Torus

The torus is also a very important geometrical three-dimensional form and we’ll bring it up here because it is the building block of matter in the new aether science of the next chapter.  It is best compared with a doughnut or the smoke ring from a cigar. Here’s it is:

Torus

It is a sphere, curving inwards on top and bottom, such that it has a hole in the middle! It also resembles an apple. The torus is the result of rotating the Genesis pattern 360 degrees around the center.

Crop circle, West Overton, 24th June 1999 octahedron projected in 2D layout.

All of these five forms are in the Cube of Metatron, it may take a little while to discover them but they are all in there. The Platonic solids have very remarkable characteristics, for one they all fit perfectly within a sphere. The vertices of the solid are on the surface of the circumscribing sphere! Also they perfectly fit inside each other and can be perfectly nested. All forms have a double, an opposite form that can be created from the other. The cube and the octahedron are doubles for instance. If we take the centers of the faces of the cube and connect all the lines between these centers we get the octahedron. The same process can be reversed creating a cube from an octahedron. The tetrahedron has itself as the double. The dodecahedron and icosahedron are doubles. Every line, face and angle in a Platonic form is identical to every other line, face and angle within the same form. In other words the Platonic solids are extremely symmetrical!

Another puzzling symbol that is derived from the progression of the Flower of Life is the Tree of Life. The Tree of life is central subject of study in the mystical Jewish Kabbalah. The Tree of Life can be overlaid with the Flower of Life and they will perfectly match. The Tree of Life is an extraction from the Flower of Life, leaving out a number of spheres of no interest.

Now the Fruit of Life is called a female form because it only contains rounded forms, spheres, just like a female body that is curved. The male counterpart can be constructed if straight lines are used to connect all the centres of all the spheres in this picture. The result is called the Cube of Metatron.

Cube of Metatron

The Cube of Metatron is very important since it contains the solid geometrical forms that have become the focus of a new aether physics that we will describe in the next chapter!

Philosopher Plato described these forms that we find in the Cube of Metatron 400 years BC, hence they are called the Platonic solids.

In fact the Platonic solids can be found in the Metatron twice, the smaller versions of the solids are repeated in the inner 7 spheres. One of the five Platonic solids is the well-known cube. If you will, you can try and find the cube in the Cube of Metatron. I will help you a little bit with this one, here it is:

Cube in the Cube of Metatron

The green spheres are the corners of the cube. One corner in the back is hidden from view though.

Platonic solids

The five Platonic solids are named after Greek philosopher Plato who first described them 350 years BC in his book Timaeus. Here they are:

When you see the upper edge of the moon  (or a first magnitude star) approaching the first marker on the astrolabe, swing the weight of a pendulum and count the pulses from one extreme and back (full swings) for 6 minutes – until the moon/ star moves 1.5 degree (for the moon it would be its 3 diameters). There are only two factors that effect the swing of a pendulum; the length of the string and gravity – which is determined by the mass of the earth ( if you swing a pendulum faster it will move outwards further but it will not change the number of pulses.)

You need to adjust the length until you get exactly 200 swings during this period of 6 minutes. It is likely to take you several attempts to get the length right so be prepared to do quite a bit of moon/star gazing. To improve accuracy, you can increase the time (and accordingly number of pendulum’s swings).

It is likely that in ancient times, astronomers would keep the rod with 1MY length (once it was established this way) and use the described method for calibration.

One you have the correct length of pendulum, mark the distance from the  exact point of suspension to the centre of the weight (it would be best to use a spherical weight for the pendulum). Congratulations, you now have a stick that is exactly one Megalithic Yard long.

