The Enigma of 24 | Robert Edward Grant

 

1. 24  =  4 x 3 x 2 x 1 — Pythagoras’ Tetractys
2. (((10^.5) / 10) + 1) ^ 1 / .24)-(((((4 / π) / 2) + 1) * 10^2) / 360) * 10^-3 = 3.1415926 (perfect π to six decimal places)
3. 360°- (φ x 360°) = 2.4 Radians (137.51°—The Golden Angle), (One Radian = 57.296°)
4. Fibonacci Numbers in Digital Root (Mod 9) analysis (reduction to single digit thru simple addition in Mod 9) PATTERN REPEATS every 24 numbers
5. Musical scales possess 12 notes per Octave (sine wave) and an additional 12 notes for the next octave (cosine), there are 24 total Major and Minor Keys
6. The Vector Equilibrium (Cube Octahedron) has 24 edges
7. >3 All Prime Numbers (and Quasi Primes) are arranged in Mod 24 (spoke 1, 5, 7, 11, 13, 17, 19, 23) without exception
8. >3, All Prime^2 values are multiples of 24,+1 without exception
9. The full Flower of Life has exactly 24 circles in its outermost perimeter
10. (π^π) / (e^e) = 2.4

What is it about this number? Is it because it is the smallest of only three Prime and Quasi Prime number pairs (.571 (Ω) and 175 (1/Ω)/.731 (α) and 137 (1/α)) whose Reciprocal Value is equal to it’s Palindrome (24 has a Palindrome of 42 AND 1/24 = .042). Interestingly and even more enigmatically 137/57 = 2.4 AND 175/73 = 2.4 as well …

Also, we have 24 hours in one day, and the Sum of Interior Angles of a 24-sided polygon (Icositetragon) is 3960°… which also happens to be the exact Radius of the Earth in miles … Was Hitch Hiker’s Guide to the Galaxy right after all in proposing that the ANSWER to the Universe really is 42 (and therefore it’s reciprocal value of 24)?

Reference:
Robert Edward Grant (2019) - The Enigma of 24.

 

See also:

TPR (2023) - Chinese 24 Solar Terms & Lunar Cycles in 2023.

Unity and Source | Seyyed Hossein Nasr

Omnia in uno sunt, et in omnibus unum.
All things are in one, and in all one.
Athanasius Kircher (1663)

 

» Ultimate Reality is at once Absolute and Infinite, the source of all being, of all consciousness and of all life. Itself beyond form, it speaks to mankind through revealed forms which, while externally bound and limited, open up inwardly towards the Boundless. Through revelations of this Word or Logos come into being the sacred traditions which although outwardly different are inwardly united into a Center which transcends all forms. They are, however, the bridge from the periphery to the Center, from the relative to the Absolute, from the finite to the Infinite, from multiplicity to Unity. «

Seyyed Hossein Nasr

Quoted from:
Seyyed Hossein Nasr (1976) - Ultimate Reality. 

Foreword to Keith Critchlow - Islamic Patterns. An Analytical and Cosmological Approach.

Fourth of July | A Masonic Holiday

 The Eye of Horus, the Eye of Providence or the All-Seeing Eye of God inside a triangle surrounded by the glow of Sirius, the Blazing Star of masonry (on the gate of Aachen Cathedral, Germany) is also part of the reverse side of the Great Seal of the United States.

Independence Day on 4th of July is commonly associated not with masonry but with fireworks, parades, barbecues, baseball games, family reunions, political speeches and ceremonies. However, the legal separation of the Thirteen Colonies from Great Britain in 1776 actually occurred on July 2nd, when the Second Continental Congress voted to approve a resolution of independence that had been proposed in June by Richard Henry Lee of Virginia declaring the United States independent from Great Britain's rule. After voting for independence, Congress turned its attention to the Declaration of Independence, a statement explaining this decision, which had been prepared by a Committee of Five, with Thomas Jefferson as its principal author. Congress debated and revised the wording of the Declaration, finally approving it two days later on July 4th. It was read from the balcony of the Council chamber of the State House to the citizens of Philadelphia on July 8th 1776. So why do the United States celebrate the 4th of July? Since many of the founding fathers were enlightened masons (illuminati) of the Ancient and Accepted Scottish Rite, and freemasonry is rooted in ancient mystery schools of solar worship, of course the date of the American Declaration of Independence was not arbitrary: In 1776 the solar aphelion (greek apo = from + helios = Sun = aphelion = away from the Sun) and the conjunction of the Sun with Sirius both happened to occur on July 4th.

