Source of Measure

After many years of studying the metrology of ancient monuments around the world, we have recovered what we consider to be significant mathematical correlations between the dimensions geometry, and geographic locations of many of the great sites of antiquity.

 The following article is an encapsulation of the framework we presently regard as the Canon of Measure, the basic tool of decoding the monuments. The Canon unifies Time, Distance and Number with the dynamics of Nature. The far reaching implications of the framework from which the Canon is derived are beyond the scope of this brief presentation, however the authors welcome further inquiry into the potentials of its application in many disciplines: art, architecture, ancient literature, and the physical sciences as well.

From all the legends since the days of yore
Saturn, old Chronos, will tell us more.
The measure in the cadence beat
in sound and light makes all compleat!
Saturn, source of measure.

— Bernard Pietsch, August 15, 1997

Saturn, Source of Measure
Of all the planets in the solar system, Saturn is the most rigorous, the most regular and the most stable in its orbit. Its path exhibits the least deviation and is able to absorb the perturbations and disturbances of space more than any other body in the solar system. Saturn is imperturbable.

Also known as Kronos, Saturn is the Time Keeper of the solar family. Saturn's orbital performance provides a dependable gauge against which Earth's fluctuations in space can be observed, for only against a reliable standard can deviation, development, growth, or decline be measured. From our position on Earth, when it appears that Saturn is off schedule, so to speak, we can be fairly certain that it is we who are off. Saturn acts as a good mirror for planet Earth's capricious dance through space.

As we might suspect, Saturn dramatically demonstrates the pervasiveness of the Golden Proportion in our solar system. Known as Phi, 1.618122977 or .618, the Golden Proportion is the framework origin of all Nature. Though only an abstraction, it is through comparison with this mean, that we establish the individuality of any natural event or living geometry. The identity of a plant for example, is recognizable by its individual adaptation to or departure from the Golden Mean—Nature's guarantee of individuality within the law.

Numerically, the Golden Number is expressed as the minutes in Saturn's rotational day, 618. Geometrically it is exemplified on a planetary level by the conjunction period of Saturn and Jupiter. Every twenty years or so, Saturn conjuncts with Jupiter at the phi point or .618 mark of its orbit. In other words, when Jupiter completes one revolution around the Sun plus .618 of its next 360 orbit, it is closely aligned or conjunct with Saturn. From Earth we see Jupiter and Saturn together in the heavens. After twenty more years we will again see them close in the sky but advanced about 222+ degrees or the phi proportion of the orbital circuit of the heavens.

Sacred and Phenomenal Measures
The essentials of the measurement system we are about to unfold could be derived from close observation of any natural event or structure. But our ringed celestial neighbor Saturn is a particularly eloquent model. As a planetary resource it sets the standard of timing for the solar system. From Saturn we will build the system of measures we refer to as the Canon of Measure. (See previous references on website.)

As you can see, the Canon is formulated in perfect units, yet perfect units are not perceivable in the natural world. Like the Golden Number, the Canon is an abstraction against which the physical world can be measured. For example, number concepts like the mean solar day of 1440 minutes, the year of 365 1/4 days, the lunar year of 354 days etc., are average periods. In reality the lengths of these periods vary slightly from day to day and year to year. But without the mean as concept, it would be difficult to establish just how much any one day or any one year does deviate.

Just how the Canon of Measure was transmitted historically,we cannot say. But we can always recover the Canon by going to the works themselves. The works are the evidence: temples, tombs, monuments and other sacred art forms are the repository of the concepts, and they are available to all.

Besides architectural remnants, some ancient literature also conveys sacred measures. Often the form is illusive and indirect. Herodotus for example, 4th Century B.C. Greek historian, exhibits an elaborate facility with words which is at times both circuitous and vexing. In his description of the Lake Moeris in section 149 of Book II The History, we find a coded reference to Saturn's function as the foundation of measure. Herodotus tells us that Lake Moeris, "a work even more astonishing than the Labyrinths," was sixty shones or 3600 furlongs in circumference. After his description of the Lake, Herodotus assigns numerical values to the furlong, the cubit, and the palm. (These figures may have been corrupted in translation, or perhaps Herodotus is trifling with us as he rarely gives significant information directly.)

Using the conventional or phenomenal unit of a furlong, 660 feet, the figure of 3600 furlongs is unengaging. Herodotus' intended communication becomes transparent when the Canon furlong of 657.27 feet is invoked. The numbers become instantly significant when it is seen that the Lake Moeris is a veiled reference to Saturn. The feet in 3600 Canon furlongs divided by ten is equal to the number of miles in Saturn's circumference: 236,617.2 miles. This figure is the numerical basis for developing a system of Earth measures relative to Saturn and its performance. We'll be seeing it again shortly.

