches as 400 / 9 of these Persian digits of 0.81 inches, and the imperial foot as 400 / 27 of these digits. We can interpret a metre of 39.375 inches as 7 000 / 144 such digits. However, units such as the Saxon foot of 13.2 inches, the shusi or angula of 0.66 inches, if read precisely in this way, do not fit, and are based on the number 11, for example, there are 40 / 27 x 11 digits of 0.81 inches in 13.2 inches, and 2 / 27 x 11 digits in a shusi of 0.66 inches. There is a whole system of units which do not fit with multiples of 12/7 metres, from the Saxon foot to the mile. However, if we read the shusi as 0.65625 inches, then we get 700 / 864 digits of 0.81 inches. If we read the shusi as 0.6561 inches, then it relates to a digit of 0.81 inches as 9 / 10.

The megalithic yard

   The megalithic yard was estimated by Thom to be 2.72 feet, or close to this value. However, a value of 2.7216 feet fits well with the metre, and several historical units of measure, as it is 12⁴ x 4 / 100 000 metres. For example the megalithic yard as 829.44 mm divided by 16, 12² and 2, and multiplied by 1000 would give a Delphi foot of 180 mm (7.0875 inches). Another example is the Bruges foot, as 288 mm, which if multiplied by 288 and divided by 100, gives a megalithic yard. The royal foot of Alexandria, which Mauss attributes 360 mm to, can be multiplied by 12² and 16 and divided by 1000 to produce a megalithic yard. There are simple connections such as these between the megalilthic yard as 829.44 mm and many other historical units, for example the Egyptian foot of 270 mm, the Egyptian qassaba foot of 274.2857 mm, the foot of the Museum of Naples of 292.57142857 mm, the foot of the stadium of Laodikeia of 222.1717 mm, the Royal Persian foot of 329.1428 mm, the Balady cubit of Egypt of 576 mm, the Dera Kesra / Cosroes cubit of 640 mm, the Chaldean Cubit of Tello / Constantinople of 648 mm, the Persian royal cubit Grande hachémique of 658.285 mm, the Pik stambouli of 685.7142857 mm, the Persian foot at Amman of 720 mm, and the Tello cubit of 756 mm, the architects’ cubit of Egypt of 768 mm, the Apadana Cubit / Vara of Seville / Susa Cubit of 864 mm, the religious cubit of 987.428 mm, to name but a few. The digit which goes into the Persian royal cubit 32 times goes into a megalithic yard 28 x 12² / 100 times.

   John Neal writes about the megalithic yard:

   A megalithic yard, if interpreted as 2.7216 feet, or 32.6592 inches, converts to 0.82944 metres with the 39.375 inch metre. It too fits well within this system, as it is made up of 12²  x 28 / 100 = 40.32 Persian digits of 0.81 inches. The megalithic inch, a 40th part of the yard, comprises 7 x 12² /1 000 = 1.008 Persian digits. We can think of the megalithic yard as simply 144 / 100 Balady cubits of Egypt of 0.576 m, or 2 x 12² / 100 Bruges feet of 0.288 m, 8 x 16 / 100 Chaldean Cubits of Tello / Constantinople of 0.648 m, 9 x 12 / 100 architects’ cubit of Egypt of 0.768 m, 12 x 8 / 100 Apadana Cubit / Vara of Seville / Susa Cubit of 0.864 m, 12 x 7 / 100 religious cubits of 0.98742857 m, or 7 x 8² / 100 000 Attic stades of 185.142857 m. The Roman foot can be understood as 11.664 inches, and converted to metres with the 39.375 inch metre, we get 0.2962285714 m, which is equivalent to 12⁴ /70 000 m. Mauss’s value of 0.29622857 m for a Roman foot can be multiplied by 28 / 10 to get the megalithic yard of 0.82944 m. The 0.2945454545 m value Mauss gives also can be multiplied by 4 400 and divided by 6⁴ to obtain a metre (or multiplied by 1 400 π / 6⁴). Of course there are other approximations for the megalithic yard and the Roman foot which can be given, and other interpretations, be they in feet, inches, or any other unit. But the megalithic yard and the Roman foot are both suited to being expressed in metres, and can clearly be understood as part of a duodecimal system expressed in metres, and linked to historical units of measure.

   The table below shows most of the units of measure discussed by Mauss, with their values in millimetres, and inches, and their relation to a digit of 20.57142857 mm, or 0.81 inches. I have added the megalithic inch and yard too. Many of these measures, when read in millimetres, are clearly divisions by 7 of a greater length. Many ancient units appear to have been derived from simple fractions of a larger, standardised unit. The use of fractions like 1/7, 1/6, and 1/12 across various cultures suggests a shared understanding or a base unit that these cultures modified to suit their needs.The metre, as a fundamental unit, allows for easy conversion and interpretation of these fractions. For instance, multiples of 72/7, 128/7, 2 048/7, and so forth are seen across different measures, showing a consistent mathematical approach that can be easily understood when using the metre. The metric system can be seen as a modern continuation or refinement of ancient principles. This continuity supports the idea that the metre is not just a modern invention but is connected to a long history of measurement practices. The terms given to the units are Mauss's, sometimes the word “foot” is used when it might better be called a “cubit”, or “cubit” when it might better be called “yard”.

 The data in the tables below includes measures from various cultures (e.g., Egyptian, Persian, Roman, Chinese). Despite geographical and temporal differences, there’s a notable harmony in the measures, especially when related to the metre. The first column gives the name of the unit as per Mauss (to which the megalithic yard and inch have been added), the second the length in millimetres, and the third the number of digits of 20.57142857 mm in the unit. The numbers in the third column show that it is possible to think about a system, which many of the various units listed are part of. This digit of 20.57142857 mm is 144 / 7 000 of a metre.

Also of interest in the list above is the Roman foot. For example Roman foot A, of 294.545 mm, is equivalent to 25 920 / 88 mm, and close to 25 920 / (pi x 28). And Roman foot B is close to a lunation in days, 29.53059. And Roman foot D is very close to being 144 Persian digits.

The mathematical foot of China is very close to being a third of a metre, as Mauss remarks.

The megalithic yard, the Burgos Vara which Mauss attributes to Ciscar, the coudée des entr'axes and the Burgos vara which Mauss has an accurate drawing of, are all close to 25 920 / π³ = 835.9598 mm.

Table 1

   Mauss’s values for the Roman foot are of interest. For example Roman foot A, of 294.545 mm, is equivalent to 25 920 / 88 mm, and close to 25 920 / (pi x 28). And Roman foot B is close to a lunation in days, 29.53059. And Roman foot D is very close to being 144 Persian digits. Also, the mathematical foot of China is very close to being a third of a metre, as Mauss remarks.

   Mauss of course does not discuss a megalithic yard, but if we take a value of 12⁴ x 4 / 100 000 = 0.82944 metres for it, then there is a clear connection to the Persian digit. A megalithic yard would be made up of 12² x 28 / 100 = 40.32 of these digits, and we can therefore connect the megalithic yard to the other units discussed by Mauss. A reading of ancient megalithic sites in Persian units, rather than only in megalithic yards and rods, might be of value.

