**Bernard I. Pietsch**

*Excerpt from work in progress*

**Introduction to the Canon of Measure**

One would think that the paradigm of mathematics cannot be questioned,
since the laws of mathematics are already surely known. This report
deals with elements of a paradigm not found in contemporary mathematics
nor in anthropology nor in art history. It begs the question: "Is
there a paradigm in Art which transcends the classical categories of
line, form, composition and spatial arrangement? Is it possible that
some level of communication exists which has eluded the reconstructions
of contemporary archeology?" The answer to these questions lies in
the recovery of an ancient wisdomatic we refer to as the
**Essential Canon of Measure**.

Following a brief introduction to the **Essential**
**Canon of Measure** and how it applies to ancient art and
metrology, the science of measurement, we will take a closer look at a
Chinese art work rendered in jade about 3,000 years ago. The
metrological elements of the Stone of Heaven illustrate a synthesis of
art, form and science not expressed in modern thinking. We will suggest
that ancient monumental works affirm in their metrological levels,
individual attainment of high intuition and natural understanding. We
will also contend that a return to an ancient paradigm of
value is within our grasp. Monumental works perceived through the lens
of the **Essential Canon of Measure** will be the vehicle of
this exploration.

**Physiology Organizes Metrology**

The jade disc to which we will refer, actualizes a universal system of
measure we designate as the **Essential Canon of Measure.**
It is an *essential* system abstracted by the mind from the
Natural Order and derived from eons of evolution of biological rhythms,
astrophysical cycles and planetary harmonics. Heartbeat, breath and
other cycles of the body are the result of the participation of our
earth bound life form in the universal process of evolution. These
human physiological frequencies reside at the core of the
**Canon**. The **Canon** is not invented. It
is derived. It is a system that *emerges* into consciousness and
is perceived at the level of the individual's awareness, i.e., awareness
of the Self precedes access to the **Canon**.

As *idealized* numbers, **Canon** measures represent
dynamic processes which in the real world are variable. Periodicities of
the planets, tidal cycles and beats of the heart fluctuate.
**Canon Measures** are *perfect*
abstractions—they do not exist, yet we recognize the
*patterns* that they indicate. For example **60**
heartbeats for **60** seconds of time or the number
**360** as both degrees in the circle as well as the number
of days in the sacred year of the ancients.

**The Canon is Perennial, not Conventional**

Historically, units of measure differ from one culture to
another—conventional manifestations of a Chinese, Egyptian or Mayan
"inch" for example, are all different. Generally, these measures
are believed to be related to some aspect of anatomy such as
length of forearm, foot, knuckle, or other contrived standard.
Canon measures are are categorically different; they are derived
from human physiology, they transcend all culture, yet inform it.

Because the cycles of the body are the universal organizer of all
systems, sychronistically each system is convertible into the others.
Monumental Art therefore, regardless of its country of origin or epoch,
is the expression of a *Perennial* *Domain of Harmony*,
perceived and rendered into form by the understanding of the artificer.
The talent of the artist lies in his or her ability to conceive
through ratios, proportions, line and measure, an art form which
reveals in its structure, an understanding of universal processes.

**Art, Geometry and Measure Precede Semantics**

One in possession of the **Canon**, and who understands the
process, can "read" a monument as it was intended to be seen
by its maker, in any century or civilization. Because the process
functions the way the mind and body work, the system can surface
anywhere in the world. To use an alchemical term, the
**Canon**, is a universal solvent, or solution; it is to
metrology what the archetype is to mythology— or the image is to a
hologram. As with the hologram, the **Canon** has no
existence per se; it is the individual's perception that gives it
intelligible form. Prior to language, prior to culture, the
**Canon** emerges—through the Art we intuitively
revere as Monumental or indicative of the Sacred.

**Monumental Art Indicates the Sacred**

The sacred does not *exist*; but it can be experienced. There are
many sublime examples of metaphysical art in the monument world, but an
architectural metaphor can merely "point" to the sacred. It is
only through the *participation* of the witness/observer that
sacred or unseen levels can be accessed. Through participation with the
art form, a moment of openness may transpire and a new way of
*seeing* may be experienced. Transformation may occur. It is the act
of transformation which renders the instant sacred.

