BERNARD PIETSCH'S RESEARCH
The Well Tempered Solar System
ANATOMY OF THE KING'S CHAMBER
As we make our way through the various interior passageways leading to the center of the Great Pyramid, the awesome quality of the sounds captures our notice. One's voice and even presence becomes an instrument of resound as it strikes some distant wall and summons us to go further into this marvel of architecture.
Near the middle of the pyramid, we ascend the Grand Gallery, pass through the Ante-Chamber and then bend down to enter the low narrow channel that leads to our destination. The floor of this passageway is rough and uneven and we must stoop for 100 inches until we enter the King's Chamber. When again standing upright we see that the chamber, brightly lit by fluorescent bulbs, is twice as long as wide, about 35 feet by 17 feet and nearly 20 feet high.
The chamber is empty save for the rectangular granite coffer at the far end. This is the famous sarcophagus in which the Pharaoh Cheops was thought to be interred. There is no evidence that a body ever occupied the cofferall is supposition.
Through the years, legions of spiritual pilgrims have come to this room to chant and meditate. Do the seekers fulfill their expectations as they contemplate quietly in the cool granite sarcophagus? Who can say? But what we can submit is that any person, regardless of the nature of his or her quest, merely by entering the chamber, stands in the midst of a truly sacred space. The narrative we are about to unfold is one told by ancient monuments and sacred sites around the world. But here, in the King's Chamber it is revealed with the elegance and simplicity and 20 rectangular forms which make up the floor of the chamber.
As we define sacred, only spaces can indicate the sacred. Sacred knowledge as we intend it, alludes to information that is perfect, idealized, and therefore intangible. One must participate with the sacred in order to realize the higher order of intention it represents.
The 20 rectangular granite blocks of the floor of the King's Chamber, though solid, can also be seen as spaces. Albeit crude approximations of perfect space, the stones delineate the keys to the astronomy that is the foundation of the entire chamber. The floor stones represent six planets: Mercury, Venus, Earth and its Moon, Mars, Jupiter, and Saturn. The message of the chamber is, "The heavens are the foundation of this space. Understanding our place in the synchrony of the solar family is the key. This is where to begin."
We'll adapt a musical analogy to uncloak the harmonies of the planets as they reside in the stones of the floor of the King's Chamber. The process is not exact and a degree of license is required, but the results will lead us to appreciate the intricacies and inter-relatedness of the solar system as never before. Even more astonishing is the realization that the elements of the planets were designed into these simple forms over 5,000 years ago, and that the true music of the spheres is recorded here.
Introducing the Well Tempered Solar System
Prior to the invention of tempering, keyboard instruments were tuned by mathematical formula. The distribution of frequencies between notes was regular and specific. The inflexibility of the early system meant that differently tuned instruments were needed to play music written in different keys. The tempered method was developed to allow all musical keys to be played on one keyboard. By adjusting slightly the intervals between tones, all keys could be accommodated. Sacrificing the mathematical purity of the just system allowed for a degree of musical versatility and harmony not previously enjoyed. In much the same manner we are going to "temper" the Solar System.
Purists may argue that the 10 digit numbers we are about to produce cannot be obtained from crude masonry and that "Man cannot disturb the march of the planets." But that is what we will do. The actual will become artful as the intention behind the design is revealed.
By once again summoning K (1.01430555) we part the veil and behold! The distaff elements of the planets are harmonized. Relationships not previously seen are made visible. K renders our Earth-centric filter of 365+ days/year to a geo-metric 360-days/year filter. Days and degrees are now synchronous; e.g., one day in an Earth year will represent one degree of the circle. We propose that the designers of the Pyramid used such a device as K, to translate time and orientation into geometry and measure.
(Note: There are numerous permutations and correlation amongst the planets' periods and rotations. Only a few illustrations are presented here, to give the general reader the flavor of the accomplishment. For serious students of the subject a complete table of the elements of the Well Tempered Solar System is available from the author. If the dance of numbers is not your pleasure, simply savor the imagery they evoke, as we skip about the features of the chamber.)
Entering the King's Chamber
Having been forced to bend down to negotiate the approach to the King's Chamber, the first thing one observes when entering the room, is the floor. The floor stones are rectangular and arranged in parallel "strips," each strip being a different width.
Directly beyond the entry, lie four stones extending to the far wall. We call this row the Mercury strip. To the right and parallel to the Mercury strip are five more rows of stones we've named the Venus strip, the Earth/Moon strip, the Mars strip, the Jupiter strip and at the far end of the room the Saturn strip.