   The megalithic yard, the Burgos Vara which Mauss attributes to Ciscar, the coudée des entr'axes and the Burgos vara which Mauss has an accurate drawing of, are all close to 25 920 / π³ = 835.9598 mm.

   The graph below shows an overview of the units referred to by Mauss. It is remarkable that the various values of these units show such a gradual and constant progression when seen in order of magnitude.

Figure 7: Historical values analysed by Mauss in order of magnitude

It's also interesting to look at the measures in millimetres multiplied by 7 and divided by 8 and 9 (or 72). The table below is similar to the first table, but with a different third column, which shows the value in millimetres when the unit is multiplied by 7 and divided by 8 and by 9. It presents an intriguing progression of units. 72/7 is 10.2857142857, which is half the Persian digit of 20.57142857 mm. The neatness of the progression, where units seem to almost "snap" into place under the transformation, suggests there could be an underlying mathematical harmony to these ancient systems. The systematic relationships between these units could indicate that the cultures associated with these units, from diverse geographical places and historical times, shared a unified or at least communicative approach to measurements.

It's also interesting to look at the measures in millimetres multiplied by 7 and divided by 8 and 9 (or 72). The table below presents an intriguing progression of units, evident in the third column. 72/7 is 10.2857142857, which is half the Persian digit of 20.57142857 mm. The neatness of the progression, where units seem to almost "snap" into place under the transformation, suggests there could be an underlying mathematical harmony to these ancient systems. The systematic relationships between these units could indicate that the cultures associated with these units, from diverse geographical places and historical times, shared a more unified or at least communicative approach to measurements than previously thought.

The terms given to the units are Mauss's, sometimes the word foot is used when it might better be called a cubit, or a cubit when it might better be called a yard, but the important thing is the values in mm.

 Table 2

The data includes measures from various cultures (e.g., Egyptian, Persian, Roman, Chinese). Despite geographical and temporal differences, there’s a notable harmony in the measures, especially when related to the metre.

The table of historical measures derived from the work of C. Mauss reveals a striking pattern when viewed through the lens of mathematical relationships. Specifically, the column titled "Unit x 7 / (8 x 9)" reflects an underlying proportional structure linking various ancient measurements to a consistent ratio. This ratio is produced by multiplying each historical unit by 7 and dividing the product by the factors 8 and 9, effectively normalising the measures and allowing for cross-comparison. When this operation is applied, many of the results fall into similar ranges, suggesting that these measures, from different times and cultures, were not arbitrary but part of a coherent system of metrology.

This relationship emphasises that historical units were not isolated but interconnected through mathematical principles. By analysing these units in millimetres (mm) or meters, modern researchers can detect repeating patterns, which may indicate a shared understanding of proportion and geometry across cultures. These units likely derived from natural or cosmic phenomena, and their recurrence across different civilisations points to a common, perhaps even sacred, method of understanding space and measurement. Hence, viewing historical measures in terms of their mathematical relationships, rather than merely as standalone values, is key to uncovering the broader metrological system that underpinned ancient engineering, architecture, and cosmology.

   The table of historical measures derived from the work of C. Mauss reveals a striking pattern when viewed through the lens of mathematical relationships. Specifically, the column titled "Unit x 7 / (8 x 9)" in the second table reflects an underlying proportional structure linking various ancient measurements to a consistent ratio. This ratio is produced by multiplying each historical unit by 7 and dividing the product by the factors 8 and 9, effectively normalising the measures and allowing for cross-comparison. When this operation is applied, many of the results fall into similar ranges, suggesting that these measures, from different times and cultures, were not arbitrary but part of a coherent system of metrology.

   This relationship emphasises that historical units were not isolated but interconnected through mathematical principles. By analysing these units in millimetres (mm) or metres, it’s possible to detect repeating patterns, across units from different cultures. The presence of numbers like 28, 29, 30, and 32 suggests a close-knit structure where many of the ancient measurements, despite connections to different cultures, adhere to a consistent proportional framework. For example, 28, 30, and 32 are close to whole numbers often found in basic divisions of time, space, or natural cycles, which were important in both daily life and spiritual or astronomical observations.

   The fact that these numbers are clustered around familiar, whole-number values demonstrates that ancient metrologists used a system based on shared mathematical principles. This consistency suggests that they were keenly aware of geometric, cosmic, or natural proportions, which they encoded into their measurement systems. By interpreting these measures in millimetres and applying this formula, it’s possible to see a unified approach to measurement that spans different regions and eras, helping us to better understand the coherence of ancient metrological systems.

The right unit?

   The metre can serve as a translator, showing that these ancient measures might have been different expressions of a common mathematical understanding. There are many units which do not derive from the polar circumference, and so do not fit with the metre, which is derived from the polar circumference.

   The mile, for example, is suited to express the mean circumference of the earth, in a duodecimal fashion: 24 883.2 miles. The mile also is suited to, or derived from, the radii of the moon and the sun, 1 080 (equatorial radius) and 864 000 miles respectively. The mile relates to some of the measures in Mauss's research via the number 11. If we convert a mile to metres, still with the 39.375 inch per metre conversion, and multiply it by 10 / 11, which is the ratio also between a Saxon foot and an imperial foot, and divide by 1 000, we get 5 feet of 292.57142857 mm, which is the length of the foot from the museum of Naples which Mauss discusses (11.52 inches). If we multiply the mile by 10 / 11 and divide the mile by 1 000, we also get 36 / 80 Grande Hachémiques, or royal Persian cubits of 658.285714 mm, or 4 of what Mauss refers to as "Pieds constatés au Saint Sepulcre de Jérusalem", of 365.7142857 mm, or 8 / 3 cubits of 548.57142857 mm, which are Mauss's estimate of the workers' cubits of Mayence, Riga and Sardinia, and the Amman worker's cubit. So if a mile is a thousand of something from Mauss's list, we could say it is ten thousand of half the Roman foot of the Naples Museum (292.57142857 mm or 11.52 inches), multiplied by 11 / 10. The mile is more closely connected to the shusi / angula of 0.66 inches, and the Saxon or Sumerian foot of 13.2 inches. Nine miles make a yojana, also equivalent to 43 200 Saxon or Sumerian feet. In the ancient Indian system, 96 angulas make an ordinary dhanusha, and this is exactly a thousandth part of an English mile: 96 x 0.66 x 1 000 = 63 360.

   The foot and inch are related to the equatorial circumference, which can be thought of as a spatial manifestation of the passage of a day, and also to time measures more generally, expressed in architecture. The presence of recurring numbers across many different units, as demonstrated by Mauss, when converted to metric units, shows a commonality in thought processes that can be aligned with the metre, but also with the mile, the foot, and the inch, which all correspond to different aspects of the universe.