In a universe wherein all is becoming, changing, evolving, it is unthinkable that anything or process is final. Hence in many of the great monuments and art forms of the world, we find an element of the unfinished, missing or incomplete. This open-ended aspect of Monumental Art is a hallmark of the ancient builders. The act of completion and the opportunity to savor the experience of discovering the sacred for him or herself is reserved for the participant/observer.

The space above the 206^{th} course is so
geometrically perfect that it cannot have existence—but it can be
conceptualized. The information in the top is of a different order than that
conveyed in the physical pyramid, but it is derivable. Herodotus said,
"The pyramid was built from the top down." Herodotus meant not
that it was *constructed* from the top down, but that it was
*conceived* from the top down. The 206 courses of the pyramid
*exist*, in stone as a physical record of tidal and planetary
history during a corresponding period of 206 years. The pyramidian on
the other hand *is* not. It can only be conceptualized. It is an
ideal form, but a necessary adjunct to the ordering of the physical
pyramid. It is the potential of the invisible top that inaugurates the
physical pyramid. **The idea drives the form.**

**Monumental Art Invokes Synchronicity**

There are no "secrets" and no "sacred" in Art.
Secrets and the sacred reside in the observer, not in the observed.
Liberating the secret/sacred requires movement on the part of the
observer—movement from one category of observation to a higher. Sacred
Art constantly reminds us: There are many levels. Do not be attached to
one viewpoint.

Monumental Art is also characterized by the interrelatedness of the
individual components of its form. By design the parts not only work
together, but incorporate a high degree of commensurability between
divergent categories. For example, inches may be read as units of time,
angles may be seen as lengths, linear measures as weights, weights as
volume. The term *synchronicity* is often applied to such
coincidences; but when diverse individual events are seen as part of a
larger framework, synchronicity gives way to understanding that
coincidence is *co ( inside) dence*.

In the grandest sense of sychronicity, the **Canon** value of the
Golden Number Ratio **1.618122977 ** is at the core of all natural
and dynamic processes in nature. Every organism, every drop of water,
every twist of plant growth or movement of the planets conforms in its
way to the law of the Golden Mean. Its dominion is omnipresent. The
simplest organism demonstrates in each moment of its growth and being,
its individual response to the contribution of the total universe. The
organism *participates *with the universe and structures its
response into form. The __structure__ of the form is the history of
that response.

**The Canon is the Perrenial Interface Between Art and Science**

The **Canon** represents the harmonization of inner and outer worlds,
above and below. Because the **Canon** is the repository of
frequencies as *number,* a single number can refer to different
scales or degrees. Like the *moment,* the concept of *place*
can be as immense as the galaxy and as immediate as the center of the
Self; each is singular but on a vastly different scale. The Great
Pyramid, for example represents simultaneously one second of time and
one rotation of the galaxy. Its form expresses both one heartbeat and
many millennia. The mystery is that both exterior/interior, past/future
can be harmonized by the realization that circumference and center are
one. Here/Now is precisely *that*. When one is in submission, in
no-time, in no-thought, the integrity of the moment may be allowed to
surface. Transformation, the deepest reconciliation of the self, can be
experienced.

An ancient work like an obelisk, stone circle, dolman, standing stone or
temple may refer by measure or geometry to its Time/Location. Because
Time is an e*ssential* feature of the **Canon**, there may be no
apparent reference to Time in a work itself. If the observer/participant
is willing to engage in new ways of observing, unexpected levels of
information may be yielded by the work. By applying some form of timing
device: calibrated drops of water, celestial observation, falling
weights,etc. We can decode information about Time and timing not
otherwise available.

For example, the essence of Time/Place in an art form may be
*divined* by invoking the laws of the precessing pendulum (Foucault
formula). The precessing pendulum can be used to determine geographic
location in latitude above or below the geographic equator. By invoking
the laws of the pendulum, any feature of a work, whether it be the
height of a doorway, area of a wall or length of a perimeter edge can be
transformed into a period of time.

One famous site that demonstrates the knowledge of Time/Place is the
Inti-Huatana (Hitching Post of the Sun) at the top of the pyramid at
Macchu Picchu, Peru. The sculptured form is a truncated, four sided
pyramid. The design is such that the angle of inclination of the top
plane, with respect to level is coincident with the value of the
latitude of Macchu Picchu south of the Equator: **-13.1415**.