The History is filled with literary absurdities and ruse which double as vehicles for coded information. Many of the keys to unveiling Canon values are given right in the language of his accounts, especially in his various and lengthy enumerations. The phrases "well worthy of notice" or "very worthy of mention" or "well deserves to be described" alert the reader to pay close attention to what is about to follow. Directions for manipulating the figures given are often inferred in such words as "subterranean passage," "ditch," or "tunnel" which can mean take the reciprocal of the number just given. The use of the word "generation" refers to the use of multiplication. "Round about" or "all around" indicates use of the circle as degrees or fractions thereof. A phrase concerning a certain number of "days journey" suggests that the total number of hours or minutes during that period may be a significant key figure.

Sacred measures are hidden only in the sense of being obscured by the filter of phenomenal or local observation. They are founded on that which is beyond mere appearance. Because they are relative to a larger framework than that which is visible here on Earth we sometimes refer to Cannon measures as cosmic values.

One of the keys to the domain of the cosmic is represented by the "K" symbol. K represents the ratio with which we part the veil. From the phenomenal world we enter the cosmic realm—a dimension where Time, Distance, Velocity, Number, and Geometry become co-in-ci-dent with one another, where one is an expression of all, where everything is in one thing, and where the law "as above, so below" becomes observable. Here the application and utility of Number in all its forms transcend the limitations imposed upon it by ordinary logic. Here, Number can become Time, distance, angle, ratio, logarithm. We have but to invoke the magic inherent in Number, and all is made available.

K is the number 1.01430555. With it, the first measures to be unveiled are those of Time. The ancients understood the intimate and inseparable relationship of Time with all dimensions. (With K we will reveal the legendary "harmony of the spheres." But first some groundwork must be laid.)

For a number of important reasons we adopt the solar year indicated by the base of Cheops Pyramid as the value 365.15 days which is 36,515 inches around the perimeter of the base. This number divided by K produces the Sacred or Cosmic Year of 360 days. The same length of time is involved but the relationship of the year to the circle of 360 is clearly established. From this ancient Sacred Year we derive the following units:

360 Days
525816 Minutes
8763.6 Hours
24.34333 Hours
1460.6 Minutes
87636 Seconds

The derivation of the Sacred Day of 24 hours 20 minutes and 36 seconds is not only a mathematical construction. This is also the day (mean cosmic) responded to by plants and organisms. These circadian rhythms tend to be about 20+ minutes longer than the mean solar day of 24 hours; biological rhythms in humans as well seem to follow this cycle. Also notice the number of minutes in the Cosmic Year: 525816. Dividing this by 100 renders the number for the feet in the Canon Mile. The mile has its origin in sacred time.

Equatorial Earth Measures
Derived from the Circumference of Saturn
How are linear units of Earth measure derived from Saturn? Each unit as standard will reflect some connection with Saturn, and because they are commensurate with each other, all equatorial Earth measures can be derived, from just two primary units:

    The number of feet to the ancient Canon mile, 5258.16, and The number of Canon miles in the circumference of the Earth as 25,000.

(The number of miles in the Earth's equator at 25,000 is taken from the Sacred Cubit of 25 inches.) (Clarke Spheroid: 24,901.55 miles @ 5280 feet/mile.)

We begin with the primary unit for measuring the Earth—the second of arc at the Equator. We again look to Saturn for the length of this unit. Saturn's daily rotational period is 10 hours 14 minutes and 35 seconds. Expressed decimally it is the number 10.1430555. Multiply this by 10 to arrive at 101.430555. Taken as feet, we now have the number of feet to the second of arc on the Earth's equator. Notice K within the number?

If we allow the testimony of Herodotus that there were "eight gods who existed before the rest," and that these eight were the gods of Measure, each is represented by one eighth of the circle or 45. Divide the foundation of measure, Saturn's circumference 236617.2 by 45 and we arrive at the ancient value for the number of feet in the Canon mile.

236617.2 / 45 = 5258.16 feet

(Recall that this number, 5258.16 times 100 is also the same as the minutes in the Cosmic Year.)

Using the framework of the 360 circle of 1,296,000 seconds or 21,600 minutes of arc, the number of feet to the second of arc (101.430555) and the number of feet to the Canon mile (5258.16), we can now develop all the Earth Equatorial units:

CIRCUMFERENCE (360 degrees) 
25,000 miles
40,000 kilometers
200,000 furlongs
131,454,000 feet
69.4444444 miles
111.111111 kilometers
555.555555 furlongs
365150 feet
ONE MINUTE OF ARC: 6085.833 feet
ONE SECOND OF ARC: 101.430555 feet or 1217.1666 inches

Canon units of measure are not created, they are derived, from Time. A period of time is also used to represent a unit of length, e.g. 5258.16 feet to the mile has the same number as the minutes in the Canon Year: 525816, a synchronicity which encourages the observation—the mile is inextricably linked to Time.