Independent farthest from the Sun (aphelion):
2018 Jul 06 (Fri) 12:46
2019 Jul 04 (Wed) 18:10
2020 Jul 04 (Wed) 07:34
Sun conjunct Sirius:
2018 Jul 03 (Tue) 02:00
2019 Jul 03 (Wed) 07:41
2020 Jul 02 (Thu) 13:31

Every year during the first days of July the Sun conjoins Sirius at 13.5 degrees Cancer, that is, the Sun moves in front of Sirius. Interestingly, this occurs when the major axis of the Earth’s orbit is also farthest from the Sun. Sirius is located in the constellation Canis Majoris – the Big Dog – (RA 6h45m8.9s and Dec -16°42'52.1" or 101.2833 degrees longitude and -16.7144 degrees declination) and is therefore known as the dog star. It is over twenty times brighter than our Sun and is twice as massive. At night time, Sirius is the brightest star in the sky and its blue-white glare never failed to amaze stargazers since the dawn of time. Sirius is said to be the Sun of our Sun, and as such more important for men on Earth than even the Galactic Center.

The Washington Monument is constructed within a Vesica Pisces
that is created by the orbiting bodies of our Sun and Sirius.

In Ancient Egypt, Sirius was regarded as the most important star in the sky. In fact, it was astronomically the foundation of the Egyptians’ entire religious system. It was revered as Sothis and was associated with Isis, the mother goddess of Egyptian mythology. Isis is the female aspect of a trinity formed by herself, Osiris and their son Horus. Ancient Egyptians held Sirius in such a high regard that most of their deities were associated, in some way or another, with Sirius. Anubis, the dog-headed god of death, had an obvious connection with the dog star and Toth-Hermes, the divine messenger and great teacher of humanity, was also esoterically connected with Sirius. The Egyptian calendar system was based on the heliacal rising of Sirius that occurred just before the annual flooding of the Nile during summer. In the Egyptian Book of the Dead, Sirius is described as the place where souls go after they leave the body, and Egyptian temples were oriented toward Sirius. The star’s celestial movement was also observed and revered by ancient Greeks, Sumerians, Babylonians and countless other civilizations. Sirius was therefore considered sacred and its apparition in the sky was accompanied with feasts and celebrations. The dog star heralded the coming of the hot and dry days of July and August, hence the popular term the dog days of summer. Since antiquity there has been much compelling speculation about a binary system of our Sun Helios and Sirius. 

The presidential inauguration ceremony performed once every four
years at exactly high noon and 19.5 days into the new year on the
balcony of the U.S. Capitol (the ever pregnant belly of Isis) facing
the Washington Monument (the erect phallus of Osiris) is giving birth
to the next U.S. president.

In this system the perigee cycle between the two causes periodicities of massive celestial upheavals and is the foundation of the Yuga cycles. (What the naked eye perceives as a single star is in fact a binary star system, consisting of a white main-sequence star of spectral type A0 or A1, termed Sirius A, and a faint white dwarf companion of spectral type DA2, called Sirius B). 

The esoteric foundation of the United States as well as that of the entire modern Western world rests upon this ancient Egyptian astro-theology. It is therefore important to understand that Egypt became Greece, Greece became Rome, Rome became Venice, Venice became Amsterdam and England, and England finally became the imperial United States or the latest incarnation of ancient Egypt. True, if there is an actual guiding intelligence to man's evolution, it most certainly should be associated with Sirius. And the United States, with its natal Sun conjunct Sirius, would represent the clearest channel for this extra-human agency to manifest its will, whatever that may be. However, for those assuming that supernatural guidance was America's eternal fate and triumph, it might be wise also to recall that so far all empires have had an expiration date: Regardless of financial strength, political power and knowledge of previous history life cycles, no empire leader has ever been able to prevent its supremacy from collapsing. For instance, the successive Chinese dynasties would always rise, stay and fall regardless of lessons learned from the past. Empire life cycles would repeat over and over following a same cyclical pattern of around 248 years: 1776 + 248 = 2024 (see also HERE).

The Dot, the Line, and the Circle | Study and Application of Rational Procedure

The dot, being most proximate to perfection, is the simplest, and therefore the least imperfect of all symbols. The dot, moving away from self, projects the line; the line becomes the radius of an imaginary circle, and this circle is the circumference of the powers of the central dot.

Hypothetically, every sun has a periphery where its rays end, every human life a periphery where its influence ceases, every human mind a periphery beyond which it cannot function, and every human heart a periphery beyond which it cannot feel. Somewhere there is a limit to the scope of awareness. The circle is the symbol of this limit. It is the symbol of the vanishing point of central energy. The dot symbolizes the cause; the line, the means; and the circle, the end.

