Titian Pieta is his last painting. In the painting we see Mary Magdalene with two cherubs one above and the other below. A woman carrying the cross crowned with rose crown of thorns. She was a Cumaen Sibyl who predicted the coming of the savior.

It is interesting that the cherubs under Magdalene  at Rennes Chateau are pointing down and one wonders if there is a crypt under the church. The cherubs are seen in many paintings dealing with the burial of Christ.  Bourdon, Poussin, Titian, and others have placed the cherubs with Magdalene and the other women at Jesus grave. These women who came to Jesus's grave possibly had children. The cherubs in the paintings maybe a symbol representing the children of the Holy Family or children of Jerusalem. Luke 23:28-31 says

"Daughters of Jerusalem, do not weep for me, but weep for yourselves and for your children. For behold, the days are coming when they will say, 'Blessed are the barren, and the wombs that never bore, and the breasts that never gave suck!' Then they will begin to say to the mountains, 'Fall on us'; and to the hills, 'Cover us'. For if they do this when the wood is green, what will happen when it is dry?"

It doesn't surprise me that Venus the goddess of Love whose symbol is the five pointed star would be connected to Mary Magdalene. It could be the reason for the symbol on the tree cross that she carries. Venus symbol has a cross in it for its astrological symbol. It is connected to the Ankh. The key of life to the Egyptians connected to Isis and eternal life. 

Venus retrogrades every 584 days (19 months) making five retrograde points around the Sun. After eight years, Venus forms a five-pointed star in the sky. Ishtar and Astarte carry the jar of life and so Mary Magdalene carries her jar . Mark 14:3 talks about the woman with the alabaster jar. The jar the Egyptians used for the funeral rites. It seems the symbolic connections with Magdalene and Venus makes sense. She loved Jesus with such passion and he loved her by showing his resurrected self first to her. It is all about the power of  love and that is what Venus and Isis is all about.

At the Cathedral of Notre Dame in Paris is a wooden panel which depicts the life of Christ. A panel depicts the Wedding of Cana. Three people have halos one is Jesus another is a woman who sits next to Jesus. . Is she Mother Mary or possibly Magdalene?One wonders who the fellow next to Jesus who has a halo too? Is he Jesus brother? Is he the bride's father? Is he the bride's groom? The lady next to him does not have a halo and she is darker skinned than the others. She does wear a gold crown and her hair is not covered. I'm interested to hear what other people think of this interpretation of the Wedding of Cana especially the saint next to Jesus. The French had a oral tradition which said Mary Magdalene came to France by boat with other saints. She brought with her the dark servant girl Sara the Egyptian. Napoleon made the Paris coats of arms the five pointed star and the ship who brought Isis to the city called Paris. It is interesting the similar story of Isis and Magdalene coming by boat to France.  Napoleon created the Arch de Triumph as a symbol of Isis and her star Sirius. Isis was devoted and loved Osiris very much. I could see how Magdalene and the story of Isis could be similar. What do you think?

http://homepage.ntlworld.com/fusniak/talisman/articles/isisofparis.html

http://www.thestarhouse.org/MMWho.html

http://www.steeppath.com/article.php?ID=1

http://en.allexperts.com/q/Esoteric-Symbology-3874/2008/10/tell-mythology-symbolism-behind.htm

LA V CORTA QUE CONTIENE LA LETRA M EN EL CENTRO EQUIVALE A LA V CORTA DE VENUS/VIRGEN

CICLO PENTAGONAL ENTRE VENUS Y GEA. LAS CURVAS DE VENUS.

Pentagonal se refiere al Ciclo formado por 5 ciclos sinódicos.

