above: Catching birds on the Nile Delta compared with the catching of different prime numbers by measuring phenomena. (from The Temple in Man by Schwaller de Lubitz, illustration by Lucy Lamy.)
Plato expresses the highest form of government as being by philosopher kings, whilst his preferred form of philosophy is Pythagorean, based upon pure number. Such a philosophy discovers the characters different numbers have within the definite field of number itself. This seems out of character with real power because we do not know of such a form a government and we appear to have lost the form of philosophy upon which it can be based. By a seeming miracle, this philosophy appears to be reconstituting itself again.
Recent discoveries about Plato demonstrate that once the ancient world knew the power of number, as a philosophy, the notion arose that a high form of government was possible through ordering the human world as the cosmic world had been. This was done by choosing units of measure that (a) showed the Earth (and Moon) to be a numerical artefact by (b) bringing out important numerical coincidences present within the Earth’s dimensions.
The Perfect Ruler was placed within the dimensions of the Earth by using the relevant units in ancient monuments that repeated the pattern, some having survived. To understand their message required inspiration, and the central core required the persistence of the John MichellWriter, sacred geometer, metrologist and mystic: his books were highly influential in defining the form of the British earth mysteries movement., a traditionalist who in his Ancient MetrologyThe application of units of length to problems of measurement, design, comparison or calculation. sketches out its basic scheme, his Dimensions of Paradise showing how this applies to ancient buildings (see bibliography below).
But to understand the majesty of ancient metrological thought, one needs to focus on what numbers are and their uniqueness relative to each other. Thus, one needs to work with prime numbers, since they are the roots of the numerical field.
Working with Prime Numbers
Any number with limited “significant digits” can be and should be expressed as a product of positive and negative powers of the prime numbers that make it up. For example, 23.413 and 234130 can both be expressed as an integer, 23413, multiplied or divided by powers of ten.
Primes are unique and any number must be prime itself or be the product of more than one prime.
The first three primes are those most commonly encountered: 2, 3 and 5. The products of 2 and 3 give 6, 12 and the perfect “sexidecimals” like 60, 360 when combined with 2 and 5, i.e. 10. The ten based arithmetic we use implicitly uses 2 and 5, with negative powers applying to fractional parts. The primes {2 3 5} are called harmonic because the intervals of western music use them.
To analyse a number for its primal identity, simply remove the decimal place by multiplying by powers of ten (10 being 2 times 5, of base-10, the decimal system. We should note that, in general, metrological measures have a limited number of non-repeating significant digits and that the complexity of their fractional parts is entirely due to the hidden action of prime numbers seen within a decimal, base 10, system of notation. (Note also that, in later books, I increasingly revert to rational fractions, with integer top and bottom, since early ancients did not have base-10 or position notation, or zero, since call came from ONE)
Since metrology is our subject, and since an example is definitely required, we will analyse the tables of Greek Measure given in Michell’s Ancient Metrology, in both their Northern and Tropical Values.
Primal Therapy for Numbers
Whilst spreadsheets and programs can increase productivity, it is useful with smaller primes to follow the modern calculator method.
- Remove Decimals: Use the reciprocal powers of 10, e.g. 1.008 becoming 1008/ 1000
- Divide by Successive Primes: Start with the lowest primes, and when the result yields a fractional part, go back and move onto the next prime in order, as in 2, 3, 5, 7, 11, 13, 17, etc [see Appendix A posting for list of primes and web references to more]
The 1.008 becomes 1008 over 1000
| Prime | 0 | 1 | 2 | 3 | 4 |
| divide by 2 | 1008 >>> | 504 >>> | 252 >>> | 126 >>> | 63 v |
| divide by 3 | 63 >>> | 21 >>> | 7 | A prime ! |
| 1008 = | 24.32.7 |
| 1000 = | 23.53 (103) |
Therefore, the “shorter, tropical, or southern) Greek Foot is uniquely:
| 1008 over | which is | 2.32.7 (126) over |
| 1000 | 53 (125) |
It is soon noticed that when there is a decimal fraction, the numerator has powers of 2 that will simply cancel out with the denominator. Thus the numerator integer is long because of doubling invoked by the decimal system itself. The same is happening with positive powers of ten too, so that our base 10 system of notation is making the metrological values appear ludicrously accurate in their number of significant places, 1/7 giving a recurring “.142857”. However, it is only the prime powers that really count and are, in every case, simple. We can hazard a guess that the ancients used prime notation and certainly that any future metrology will benefit, as I have, from seeing numbers from their prime factors.
In the next part, the relationship of the English footThe standard prehistoric foot (of 12 inches) representing a unity from which all other foot measures came to be formed, as rational fractions of the foot, a fact hidden within our historical metrology [Neal, 2000]. as standing at the root of ancient metrological measures. This was discovered by John Neal through realizing that Michell’s southern and northern measures had a different relationship to pure fractions of the foot, these fractions being the root for the variation of each module, just as the foot is the root for the fractional root feet which define each module.
Books about Ancient Metrology
- Berriman, A. E. Historical Metrology. London: J. M. Dent and Sons, 1953.
- Heath, Robin, and John Michell. Lost Science of Measuring the Earth: Discovering the Sacred Geometry of the Ancients. Kempton, Ill.: Adventures Unlimited Press, 2006. Reprint edition of The Measure of Albion.
- Heath, Richard. Sacred Geometry: Language of the Angels. Vermont: Inner Traditions 2022.
- Michell, John. Ancient Metrology. Bristol, England: Pentacle Press, 1981.
- Neal, John. All Done with Mirrors. London: Secret Academy, 2000.
- —-. Ancient Metrology. Vol. 1, A Numerical Code—Metrological Continuity in Neolithic, Bronze, and Iron Age Europe. Glastonbury, England: Squeeze, 2016 – read 1.6 Pior π: The constant ratio of a circle's circumference to its diameter, approximately equal to 3.14159, in ancient times approximated by rational approximations such as 22/7. and the World.
- —-. Ancient Metrology. Vol. 2, The Geographic Correlation—Arabian, Egyptian, and Chinese Metrology. Glastonbury, England: Squeeze, 2017.
- —-. Ancient Metrology, Vol. 3, The Worldwide Diffusion – Ancient Egyptian, and American Metrology. The Squeeze Press: 2024.
- Petri, W. M. Flinders. Inductive Metrology. 1877. Reprint, Cambridge: Cambridge University Press, 2013.