The first stone upon which we stand upright is named after Mercury, Messenger of the Gods and Communication. It is Mercury, first planet in the solar system which initializes our circuit around the room. Mercury is the swiftest in its orbit and its quick cadence imprints the whole solar family. In the Well Tempered Solar System, Mercury's movements are part of the huge choreographed dance of the planets' periods, rotations and harmonics. Mercury's influence permeates the other planets in the system, and the dimensions of its stone counterpart infuse the geometry of the other stones in the chamber as well.
Recalling that K (1.01430555) is the ratio between the solar year of 365+ days and the Canon Year (also called Sacred Year of 360 days, wherein 1 day = 1460.6 minutes) we undertake the process of "tempering" by adjusting ever so slightly the conventional astronomical value of the planets by K. Mercury's year of 87+ earth days divided by K becomes the Canon period for Mercury:87.06 ๗ 1.01430555 = 85.83333 Canon Days in Mercury's year.
Likewise, we "tune" Mercury's rotation period (astronomically 58+ days) by K:58.04 ๗ 1.01430555 = 57.2222 Canon Days = 1 Day on Mercury
It is now easy to see that Mercury's orbit divided by its days of rotation is 1.5. In other words, in one Mercury year, Mercury has one and one-half of its own days.
A stepping stone to its solar cousins, the first stone in the Mercury strip, stone 1A is peculiarly endowed with numbers relating to Saturn. If speedy little Mercury corresponds to the snare drum in the rhythm section of an orchestra, large and ponderous Saturn is like the bass. Solemn and unwavering Saturn carries the beat for the whole band. We can see the interplay between Saturn and Mercury in the following example.
In the chamber we find the number for Mercury's year sandwiched between the relationship of the widths of two stones in the Mercury strip, stone 1C and stone 1D. The length of stone 1C at 29.469444 inches represents the Canon orbit of Saturn at 29.469444 years. The length of stone 1D has to be tuned just a bit from 34.34317751 to 34.33333 to get a perfect number. Multiply the ratio of the two by 100, and we have the Canon value of Mercury's year in days:(29.469444 ๗34.333333) x 100 = 85.83333 days/year of Mercury
The Mercury strip is 63.81262190 inches wide. Divide this by ten and see that the number in the Mercury strip is the same number as the distance Saturn's equator rotates in one second of time: 6.381262135 Canon miles.
Notice that we began inches and ended in miles. This telescoping of relationships between units is more than numerical slight of hand. It is a statement about the underlying relationships between units in the Canon system and the scale of relationships between the planets. There are many instances where the lower order of a measure, much like the lower octave of a note, is manifest in the higher order or octave of a planetary attribute. The units may be different (e.g. years or degrees) but the resonance is apparent. The relationships occur because the Canon itself is grounded in the natural order. Indeed, if illumination is effected, it is to realize profoundly that we are a part of the natural order. The only planets we may ever know are the planets within.
In one Canon Earth day, (1/360th Canon Earth year or 24 hours 20 minutes 36 seconds) Mercury rotates 2 x degrees or 6.283972726 degrees.
The number of square inches on top of the whole Mercury strip is 131,454,000. Taken as feet, we have an indicator for the number of feet the Earth rotates on the equator in one Canon Day of 24 hours 20 minutes 36 seconds: 131,454,000 feet.
The reciprocal of 131,454,000 x 111 is the same number as the number of feet on the front of Cheops Pyramid:(1 ๗ 131,454,000) x 111 = 760.722382
The number 760.722382 has a nearly metaphysical relationship to gravity and time. If divided by 100 and taken as seconds7.60722382, it is the answer to the following riddle: An object falls 47.2 feet in 2 seconds. If a pendulum is the same length in height, (47.2') how long would it take it to swing back and forth one time? It would take 7.60 seconds. This observation is significant because it incorporates the knowledge of the "second-second" in its formulation. In order to understand the "first" second i.e. to be able to measure the distance of fall of an object in one second, the present moment must be extended/suspended in order to examine (measure) the "second" second of fall. Without appealing to the second-second, we would never notice that the distance of fall in the second-second is greater than the first and thus that the rate of fall is accelerating. Ironically, because we can never get out of the first second of our experience, the conceptualization of the second-second is a highly sophisticated device. Our experience is always now, but by borrowing on our past experience we presume the future and realize that our present is accelerating.
760.722382 as millimeters or (30 inches) of Mercury is the standard mean reading of barometric air pressure.
The volume of the second stone in the Mercury strip 1B, 53519.60278 cubic inches, divided by 100 and taken to its natural logarithm is 2 times:[(53519.60278 ๗ 100)-e] = 6.2826330876.282633087 ๗ 2 = 3.141316543
It also happens that the square root of the same volume (53519.60278), divided by 100 and taken to its natural logarithm is the same number:535.1960278 = 23.13430413-e = 3.141316543
When Mercury rotates through one degree of its circumference, Earth has rotated 57.2222ฐ. It takes Mercury 57.2222 Canon days to turn one rotation on its axis or complete one of its own days.