   We observe that the same sets of significant numbers are expressed in metres in Mauss’s work, just as they are in feet and miles in the research of John Michell and John Neal. These numbers—144, 1296, 864, 2592, 4320, 248832, 20736, 5040, 63, 64, and others—hold particular importance across metrological studies, representing foundational values used in both sacred and scientific contexts. These key numbers are not arbitrary but are consistently applied to critical features of ancient cosmology and geometry.

   Recognising the usefulness of reading historical units of measurement in metres, rather than exclusively in feet or miles, does not necessarily diminish the legacy of English or imperial measurements. Nor does it imply a betrayal of one's principles or an anachronistic misreading of history. Some metrologists argue that only by examining ancient units in feet or inches can we discern the underlying patterns. This is certainly true in many cases, but it is equally important to acknowledge that similar patterns can emerge when these measurements are expressed in metres or millimetres.

   There is a tendency among English-speaking researchers to insist that historical measurements must be understood in feet and inches, while their French-speaking counterparts are more likely to assert that reading these values in metres or millimetres unlocks the true structure of ancient systems. Both approaches reveal different layers of meaning and pattern, underscoring the idea that historical units of measurement may have been part of a universal system, transcending the distinctions between imperial and metric standards.

   Ultimately, what becomes clear is that ancient metrological systems were designed to reflect mathematical and cosmic principles, and these principles can be revealed through multiple lenses, whether in feet, miles, metres, or millimetres. This suggests a shared ancient knowledge of the Earth’s dimensions, encoded in different forms but consistently pointing back to a unified, global system of measurement that reflects both scientific understanding and symbolic meaning. What reading historical units of measure in metres can do is allow us to see that they are connected to the polar circumference of the earth, just as the metre is. 

Dividing the earth’s polar circumference

   The widespread idea that the earth could not possibly have been accurately measured until just a century or two ago can be challenged by looking at historical units of measure, read in inches, feet, and metres. The work of John Neal and John Michell has shown how important the English foot is. But another part of the picture is the metre, or divisions of the polar circumference. 

   One example, among many, is the unit of 548.57148257 mm, which is Mauss's estimate of the Riga and Permau workers' cubits and Amman worker's cubit, and the Florentine Braccio, corresponds to a division of the polar circumference. The metre is itself a division of the polar circumference, though today a slightly different value is given to the circumference than it was when the metre was calculated in the 18th century. If we take this circumference as 40 000 000 m exactly, rather than the more accurate 40 007.863 km, the 548.7142857 mm unit corresponds to the polar circumference x 8 x 12 / 7 000 000. Reading these cubits in this way, in millimetres, implies a division of the polar quadrant by 7. If we can link reading this unit in metres to an ancient practice of dividing up the space between the equator and the north pole into seven parts, then this lends some weight towards the theory that this, and other units of measure were designed against an accurate measure of the polar circumference which was divided into seven parts. It's possible to approximate the polar circumference of the earth fairly well with 9² x 6² x 7³ x 40 = 40 007 520 m. Perhaps a division into seven parts was also linked to this.

   There are several indications that this practice of dividing the distance between the equator and the north pole into seven parts did indeed take place. There is historical reference to this by Pliny and, later, by Ibn Khaldun. And if we look at a key ancient site such as Avebury, we can see it is placed at one of the divisions into seven parts of the polar quadrant.

   Ptolemy’s Geography (2nd century) outlines his division of the Earth into climatic zones, which served as a foundation for mediaeval and later geographic concepts. The Earth is divided into five zones: the torrid zone in the middle, two temperate zones on either side of it, and two frigid zones in the utmost parts. The torrid zone is the closest to the equator, characterised by intense heat, and was considered uninhabitable by ancient geographers. The first temperate zone came next, and included the Mediterranean region, which Ptolemy considered ideal for human habitation. The second temperate zone was cooler than the first but still suitable for habitation, and included northern Europe. Beyond that came the first frigid zone, marked by long winters and short summers. The second frigid zone was characterised by extreme cold and long periods of darkness, and considered largely uninhabitable. Finally came the polar zone. Within this there was a system of parallels, seven in number in the later works, which corresponded to numbers of hours of daylight at the summer solstice at various latitudes.

  In the Muqaddimah (1377), Ibn Khaldun, working in this tradition, also outlines a division of the Earth into seven zones, which he associates with varying levels of civilisation and human development. These zones are based on latitude, also starting from the equator and extending to the poles. Ibn Khaldun writes:

   The arctic circle really does begin very close to latitude 64.

    Here we have a description of the ecliptic being divided into 360 degrees, one degree being 25 parasangs, 1 parasang being 12 000 cubits, 1 cubit being 24 fingers, and 1 finger being 6 grains of barley placed closely together in one row.

    The Attic foot derived from the Parthenon is according to Mauss 308.5714 mm (12.15 inches). A 20th part of this would be 15.4285714 mm, and would correspond to a "finger" or digit as it is described in the quotation above: 15.42857 mm multiplied by 24 would give a cubit of 370.2857142 mm. This digit or finger of 15.4285714 mm is 4 /3 of the 20.57142857 mm digit discussed earlier. 6 / 5 of these smaller digits make an Egyptian digit of 0.0185142857 m (0.729 inches). While 20 digits of 15.4285714 mm make an Attic foot, 22 make what Mauss describes as the “pied de Serpouli-Zoab” of 339.42857 mm, 24 make the foot of the Stadium of Laodikeia, 35 make a black cubit of 540 mm, 36 make a Persian cubit of 555.42857 mm, 40 make a Beit-Lehm cubit of 617.42857 mm, 42 make a Chaldean cubit of Tello / Constantinople, 45 make a Delphi foot of 694.2857 mm, 56 make an Apadana Cubit / Vara of Seville / Susa Cubit of 864 mm, 63 make a Tello cubit of 972 mm, 64 make a Religious cubit, 12 000 make an Attic stade of 185 142 m, 14 000 make a Philitarian / Alexandrian stade (600 feet of 360 mm), and 140 000 make an Armenian mile (700 feet of 308.571mm), or 2 160 000 m. We might add to this list that a megalithic yard (as 2.7216 feet) contains 3 x 4⁴ x 7 / 100 fingers of 15.4285714 mm. 

Figure 8: Historical units related to a digit of 15.42857 mm

   Mauss’s "foot of the Stadium of Laodikeia", which is 370.28571 mm long, and is a hundredth part of the stade, sometimes called the "Asian foot" (pied asiatique), could well be equal in length to the cubit mentioned in the Muqaddimah. This text tells us that 4000 such cubits (designated as feet by Mauss) make a mile, of 1 481.142857 m, and that 12 000 such cubits make a parasang, which is then 4 443.42857 m. A geographical degree is 25 parasangs, so 111 085.7142857 m. And with 360 degrees in total, the polar circumference is then 39 990 857.142857 m, about 17 km short of the current estimate.