1 Megalithic Yard = 2.72 feet = 1 foot + 1RC = 0.82966m

1 m = 3.281 feet  |  1 foot = 12 inch = 30.48 cm  |  1 inch = 2.254 cm
1 Royal Egyptian Cubit = 20.62 inch = 0.531 m

1 mile = 1,609.344 meters = 1,941 MY = sqrt(44) MY
1 nautical mile = 1.15078 mile = 6,076 feet = 1.852 km = 2233 MY

Modern and accurate numbers describing the size of our planet:

Earth’s Circumference Between the North and South Poles:
21,602.6 nautical miles = 24,859.82 miles (40,008 km)

Earth Equatorial Circumference:
24,901.55 miles (40,075.16 kilometers)
Earth’s Diameter at the Equator:
6,887.7 nautical miles = 7,926.28 miles (12,756.1 km)

1 year = 365.25 days
1 day = 24 hours = 1,440 minutes = 86,400 seconds
24 hours = 360 degrees, 
1 hour = 15 degrees,
1 minute (time) = 0.25 degree = 15 min of arc
1 degree = 4 minutes (time)
360 degrees = 21,600 minutes = 1,296,000 seconds (of arc)
1 degree = 60 min = 360 seconds (of arc)

Note:1/1,000th of a degree of arc around the equatorial circumference of the Earth is just 365.22 ft in length!

1 degree of arc = (1/360) * 40,075.16 km = 111.32 km = 365,223 feet (divided by 1000 = 365.22 which is number of days in a year)

Egyptian Cubit

The Egyptian cubit, the Indus Valley units of length referred to above and the Mesopotamian cubit were used in the 3rd millennium BC and are the earliest known units used by ancient peoples to measure length. The measures of length used in ancient India included the dhanus (bow), the krosa (cry, or cow-call) and the yojana (stage).

The Egyptian Royal Cubit rod,  from the Turin collection, has an official length of 20.618 inches. Its refined value, under the sexagesimal geodetic system, was calculated mathematically to be 20.61818182 inches.

Note: Royal Cubit consists of 28 units, digits, which is the same as 7 palms of 4 digits. The names of divisions of royal cubit may suggest anatomical origin, however the divisions indicate astronomical origin of the cubit (7 days per week, 28 days lunar calendar, 4 weeks per lunar month)…

Interesting Relationship between ancient units of lengths

From measurements of the King’s chamber and other dimensions in the Great Pyramid by John Greaves, Sir Isaac Newton realized that the King’s Chamber was 10 x 20 Royal Cubits (or Thoth Cubits) so that the Royal Cubit is determined as equal to 1.719 (1.72) feet.

Therefore, we can take the following as “ideal values” in metric system of 3 fundamental ancient units of length:

 1MY = 1 foot + 1RC = 2.72 feet = 0.829m
1 Royal Cubit = 1.72 feet = 0.632 MY = 0.524m
1 Remen = Royal Cubit/sqrt(2) = 14.58 inch =  0.37 m

Notice the relationship between all 3 units  can be well approximated as follows:

1 Megalithic Yard = sqrt(5) x 1 Remen = 1 Royal Cubit x sqrt(5/2) = 1.5811388 RC

Let’s notice the relationship between all 3 units  can be well approximated as follows:

1 Megalithic Yard = sqrt(5) x 1 Remen = 1 Royal Cubit x sqrt(5/2) = 1.5811388 RC
1 Royal Cubit = sqrt(2) x 1 Remen = 0.525 m
1 Megalithic Yard = sqrt(5) x 1 Remen = 0.83 m

It may be seen that, from the basic square side of the Remen, the length of the Royal Cubit can be derived by multiplying the Remen by the square root of 2; similarly, the Megalithic yard can be derived by multiplying the Remen by the square root of 5.
Another geometric illustration of the relationship between Remen, Royal Cubit and Megalithic Yard, where1M.Y. is circumference of the circle (0.823m) inscribed in (1/2) R.C. square (with 99.3 % accuracy):

     
If Megalithic Yard was defined as equal to the circumference of the circle inscribed in ½ of Royal Cubit square:

1 MY=1/2 x RC x “Pi” so 1 MY = 1.570795 RC

1 MY (in RC) = Pi/2

For RC=1 we get and  1MY=1.570795   and 1 Remen = 1/sqrt(2)=0.7071 

NOTE:
For the Great Pyramid:
Height = 280 Royal Cubits
Base Side = 440 Royal Cubits = 280 MY

Click to Enlarge

In whichever case, the Greeks and Romans inherited the foot from the Egyptians.

12 inches = 1 foot
36 inches = 3 feet =  1 yard
1760 yards = 1 mile

440 yards = quarter mile

Interest in ancient metrology was triggered by research into the various Megalith building cultures and the Great Pyramid of Giza.