In 53.045 days Mercury will have reached the , phi point222.48ฐ (the golden proportion of 360ฐ of its yearly orbit, and will have rotated through 333.333 degrees of its day.
Mercury's rotation through 333.333 degrees takes .927 of its day.57.2222 ๗ 53.045 = .927.927 x 2 x 100,000 is the Canon signification for the speed of light: 185,400 Canon mps.92,700,000 miles is the mean radius of Earth's orbit, or one Astronomical Unit.
Another reference to the Canon speed of light number is found by applying the tempering process to the period Saturn, wherein one year of Saturn becomes 10609 Canon days, during which time there are 185.4 days of Mercury:10609 ๗ 57.222 = 185.4 signification for the speed of light
at 185,400 Canon miles per second.
The diagonal angle of Mercury Stone 1A is 30ฐ 40' 06". This is also Mercury's approximate orbital inclination to the (mean) celestial Equator.
Stone 1C in the Mercury Strip is 29.469444" long. As years it represents one orbit of Saturn. By "tuning" slightly the length of stone 1D from 34.3417751" to 34.3433333", we can derive a perfect ratio between the two stones:(29.4694444 x 100) ๗ 34.333333 = 85.833333 the days in Mercury's Canon year.(2 x 34.3333 x 10 = 686.6666, the Canon days in Mars year.)686.666 (x 10) is also found as the surface area of Mercury 1A: 6866.666 sq. inches.
The surface area of the top of the first stone in the Mercury Strip 1A, divided by 10 signifies the number of Canon days in Mars' orbit:
(63.812 x 107.607) ๗ 10 = 686.666 days.
There are 12 days of Mercury in one Mars' year: 686.666 ๗ 57.22222 = 12.
There are 8 Mercury years (orbits) in one Mars year: 686.666 ๗ 85.8333 = 8.
During one Saturn year, 10,609 days, Mercury will have completed 66666.666ฐ of rotation, or will have reached the 333.333ฐ point 200 times.
The length of Mercury 1A x 100 is representative of the number of Earth calendar days (24 hours) in Saturn's year: 10760.76763. The width of 1A, 63.81262195" divided by 10 signifies the number of Canon miles 6.381262195 that the equator of Saturn will rotate (5258.16 feet to the mile) In one second of time, Saturn rotates 6.38126295 miles on its equator. Saturn's equator would then be 236,617.2 miles in circumference. As previously discussed in Saturn Source of Measure, Saturn figures heavily in ancient art and the origin of measure.
The surface of Mercury stone 1A has 6866.727967 square inches. Divide by 10 and see a referent for Mars' Canon period of 686.66666 days/year.
The volume of 1A is 73512.14044 cubic inches. Multiply that by 100 and take the common log: 6.866359069. Multiply by 1000 and we are very near to the square inches on the top surface of 1A: 6866.727967 square inches.
107.6076763 the length of stone 1A x 100 is the exact same number of square inches on the surface of Saturn Stone 6B: 10,760.76763 square inches.
In the Mercury Strip the total number of square inches on the top surface of the four stones, multiplied by 10,000 and taken as feet, signifies the number of Canon feet in the circumference of the Earth:206" x 63.81262195" = 13145.400 x 10,000 = 131,454,000
The cubic inches in the whole of Mercury 1C is 6325.459147 cubic inches or 3.660566636 cubic feet. Times 100 see Earth's sidereal year in days: 366+ days.
The length of the entire Chamber is 412 inches. The width is 206 inches. The perimeter of the Chamber is 1236 inches. In one orbit of Saturn, there are 123.6 orbits of Mercury:
10609 ๗ 85.8333 = 123.6
The width of the chamber 206 inches (17.166 feet,) divided by 10 connotes the Common Cubit of 20.6 inches. Read as a sexigesimal number 20.6 would be 20 minutes 36 secondsthe difference between Earth's Calendar Day of 24 hours and the Canon Earth day of 24 hours 20 minutes 36 seconds. 20.6 is a principal figure in the Canon system. Divided by 2, it represents the ratio between the major to minor axis of the orbit of earth: 1.03. When multiplied by .03, 20.6 becomes the ratio of the golden proportion. .618.
The surface area of 4C in the Mars strip is 3333.333 square inches. Divided by the Common Cubit of 20.6 inches and again by 100, we derive the golden proportion number 1.618122977 (perfect Canon value).