   If we start from today's estimate for the polar circumference of 40 007.863 km and work back downwards, we would get a cubit 370.443176 mm (14.584377 inches) and a digit of 15.435132 mm (0.60768 inches). This is 0.00656 mm in difference from a digit derived from Mauss’s value of the foot of the stadium of Laodikeia.Twenty digits of 15.435132 mm make a Greek foot of 0.3087026 mm (12.153647 inches), and forty such digits make 9 x 9 x 3 / 10 inches. This digit multiplied by 6 / 5 gives approximately an Egyptian digit, as 18.522159 mm (0.72921885 inches).

  If the parasang is the polar circumference divided by 360 and then by 25, and we can connect it to a historical measure valued at 4 443.42857 m (though this implies a polar circumference closer to 39 990.857 km), then what are the lengths of the subdivisions of the parasang mentioned in the Muqaddimah? There are 12 000 cubits in the parasang, and this has been equated to the foot of the Stadium of Laodikeia or asian foot, as Mauss calls it, of 0.3702857 m (a remen of 14.58 inches). Alternatively if we start with a polar circumference of 40 000 km exactly and use the same process, we obtain  a unit of 0.37037037 metres (14.58333 inches with the 39.375 inch conversion). 

    Each of these cubits is then further divided into 24 fingers and each finger into 6 grains of barley. A twenty-fourth part of the 0.3702857 m unit is 15.42857 mm and a 6th part of that, the barleycorn, is 2.57142857 mm, or 18 / 7 mm. Eight of these barleycorns make a Persian digit of 20.57142857 mm (0.81 inches). Converting to inches with the 39.375 inch metre, the barleycorn of 2.57142857 mm is 0.10125 inches, which is 81/800 inches.

   A mile of 1 481.142857 m is 864 x 12/7 m. The Apadana cubit / vara of Seville / Susa cubit are 864 mm so this mile is 1 000 Apadana cubits / Seville varas / cubits of Susa multiplied by 12 / 7. A Roman pace is 1 481.142857 mm, and a thousand make one of these miles, which corresponds well to the name "mile" meaning a thousand.

   A parasang of 4 443.42857 m is 18 x 12 x 12 x 12 / 7 m. The Delphi foot is 18 mm, according to Mauss, so the parasang is therefore 1 000 x 12 x 12 x 12 / 7 Delphi feet. The fact that multiples of 12 appear not only in the miles associated with celestial bodies (sun and moon) but also in cubits and metres suggests that these ancient systems were not arbitrary. They were designed to serve distinct purposes, reflecting a sophisticated understanding of both the Earth and the cosmos. These relationships challenge the modern notion that such precision in measurement arose only with Enlightenment-era science and encourage us to reconsider the level of sophistication achieved by ancient metrological systems.

   Many traditional systems feature the barley corn, as a standard both of length and of weight. However, confusingly, the barleycorns can be taken as the breadth of grains, or the length of grains, placed end to end. A 14th century English law defined the inch as “three grains of barley, dry and round, placed end to end lengthwise”, so a barley corn is ⅓ of an inch, or 8.4656 mm. In the ancient Indian tradition, as explained in the Brahmanda Purana, 8 Yūkā make 1 Yava (यव), a barleycorn,  8 Yavas make 1 Aṅgula (अङ्गुल), or finger-breadth. Since 1 angula is 0.66 inches, then 1 barleycorn is 0.0825 inches, or 2.0952 mm. The barley corn derived from the foot of the Stadium of Laodikeia according to the system put forward in the Muqaddimah is closer to the Indian barley corn, being 2.57142857 mm. Going by the Brahmanda Purana, 8 barley corns make an angula of 0.66 inches, or 16.7619 mm, also called a sushi in Sumeria. However, if we use the barley corns of 2.57142857 mm, these are too small to make an angula, so there is a discrepancy. However, 8 of these barleycorns of 2.57142857 mm make the Persian digit of 20.57142857 mm, 32 of which make the Persian cubit of 658.2857 mm, etc. The barley corn of 2.0952 mm (0.0825 inches), of which 8 make an angula, can be linked to the barley corn of which 6 make a finger of 15.42857 mm by multiplying the first by 27 / 22.

Jim Alison explains:

   Many of the units recorded by Mauss are linked to the polar circumference through numbers such as 3, 4, 7, 9 and 12, and so when we read them in millimetres or metres, we can see that the figures are often divisions of 7.

      If the ecliptic is divided into 360 degrees, then so must be the polar circumference. The royal Persian foot is given by Mauss as 329.1428 mm. If we take the polar circumference as 40 000 km exactly, and divide it up into 360 parts, then 7 parts, and 1 000 000 000, and multiply by 12⁴, we get a value of 329.142857. This foot is made up of exactly 16 Persian digits of 20.57142857 mm, the petite hachémique is 29 such digits and the grande hachémique 32 digits. Other measures are related by simple fractions to the grande hachémique, as Mauss points out: the cubit of 648 mm is 63/64 of the grande hachémique, the cubit of 540 mm is 5/6 of the grande hachémique. The finger of 15.42857 mm, or which 24 make a foot of the Stadium of Laodikeia or asian foot, can be simply linked to a polar circumference of 40 000 km, multiplying it by 27 and dividing by 7 x 10¹⁰. Working in metres, 40 000 000 x 27 / 70 000 000 000 = 0.01542857. This With 35 of these fingers of 15.42857 mm we get the black cubit of 540 mm, 20 make the Attic foot of the Parthenon, 22 make Mauss’s Pied de Serpouli-Zoab, 30 give the Attic cubit of 462.857 mm. 

Figure 9: Page from Rome de l'Isle’s 1721 Histoire de l'Académie royale des sciences, avec les mémoires de mathématique et de physique. ”The length of a Meridian degree has been determined in Toises du Châtelet of Paris, but it would be more common to have it in Leagues of France, if these Leagues weren’t of a very uncertain size, & which varies a lot. But we can take for the common Leagues, & if we want, average ones, those which fit 25 times in a Meridian degree. They will be 2282 Toises, neglecting a fraction, & will give a semi-diameter of the Earth of 1432 Leagues & plus a semi-League.”

 It is difficult to argue that the earth wasn't accurately measured in the distant past. It's interesting to note that Ibn Khaldun tells us that there were 25 parasangs to the degree., when this is also what de l'Isle tells us about the Lieue de France, in the 18th century: there were 25 to the degree (25 Lieues of 2282 toises du Châtelet per meridian degree).

  We can go back to the table of values given by Mauss, and compare a 25th part of the meridian degree to his units, and to the lieue (league) mentioned by de l'Isle.

   Mauss gives the value of a Tello cubit as 972 mm. Divided by 3 this is 324 mm, which is close to the pied de roi, the French foot. If we take this Tello cubit of 972 mm, it is very close to the modern estimate of the polar circumference of the earth in metres divided by 120 and 7³, suggesting a threefold division by 7 as well as by 12. So starting with the modern estimate for the earth's polar circumference, in metres, 40 007 863 / (120 x 7³) = 972.008333. Or starting with the Tello cubit, we get a polar circumference of 40 007 520 m, about 343 metres difference from the modern estimate. 

