This is a compilation of material I have spoken to and written about in the past summarizing an intact version of ancient cubit rod measures.
In hopes of improving the human condition, I wanted to reason out this thread with a full understanding of cubits in the rods from which they operate before I move on to the next thread. The attached PDF's are to be read side by side to square actions. Due to file requirements, I had to scale down and separate the associated pictures PDF.s , they will expand to 400%.
Cubit Rod Composition part 1 (Introduction)General topics:
The thought process behind the cubit rod
In graduates, the standard length of a digit/cubit would correspond, in parallel, with that of inches, yards and millimeter/meters because a cubit rod hierarchy consists of all these measures. More specifically, the millimeter, meter, yard, inch and their fractions of, in a radial display. SI units (mm) and the inch system was derived from an integral to a cubit rod. It is curious how mankind re-scripted cubit structure through the ages. Ancient wisdom as well as astronomy, divinities, the Egyptian and Mayan calender's, prophet forecasting and most notably, stone mason mathematics, held theorems absolutely true from one scale. In general, cubit scales are a theory of everything, a final theory in the description of nature. Ancient cubits once were a number unification theorem with an explanation found in the progression of the cubit rod ratios:
7, 28, 4 (Egyptian)
4, 16, 4 (Sumerian)
6, 24, 4 (Biblical)
9, 36, 4 [Babylonian (the last evolved cubit rod ratio 539 B.C.)]
One can see an advancement in the incorporation of the circle formed 36 unit rod of Babylon with each of the 36 units/digits in 10 degree increments for radial 360º calculation. This is in parallel to Ancient Egyptian astronomy having 36 groups of stars (small constellations), every 10 days a new constellation would have a heliacal rising. A total of 36 decans were observed and were presided over by a deity throughout the year. For thousands of years, the hour and the ancient calendars were calibrated to the degree. The last evolved cubit rod of Babylon simplified these radial mathematics from above (the Heavens) to below (the Earth) before it was removed from mankind’s time-line. Mankind's inheritance is above.
So, did the ancients have a mathematical unification theorem to “all is number” ? The answer is yes. One unit of measure (cubits) produced a lot of divine societies and the plagiarized sacred geometry that drove them, more relevant, in the years after the fall of Egypt and Babylon (525-539 BCE), the divine sect of Pythagoras and his endeavor. Pythagoras, instead of using root length numbers as a basis, squared the right triangle from whole numbers up. Why re-compose? Well, it is written that Cyrus the conqueror of Egypt and Babylon met with Pythagoras and would have executed Pythagoras if he kept cubits in the forefront. Cubits would have been viewed as a method of undermining Cyrus' rule (thus, producing a secret society). The one and only thing that united the ancient world of Egypt and Babylonia was the philosophy of Thoth's cubits. All of Pythagorean's work from right angle theorem, Musica Universal, and Pythagoras' musical scale was accomplished from one unit of rule, cubits the math of the previous kings. It is only logical that Pythagoras studied with the Egyptian priests and the Babylonians for years with full knowledge of a cubit rod.
Before furthering this article, I would like to answer the question “Why was cubits of various lengths employed in many parts of the world in antiquity?” This is because the length is broken down from a unit, a cubit could be assigned any standard length measure. The standard unit only sets the scale. For example, √2 will always be the hypotenuse means of a square and √3 will always be the diagonal means of a cube. In another words, the square segment set to a unit, is all that is needed to set these constants in motion. These constants have been here long before mankind. Mankind only sets the unit to define this reality.
Cubit rod composition part 2 (Cubits , SI unit and its noted relation to the British inch)General topics:
Root table mechanics
Inner workings of a cubit rod
So, what is a cubit rod and how does it function? The utilization of a unit and a constant or an opposite and an angle as shown in Rhind Papyrus number fifty-three.
(Pic 1) ● A cubit rod needs to employ two pieces of wire-frame geometry to compute (as seen, segment and an angle).
I'll further explain in a right angle example
(Pic 2). By assigning the square segment into a tier of rod root lengths and its diagonal or angle length to a tier of digits, in this instance, the segment of the cube equals a √length and the hypotenuse is assigned to digits of a unit. This is the bygone ingredient of allowing geometry to energize the rod. Why a root length increment? Respectfully, we are taught to associate roots to the unit number, where geometry and unit line length never align.
(Pic 3) The line-like root length gets smaller and smaller as it graduates (units in this fashion are not used as measurement in geometry) whereas equal root length increments, square units and opens geometric volume and space. All digit rods
are squaring rods.