The height of the chamber from floor surface to ceiling is 230.2585093 inches. Divided by 100, the height of the chamber signifies the ratio between the system of common and natural logarithms:10-e = 2.302585093
When the height of the chamber is taken from the bottom of the wall (which is beneath the level of the floor) to the ceiling, it measures 235.6463942 inches. Taken as seconds of time we find a referent for the difference between the mean solar day of 1440 minutes and the mean sidereal day of 1436.07 minutes:1440 - 1436.0725 = 3.92743 minutes difference.3.92743 minutes x 60 = 235.6463942 seconds.
The Earth Strip, 3A, 3B, 3C, and 3D+3E is 87.636 inches wide. As seconds, 87,636 is the number of seconds in one Canon Earth Day of 24.343333 hours. There are also 8763.6 hours in one Canon Earth year of 360 days.
In stone 3B of the Earth Strip, the length is 46.69246833 inches. As 4.6692 we recognize the value for chaos. The diagonal angle of the top plane of 3B is 28.04869487 degrees. We take that as a referent for the number of degrees in the Moon's upper node, from which tidal harmonics are initiated. That this figure would be linked to the value for chaos, is interesting.
The diagonal angle on the surface of Earth Stone 3A is 32.14521358, indicator for "g" approximating the gravitational number of feet in the second
second-of-fallof an object.
The tangent of that angle, .6283990122 divided by 2 and x 10 is a close approximation for the value of .
The largest stone in the Earth Strip 3C is 83.63715584" long and 87.836" wide. The surface area in square feet represents the mean number of seconds of precession of the equinoxes: 50.90 seconds of arc per year:(83.63715584 x 87.636) ๗ 144 = 50.90017909 square feet
The diagonal angle of stone 3D of the Earth strip is 26.19222679 degrees, indicating the inclination of the Earth's orbit read magnetically: 26ฐ 19'+. This is also the degrees of inclination of the passageways.
Earth stone 3E is 45.75693065" long by 20.6" wide. The length, times ten is 457.5693065. The common log of this number is 2.660456884, or the co-tangent, when seen as an angle, of 20.6", the width.
The Saturn stone 6B in the Saturn Strip, is 185.4" long, 58.0408179012" wide and 10.70555595" deep. Each of these dimensions is significant:185.4 is the number of times Mercury rotates on its axis in one orbit of Saturn.185.4 also stands for 185,400 Canon miles/second, as the speed of light.58. 0408179012" indicates the E days (24 hours/day) of Mercury's rotation.
The surface area on top of Saturn 6B = 10760.7676383 square inches. As days, the area represents the number of calendar days in Saturn's year: 10760.7 days.
Also: Saturn's Calendar Period divided by the perimeter of the room (divided by 10) equals the Calendar days in Mercury's year:10760.7676383 ๗ 123.6 = 87.06122685137 days.
The diagonal length on the top surface of the Saturn Stone 6B is 16.18939479', divided by 10 signifying the golden number: 1.618.
The volume of Saturn Stone 6B is 66.66666 cubic feet.
If the Saturn Stone 6B were gold, it would weigh 80,000 lbs. Troy.
If the Saturn Stone 6A were gold, it would weigh 8,888.888 lbs. Troy.
Saturn stone 6B is 9 times the weight of Saturn stone 6A.
The volume of the entire chamber (from ceiling to the bottom of the walls which are beneath the floor) 206" x 412" x 235.64" = 20,000,000cubic inches.
The volume of the floor alone, multiplied by 1000, approximates the value for the number of minutes in the year:
(206" x 412" x 10.70555595" = 908601.86 cubic inches, the volume of the floor)908601.86 cubic inches ๗1728 (cubic inches to one cubic foot) x 1000 = 525,811.3105. As minutes/year, this figure is a departure of 8.1103456 cubic inches, from a perfect 525,816 minutes in one Canon year.)
The width of the Chamber, 206 inches is related to another Canon measure rooted in the heavens. The reciprocal (1 ๗ 20.6) of the number of the Common Cubit, x 100 is 4.854368932 inches, the measure called the Handbreadth or Palm. The Handbreadth times 360 and divided by 100 gives us another ancient and powerful measure we believe was the original Jewish Remen: 17.47572816". The reciprocal of the Remen x 100 is the day of Mercury:(1 ๗ 17.47572816) x 100 = 57.22222 the Canon day of Mercury
The length of the Saturn Stone 6B, 185.4 inches, divided by the Remen x 1000 produces the Canon period for the orbit of Saturn, 10609 days:185.4 ๗ 17.47572816 x 1000 = 10609 Saturn's year in Canon days.
The length of the Saturn Stone 6B, 185.4 inches, divided by the Handbreadth, taken to its reciprocal and multiplied by 1000 renders the sexigesimal number (unconverted) of the inclination of the magnetic orbit* and angle of the Ascending and Descending Passages:185.4 ๗ 4.854368932 x 1000 = 26.1832197 or 26ฐ 18' 32"
Stepping over to the 5th strip we call the Jupiter strip, we'll see how incestuous our little solar family is.