 If we start with a polar circumference of 40 007.863 km, then a mean degree measures 111 132.952778 m, a 25th part of the degree measures 4 445.3181111 m, and a 2282th part of this measures 1.94799216 m. A toise was made up of 6 pieds, and a 6th part of 1.94799216 m is 0.32466536 m. This is very close to the actual value of the pied de roi, though this varied over time, and of course de l'Isle's estimate of the length of a degree is also an estimate, and we don't know exactly the length of the toise he talks about. 

Figure 10: Tello pillar, Wikimedia Commons. The Louvre website gives a diameter of 80 cm (https://collections.louvre.fr/en/ark:/53355/cl010163641) but Mauss gives a circumference of 2376 mm (assuming these are the same pillars), which would imply a diameter of 756.305 mm, or 756 mm (75.6 cm). Perhaps the Louvre museum has rounded the value up, thinking the actual measured value to be of no consequence, or perhaps Mauss has measured differently. Mauss gives the dimensions of the Tello pillar bricks as 108 mm,  216 mm, 540mm, 648mm and 756mm (Mauss p 95). Mauss remarks that a diameter of 756 mm corresponds to a circumference of 2 x 1188 mm, or 2 aunes de Paris or Marseille, with pi as 22 / 7 (Mauss p 101). 

     Ptolemy accorded 500 stades to a degree of latitude. In ancient geography, a degree refers to one 360th part of a circle, or in this case, one 360th part of the Earth's full circumference. Each degree represents the distance from one line of latitude to the next, approximately 111 km in modern measurements. Mauss writes:

   According to Mauss, Ptolemy's stade (if we assume he was using the 'Asian stade' or stade of the stadium of Laodikeia) yielded a length of 111,085.714 metres per degree. This is remarkably close to the modern average measurement of a degree along the meridian, which is 111,111.111 metres. The difference is a mere 25 metres, an impressively small margin. 

Figure 11: Stadium of Laodicea, Photo by Brcksprt, Wikimedia Commons

   What this implies is that Ptolemy's division of the Earth into 500 stades per degree reflects a highly accurate understanding of the Earth's dimensions. Even though he worked within a different system of measurement, Ptolemy’s stade of approximately 222.17 metres per unit aligns closely with the metric system's approach. By dividing the polar circumference into 360 degrees and assigning 500 stades per degree, Ptolemy effectively used a system that, though different from modern units, achieved a high degree of precision. By comparison, with the modern value for the polar circumference, a 500th part of a mean degree is 222.26389 metres.

   This remarkable closeness between the ancient stade and modern measurements suggests that ancient geographers had a sophisticated understanding of the Earth's size. They may not have used the metric system, but their methods of dividing the polar circumference were remarkably accurate, reflecting advanced metrological practices that would later converge with modern scientific approaches.

   The irony here is that both the metre and the toise/pied de roi system were derived from remarkably accurate measurements of the Earth's polar circumference, yet belonged to two different approaches to dividing up the Earth. While the metre was part of a new, rational system based on the polar circumference, the old French system, which included the pied de roi, was part of a broader very old system. This would probably once have been close to universal, but through a sort of cultural entropy, in the aftermath of the collapse of the Roman Empire, for example, had become broken up over time. Despite their differing intentions, both systems reflect an impressive, shared understanding of the Earth's dimensions.

   What's particularly interesting is the contrasting mathematical logic behind these systems. The old systems, like those using the pied de roi, were based on divisions by numbers like 7 and 12, numbers with deep cultural and symbolic significance. In contrast, the modern metric system relies on the more simplified and decimal-friendly format, 10, dividing a quarter of the circumference decimally. Yet despite these philosophical differences, both systems manage to express highly accurate measurements of the Earth's dimensions.

   The Tello cubit of 972 mm, derived from ancient systems, is strikingly close to the modern measurement of Earth's polar circumference when divided by 120 and 7³ (40 007 863 / (120 x 7³) = 972.008 mm). This suggests that ancient systems incorporated divisions based on numbers like 7 and 12. If we start from the Tello cubit, and multiply it by 120 and 7 x 7 x 7, we can derive a polar circumference of 40,007,520 metres—only 343 metres less than the modern estimate. This connection shows that ancient cultures likely used complex divisions based on sacred numbers like 7 and 12 to express highly accurate measurements. The old French pied de roi was around the 0.324 metre mark, as it varied over time. However, three feet of 0.324 metres exactly make a Tello cubit. 

   A key difference between the ancient  and modern systems is the underlying structure, based on numbers like 7 and 12 in the old, and 10 in new. The number 10 also applied to the old systems, in that we see ky numbers being expressed in multiples of 10, such as the Philitarian / Alexandrian stade (600 feet of 360 mm) of 216 metres and the Armenian mile (7 feet of 308.571mm) of 2 160 metres. Also, the key units in the ancient system such as the Persian digit of 20.57142857 mm and the digit of  finger of 15.42857 mm, and the unit of 45 mm, relate to the polar circumference both through these key numbers, such as 4, 6, 7, 8, 9, 11, 12, but also 10¹⁰ or 10⁹. The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 all have cultural and cosmological significance. The modern system's logic is functional and mathematically straightforward.

      Prolomey and Ibn Khaldun’s understanding of the Earth’s structure, particularly the division of the planet into seven climatic zones, aligns remarkably well with ancient measurements. The reference to parasangs and cubits provides insight into the level of precision achieved by ancient metrologists. If a parasang consists of 24,000 cubits of 0.185142857 m, and 25 parasangs constitute a geographical degree, this gives a degree of 111,085.7 metres, astonishingly close to the modern estimate of 111,132.95 metres per degree at the equator. Such precision suggests that ancient scholars had a more accurate understanding of Earth’s dimensions than previously thought.

   The cubit, in particular, appears as a recurring unit of measure across various ancient cultures. Ibn Khaldun’s description of a cubit measuring 24 fingers, where each finger is defined as six grains of barley placed end-to-end, provides insight into how even the smallest units were standardised. When comparing this to the Attic foot of 308.57 mm, as documented by Mauss, it becomes clear that these measurements were part of a broader, interconnected system. Dividing the polar circumference into 360 degrees and further into parasangs reveals how closely these ancient measurements align with modern estimates.

Dividing by 7 (or 28?)

   Why divide the northern hemisphere, or the northern quadrant, into 7 parts? This may imply that the entire polar circumference was divided into 28 parts. Dividing by 28 is seen elsewhere in the ancient world. The ecliptic or zodiac was divided into 27 or 28 lunar mansions, from the Middle East to China. In India, for example, Jean-Sylvain Bailly teaches us that:

   This was because the sidereal lunar month is 27.321661 days and can be rounded down to 27 or up to 28. Also, 28 is a perfect number. We see the division by 28 at Giza in particular. For example, the north-west length of the area marked out by the Great Pyramid and the third pyramid is almost exactly 1 000 000 / 28 = 35 714.2857 inches (Petrie: 35 713.2 inches). The side of the Great Pyramid itself can be interpreted as 1 000 / 28 x 254 = 9071.42857 inches (Petrie: 9068.8 inches).