The Inti-Huantana Pyramid, Macchu Picchu, Peru

When the vertice corners of the Inti-Huatana pyramid are extended
upward, an *inferential *pyramidian is created. The height of its
*indicated* apex is **72.5"** above the middle of the
existing top plane. Sychronistically, **72.5** also represents the
degrees of longitude of Macchu Picchu west of the Prime Meridian.

**Stone of Heaven**

`[8-color GIF]`

(Image © New Image.)
A high-quality 16-million color image is available.

`[279K]`

We now embark on a new voyage on the seas of time. The model for our
vessel is the Jade Pi Disc illustrated in the *National Geographic
Magazine* article "Jade, the Stone of Heaven," on page 285
of the September 1987 issue. This ancient art form uses elements of a
modified framework of mathematics to encode its message. Traditionally
the Pi Disc is regarded simply as a ceremonial object used for the
worship of the heavens. As an Art form, it not only regards the heavens
but is the carrier of a metrological tradition as well. See illustration
following page.

RING | DIAMETERinches | AREAsq.inches |

h | 6.514294315 | 33.33335722 |

g | 6.3654 | 31.827 |

f | 3.298963744 | 8.54686478 |

e | 3.070171385 | 7.404053422 |

d | 1.8659116 | 2.73405431 |

c | 1.681792831 | 2.221719865 |

b | 1.128308469 | 1.0 |

a | .954810684 | .716108525 |

TOTALS: | 24.87965342 | 87.83315812 |

**Observation One**

There are 8 concentric circles underlying the ornamentation of the Jade Disc.

Starting with the largest, the dimensions in inches are as follows: See
**DIAGRAM A**.

**Process:**Sum the length of all eight diameters. The
total length is **24.87965342** inches.

Construct one circle with **24.87965342** inches as a diameter.
See **DIAGRAM B**.

The circumference of this circle will be **78.17153176**
inches^{2} or **6.514294313** feet.

**Note:** The circumference of the derived circle
**B** has the same number but in *feet* as the
number of *inches* in the diameter of the largest diameter
**h** of the Disc: **6.51429315**. The derived
form **B**, like a catalyst, actualizes a potential
previously not available to **A**.

**Observation Two**

Since there are eight different circles in the Jade disc, divide
the derived circumference of **B** by **8**:

78.17153176 ----------- = 9.771441472 8

**Note**: The number **9.771441472** will be
referenced often in Monumental Art. One of the significant attributes of
this number is that it is identical to the length of a __ pendulum
which will beat one second of time__ (one full swing forth and
back), exactly

Now find the square of **9.771441472** and divide by
**100:**

9.771441472^{2}------------ = .954810641 100

**Note redundancy**: The innermost diameter
**a** of the Pi Disc is also **.954810641**
inch.

**See that:** One eighth of the derived circumference of
**B** (__ 9.771441472)__ is exactly

78.17153176 9.771441472 ----------- = 9.771441472 then: ----------- = 6.514294315 8 1.5

**Most importantly notice that: ** The number **8** divided
by the diameter of the actual disc is:

8 ----------- = 1.228068554. 6.514294315

This last number, **1.228068554** is pivotal in the
translation of time to length. It recurs frequently in the Monument
System, and will be referenced several times as we unwind the labyrinth
of the disc. When it is taken as the exact number of feet in the length
of a pendulum, that pendulum would beat a period of time in seconds
identical to its length: **1.228068554 seconds. 1.228068554 feet**.

**Observation Three**

The diameter of the second innermost **b** circle is
**1.128308469** inches.

**Note:** The area of that circle is exactly one square inch.

**See that: 1.1283084692 ^{2} = 1.27308**.

**1.27308 × 45°** = **57.2886** The
**Canon** Radian of the Circle

**Observation Four**

The number **8** plays a significant role in the design of
this piece.

**Note:** The square root of the number **8**
is **2.828427125**. Holding that figure in mind, notice
that if the circumference of our derived circle
**B (78.17153178** inches) is used as the length of a
pendulum, the period of this pendulum will beat
**2.828427125** seconds of time, the same number as the
square root of **8**.

The third diameter **c 1.681792831** inches, is the
**fourth root** of the number **8**.