The Jupiter Stone 5B is 151.767633 inches long. 151.767633 is also the difference between the calendar days of Saturn and its counterpart in Canon Days:10760.76763 ( Year In E Days) ๗ K = 10609 Canon Years.10760.76763 10609 = 151.767633 the difference between the two types of year, calendar and Canon.
Jupiter's year is 4,333.333 Earth days of 24 hours each. There are 104,000 hours in that time. If that period is divided by the number of days in one Canon year of Saturn, we get the number of hours in one day on Jupiter:104,000 ๗ 10,609 = 9.802997455 hours of Jupiter's rotational day
In 4333.3333 Earth days (one year of Jupiter) there are or 11.8637550 Earth calendar years. During that time, Jupiter will have had 10,609 of its own days during one full orbit. Notice the simile between Jupiter and Saturn: each shares 10,609 but in its own way. There are 10609 Canon Earth days (24 hrs. 20 min. 36 sec.) in Saturn's orbit. There are 10609 Jupiter Canon days in its orbit.
There are 10760.76763 square inches on the top of Saturn Stone 6B. The calendar year of Saturn 10760.76763 days, has 258,258.4232 periods of 24 hours. Divide by ten and see this as representing the number of years in the precessional cycle: 25,825.84232 years.
On the top plane of the Jupiter Strip 5A, the side length of 34.3333 inches is shared with the side length of Saturn stone 6A, 20.6". The relationship of the two is: 34.3333 ๗ 20.6 = 1.6666, the ratio for decimal to sexigesimal timing: 100 ๗ 60.
The synchronistic relationship between Saturn and Jupiter is again embellished by the interplay of the two stones 6B and 5B. On the east side of Saturn 6B the side length (185.4") is adjacent to the longest length in 5B, the Jupiter strip (151.7676"). Subtracting the length of the Jupiter stone 5B from the number of square inches on the top of Saturn stone 6B extracts the number of Canon days in Saturn's year from the number of Calendar years:185.4 x 58.04 = 10760.76763 (area sq." top surface 6B)
The number of square inches on the top surface of Saturn 6B which identifies the calendar days in Saturn's orbit, minus the length of Jupiter stone 5B in inches, yields the Canon period of Saturn's orbit:10,760.7676 - 151.7676 = 10,609 the number of Canon days in Saturn's year.
The walls of the Chamber descend about half way beneath the top and bottom surfaces of the floor stones. When the floor stones are seen as "inserted" between the walls, the perimeter of the bottom of the wall as it were, bifurcates the floor stones into two layers, creating a double set of stones.
In a sense, there are now 60 stones indicated in the floor20 actual and 40 derived. A set of 20 stones contrived on the top "half", and a set of 20 on the bottom "half". Each set gives different information. We may consider the major diagonals, the areas, surfaces and volumes of the top and bottom portions of each stone and the ratios between them.
The depth of the stones to the level of the bottom of the wall is 5.387884927". This top layer we'll designate as level a. The bottom layer, b is slightly smaller at 5.317671023". The total actual height of the floor stones is 10.70555595".
The height of the lower portion of the floor stones b, 5.317671023" is related to the speed of light. Its reciprocal divided by K is the Canon value for the speed of light:(1 ๗ 5.317671023) x 1,000 = 18805.22499
18805.22499 ๗ K = 185,400 Canon miles/sec.
The bottom portion of Mercury 1D/b has a cubic volume of 3661.616349 cubic inches. Divided by 10 and seen as 366.16 days it represents the Earth's sidereal year. The cubic inches in the bottom portion of Mercury 1A/b is 36515.00. Divide this by 100 and we have the indicator for Earth's solar year: 365+ days.
There are three interesting ways that pi is indicated in the Mercury strip:
First, the total volume of Mercury stone 1B divided by 100 has a natural logarithm of two times () pi:(53519.60278 cubic inches ๗ 100)-e ๗ 2 = 3.141316543
Secondly, the top portion of Mercury stone 1C/a has 3183.472784 cubic inches in volume. The reciprocal of 3183.472784 ๗ 10,000 = .0003141224 x 10,000 = 3.141224 .
Third, the volume of the lower portion of Mercury stone 1C/b is 3141.986361 cubic inches. Dividing by 1000, renders the exact value of Canon at 3.141986363.
The volume of Mercury 1B is 30.97199235 cubic feet, another referent for Mercury's orbital inclination: 30+ degrees.
If Mercury 1B were gold, it would weigh 37166.39082 lbs. troy. Divide by 100 and then by 60, to derive the decimal number for the last quarter day of Earth's year: 6.19439487 or 6 hrs 11 min 39 sec .8344.