In 1637 John Greaves, professor of geometry at Gresham College, made his first of several studies in Egypt and Italy, making numerous measurements of buildings and monuments, including the Great Pyramid. These activities fueled many centuries of interest in metrology of the ancient cultures by the likes of Isaac Newton and the French Academy.

The first known description and practical use of a physical pendulum is by Galileo Galilei, however, Flinders Petrie, a disciple of Charles Piazzi Smyth, is of the opinion that it was used earlier by the ancient Egyptians. Writing in an article in Nature, 1933 Petrie says:

If we take the natural standard of one day divided by 105, the pendulum would be 29.157 inches (0.7405878 m) at lat 30 degrees. Now this is exactly the basis of Egyptian land measures, most precisely known through the diagonal of that squared, being the Egyptian double cubit. The value for this cubit is 20.617 inches, while the best examples in stone are 20.620±0.005inches.

By the time measurements of Mesopotamia were discovered, by doing various exercises of mathematics on the definitions of the major ancient measurement systems, various people (Jean-Adolphe Decourdemanche in 1909, August Oxé in 1942) came to the conclusion that the relationship between them was well planned.

Livio C. Stecchini claims in his  A History of Measures:

The relation among the units of length can be explained by the ratio 15:16:17:18 among the four fundamental feet and cubits. Before I arrived at this discovery, Decourdemanche and Oxé discovered that the cubes of those units are related according to the conventional specific gravities of oil, water, wheat and barley.

Stecchini makes claims that imply that the Egyptian measures of length, originating from at least the 3rd millennium BC, were directly derived from the circumference of the earth with an amazing accuracy. According to “Secrets of the Great Pyramid” (p. 346), his claim is that the Egyptian measurement was equal to 40,075,000 meters, which compared to the International Spheroid of 40,076,596 meters gives an error of 0.004%. No consideration seems to be made to the question of, on purely technical and procedural grounds, how the early Egyptians, in defining their cubit, could have achieved a degree of accuracy that to our current knowledge can only be achieved with very sophisticated equipment and techniques.

Alexander Thom

Oxford engineering professor Alexander Thom, doing statistical analysis of survey data taken from over 250 stone circles in England and Scotland, came to the conclusion that there must have been a common unit of measure which he called a megalithic yard. This research was published in the Journal of the Royal Statistical Society (Series A (General), 1955, Vol 118 Part III p275-295) as a paper entitled A Statistical Examination of the Megalithic Sites in Britain.

As Professor Thom observed in his book Megalithic Sites in Britain (1967):

“It is remarkable that one thousand years before the earliest mathematicians of classical Greece, people in these islands not only had a practical knowledge of geometry and were capable of setting out elaborate geometrical designs but could also set out ellipses based on the Pythagorean triangles.”

Robin Heath

Later, these ideas were further developed as defense for the Imperial units against the emerging metric system, and adopted by parts of the anti-metric movement. Robin Heath, in his book Sun, Moon & Stonehenge, connects the megalithic yard (and thus Stonehenge) to the imperial foot, and manages to connect a few astronomical phenomena, and the Egyptian Royal Cubit (and thus the Great Pyramid) into one grand equation (MY is an abbreviation for megalithic yard):

If the lunar year is represented by 12 MY then 1 ft corresponds precisely to the extra 10.875 days to coincide with the end of the solar or seasonal year. Furthermore, the period between the end of the solar year and 13 lunations – 18.656 days – is represented by another unit of length from antiquity, the ‘Royal Cubit’ of 20.63 inches or 1.72 ft.

Note: 1 solar year = 365.24 days,
1 lunar year = 12 lunar months = 354.36 days.
(1 lunar month = the time between full moons = 29.530589 days, therefore 1 lunar year = 12 * 29.53 = 354.36 and 365.24 – 354.36 = 10.88.
Therefore
1 solar year = 1 lunar year (12 lunar months) + 10.88 days. 