By juxtaposing distance with time, yet another unit of measure is generated by Saturn's timing—the Canon Meter. Divide the circumference of Saturn, 236617.2 by the number which is also the number of minutes in Earth's mean solar day, 1440, divide by 100, and the result is exactly one-half the measure we identify as the Canon Meter:

236617.2 1440 = 164.3175 x 2 = 3.28635 feet in 1 Canon Meter 100

There are 39.4362 inches in the Canon meter.

This Canon metric value is commensurate with the duodecimal system. When invoked, Canon metrics expose relationships not otherwise apparent. In an almost alchemical fashion, the precipitate of the two systems exceeds the limitations of either. Ideally, the two systems work together and need not be a source of contention. Thomas Jefferson was intuitively correct in resisting adoption of the French meter in the United States. He recognized the importance of endorsing a truly commensurate figure which would unify time, space, and matter. He discerned that the French system did not fulfill this requirement.

ONE CANON METER = 3.28635 feet

39.4362 inches

        ----------- = .0253574127 

.0253574127 x 100 =2.5374127cm/inch

ONE CANON MILE = 1600 Canon Meters

The ancient measure of the Canon Furlong is also recognizable on Saturn as one degree of its circumference in miles, expressed on Earth in feet as:

236617.2 / 360 = 657.27 This number is now taken as feet to the Canon furlong.

The Canon furlong is exactly 200 meters or 1/8th of a Canon Mile. The furlong times 20,000 it is the number of feet in the circumference of the Earth

657.27 x 20,000 = 131,454,000 feet on the Equator.

As shown, the figure 101430555 has a number of transformations and applications. As it is the multiplier which changes the number of seconds in the circle into the number of CANON feet on the Equator:

1,296.000 x 1.01430555 = 131,454,000 feet

As a divisor it transforms the Sacred Year into the Lunar Year:

360 / 1.01430555 = 354.9226347 days

As 101.430555 it is the number of feet to the second of arc on the Equator.

As 10.1430555 it is the hours in Saturn's day. This day is the period of our "phenomenal"observation. The Canon day for Saturn is 10.3 hours, or 618 minutes.

These various manifestations demonstrate the sychronistic aspects of the Canon system. One number can have different levels. The equatorial second of arc 101.430555 feet for example, is in a sense the first Earth measure. It also embodies what we might term the last measure—the rate of the precession of the equinoxes.

The rate of precession is a finely tuned figure, computed after all the motions, variations, and impressions of all the planets and masses in the solar system have been calculated. The rate of precession will always vary, but it averages to approximately 50.9 seconds of arc per year, also recognizable as 1/2 of .

101.430555 = 50.7152+/- seconds of arc per year.

The Canon value for annual precession is 50.90017909 seconds of arc.

If measures, though abstractions, are based on relevant frequencies or events occurring in the universe, they will be inherently related to one another. The rhythms and cycles of the cosmos abide in all of Nature, whether, mineral, vegetable or animal. The planets resonate in the physiology of the human body.

Because humans evolved in a framework affected by these vibratory rates—diurnal rotations, lunar phases, revolutions around the Sun etc., it is reasonable to infer that the spectrum of these various vibrational frequencies would be designed into what humans have become both as form and process. Mankind is, as is all of Nature, the repository of all the cycles and all the patterns of its developing environment. We are the result of our biological, geophysical, and astronomical heritage. The genetic code contains not only the blueprint of the individual organism, but also the cumulative record of the entire species.

It is from the internal measures of the perfected or harmonized individual—the frequencies and ratios of the heartbeat, the breath, the voice, the orgasmic impulse etc., that the Canon emerges. Physiological events occurring in Time are the ground of the Canon—as the Zen philosophers tell us, "Everything is in one thing." The foundation of measure is the human body itself.

When Canon measuring units are the basis for evaluation, the relationships between above and below arise as pattern. Harmony is observable and deviation from the harmonized is experienced as dis-harmony. Saturn is the source and model of our understanding of harmony, but it is from within that we yield to our relationship with the whole.

In our next installment, we'll see how each of the planets contributes to the harmony of the spheres more specifically, as we continue to link Earth Canon measures to the rhythms of the Solar family.

The relationship between all these CANON measures, and the dynamic linkage with the number of CHAOS, 4.669246833, will satisfy the framework question in a mathematical format which includes the demonstration of variance, everywhere and always. Necessary to the continuance of this presentation, a short primer on the mathematical alchemy will be presented in the next installment.

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Copyright 1996–2005 Bernard  I. Pietsch.