The width of Mercury 1C is 29.4694444 inches. This is the same number as the number of calendar years in Saturn's orbit: 29.469444 years.
The area of the long side plane of the bottom portion of Mercury 1A/b is 572.2222218 square inches. Divide by 10 to find 57.2222, the number of Canon Earth days in one day of Mercury, ie. one rotation on its axis.107.6076763" x 5.31767102" = 572.2222218 ๗ 10 = 57.22222
Notice that the volume of the bottom portion b of Saturn Stone 6b is also 57222.222 cubic inches. Divided by 1000, it is again, the number of Canon days in one rotation of Mercury: 57.2222days.
The total volume of the Saturn Stone 6B is 115,200 cubic inches, or 66.666 cubic feet. Curiously, 66.666 times 1.03, (which is the ratio of the Earth's major to minor axis) gives us 68.6666, which multiplied by 10, is the period of Mars: 686.666 Canon days.
The complexities we have just touched upon, beg the questions, "What was the initiating point for reconciling the multiplicity of variables in the design? "Where did the designer start?"
There is a certain book of aphorisms which says: "To know means to know all. To know a part of something means not to know. It is not difficult to know all, because in order to know all one has to know very little. But in order to know this little one has to know pretty much." (P.D. Ospensky in The Fourth Way.) The design of the King's Chamber begins with "one thing," and that one thing is a totality. Like other aspects of the Great Pyramid, it is built out of the knowledge of wholeness. All the parts must work together. Ultimately the one thing is us--our physiology, our life experience, our ability to perceive the instant--we are our vehicle. In an imperfect world, physical forms can only suggest meaning. By tuning the measure of a form ever so slightly, we can apprehend beyond the limitations of the actual form perceived, and divine as it were, more than is given. If we can see the intention of the architect, it may be possible to glimpse the whole.
Just as the whole pyramid is informed from "the top down" the individual parts are derived from the whole. As discussed previously, the "missing" top of Cheops Pyramid is neither missing nor existent. As metaphysical construct, its elusiveness lies in the nature of its apprehension. Since it is not physical, it can only be comprehended intellectually. In the Timaeus, Plato speaks of a "third nature, which is space, and is eternal, and admits not of destruction and provides a home for all created things, and is apprehended without the help of sense, by a kind of spurious reason, and is hardly real." (page 457 section 52, The Great Books version.) In this purity of space, the laws are expressed in mathematics and geometry, uncorrupted by physical form. Here the gods consort with number, geometry and physics, co-mingling their various parts. Diversity results from the coalescing of a few simple attributes: height, width, volume etc. The seeds of measure--the second of time, the weight of gold, and the one-second pendulum are conceived here. When transposed to the physical world these heavenly notions become susceptible to the limits and vagaries of time and material. We can glimpse them dimly through the portal of number and divine what perfection they intend.
The space above the 206th course of Cheops, projected from the physical stone to a point above the pyramid though invisible can be said to have a form extrapolated and extended from the physical pyramid. Within this empty pyramidal shape, angles, dimensions and volume can be derived. From the measures, significance can be intuited. For example: The cubic volume of the extended pyramidian would be 17,526.01662 cubic feet.
The common logarithm of that volume is 4.2436. Multiplied by 10,000 is 42,436 which has a square root of our old friend, 206, as inches, the width of the King's Chamber.
The natural logarithm of the same volume (the empty top) is 9.771441472. If this number is taken a 9.771441472 inches, and used as a pendulum's length, that pendulum would have a period of one second of time.
The ratio between all natural and common logarithms of numbers is 2.30258503. For example the natural log of the pyramid's empty top, 9.771441472 ๗ the common log of empty top, 4.243683112 equals 2.30258503
In the King's Chamber we find this number 2.30258503 (times 100) as the height, 230.258503 inches, of the walls above the surface of the floor.
The whole Mercury Strip, if it were gold, would weigh 97728.34478lbs. troy. That number divided by 10,000 and seen as inches would be the length of a one-second pendulum: 9.77 inches.
Whether as 9.771441472, or as .9771441472 or 97.71441472 this number appears in numerous places in the pyramid and other structures. Hatshepshut's obelisk at Karnak is 97.71441472 feet high. In Luxor there were two Obelisks dedicated to Ramses. The first is 977.1441472 inches high. If that length were a pendulum, it would have a 10-second period. The second smaller obelisk, now in Paris at the Place De La Concorde, is 77.74 feet high. If its height were a pendulum, its period would be 9.771441472 seconds.
In the King's Chamber, 977. appears in the relationship between the volume of the upper part of the floor (that portion of the floor which is between the walls) and the empty space above the floor. The pure space above the floor is 19,542,882.944 cubic inches. This space in the chamber plus the portion of the solid floor which extends to the bottom of the walls, has a volume of 20,000,000 cubic inches.The ratio of the two volumes: 20,000,000 ๗19,542,882.944 = 1.0233904.
