Sacred Number

Prime Numbers in Metrology

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.

To analyse a number for its primal identity, simply remove the decimal place by dividing by powers of 2 and 5. 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.

Since metrology is our subject, and since an example is definitely required, we will analyse the Greek Foot in its Standard Canonical and Standard Geographical Values [as in John Neal's All Done With Mirrors], please see my Introduction to the Metrology of Neal and Michell, online here and printed in Appendix 2 of Sacred Number. First, how do you work out the primes in a number?

Primal Therapy for Numbers

Whilst spreadsheets and programs can increase productivity, it is useful with smaller primes to follow the calculator method.

1. Remove Decimals: Use the reciprocal powers of 10, e.g. 1.008 becoming 1008/ 1000
2. 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 for list of primes and web references to more]

Therefore, the Standard Canonical Greek Foot of 1.008 feet is uniquely

2.3².7/5³

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. 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 from using it.