If 1 lunar month is represented by 1 MY we get 29.53 days represented by 2.72 feet (or 10.8566 days are represented by 1 foot).
One lunar year (12 lunar month) = 354.36 days represented by 12 MY = 12* 2.72 feet= 32.64 feet
Also 13 lunar months = 13*29.53 = 383.89 days. 
13 lunar months – 1 solar year = 383.89 – 365.24 = 18.65 days (representing 1.718 feet = 1 Royal Cubit).
18.65 /10.8566 = 1,718 feet = 1 Royal Cuibt

This seems to bring pseudo-scientific metrology to new heights, especially in view of the conclusion:

Hence the equally astonishing revelation that 1 MY = 1 ft + 1 RC. Assuming that the MY was the primary unit, then the derivative foot and cubit appear to have formed a logical and essential part of the astronomical and calendrical researches of our Neolithic ancestors. If, however, the foot preceded the MY in time – and here we must remember that 1/1,000th of a degree of arc around the equatorial circumference of the Earth is just 365.244 ft in length! – then knowledge of the roundness of the Earth must have predated use of the MY…i.e. well before 3,000BC. There are no other choices readily apparent!

J. Michell claims that all over the world traditional units of measurements are related.
He goes on to point out the value of the pu that still survives in Indo-China is given in L.D’A. Jackson’s Modern Metrology (available on the net) as 2.7272 miles with the fraction repeating. Without knowledge of the pu’s existence its former use in Britain was deduced by J. F. Neal, who called it the Megalithic Mile because the ratio is similar to that between the foot and the Megalithic Yard.

Since the ratio between the dimensions of the Earth and Moon is 10:2.7272 the following relationships unambiguously exist.

Earth’s diameter = 7,920 miles
Moon’s diameter = 792 megalithic miles
Perimeter of the square containing the circle of the Earth = 31,680 miles
Perimeter of the square containing the circle of the Moon = 3,168 megalithic miles.
Sun’s diameter = 864,000 miles = 316,800 megalithic miles.

More information: http://blog.world-mysteries.com/science/ancient-timekeepers-part-5-units-of-measurement/

Units of Time

Observing movement of the Sun and the stars suggested that Earth is spinning around its own axis and that the Sun is moving against the background of constellations. This suggested there are 2 cycles: earth axis spin cycle and earth around the sun orbital cycle.

In ancient times it was easy to observe the Sun in order to establish units of time so it is good assumption that such units would be “solar units of time”. We use them today and call them “solar days” or simply days (as opposed to stellar background based “sidereal days”). It was also easy to observe the moon and the stars at night. 

Hipparchus (190-120 BC) and his predecessors used various instruments for astronomical calculations and observations, such as the gnomon, the astrolabe, and the armillary sphere. Hipparchus is credited with the invention or improvement of several astronomical instruments, which were used for a long time for naked-eye observations. According to Synesius of Ptolemais (4th century) he made the first astrolabion: this may have been an armillary sphere (which Ptolemy however says he constructed, in Almagest V.1); or the predecessor of the planar instrument called astrolabe (also mentioned by Theon of Alexandria). With an astrolabe Hipparchus was the first to be able to measure the geographical latitude and time by observing stars. Previously this was done at daytime by measuring the shadow cast by a gnomon, or with the portable instrument known as a scaphe. [ -- Wikipedia ]

Illustration below shows ancient Egyptians’ interest in astronomy.

The Northern [Bottom] and Southern [Top] Panel ‘Decan Chart’ from the Tomb of Senmut [c 1500 BC]. [In reality this panel is about 4 m long.] The decan system was actually used as a clock for time keeping in the night hours and through the year – modern Egyptologists call them Egyptian sidereal clocks.

After these cycles were noticed (discovered) the next step would be to quantify them (describe them using specific units of measurement).