The reciprocal of 1.0233904 is .9771441472977. approximates the number of ounces in one cubic foot of water.
The interconnection between Saturn, "Initiator of Time" or "Kronos," with the Common Cubit of 20.6" is pervasive throughout the Great Pyramid.
- The width of the King's Chamber is 10 times the Common Cubit, or 206" inches.
- There are 206 original courses in the body of Cheops Pyramid.
- In 206 years there are 7 orbits of the planet Saturn.
- 20.6 is the minutes difference between the solar day of 1440 minutes and the Canon Day of 1460.6 minutes. (Refer to our previous chapter on the Great Pyramid.)
An average or mean number is another method of encoding wholeness. 206 is a prime demonstration of a Saturn number embedded in the wholeness of the chamber. Take for example the average top surface area of an averaged stone from the floor:206" x 412" = 84,872 square inches in the floor. Divide by 20 to find the average stone's top surface: 4,243.6 square inches. Translate the number of square inches into the number of square feet by dividing by 144. There are 29.469444 square feet per average stone, or the same number as the number of Earth years in Saturn's orbit: 29.469444 years.The number of square inches in the average stone, 4243.6 divided by 10 is also the same number as the Common Cubit squared: 20.62 = 424.36.
Invoking Mercury, messenger of the gods to transport us to another dimension, we take 20.62 divided by the area of Mercury 1D to get a close approximation to the weight of 1 cubic foot of water:The top surface area of1D (34.64317751 x 20.0498165) is 694.5893521 square inches.(20.62 ๗ 694.5893521) x 100 = 61.095.61.095 identifies the number of avoirdupois pounds per cubic foot of water.
The Mercury Stone 1D if it were gold would weigh 5163.864702 lbs. troy. By tuning the weight to a perfect 5162.8333, we'll see an inkling of the origin of a system of weights and measures which relate to time. Dividing 5162.8333, a weight, by 101.430555, (K x 100 and also the number of feet in the Canon second of arc on the equator) we arrive at a cosmic measure of time associated with the annual number of seconds of arc of the precession of the equinoxes: 50.9009788". The perfect Canon value would be 50.90017909. Interestingly, the reciprocal of a pure 50.90017909 x 100 renders the ratio between the weight of one cubic foot of gold and one cubic foot of water: 19.64462963.
The whole Mercury Strip, stones 1A, 1B, 1C, 1D, has a volume of 81.44028733 cubic feet. If the entire mass of the strip were gold, it would weigh 97728.34478 lbs. Troy. That number divided by 10,000 and seen inches would be the length of a one-second pendulum: 9.77 inches.
Another underlying octave of the precessional cycle reveals itself when Saturn's orbital period in calendar days, multiplied by the number of 24 hour periods in that time, is seen as years:
10760.76763 days x 24 hours = 258258.4232 ๗ 10 = 25,825.84232 years.
The synchronicity continues between Jupiter, Saturn and Earth. The ratio between Jupiter's rotation 4333.33333 (in Earth calendar days of 24 hours) and Saturn's rotation 10760.7676383 (in Earth calendar days of 24 hours) is 2.483254070512. Earth's Canon day of 1460.6 hours divided by this ratio is the number of hours assigned to the rotation of Jupiter: 9.802997454996 or 9 hours 48 minutes.
There's more: The major diagonal length of Saturn Stone 6B is 194.5696792 inches. If a pendulum that length were to beat for one Canon Earth day of 1460.6 minutes, there would be 19639.22215 full periods. Dividing 19639.22215 by 1000 = 19.639another close approximation to the ratio between the weight of one cubic foot of gold and one of water.
The surface diagonal of the same stone 6B read in feet is approximately 10 times the golden number: 16.18939479.
What is the origin of the Canon grain? The grain is transliterated from the abstraction of time. The mean solar day of 1440 minutes minus the mean sidereal day of 1436.07 minutes, derives a difference which when squared is the ratio of grains to one gram:3 minutes 55 seconds or 3.9274222 = 15.42447076 gr./gm
As previously discussed, there is a qualitative difference which distinguishes the Canon inch from the conventional inch. Even though we use the word "inch" and an ordinary ruler for measuring objects, the essence of the Canon inch is much more complex and dynamic. The Canon inch is subservient to time and the instant. It is the philosophical measure of being in the moment. As every moment in an expanding universe is singular, so is the inch. From the observation of the action of a simple pendulum, we may experience the variety of "the moment." Just as no two moments are the same, no interval of the pendulum is the same as the last. To casually say they are identical is to rob the instant of its individuality. Ideally, any experiment or observation would be qualified by the degree of departure however slight, of the behavior from the mean measure used to quantify it. This residual factor or departure from the mean, regardless of how small, is information about the influence of the environment of the experiment, whether it's human input, a local influence or a cosmic one.