Venus y la Tierra danzan en sincronía matemática y geométrica en el salón del Espacio, al son de la sutilísima vibración de la música de las esferas, pues esferas son. El milenario mito de la llamada "Música de las Esferas" es mito mientras no se comprende qué es o a qué se refiere. Es como si una persona no reconociera que los instrumentos musicales suenan y por eso concluye que la "música de los instrumentos" es mito. Sólo le basta escuchar, sentir, vibrar y comprender. Nosotros estamos en una de esas esferas: el Planeta Tierra, aunque si pensamos un poco comprenderemos que es normal que sea posible que no conozcamos la maravilla en la que estamos inmersos ni que participemos activamente en ella, como aquel espectador que está de gratis en un maravilloso concierto y él mismo es un instrumento y se queda dormido, pero no porque la música sea aburrida sino porque no sabe que está ahí. Cada 8 años, que son 8 órbitas de la Tierra y 13 de Venus, ambos planetas se encuentran 5 veces en sus puntos más cercanos, al mismo lado del Sol, 5 puntos que son equidistantes y que forman los 5 vértices de una estrella de 5 puntas. Puedes pulsar sobre la imagen para ver la animación.

Si continúas observando podrás comprobar cómo Venus y la Tierra continúan trazando la figura pentagonal, aunque ya no desde el mismo punto que la anterior. De hecho, comienzan una nueva 2,33 días antes que la anterior. La actual la comenzaron el 8 de junio de 2004 y termina el 6 de junio de 2012. Esto significa que esa estrella de 5 puntas gira también alrededor del Sol hasta dar una vuelta en 1.252 años: un Ciclo mayor compuesto por 156 subciclos Pentagonales (1.252 órbitas de la Tierra y 2.035 de Venus). Así es como los planetas crean los Ciclos Cósmicos. 1.252 años son 457.457 días, que es prácticamente 676 x 676 ó 26x26x26x26 ó (13+13)x(13+13)x(13+13)x(13+13) días. Aquí puedes verlo de otra manera comenzando desde el 8 de junio de 2004 (cuando se produjo un tránsito de Venus) hasta el 6 de junio de 2012 en que se produce otro tránsito. Puedes hacer click sobre la escena repetidamente. Los números 5, 8 y 13 son números consecutivos de la serie Fibonacci en la que cada número dividido por su anterior tiende al valor del número Phi, el que marca la llamada "proporción divina" de ciertos elementos de la Naturaleza, por no decir muchos o todos, y entre los cuales están las propias piezas que componen el esqueleto de nuestros cuerpos: los huesos. En la vigésima división de la serie Fibonacci, entre los números 6.765 y 4.181, se obtiene un valor de phi afinado hasta el sexto decimal: 1'6180339. También se puede ver que los números de la serie Fibonacci 6.765 y 4.181 como días terrestres convertidos a Tzolkins son 26 y 16 Tzolkin, y mientras el año de la Tierra (365 días) es 1,62 veces más largo que el de Venus (225 días), siendo 1,62 el redondeo de 1,618 que es el valor de Phi, en el ciclo sinódico Venus da 2'6 órbitas y la Tierra da 1'6 (fracciones de 26 y 16). Y por fin, reproduciendo los tres números de la serie Fibonacci 5, 8 y 13 en el ciclo pentagonal resulta que 5 es el número de encuentros entre La Tierra y Venus durante 8 órbitas de la Tierra y 13 de Venus. Viendo desde el planeta Tierra, desde el meridiano del mediodía, sin que gire el planeta (pero sí trasladándose) y acelerando mucho el movimiento de los astros hasta que en 20 segundos transcurrieran 8 años, podríamos ver a Venus realizar 5 movimientos retrógrados cada 8 años, 2 en forma de lazo, 1 en zig zag (cruzando la eclíptica) y otros 2 de nuevo en forma de lazo (casi simétricos a los dos primeros). Los trazos en forma de lazo los realiza por encima o debajo de la eclíptica según ande circulando por el nodo superior o inferior de su órbita (inclinada respecto a la de la Tierra). Empleando una expresión metafórica, son las Curvas de Venus. También podemos verlas como las letras gráficas del lenguaje venusiano. Tales trazos derivan gradualmente en el cielo terrestre cada 8 años en sentido contrario al del Sol ante el fondo fijo de las estrellas y las constelaciones, de modo que desde hace unos 100 años, el movimiento en zig zag de Venus ha venido ocurriendo sobre la constelación de Orión. El 13 es número basico en el Ciclo Pentagonal, pues es el número de órbitas de Venus, de modo que en 13 Ciclos Pentagonales Venus da 169 órbitas (13x13). Este ciclo de 13 ciclos Pentagonales es 37.960 días durante los que Venus realiza 65 ciclos sinódicos (o alineamientos con la Tierra) y en los que también intervienen 146 ciclos del Tzolkin 146 e incluso 104 del Haab (103,96 años de 365,2422 años). Vemos que el el 65 y el 104 son múltiplos del 13. 13 Pentagonales = 13 x 2920 días = 37.960 días 65 ciclos sinódicos = 65 x 584 días = 37.960 días 104 Haabs = 104 x 365 días = 37.960 días 146 Tzolkines = 146 x 260 días = 37.960 días A su vez este ciclo de 37.960 días ó 13 Ciclos Pentagonales es una unidad de otros ciclos mayores.   Ver también Ciclo Octogonal de Venus.   Deseas hacer algún comentario? Blog sobre la Dinámica de Venus http://asteromia.net/sistema-solar/sistema-solar-planetas-venus4.html