**Observation Five**

The number of square inches occupied in the area of ring **K
** (see diagram) is similar to a number modernly given as the
rate of period doubling to chaos, or "Fiegenbaum's Number":
**4.669246833**. This number has its own anti-common log
multiplied by 10,000:

**4.669246833 ^{10} = 46692.46833**.

(In his writings, Fiegenbaum apparently did not notice this
synchronicity. Actually the Fiegenbaum value is given as
**4.6692016**. Fiegenbaum's Number departs from the
**Canon** figure by a little over one hundred thousandth.)

**Observation Six**

The pendulum, as an instrument *just* does, it is pure physics.
When coupled with the heartbeat however, we initiate the fundamentals of
measure based on physiology.

The commensurability factor of units of length which translate into units of time via the pendulum enables metrological transformation. One number can indicate another. One number may be imbedded within another. But a mathematical (and sometimes magical) function must be utilized to liberate the unseen value. he function could be a square root, a logarithm, or the reciprocal of a number. The participant/observer must invoke an intuitive leap in order to access the hidden. Through the lens of intuition, the new relationship emerges.

For instance, out of the emptiness of the inner circle of the Jade disc, we will derive the ultimate Time/Length factor. In the beginning, the path seems circuitous, but then the familiar is revealed.

**The Process**: The area of the inner (empty) circle
**a** is **.716108525** of an inch.

Although not obvious at first, further exploration will reveal that this
number, times **10** is an "indicator" of the
pendulum whose period has the same number of seconds as its length has
in inches.

**.716108525 × 10 = 7.16108525**

The square root of **7.16108525** is
**2.676020414**

The reciprocal of this,

1 ----------- = .3373689227 2.676020414

Use this number to multiply the value of the **Cannon
Meter**, in inches, as

**.3373689227 × 39.4362 = 14.73688309 inches**

Dividing **14.73688309** inches by 12 to derive feet we
arrive at:

14.73688309 ----------- = 1.228073591 feet 12

**This is almost 1.228068554** the number of feet
in the length of a pendulum that beats the same number of seconds as the
measure of its length in inches.

**A further redundancy is indicated when it is seen that:**

The square inches in the empty center:.7161084613

Taken to its anti-natural logarithm= 2.04645384and multiplied by10

isalmostthe same number of inches as in the circumference of the real jade disc:

20.4678239

20.4678239 ----------- = 3.14148201. This last a very close value of pi. 6.513248639

**The idea can be rendered but only as a sensible copy of the ideal.**

A moment of openess initiates transformation. The artist captures the
moment as an *image*. The image is reduced to an idea. The idea
can then be expressed as language, geometry, number, shapes, sculptures
etc. The last aspect of the artist's act is submission to the limitation
of his medium: his *idea* can be conceived; but the object can
only be rendered as an approximation of the idea. The is no guarantee
that a person who has experienced the sacred, is going to precipitate a
sacred work in the world. The best that the artist can hope for is that
someone else may appreciate his intention, and see through the form to
the idea in the mind of its originator, to the level of the perennial.

**Appendix: Canon and Convention**

**Canon Measures** are observably a departure from modern
conventional units. Bear in mind that the purpose of modern measures is
primarily functional. Conventional measures are traditional and for the
most part arbitrary. They are none the less, useful for keeping
schedules, navigating, and negotiating commerce. The authority of the
convention rests in the *agreement* of those who adhere to it.

Conversely, the **Essential Canon of Measure** is initiated
by universals—ideal units of frequenecy assigned after millennia of
observation. Canon units are characterized by internal
commensurabilities and strange mathematical relationships. Although the
intuitive levels are not unfamiliar to poet and mystic, many of these
relationships defy the limitations of our logic, yet they occur. The
opportunity exists for the scientist to explore the realm and from
another frame of reference, discover new questions.

The origin, evolution and rationale of the following short list of
**Canon** measures are detailed in another work.