Figure 12: Perfect numbers

   The polar circumference, like the zodiac or ecliptic, may have been divided into 28 parts. This would explain why the section between the equator and a pole would be divided into 28 / 4 = 7 parts.

   It's also possible that each hemisphere was divided into 7 parts, to the north and to the south, in a series of concentric rings round the pole, as opposed to divisions on a polar circumference. Each hemisphere would then reflect the hemisphere of stars above it in some way. The number 7 holds profound significance across various ancient cultures, symbolising completeness, divine order, and cosmic harmony. In many traditions, including Mesopotamian, Greek, and later Abrahamic religions, the number 7 represents the totality of the cosmos, often reflected in the seven visible celestial bodies: the Sun, Moon, and five planets visible to the naked eye. These celestial bodies were believed to govern the fates and rhythms of life on Earth, and their influence was thought to be all-encompassing. The division of the northern hemisphere into seven parts could be seen as a mirror of the heavens, with each section corresponding to one of these celestial entities. A Sumerian incantation goes "an-imin-bi ki-imin-bi" (the heavens are seven, the earths are seven." This division would not only symbolise the unity between the heavens and the Earth but also suggest a deep connection between terrestrial geography and celestial order. Such a system might have been used to encode the belief that the physical world was governed by the same principles that ordered the heavens, reinforcing the idea of a universe that is both interconnected and divinely structured.

   If we associate each of the seven visible celestial bodies (Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn) with one of the seven divisions of the northern hemisphere, they might be arranged from the outermost to the innermost or vice versa, depending on the cultural or symbolic significance given to each body. For example, the Sun could correspond to the outermost division (near the equator) due to its central role in life, while Saturn, often associated with boundaries and limitations, could correspond to the innermost division (closest to the pole). However if we look at mediaeval depictions of this idea, the sun is always between Venus and Mars.

   Avebury, being at latitude 51.428611, almost exactly 90 / 7 x 4 = 51.4285714, would, according to this scheme, be at the boundary between the zones dedicated to the Sun and to Mars. It's difficult to know whether the spaces between the lines or the lines themselves are more significant, but if the location of Avebury is related to a division of the northern hemisphere into seven parts, then it would seem that the lines creating the divisions would have been important.

Figure 13: Celestial planispheres

Figure 14: Celestial planisphere divided into seven concentric circles

   The idea that the Earth's northern hemisphere could be divided into seven parts, each connected to one of the seven visible celestial bodies, is a logical extension of ancient cosmological thought. This system would align with the principle that earthly realms were governed by the same forces that ruled the heavens, creating a unified cosmological and geographical worldview. This connection might have influenced everything from ancient territorial divisions to cultural practices, reflecting the deep integration of astronomy, mythology, and geography in ancient thought.

Figure 15: Division of the northern hemisphere into seven parts, by concentric circles.

Figure 16: Page from “L’église de Saint-Jérémie à Abou-Gosch Observations sur les mesures de l’Antiquité” by C. Mauss, 1892. Here Mauss makes the point that while there were many regional variations, most of the units of measure used in northern Italy, Spain, Egypt and Syria were fractions of the “Grande Hachemique”, the Persian royal cubit, which Mauss estimates as 658.285 mm, equivalent to 25.92 inches (with a 39.375 inch per metre conversion), of 32 digits of 20.5714 mm (0.81 inches). Each of these digits is equivalent to a fraction of the polar circumference: 40 000 km divided by 7 and 10¹⁰ and multiplied by 36. The Perisan royal cubit is the polar circumference divided by 7 and 10¹⁰ and multiplied by 8 x 12 x 12.

Figure 17

   The remarkable consistency in ancient units of measure across vast geographical regions—ranging from the Egyptian cubit to the Persian royal cubit—indicates a shared understanding of metrology among ancient civilisations. This suggests that far from being isolated, these cultures engaged in extensive knowledge exchange, facilitated by trade routes, imperial conquests, and shared astronomical observations. Such a degree of standardisation points to the existence of a proto-metric system that was likely disseminated through a global network of scholars and merchants. This interconnectedness in ancient times challenges the modern view of pre-modern civilisations as fundamentally disconnected and highlights the sophisticated nature of ancient scientific knowledge.

Figure 18: Dividing the polar circumference by 7/36

Dividing by 25 920?

   It’s also possible to think of a division of the polar circumference into 25 920 parts; or, to produce the finger or digit of 15.435 mm (if we start from a 40 007.52 km circumference) or 15.4321 mm (if we start from a 40 000 km circumference), into 2 952 000 000 parts. This is a match for the historical division seen earlier into 360 degrees, then 25 leagues or parasangs, then 12 000 cubits, then 24 fingers or digits.

Figure 19: Dividing the polar circumference into 25 920 parts, according to the number of years in a precessional cycle.

Metre and moon

   The base side of the Great Pyramid can be interpreted as 230.4 metres, which is 12 x 12 x 16 / 10, or as 230.338602 metres, which is 29.53059 x 3 / 2 x 364 / 70 metres, which again shows a division by 7 expressed in metres. The 364 is sometimes given as the number of days in a year, as per the Book of Enoch, and Genesis, because this is exactly 13 months of 28 days, and 10 days more than a lunar year approximated to 354 days. Coincidentally, 230.34 is the number of inches in the height of the King's chamber, as pointed out by Dennis Payne, and so the same lunar associations can be made there, but in inches instead of metres. If this is correct, it might explain why we sometimes come across lunar numbers expressed in metres, for example at Giza. Another way of interpreting the side of the Great Pyramid in terms of metres and the moon is with the synodic orbital period for Mars of 779.94 days (close to 780). With 779.94 / 10, we get 779.94 / 10 x 29.53059 = 230.32088, the value of the base side in metres, equivalent to 9067.75132 inches. Or rounding the Mars period up, we get 780 / 10 x 29.53059 = 230.3386 for the measure in metres, equivalent to 9068.4489 inches (Petrie gives 9068.8 inches). The metre may express lunar cycles in conjunction with other cycles, such as Mars.

Conclusion

   The evidence presented here suggests that the metre, or a unit remarkably close to it, was known and used by ancient civilisations long before its official adoption in the 18th century. This challenges the conventional narrative that modern measurement systems are solely a product of Enlightenment science. Instead, it appears that ancient societies possessed a sophisticated understanding of the Earth’s dimensions, which they encoded in their metrological systems. This revelation invites us to reconsider the technological and scientific capabilities of our ancestors. If the ancients could measure the Earth with such precision, what other knowledge might they have possessed that has yet to be fully appreciated?