(Pic 4) Tablets such as Plimpton 322 (1800 B.C.) would be the necessary steps to define and calibrate a new rod. Mathematical squaring tables are an easy understanding of the applied math in a good explanation.
(Pic 5) If you envision the entire column as line length
● (the vertical line shown next to the upper right table) and the rows as increments in that line, the sum(s) of the column are how root length measures increment or graduate geometrically in that line. These measures like Plimpton 322 would have been displayed and utilized in parallel on a cubit rod. Let's glance at some unearthed rods of the past,
(Pic 6) the tiers are labeled for this assessment. Herein digits will be shown in a combined outgrowth communication with √length in a square segment to hypotenuse relationship or more so, Pythagorean √2 (the square mechanics, as depicted in
picture 2). This methodology is shown and applied into the modernized 36 digit rod of Babylonia
(Pic 6) ● (the last one of the three rods displayed). The standard unit will be portrayed inside of the inch to get a broader grasp of cubit scaling in a mathematical perspective.
The following applied terminology,
● is explaining its build, one tier at a time:
Digit subdivisions: a mediator between √lengths and an inch unit that subdivides into 2 cubits
Cubits: 0.5 graduations of the set unit and radiant work flow, where1 turn equals 2 cubits (same mindset as radians)
Fractions: as well as decimals and the inch are respectfully graduations of the 2 cubit set unit. Fractions by simple means are a ratio by palms in 4 subunits. The denominator is the mechanism from which the cubit and digit ratio is sized
●Decimals: derived in the set unit
●Inch: bounds the unit to a set amount of digits
●√Length: √length integration allows right angle theorem to calculate and exercise in synchronicity to the unit scale
In a further conception of √length integration, (still in view of the last rod depicted in
Pic 6) the hierarchy of a cubit rod utilizes root lengths calibrated with digits. In this example, in using Pythagoras √2 as increments, a rod deployment unit of √2 at 36 increments as shown, would equal 25.455844122715710878430397035775 (√648) length. Keep in mind, modern calculators round up. Thirty-six increments equal 1 unit inch (9/9ths) or incrementally by a 36th viewed as 36 increments equaling 1 yard.
(Pic 7, the concept shown outside the inch)
● Note, scaling at 2 cubits equals a 1 inch unit. Pythagorean and Euclid math is commonly spoken in 2 dimensions, where this type of dimensional √length integration also calculates respective mass properties utilizing root measures and the right angle third leg in partnership. And since units only set scale, to remove the restraints, and zero out a magnitude of geometric actions and ancient engineering,
(Pic 8) if you took the standard inch unit block and added .00219” to the inch block. The millimeter would then calibrate to 25.455mm which is √648 (√2 at 36 increments in a one inch unit). This would unite the homogenized mechanics of the modern yard, the millimeter, the inch, the rationale of the Babylonian cubit rod, radial degrees and right angle theorem in ancient sacred geometry as it was practiced. It is really that simple. In the ongoing example of the modernized Babylonian digit rod, the √2 hypotenuse now becomes the gateway to the square or in general terms, opposite to adjacent, the hypotenuse into a diameter, into platonic solids in an outreach in natural educations of right angle theorem across geometries.
(Pic 9) Just by assigning a unit to the square segment and a constant to an angle, all mass property and vertexes are well known ingredients bound in a unit with the numbers in a geometric locking pattern. The area and volumes in unison, harmonically exercised together in Pythagorean arithmetic. This mannerism is at the core of ancient mysticism (geometry figured from known geometry). Note, in a further view of the Babylonian rod and how the tiers are rationalized, if reading transcript instead of watching the video, to access arithmetic value, separately apply these equations to
(Pic 6) the last rod depicted. This is how you gauge the merit of the rod and the numeric woven abilities.
Periodic Conversions: (Examples in calculations from digit 27)
√Length x √2 = Digit
19.091 x √2 = 27
Digit / 4 = Numerator
27 / 4 = 6.75
Digit / 36 = Inch
27 / 36 = 0.75
Digit x (Numerator x 2) = √Length squared
27 x 6.75 x 2 = 364.5
Fraction numerator x √8 = √Length
6.75 x √8 = 19.091
Inch x 9 (Fraction Denominator) = Numerator
0.75 x 9 x 27 = 6.75
Digit x 9 (denominator) x Cubit = √Length
27 x 9 x 1.5 = 364.5
Digit / 2 x Digit = √Length squared
27 / 2 = 13.5 x 27 = 364.5
Inch x √648 = √Length
0.75 x √648 = 19.091
Cubit / 2 = inch
1.5 / 2 = 0.75
Cubit x 18 = Digit
1.5 x 18 = 27
Cubit x 180 = deg.