Numbers like 360, 72, 30, 12 and multiples thereof were intentionally plotted in ancient myths. It was as if the storyteller were trying to convey a secret code. Here’s what the figures signify in the precession cycle:

•  360 degrees = 12 x 30 degrees, or one full circuit through the zodiac constellations
• 72 years = the time it takes for the stars to shift 1 degree
•  30 degrees = one astrological age (a different zodiac constellation rises with the Sun every 2,160 years)
•  12 = the total number of zodiac signs or astrological ages. 12 times 2,160 = 25,920 years, or one full precession cycle

•  In Babylonia, the ancient scribe Berossus wrote that mythical kings ruled before the Great Flood for a total 432,000 years.
• In India, the Rigvida contains exactly 432,000 syllables. And although the calculation has created some confusion of late, the Vedic Kali Yuga (representing the current world age) is said to be comprised of 432,000 years.
• On the other side of the globe, Mayan calendar units parrot the precessional figures.
  For example: 1 tun (an astronomical year) = 360 days;
  6 tuns = 2,160 days;
  1 katun = 7200 days,
  6 katuns = 43,200.
  The standard Mayan base of 20 (ours is 10) is arrived at by dividing 43,200 by 2,160.

Today we use decimal system (multiples of 10) however when it comes to measuring angles, we use ancient convention: a circle is not divided into 100 (or 1000 parts), instead it  divided in 360 units (called degrees) and each unit is further divided into 60 equal pats called minutes and each one of these is further divided into 60 equal units called seconds.
A full circle has 360 degrees, 21,600 (360×60) minutes and 1,296,000 (360x60x60) seconds.

Ancient divided the whole sky into 12 equal parts called constellations.

• Zodiac (circle division): 12 equal parts (or 4×3): 4 quarters each into 3 and further each third into 10 (4, 3, 10)
• Each Constellation had 30 degrees (360/12)
• 30 degrees = 1,800 minutes = 108,000 seconds.

Dividing the daily cycle into equal parts established units of time.
Ancient divisions were not decimal but based on 24 and 60:

1/24 of the Earth spin cycle was unit we call now 1 hour, Each hour is divided into 60 equal units (called minutes) and each minute is divided into 60 equal units (called seconds).

The finest unit of time in ancient times was one second:

1/(24x60x60) = 1/86400 part of one spin cycle (1 day). In other words 1 rotation cycle of the Earth (one day) has 24 hours, 1,440 minutes and 86,400 seconds.

Each day was divided into 24 parts called hours, each hour into 60 minutes and each minute in to 60 seconds (today we divide seconds using decimal system; 1/10, 1/100, 1/1000 (millisecond).

Each day has 24 hours = 1440 minutes (24×60) = 86,400 seconds (24x60x60).

The Earth turns 15 degrees per hour (1 degree each 4 minutes).

Astronomy and Calendars

All calendars began with people recording time by using natural cycles: days, lunar cycles (months), and solar cycles (years). Ancient peoples have attempted to organize these cycles into calendars to keep track of time and to be able to predict future events of importance to them, such as seasons (e.g. the annual Nile flood in ancient Egypt), eclipses etc. The main problem was that these natural cycles did not divide evenly.

Early people could either try to stay in sync with the moon, perhaps making months alternating combinations of 29 and 30 days, with special rules to re-sync occasionally with a solar year by adding leap months (such as the Jewish or Chinese calendar) or abandon lunar cycles and concentrate on the solar year (such as the Ancient Egyptian calendar of 12 same-sized months).

Today, the solar year is 365.242199 days long (or 365 days 5 hours 48 minutes 46 seconds) and the time between full moons is 29.530589 days.
Therefore in 1 year there are 12.37 moon cycles (365.24 / 29.53 = 12.37).

The Moon makes a complete orbit around the Earth with respect to the fixed stars about once every 27.3 days (sidereal period). However, since the Earth is moving in its orbit about the Sun at the same time, it takes slightly longer for the Moon to show the same phase to Earth, which is about 29.5 days (its synodic period).

Nature’s Nearly Perfect Calendar

The Moon could be “Nature’s perfect clock” if the solar cycle period were exactly divisible by the period of the lunar cycle.
For example if the solar year were exactly 364 days (instead of 365.24 ) and lunar cycle exactly 28 days (instead of  29.53), we would have a “perfect calendar” based on 13 months of 28 days per month, with each month having 4 weeks of 7 days. Such calendar was proposed as “13 Moon Calendar”  (discussed later in this article) with the 365th day called the “Day Out of Time”.