Motion away from self brings a decrease in consciousness and power; motion toward self brings a corresponding increase in consciousness and power. The farther the light ray travels from its source the weaker the ray.

The dot, the line, and the circle are the supreme and primary symbols. The dot is spirit and its symbol in the Chaldaic Hebrew – the Yod – is actually a seed or spermatozoon, a little comma with a twisting tail representing the germ of the not-self. In its first manifestation the dot elongates to form the line. The line is a string of dots made up of germ lives – the monadic lives of Leibnitz. From the seed growing in the earth comes the sprig – the line. The line, therefore, is the symbol of the dot in growth or motion. The sun is a great dot, a monad of life, and each of its rays a line – its own active principle in manifestation. The key thought is: The line is the motion of the dot.

The dot, or Sacred Island, is the beginning of existence, whether that of a universe or a man. The dot is the germ raised upon the surface of infinite duration. The potentialities signified by the blank paper are manifested as active potencies through the dot. Thus the limitless Absolute is manifested in a limited way.

Manly P. Hall (1929): Lectures on Ancient Philosophy. An Introduction to the Study and Application of Rational Procedure.

Triangle, Square, and Hexagon │ Basic Figures Filling the Space

The Equiangular Period Spiral includes periods, distances and velocities. It is delimited by three basic equiangular figures – the triangle, the square (more correctly the rectangle) and the hexagon. Nicolas d'Oresme wrote in his major work Le Livre du Ciel et du Monde (The Book of the Heaven and the Earth, 1377):

» Notwithstanding that He is everywhere, still is He absolutely indivisible and the same time infinite with respect to the three qualities that are divisible in living creatures, which we call duration, position, and power or perfection; for temporal duration of creatures is divisible in succession; their position, especially of material bodies, is divisible in extension; and their power is divisible in any degree or intensity […] Besides the varieties of trinity noted there, there is another which is pertinent to our present discussion, because, in accord with what we said […], there are three regular plane figures – the triangle, the square, and the hexagon – each of which we can imagine to be capable of filling so completely a flat area or surface that it is absolutely impossible that there could be more space to be filled; likewise there are three divine persons, each of whom fills all space. Isaiah the Prophet spoke of them thus: Holy, Holy, Holy, Lord God, etc. all the earth is full of thy glory. And there is one God, who spoke through His Prophet Jeremiah: I will fill the heaven and earth; and of whom Virgil said: All things are replete with Jove. « (Book IV, Chapter 10).

A page from d'Oresme's Livre du Ciel et du Monde, showing the celestial spheres:
Although the order of the spheres is conventional, with the Moon and Mercury
closest the Earth and Saturn and the stars farthest, the spheres are convex upward
centered on God rather than convex downward centered on the Earth.
[Paris, Bibliothèque Nationale de France, Manuscrits, Fr. 565, fo 69].

Equal to the Ears and to One-Third of the Face | Da Vinci's Vitruvian Man

A palm is four fingers, a foot is four palms, a cubit is six palms, four cubits make a man,
a pace is four cubits, a man is 24 palms.
The length of the outspread arms is equal to the height of a man.
From the hairline to the bottom of the chin is one-tenth of the height of a man.
From below the chin to the top of the head is one-eighth of the height of a man.
From above the chest to the top of the head is one-sixth of the height of a man.
From above the chest to the hairline is one-seventh of the height of a man.
The maximum width of the shoulders is a quarter of the height of a man.
From the breasts to the top of the head is a quarter of the height of a man.
The distance from the elbow to the tip of the hand is a quarter of the height of a man.
The distance from the elbow to the armpit is one-eighth of the height of a man.
The length of the hand is one-tenth of the height of a man.
The root of the penis is at half the height of a man.
The foot is one-seventh of the height of a man.
From below the foot to below the knee is a quarter of the height of a man.
From below the knee to the root of the penis is a quarter of the height of a man.
The distances from below the chin to the nose and the eyebrows and the hairline are equal
to the ears and to one-third of the face (HERE).

The Harmony of Being | Geometry in Man, Nature, and Cosmos

Proportional roots: (a) the √2 proportion, (b) the √3 proportion,
and (c) the golden mean (Phi) proportion.

Loai M. Dabbour (2012) - Geometry describes the assertions of a mathematical order of the intrinsic nature of the universe. Geometry is the very basis of our reality, and we live in a coherent world governed by underlying laws. Johannes Kepler stated that geometry is underpinning the cosmos, which was based on Plato’s ideas that God created the universe according to a geometric plan. The structure of the universe is determined by and revealed as certain mathematical and geometric constants which represent a confirmation that proportions are the underlying fabric of nature. This can be seen in man, nature, and cosmos.

Root proportions based on the square.