Cubit x 180 = 270º
(decimal x 2 = cubit)
In absolute respect to the ancients, the above example equations were to display the magnitude of geometry driven numerology. Since I mentioned Euclid, I'll give you a quick example of rod deployment.
(Pic10) The first square segment
● is dimensional to the Babylonian rod depicted earlier, 36 digits, √648 length at 9/9ths. The set unit or multiples of, become Pythagoras on steroids when stretching rope from vertex to vertex. The dimensions are displayed in exact digit measures, rationalized. Also, area and volume of a cube become Pythagorean volume squaring actions. (The prescript result
● shown in the upper right hand corner).
Cubit rod composition part 3 (Fraction) General topics:
Construct of Palms
As you may have noted in the Babylonian rod and Euclid depiction, fractions on a cubit rod are ordered differently such as 9/9, 16/9, 25/9. This enables the numerator and denominator to calculate separately within the rod hierarchy. As demonstrated earlier in the Periodic Conversions (equations), the denominator and numerator are calculated separately. This being the significance of Egyptian fractions, by calculating fractions in this manner, it doubles the computing power of ancient fractions. In adding to an article written from Dr. David Ian Ligthbody (
link) on the Edinburgh stone, and to appropriately highlight fractional intent, the accompanying partial royal scale will provide insight taking the opportunity to re-order the hierarchy to the respective scale (Egyptian.)
(In Pic 11) Dr. Ligthbody's discovery (May 7, 2013), pyramid Khufu's seked, (seked: the surface inclination of a triangular pyramid). In terms of a right angle, 1 unit opposite (altitude) to 5.5 adjacent,
(Pic 12) this would be in agreement with the fractional numerator of an Egyptian palm in a digit relationship. 4 digits to 1 palm is 1/7th , and
● 5.5/7th of a palm is at 22 digits. With the royal Egyptian cubit rod set unit applied to
● the pyramid of Khufu, 280 cubits opposite (altitude) or 28 digits (one unit rod) multiplied by a factor of 10 by 5.5/7 of the unit, adjacent (constant), PI. A description of nature as earlier mentioned, also seen in the pinwheel Milky Way and the arrangement of body parts, a unit to constant relationship (Phi). The one thing the ancients strongly emphasized was a unit to a constant relationship. Contrary forces are complementary, interconnected, and interdependent to each other. Therefore, Khufu's sums are a result of the same shown root mechanics (constant) and cubits (whole number units) being calculated by right angle geometry governed in a set unit.
(Pic13) We tend to view right angle theorem in a whole number format overlooking the natural function of a fraction and the ability to communicate in the same manner. The primal design of a palm constructed by 4 instances is primarily in association to
(Pic 14).
Then, why sevenths in an Egyptian rod? When adding, your answers will always be in some sequence of .142857 etc., (as 7ths do) this arrangement lets you know correct addition procedure, but more so, in the scale of things, cubit rod graduations. 7ths in 28 digits (lunar), 8ths in 32 digits, 9ths in 36 digits (solar), 10ths in 40 digits or Mayan, 5ths in 20 digits, etc. These are of cubit rod ratios from the ancient architects of the past.
Cubit rod composition part 4 (Radial)
General topics:
Circle length to line weight
√2 associated to arc length and the radial degree
A radial explanation of root measures around the radian
Shown in
(Pic 15) is the dimensions of the unit circle. The arc length of this unit circle is numerically equal to the measurement of √(2Pi x Pi) the sum 4.4428 inner square segments diameter formed. The segments are realized in the lower left hand corner of
(Pic 16).
● The smaller diameter as illustrated is a redefined radian under the same shown leadership of geometry, the Pythagorean √2 square. Instead of radii segments being used to determine arc length (s=rθ ),square segments are used as arc length communication and accordingly, become webbed calibrations within the rod. In the larger diameter shown, the √2 rod is sized around a diameter by a circle formed means of 36 digits multiplied by 10 graduated into 360º. Where one cubit equates to 18 digits on the rod
● multiplied by 10, equals 180º placement on the diameter. Respectfully, 2 cubits equate to 36 digits on the rod multiplied by 10 equals 360º placement on the diameter. In another words, the former 2 Pi radians become 2 cubit in one rotation placement.