**TABLE I: Metrological Aspects of the Canon Based on a Magnetic Framework**^{3}

- Earth circumference at the Equator
**25,000 Canon**Miles. - The
**Canon**Mile at**5258.16 Canon**feet. - The Foot at 12 inches. There are
**131,454,000 × 12 =1,577,448,000**inches in the geographic Equator. - There are
**525,816 Canon**minutes in the**Canon**year, of**360 Canon**days. - The
**Canon**Time of Earth rotation established as**87,636**seconds Time. - One
**Canon**day: **87,636.**seconds**1,460.6**minutes**24.34333**hours**1500 Canon**feet of equator rotate through one second of arc in one**Canon**second.- The conversion number of
**Canon**feet to geographic feet is approximately**1.0143055555.** - Thus, the geographic equatorial rotation is
**1521.458333**geographic feet in one second of time. - There are
**15**geographic seconds of arc in**1521.458333**geographic feet. - The
**Canon**meter at**39.4362****Canon**inches. - The inch at
**2.535741273****Canon**Centimeters. - The Common Egyptian Cubit at
**20.35990488**inches. Also rendered as**20.6**inches - The "Sacred" Egyptian Cubit at
**25**inches. - The
**Canon**value of**pi**is**3.141986363**

**TABLE II: **Conventional Mathematical Processes Used

- Add, Subtract, Multiply, Divide.
- Trigonometric values of Angles, as:
- Sine, Cosecant, Tangent, Cotangent, Cosign, Secant.
- (Degree, Grad, and Rad)
- Square Root
**n**of which a given quantity is**n**^{2} - Common Logarithm
**n**^{10}, and n^{ -10} - Natural Logarithms
**N**and_{ -2.718281}**N**^{ 2.7182818} - Formulas, for Areas, Volumes, Triangles, Spheres, Cubes
- Spherical Trigonometry, for location of stations in Geographic Latitude and Longitude.
- Formula for the Foucault Precessional Pendulum for Precession of a Pendulum in degrees per hour on a Latitude (
):*l***15° × sin**= precession in degrees per hour on a latitude*l*.*l* - The formula for deriving the theoretical period (
**T**) of a pendulum (**n**) feet in length using the conventional value for the acceleration of gravity () at*g***32.15481179**feet. This is the distance of fall of a weight in the second second of its fall in the local geometry.^{3}*T = 2 l / g* - In this formula, the
**Canon**value of**pi**is**3.141986363 × 2 = 6.283972726**

The feet to the**1st**second of fall is approximately**15.7**feet.^{4}

**Table III: The Conventional Geographic Framework**

**15**degrees of rotation in one hour of Time.**4**Minutes of time of rotation in each degree**1521.1458333**feet of rotation in each second of time.**24**hours of**60**minutes produces**86,400**seconds in a Mean Solar Day.**23**hours,**56**minutes,**04.+**seconds, the Mean Sidereal Day of the Stars.

1.) 1.618033989, the Fibonacci Number closely resembles the Canon number. But in the quest for mathematical perfection sacrifices it relationship to nature: The reciprocal of the Fibonacci Number is itself minus 1: 1 ----------- = .618033989 1.618033989 On this tiny point the link between mathematics, natural form and the Canon was lost. 2.) 78.17153176 inches is also 1.982227795 Canon meters. This number taken as minutes and squared (3.92922703) represents a reasonable decimal value for the difference in minutes between the Mean Solar Day and the Mean Sideral Day, 03 min 55 sec .7536. 3.) The time systematics in the Canon register Earth rotation in terms of the Eart h's magnetic geometry. The Canon paradigm departs from contemporary time systematics on this point. Fo r example, one day of Earth rotation in the Canon System becomes 87,636 seconds of time, as compared t o the conventional figure of 86,400 seconds. The ratio between the two systems is: 87,636 ------ = 1.01430555 86,400 4.) Conventional conceptualizations about "gravity" are locked to relativistic considerations and constraints Newton denied in personal writings any knowlege of or ascent to the notion of "a ttraction." There is at present probably not a single physics textbook which attends to this error in re porting. Newton himself may have been an unwitting participant in sustaining the delusion of attraction in the Principia while denying it personally in private communications to others. See Newton: The Third Book of Optics. 5.) There can be no true Canon value for the 1st second of fall, since the object is already in motion in the cosmodesic acceleration. 6.) Based on the adopted Clarke Spheroid of 24,901.55 miles Equatorial circumference, wherein the mile @ 5280 feet is not required to be commensurate with a time systematics.

Copyright 1996–2005 Bernard I. Pietsch.