So it is that from the timing of the pendulum one of the most elemental of units, the number of grains to one gram of weight is embedded with another fundamental unit of length, the Canon inch.
We start with the Canon inch, and find the period of one inch as a pendulum, a moving weight in space. The period is .3199 seconds of time. In one period of .3199 seconds the pendulum will have swung to and fro, and the Earth will have rotated through 479.85 feet on its equator:479.85 is the number of Canon grains in one troy gram of gold (Conventionally 480 gr./gm).
It must be appreciated that the source of Canon measure is neither cultural nor conventional, nor even historical in its development. It is rooted in the very nature of universal dynamics. Our genetic apparatus is at the effect of those dynamics and we through our physiology are recipients of that inheritance. It would not be surprising if in the not so distant future it is found that the human genome and the Canon of Measure are inscribed by the same precursors to human evolution. And that the genesis of number itself is a natural exteriorization or projection of the planetary dynamics and biological cycles resident within us.
We can propose that some systems of metrology may have grown out of geometry itself. For example, avoirdupois weight has an interesting relationship with the cosine of 45 degrees. (We use the conventional term "avoirdupois" simply for convenience. Though not derived by this method, the modern ounce is nearly the same as the Canon ounce.)Begin with the cosine of 45 degrees = 0.7071067811.Use this as the tangent of an angle. The angle is: 35.2643896 degrees.The reciprocal of of 35.2643896 degrees, times 1000, is the number of grams to one avoirdupois ounce: 1 ๗ 35.2643896 x 1000 = 28.357218400 grams to the ounce.
The persistence of these various relationships suggests an ancient recognition of the elemental connection between systems of linear measure, volume, weight, and the abstraction called gravity. The Canon inch, the gram of gold, (both avoirdupois and troy weight) the weight of water and the function of the pendulum, form an inseparable amalgam with timethe conceptual seeds from which the fruits of ancient measures arise. The smallest unit abides with the grandest, from the inch to the precession of the equinoxes. All are complementary. From knowing one, it is possible to discover the others.
In our next segment we will continue our exploration of the King's Chamber with special attention to the granite sarcophagus, the "Pillar of Orichalcum upon which are inscribed the Laws." (Plato, Critias.)
The following reference is from a conventional astronomical table for the elements of the planets. It can be noted that astronomical assessments for the orbits of the planets vary from one reference to another. Mean periodicities are derived from observation and attendant reconciling astronomical theories. With at least 5,000 years of modern astronomical invention at hand, one must by comparison, assent to the clarity of vision of the ancient astronomer
From Peterson Field Guides: Stars and Planets, 1995
Rotation: 58.646 E days
Synodic Period: 115.9 E. days
Sidereal Period 87.96 E days
Rotation: 243.01R E days
Synodic Period: 584.0 E days
Sidereal Period: 224.68 E days
Synodic Period: 779.9 E days
Sidereal Period: 686.95 E days
Rotation: 9h 50m > 9h 55m
Synodic Period: 398.9 E days
Sidereal Period: 4337 E days
Rotation: 10h 39.9m
Synodic Period: 378.1 E days
Sidereal Period: 10,760 E days
Rotation: 58.65 E days
Synodic Period: 115.88 E days (opposition to opposition)
Sidereal Period: 87.969 E days
Rotation: 243.01 E days
Synodic Period: 583.92 E days
Sidereal Period: 224.701 E days
Rotation: 24.6229 E hours
Synodic Period: 779.94 E days
Sidereal Period: 686.98 E days
Rotation: 9.841 E hours
Synodic Period: 398.99 E days
Sidereal Period: 11.8623 E years
Rotation: 10.233 E hours
Synodic Period: 378.09 E days
Sidereal Period: 29.458 E years
Rotation: 58.646 E days
Synodic Period: 115.88 E days
Sidereal Period: 87.97 E days
Rotation: -243 E days
Synodic Period: 583.96 E days
Sidereal Period: 224.7 E days
Rotation: .997 days
Sidereal Period: 365.26
Rotation: 1.026 E days
Synodic Period: 779.94 E days
Sidereal Period: 686.98 E days
Rotation: .41 E days or 9.8400 hours
Synodic Period: 399 E days
Sidereal Period: 4331.9836 E days
Rotation: .43 E days
Synodic Period: 378 E days
Sidereal Period: 10742.2966 E days
Copyright ฉ 2000 by Bernard I. Pietsch.
For more articles please visit Bernard Pietsch's web site at: http://www.sonic.net/bernard/