Before moving on, in order to provide a mental representation of the unit circle in view of the ability to form a circle using a rod, let's unpack the cubit fractions displayed around the diameter. Since 1 cubit
● is at 180º or 180º divide by 10, 18 digits locational on the digit rod, in essence, a half rod and/or turn. Respectfully, 3 cubits would equal a rod and a half or turn and a half at 54 digits or 540º. To forecast the 270º fraction (3/2)
● located at the bottom of the larger diameter, 3 (three, the numerator and digit means) multiplied by 180 equals 540º / 2 (two, the denominator and cubit means) equals 270º.
On the far mid-right of the illustration
● are numbered symbols in the column. These are the cubits and fractions of turns displayed around the larger diameter. The symbol Pi is associated from a radius to a Pi radian. Therefore, I created a new symbol in order to distinguish a square segment to radial means.
● The numbers in the first column correspond to cubits, “the new symbol” assigned as mentioned represents the square/cube means to Pi arc length shown in the equations located under the “to arc length column”. The equations and where the numbers are integrated into the rod is the geometric framework of our ancestors. To explain, perpendicular in the
● “2 new symbol cubit row”, the inner coincident square segment is multiplied by the root of 2 x Pi x Pi, the sum 4.4428 equaling arc length of the unit diameter at one revelation. Accordingly, at 3 cubits, segment multiplied by the root of 4.5 x Pi x Pi, the sum being 6.6643 is the arc length at one and a half turns, divided by the fractional denominator 2 of the
● 3/2 bottom diameters displayed fraction equaling the arc length of the unit diameter at 270º (3.33215).
What is meant by “the segment is multiplied” in the first operation of the equation(s) shown? The segment sizes the diameter, or in other words, the diameter's line itself is also the hypotenuse of its inner coincident square. So, the diameter divided by √2 is naturally the segment size. √2 is the communicator between the rod and diameter. These numbers were generated by the digit rod
(Pic 17) in the √length squared tier of the rod. Note, located at digit 2,
● the first number in the x Pi x Pi operation. Located at digit 3, the squared root of
● 4.5 and so on.
(Pic 18) Digits and cubits share the same common means being that the rod is an evolved sequence of numbers populated by the dimensions of the square segment. The hypotenuse is interchanging and inhabited in digit and √length increments. The √2 table increments shown earlier are the chosen geometry that drives the measures, quite opposite of the measures today. The modern unit fully defines geometry, while ancient geometry fully defined the cubit.
(Pic 19) Lastly, the angle made when one square segment is wrapped around a unit circumference is 81.028 degrees, that is 360 / π /√2 or for a full mathematical grasp, 360 / √(2Pi x Pi) = 81.028º / √2 = 57.2957 radian.
To convert from degrees into arc length: ( / is divided by)
Circular degree / 81.028º x segment (same segment means mentioned earlier)
Ex. 360º / 81.028º = 4.4428 arc length of unit circle.
Also applicable, degree / 10 x π / √648 “the unit rod length.”
Ex. 360º / 10 = 36 x π = 36 π / √648 = 4.4428.
The architect's set unit controls all measures. To push it a step further,
(Pic 20) take a look at the square segment unit circle allocated to weight, wherein the geometry drives the inch to metric conversion. The pound equal to the arc length at 1 cubit rotation and 1unit segment equal to 1kg. To take that a step further, you can add another tier of √3 lengths
(Pic 21) which would be considered as square segment to the diagonal of the inner coincident cube to sphere diameter.
(Pic 22) This is the insight into the
● 1:1 and
● 2:3 Pythagorean musical scale wherein,
● √432 and
● √648 in hertz are housed. Mass and harmonics being one in the same. Basically, 3 and 4 in a carpenter's sense of squaring a right angle. (Based on the simplest Pythagorean Triple, with the side lengths being 3, 4, and 5 units.) Notably, unearthed ancient musical instruments from Egypt and Greece were predominantly tuned at 432 hz.
And finally,
(Pic 23) to put rod calibrations in perspective, in this unit diameter, any of these segments and their respective angles could be set as rod functionality, dependent on your desired path of discipline. As the example shown, the triangle segment wrapped around a diameter would equal 3.6275 circle formed segments under a whole new leadership of radial navigation. Cubit rod ratios are infinite in choice and are in
complete communication with each other through geometric matrix reasoning.