Another “perfect calendar” would require solar year to have 360 days and lunar cycle 30 days:

• The “perfect” Earth would take 360 days to complete 360 degree circular solar orbit (1 deg per day).
• The “perfect” Moon would take 30 days to complete 360 degree circular orbit around the Earth (12 deg per day).
• In such case,  we could have a year based on 12 months of 30 days. Each month would have 5 weeks of 6 days each.

We can only wonder if these numbers were true for the Earth  in the the early period of the solar system…

13 Moon Calendar

A Culture of Peace through a Calendar of Peace

The 13 Moon Natural Time Calendar is based upon Dreamspell – a universal application of the mathematics and cosmology of the Classic Mayan Calendar and Prophecy of 2012 as deciphered and presented by Jose and Lloydine Arguelles.

Around the world, people of diverse beliefs and cultures are unifying with the 13 moon calendar as a global harmonic standard – thirteen moons of 28 days, with one day to celebrate “Peace Through Culture” before each new year (July 26).

Introduction to the 13 Moon Calendar:

The Thirteen Moon/28 day calendar is a perpetual, harmonic calendar. It is called a Moon Calendar because it is based on the female 28-day (average) menstruation cycle, which is also the average lunar cycle. The measure of the moon from new moon to new moon is called the synodic cycle and is 29.5 days in length.

However, the sidereal lunar cycle which measures the moon from where it reappears in the same place in the sky is only 27.1 days in length. So 28 days is the average lunar cycle.

In actuality the moon goes around the Earth thirteen times a year. This means that the 13 Moon calendar is a genuine solar-lunar calendar which measures the Earth’s orbit around the sun by the lunar average of 28 days.

Thirteen perfect months of 28 days = 52 perfect weeks of 7 days = 364 days.
 
The 365th day is called the “Day Out of Time” because it is no day of the week or month at all. This day which falls on the Gregorian correlate date of July 25 is a day for forgiveness and for the artistic celebration of life and freedom.

The synchronization, or new year’s date of the 13 Moon calendar is July 26. This corresponds to the rising of the great star Sirius. This makes the 13 Moon Calendar a tool for harmonizing ourselves with the galaxy.

Perfect Periodicity
For every one time we go around the Sun,the Moon goes around Earth 13 times.
The year has already been divided by Nature-13 ‘moon’ths of perpetual harmony.

Related Links

• http://blog.world-mysteries.com/science/ancient-timekeepers-part4-calendars/
• http://blog.world-mysteries.com/science/ancient-time-keepers-archaeoastronomy/

Cosmic Harmony

Earth Facts

Revolution Period around Sun: 365.2425 days

Rotation on Axis: 23 hours and 56 minutes and 04.09053 seconds.
Note: it takes an additional four minutes for the earth to revolve to the same position as the day before relative to the sun (i.e. 24 hours).

Axial Tilt: 23.4 ^o (23°26’21.4119″)

Earth’s Circumference at the Equator:
21,638.855 nautical miles = 24,901.55 miles (40,075.16 km)
Earth’s Circumference Between
the North and South Poles:
21,602.6 nautical miles = 24,859.82 miles (40,008 km)

Earth’s Diameter at the Equator:
6,887.7 nautical miles = 7,926.28 miles (12,756.1 km)
Equatorial Radius (1/2 of the diameter):
3,443.9 nautical miles = 3,963.14 miles (6,378.05 km)

Earth’s Diameter at the Poles:
7,899.80 miles (12,713.5 km)
Polar Radius: 3,950 miles (6,356.75km)

Average Distance from the Earth to the Sun:
93,020,000 miles (149,669,180 km)

Average Distance from the Earth to the Moon:
238,857 miles (384,403.1 km) 

The closest distance between Earth and Sun is 147 x 10⁶ km, which converted to Royal Egyptian Cubits is 280 x 10⁹  ( 280 cubits is the height of the Great Pyramid).

Observe the measurements of the Moon:
Equatorial radius 1,738.14 km (0.273 Earths) so
the Moon Diameter is: 3,476.28 km or 2,160 miles.
Let’s make this “the cosmic unit” (one moon unit)
representing the “ideal” diameter of The Moon.

Diameter of The Sun =865,294 miles*.
If we divide 865,294 by 2,160 astonishingly
we get 400.6 …