   Ancient measurements were often based on harmonic proportions, reflecting the belief that the universe was constructed according to divine or mathematical laws. The inch is similarly connected to the Earth's equatorial circumference, not just spatially but also temporally. As the Earth rotates, the inch can be seen as a measure that links time (the rotation of the Earth) with space (the distance travelled at the equator). The fact that 365.256363 sidereal days multiplied by 4,320,000 gives a result so close to the equatorial circumference in inches suggests a deep, ancient understanding of the Earth’s dimensions. If we approach this evidence without the preconceived notion that the metre is a modern invention. By doing so, we can recognise that both the metre and the inch are part of a unified system of measurement that has existed for many centuries, and goes back to antiquity. The metre and the inch are not independent developments but are rather two parts of the same ancient metrological system. This system was designed with an understanding of both the Earth’s dimensions and the relationship between time and space, as evidenced by the way the inch relates to the Earth’s rotation and the metre to its meridian circumference.

   The metrological consistency observed across different ancient cultures is evidence of a global network of knowledge that transcended political and geographical boundaries. This network likely facilitated the transmission of scientific and practical knowledge, including measurement systems, helping to create a more unified understanding of the world. The enduring influence of these ancient measurement systems is still evident today, as modern units like the metre, inch and foot, can be seen as the culmination of thousands of years of metrological development. This calls for a re-evaluation of how we view ancient civilisations and their capabilities.

   The evidence presented in this essay suggests that ancient civilisations had a far more sophisticated understanding of the Earth's dimensions than modern scholarship often credits them with. The precision seen in their metrological systems, particularly with units like the cubit, parasang, and pied de roi, reveals a shared, interconnected knowledge base that spanned continents and cultures. This global network of scientific knowledge likely transcended political and geographical boundaries, demonstrating that ancient societies were not isolated in their intellectual pursuits.

   Moreover, the recurring division of the Earth's circumference, particularly into multiples of 7 and 28, points to a deep symbolic connection between metrology and cosmology. The alignment of geographical zones with celestial bodies, as well as the intricate mathematical relationships encoded in ancient units of measurement, reflects a worldview in which the heavens and Earth were intimately linked.

   These findings challenge the conventional narrative that modern measurement systems, such as the metre, are purely products of Enlightenment science. Instead, they suggest that ancient societies possessed a profound understanding of both terrestrial and celestial dimensions, laying the groundwork for modern systems long before their official adoption. By recognising this continuity, we gain a deeper appreciation for the intellectual achievements of our ancestors and the enduring legacy of their metrological systems. This calls for a re-examination of how we perceive ancient civilisations, urging us to appreciate the vast scope of their scientific and technological capabilities, which continue to influence the world today.

    Petrie's observation about the early decimal system of Germany and Britain being remarkably close to the modern metric system is highly relevant to the arguments presented in this essay. His statement emphasises that ancient and early measurement systems were not only sophisticated but, in some cases, were already aligned with the principles of the modern metric system. Petrie's lament that the 12-inch foot system replaced these earlier decimal measures, leading to their suppression through legal statutes, aligns with the essay's argument that ancient civilisations had a deep and accurate understanding of the Earth's dimensions.

   To return to the opening quotation, Petrie's insight suggests that the transition to modern systems of measurement such as the metre was less about innovation and more about a shift in cultural or political priorities. If the early decimal systems of measurement had persisted, societies would have needed minimal adjustment to align with the metric system. This reinforces the essay's central argument: that ancient metrological systems, including those described by Ibn Khaldun and others, were not primitive or inaccurate but were part of a continuous, global understanding of the Earth's dimensions that extended far into the past.

   Petrie's comment also underscores how modern systems, such as the metre, may have roots in much older measurement traditions, thus supporting the idea that the metre was not a purely modern invention. As John Neal suggests, we might even call it by one of its ancient names, or as a unit in ratio with various ancient ones. Rather, it is the culmination of an ancient and evolving understanding of measurement, one that was disrupted but never fully eradicated by changes in political and legal systems. This makes Petrie’s point an important reminder of the sophistication of early systems and how close they were to what we use today, reinforcing the need to re-evaluate the scientific and metrological capabilities of ancient cultures.

Appendix

   Below is a list of historical values of the pied de roi, compiled from various sources. (see Charlemagne's Foot). The value closest to 0.324 m I could find is Matthew Raper’s, in 1760, converted to metres. However, by the late 18th century, when the French king lost his head and the people wanted nothing more to do with his foot, the pied de roi was established as 0.32488 m. If we divide the polar circumference by 360, to get the mean degree, and then by 500, and 400, and 12, and multiply by 7, the result is 0.324135 metres with the current estimate for the circumference, and 0.324074 with a 40 000 km circumference. The pied de roi is approximately equivalent to the polar circumference x 7 / 864 000 000, and to 21 fingers of 15.42857 mm.

.

Bibliography

Alison, Jim. “Sumerian Metrology.” March 23, 2024, 11:36 PM. https://grahamhancock.com/phorum/read.php?1,1333388,1334253#msg-1334253.

Aristotle. On the Heavens. Translated by J. L. Stocks, Book II, Chapter 14, 384–322 BC.

Bailly, Jean-Sylvain. Histoire de l'astronomie ancienne, depuis son origine jusqu'à l'établissement de l'École d'Alexandrie. Google Books. https://play.google.com/books/reader?id=wH9YAAAAcAAJ&pg=GBS.PA108.

Berriman, A.E. Historical Metrology. JM Dent & Sons, 1953.

De l'Isle, Romé. Histoire de l'Académie royale des sciences, avec les mémoires de mathématique et de physique, 1721.

Goyal, Dr. M. R. “Units of Length Measurement and the Speed of Light in Ancient India.” April 18, 2020.

Heath, Richard. The Origins of Megalithic Astronomy as Found at Le Manio. Academia.edu. https://www.academia.edu/5384545/The_Origins_of_Megalithic_Astronomy_as_found_at_Le_Manio.

Horowitz, Wayne. Mesopotamian Cosmic Geography. Eisenbrauns, 1998.

Lubicz, Schwaller de. The Temple of Man. 1957.

Mauss, C. “L’Église de Saint-Jérémie à Abou-Gosch Observations sur plusieurs mesures de l’antiquité (Suite).” Revue Archéologique, vol. 20, 1892, pp. 80–130. JSTOR, http://www.jstor.org/stable/41747027.

Neal, John. “All Done With Mirrors (a kind of apology).” Academia.edu. https://www.academia.edu/117813342/All_Done_With_Mirrors_a_kind_of_apology.

Neal, John. The Measures and Numbers of the Temple, 2024. Academia.edu. https://www.academia.edu/123098066/The_Measures_and_Numbers_of_the_Temple.

Newman, Hugh. Earth Grids: The Secret Patterns of Gaia's Sacred Sites. Wooden Books, 2008.

Pappas, Stephanie. “The Sun May Be Smaller Than We Thought.” Live Science, November 12, 2023. https://www.livescience.com/space/the-sun/the-sun-may-be-smaller-than-we-thought.