Cubit rod composition part 5 (Sacred)General topics:
Solomon's lesser keys
Merging the ancient world with the modern
(Pic 24) In the Lesser Key of Solomon, the 72 demons according to texts, are described as being commanded by four kings of the cardinal directions: Amaymon (East), Corson (West), Ziminiar (North), and Gaap (South). The ancient texts of Ars Paulina, is in turn, divided into two books, the first detailing twenty-four angels aligned with the twenty-four hours of the day, the second (derived more from the Heptameron) detailing the 360 spirits of the degrees of the celestial bodies. In both cases, these are applied entities to cubit structure. In re-reading this as math, it is rod functionality:
360 spirits of the degrees of the celestial bodies equals 36 increments multiplied by ten degree divisions of, decans at 30º longitude. Twenty-four angels aligned with the twenty-four hours of the day, the second equals 1,440 min. / 24hr segments equals 60 sections.
●72 Demons = Digits
●Four Kings = Cubits
●Two books = A rod above and a rod below (two rods raised vertical, squaring actions)
The Components of the Mayan and Egyptian Calendars:The Mayan Long Count calender is based on
● 20 katun cycles of 144,000 days each.
The Egyptian calender is constructed from Egyptian astronomy consisting of a 36 decan year. One decan is defined by a 10 degree rotation in the zodiac lasting for a period of ten days. A one year rotation divided into 36 decans/digits with 1 and 2 cubit placement at the solstices. This in an extension of the Royal, 28 digit Egyptian unit rod (28 day lunar cycle) of basically adding an additional 2 palms or 8 digits to arrive at the evolved 36 digit, Babylonian unit rod (the ancient 360 day solar cycle). Or more so, the practiced Egyptian conversion of scales between the eyes of Horus. The Egyptian measures were calibrated to the lunar cycle, in predicting planetary shifts in the moon's cycle. The Egyptians were masters of the affects of tide, a critical control for the Nile. In predicting the solar cycle, the philosophy of mathematical cubits were well preserved in Egyptian sun temples with their results still in practice today. The ancient Egyptians used the shadows of the sun temples giant stone obelisk cast on the ground to tell the time divided in a day into sections of 10 (rod) and 12 (hour) standardizations of cubit measures. Sexagesimal – in modern time (in view of the illustration)
3 increments (palm) per hour equals
● 60 subdivisions of x 24 hours equaling 1,440 minutes in a day. These were exclusively the ancient solving properties of cubits and degrees.
In furthering this description, in the illustration, each of the 72 increments in
● 20 subdivisions equals a sum of 1,440 subdivisions overall. In wielding set measures, 1/20th of a subdivision set at √φ length with two subdivisions equalizing 1φ length,
(Pic 25) ● circumferences and increments result cleanly. This in the ancient utilization of two pieces of geometry to custom time constants and units.
Where else have the masters left this knowledge?
Rod Unit measures in 72 Increments Corresponding with the Equinox or...-The 72 disciples of Confucius.
-The 72 companions of apotheosis of Houang-ti.
-After his temptation in the dessert, Jesus is served by 12 superior angels and 72 angels.
-72 is the number of the Immortals Taoism.
-The Chinese astrology has 36 beneficial stars and 72 malevolent stars.
-The "Sentur" Persian has 72 cords.
-72 divine names in one of the Jewish systems said to be used as codes in creation.
-The 70 ancients accompanying Moses that received an outpouring of the spirit, plus the 2 absent.
-In Cao Dai, the number of planets between hell and heaven.
-Thoth, of Egyptian Mythology wins a 72nd of each day of the year from the Moon in a game of Draughts.
*4 cubit instantiates : Cosmic, Systemic, Planetary and Hierarchical in 72 increments, etc...
In closing, in clarifying the endless different incremental rods of different arrangements from around the world, these rods are not ceremonial by any means. They are the architects hierarchic thought process of computing his rod. Since individuals and societies apply math differently, each architect's rod would utilize different routes to the sum. In short, the architects' rod is his identity of using a hierarchy to reach the sum. An individual's natural process might read and rearrange the path of hierarchy to accommodate preference and performance of working geometries. Keeping in mind during Solomon's time, there were 3 different cubits applied: A land cubit for plotting, a building cubit for construction, and a gold cubit for decorative work, such as silver vessels, all relating to each other, composed for different purposes, and all consisting of a constant in cubit agreement.
As this article presents, cubits as an ancient philosophy are profoundly simple enough to define any desired outcome. As mentioned, just by adjusting unit length in mankind's unit will encompass the more accurate based results seen by our ancients. Mankind will never gain the true inheritance of above without this realization. To leave the reader with a final thought, all of the 7 wonders were designed and constructed from cubits. Imagine all the other potential world wonders that were diminished into mere ideas instead of constructional realities due to the absence of cubits from society. More modernly, the input scales of global warming models.
If requested, I could forum Email Associated pictures PDF. in a proper format for picture clarity.