By contemplating geometric proportions, an understanding towards the sacred truth can be obtained since geometric proportions are one of the definitive geometric qualities of life itself. The Holy Quran tells us that man has within himself all what is reflected in the universe - the best proportions. Man is the core of God’s creatures; he possesses the most harmonious proportions, reflecting of the Divine harmony of being. "We have indeed created man in best of forms" – proportions (Surah At-Tin, 95:4). Leonardo da Vinci illustrated the mathematical proportions of the human body, showing that human being exhibits clearly golden mean proportions in his body based on ratios of 1.618.The Vitruvian Man drawn by Leonardo Da Vinci is based on Vitruvius, who believed that if human proportions could be incorporated into buildings, they would become perfect in their geometry. According to Vitruvius, the distance from fingertip to fingertip should be the same as that from head to toe. The sacred mean rules can be seen in the ratios of body parts throughout the human body. The human body contains in its proportions all the important geometric geodesic measures and functions. The proportions of ideal man are at the center of a circle of invariant cosmic relationships.

Proportions of Venus’ and Earth’s mean orbits.

The mathematical harmony of the universe can be seen from the proportions of the planets in our solar system. For example, the ratio of the sacred mean can be seen in the rotations of Venus and Earth around the Sun in that for each five years that the Earth rotates around the Sun, Venus rotates around it eight times. The connection between 5 and 8, both of which are Fibonacci numbers, is the golden mean proportion (8/5 = 1.6). The result of this motion is that Venus draws a pentagon around the Sun every eight years (Figure A). Figure B shows that a circle is drawn, which represents Venus’ mean orbit. A pentagon is constructed inside it and a small circle placed through the arm-crossing points. The radius of this small circle divides the radius of the large one into golden sections and can be used to space Venus’ orbit from Earth’s orbit. It can be seen from the agreement between eightfold and fivefold geometries that eight touching circles are drawn from Venus’ mean orbit. In turn, the circumference circle is enclosing these eight circles, defining Earth’s mean orbit. The ratio of the mean orbits of Venus’s to Earth is the √2 proportion. The geometric representation of these orbits creates the golden mean proportion.

The Pythagorean Definition of God

St. Bernard of Clairvaux: "God is breadth and length, height and depth."

By That Pure, Holy, Four Lettered Name On High | Pythagoras

The Pythagorean Oath mentions the Tetractys:
"By that pure, holy, four lettered name on high,
nature's eternal fountain and supply,
the parent of all souls that living be,
by him, with faith find oath, I swear to thee."
Credits: Michæl Paukner

Albert Mackey (1873) - "The Greek word 'Tetractys' signifies, literally, the number four, and is synonymous with the quaternion; but it has been peculiarly applied to a symbol of the Pythagoreans, which is composed of ten dots arranged in a triangular form of four rows."   

The first four numbers symbolize the harmony of the spheres and the Cosmos as: (1) Unity (Monad); (2) Dyad - Power - Limit/Unlimited; (3) Harmony (Triad); (4) Kosmos (Tetrad) - The four rows add up to ten, which was unity of a higher order (The Dekad).  The Tetractys symbolizes the four elements — fire, air, water, and earth. The Tetractys represented the organization of space: the first row represented zero dimensions (a point). The second row represented one dimension (a line of two points). The third row represented two dimensions (a plane defined by a triangle of three points). The fourth row represented three dimensions (a tetrahedron defined by four points). 

The Pythagorean musical system is based on the Tetractys as the rows can be read as the ratios of 4:3 (perfect fourth), 3:2 (perfect fifth), 2:1 (octave), forming the basic intervals of the Pythagorean scales. That is, Pythagorean scales are generated from combining pure fourths (in a 4:3 relation), pure fifths (in a 3:2 relation), and the simple ratios of the unison 1:1 and the octave 2:1. The diapason, 2:1 (octave), and the diapason plus diapente, 3:1 (compound fifth or perfect twelfth), are consonant intervals according to the tetractys of the decad. The diapason plus diatessaron, 8:3 (compound fourth or perfect eleventh), is not.

Squaring the Circle with the Earth and the Moon

The perimeter of a square around the Earth equals the perimeter of a
circle drawn through the center of the Moon.
Credits: Michæl Paukner

Common Wisdom (2015) - Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.

In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem which proves that pi (π) is a transcendental, rather than an algebraic irrational number; that is, it is not the root of any polynomial with rational coefficients. It had been known for some decades before then that the construction would be impossible if pi were transcendental, but pi was not proven transcendental until 1882. Approximate squaring to any given non-perfect accuracy, in contrast, is possible in a finite number of steps, since there are rational numbers arbitrarily close to π.