Payne, Dennis. The Full Giza Plan: It’s Always Been About the Moon. Academia.edu. https://www.academia.edu/122472999/The_Full_Giza_Plan_its_always_been_about_the_Moon_.

Ptolemy. The Geography. Translation of the Geographia and dedication of the 1460 ms. ed. (Codex Ebnerianus) by Donnus Nicholas [Nicolaus] Germanus. Archive.org. https://archive.org/details/geography0000ptol/page/n1/mode/2up.

Petrie, M.W. Flinders. “Weights and Measures.” Encyclopædia Britannica, 1911. Encyclopædia Britannica/Weights and Measures. Wikisource.

West, John Anthony. The Serpent in the Sky. Quest Books, U.S., 1979; Subsequent edition, 1993.

Notes

1.  Flinders Petrie, M.W. 1911, "Weights and Measures", Encyclopædia Britannica 1911 Encyclopædia Britannica/Weights and Measures - Wikisource, the free online library

2. “The sun may be smaller than we thought” by Stephanie Pappas published November 12, 2023, https://www.livescience.com/space/the-sun/the-sun-may-be-smaller-than-we-thought

3. Neal, John, 2024, The Measures and Numbers of the Temple, https://www.academia.edu/123098066/The_Measures_and_Numbers_of_the_Temple

4. According to Dr M. R. Goyal in “Units of Length Measurement and the Speed of Light in Ancient India“, April 18 2020, “Taking an Indus Inch i.e. 5 divisions of the Mohenjo-daro scale to be equal to 2 Angula, the precise length of an Angula works out to be 16.764mm (0.66 inches).

   A Dhanusha of 96 Angulas = 96 × 16.764mm = 1.609344m (1) A Dhanusha of 108 Angulas = 108 × 16.764mm = 1.810512m (2) A Yojana = 8000 Dhanushas(of 108 Angulas each) (3)

   
   

   = 8000 × 1.810512m = 14.484096km (4) Further, 14.484096km = 9 miles,(exactly!). (5) Also, 1000 Dhanushas of 96 Angulas each = 1 mile (6) Interestingly, when we look into the history of the unit mile, we find that the word mile is derived from mille, which means a thousand.” If the equatorial radius of the moon is 1080 miles, it is also 120 yojanas of 9 miles. Similarly, if the radius of the sun is 432 000 miles, it is 72 000 yojanas.

5. See the work of Richard Heath, in particular https://www.academia.edu/5384545/The_Origins_of_Megalithic_Astronomy_as_found_at_Le_Manio

6. See the work of Dennis Payne, for example https://www.academia.edu/122472999/The_Full_Giza_Plan_its_always_been_about_the_Moon_

7. Mauss, C. “L’ÉGLISE DE SAINT-JÉRÉMIE A ABOU-GOSCH OBSERVATIONS SUR                            PLUSIEURS MESURES DE L’ANTIQUITÉ (Suite).” Revue Archéologique, vol. 20, 1892, pp. 80–130. JSTOR, http://www.jstor.org/stable/41747027

8.  Ibid p 114 Translation from the French: Google Translate

9. Ibid p 114

10. Aristotle, 384-322 BC, On the Heavens, Translated by J. L. Stocks, Book II, Chapter 14

11. Schwaller de Lubicz, The Temple of Man, 1957 and John Anthony West, The Serpent in the Sky, 1979, Quest Books,U.S.; Subsequent edition 1993

12. Weights and Measures by William Matthew Flinders Petrie and Henry James Chaney

    1911 Encyclopædia Britannica, Volume 28, 

     https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Weights_and_Measures

13.  Ibid.

14. Neal, John, “All Done With Mirrors (a kind of apology)”, https://www.academia.edu/117813342/All_Done_With_Mirrors_a_kind_of_apology

15.  Ibid. p 81..

16. Ibid. p 81

17. Ibid. p 103

18. Ibid. p 81

19. Neal, John, “All Done With Mirrors (a kind of apology)”, https://www.academia.edu/117813342/All_Done_With_Mirrors_a_kind_of_apology

20. Wikipedia in fact gives 864 575.88 miles for the sun but the moon's equatorial radius as 1 080 miles corresponds exactly to the modern estimate, Wikipedia giving 1 080.00527 miles, though expressed in km.

21. Newman, Hugh, 2008, Earth Grids: The Secret Patterns of Gaia's Sacred Sites, Wooden Books

22.  Ptolomy, 2nd century, The Geography, Translation of the Geographia and dedication of the 1460 ms. ed. (Codex Ebnerianus) prepared by Donnus Nicholas [Nicolaus] Germanus, https://archive.org/details/geography0000ptol/page/n1/mode/2up

23. Flinders Petrie, M.W. 1911, "Weights and Measures", Encyclopædia Britannica 1911 Encyclopædia Britannica/Weights and Measures - Wikisource, the free online library

24. Also known as an Egyptian remen, which, multiplied by the square root of two, gives a value for the Egyptian royal cubit. Depending on what value is used exactly for the remen and for the square root of two, this would result in an Egyptian royal cubit of 20.61666 inches (0.3702857 metres multiplied by 39.3700787402, to convert to inches, and the value for √2 given by a calculator is 20.61665584), or 20.6192329 inches (0.3702857 inches multiplied by 39.375, to convert to inches, and multiplied by √2 is 20.61923294), or 20.620285 (the same process as before but with an approximation for √2 of 99 / 70).

25. From the Brahmanda Purana https://www.wisdomlib.org/hinduism/book/the-brahmanda-

    purana/d/doc362935.html

26. Historical Metrology, A.E. Berriman, 1953, JM Dent & Sons, London.

27. Jim Alison, “Sumerian Metrology”, March 23, 2024 11:36PM, https://grahamhancock.com/phorum/read.php?1,1333388,1334253#msg-1334253

28. De l'Isle, Romé, 1721, Histoire de l'Académie royale des sciences, avec les mémoires de mathématique et de physique

29. Mauss, C. “L’ÉGLISE DE SAINT-JÉRÉMIE A ABOU-GOSCH OBSERVATIONS SUR                            PLUSIEURS MESURES DE L’ANTIQUITÉ (Suite).” Revue Archéologique, vol.

    20, 1892, pp. 80–130. P 112. JSTOR, http://www.jstor.org/stable/41747027

30. See Appendix for a table of values for the pied de roi

31. Ibid. p 114

32. Bailly, Jean-Sylvain, Histoire de l'astronomie ancienne, depuis son origine jusqu'à l'établissement de l'École d'Alexandrie, p 109 https://play.google.com/books/reader?id=wH9YAAAAcAAJ&pg=GBS.PA108

33. Horowitz, Wayne (1998). Mesopotamian Cosmic Geography. Eisenbrauns. p. 208

34.  Personal correspondence

35. Raper, Matthew. “An Enquiry into the Measure of the Roman Foot; By Matthew Raper, Esq; F. R. S.” Philosophical Transactions (1683-1775), vol. 51, 1759, pp. 774–823. JSTOR, http://www.jstor.org/stable/105415.