Phi and the Solar System

The dimensions of the Earth and Moon are in Phi relationship, forming a Golden Triangle

The illustration above shows the relative sizes of the Earth and the Moon to scale.

• Draw a radius of the Earth (1)
• Draw a line from the center point of the Earth to the center point of the Moon (square root of Phi)
• Draw a line to connect the two lines to form a Golden Triangle (Phi).

Using dimensions from Wikipedia and geometry’s classic Pythagorean Theorem, this is expressed mathematically as follows:

The second row represents the first twelve terms of what is now called the Fibonacci series. The series can be continued indefinitely based on the simple rule: each terms is found by adding the two terms immediately preceding. (except the very first two terms.) Four hundred years after Fibonacci an important relationship was formulated for this series.   in general, Xn = Xn - 1 + Xn - 2   Since then, especially in our present century, The properties of the Fibonnaci numbers have been studied extensively. From all of the literature resulting therfrom, an important ratio is recognised. The ratio is so intriguing that it has been designated The Golden Number and is represented as the greek letter PHI. The ratio is as follows: Take the square root of five and add one. Divide the result by two and you have the Golden Number. Other interesting things about PHI are that its reciprocal is the same as the fractional part. PHI squared changes its integer but retains the same fractional part. Lets continue by examining the first 48 terms of the Fibonacci series. First Twelve Second Twelve Third Twelve Fourth Twelve 1 233 75025 24157817 1 377 121393 39088169 2 610 196418 63245986 3 987 317811 102334155 5 1597 514229 165580141 8 2584 832040 267914296 13 4181 1346269 433494437 21 6765 2178309 701408733 34 10946 3524578 1134903170 55 17711 5702887 1836311903 89 28657 9227465 2971215073 144 46368 14930352 4807526976     By applying the rules of the game the single pair of hypothetical rabbits would have generated 4,807,526,976 pairs by the end of the fourth year! If you divide any number of this series by the number immediately preceding it you will get the golden mean or 1.618. Only that the higher up in the series the closer to the average mean you will get. Besides being an interesting number game, the Fibonacci series exemplifies biological growth patterns such as phyllotaxis. The arrangement of the whorls on a pinecone or pineapple, of petals on a sunflower, and of branches from some stems follow the sequence of Fibonacci numbers. Also the logarithmic spirals found on a cross section of a nautilus shell, the basic proportions of the human body and periodic cycles of some planets relate to this series as well. The rest of this article will focus on some of these relationships. The spiral, as found in a Nautilus shell, is illustrated above. The radius point for each consecutive 90 degree arc is moved at a value equaling the side divided by PHI. In this case r represents the side and s represents r/PHI.   The Pentacle Of all symmetric geometric shapes, none represent so concisely the principles of PHI than the pentacle or five pointed star within a circle. This is probably so because the ratio of PHI is first derived from the square root of five. Using a compass, draw a circle with five points spaced at exactly 72 degree apart with the first point at the top. Connect the points at 144 degree intervals with straight lines. Notice that both numbers 5 and 144 occur in the first twelve terms of the Fibonacci series.   Draw a straight line from the center of the circle intersecting the two bottom "legs" of the star. That line is equal to the radius of the circle. Measure the radius in centimeters. Measure the portion of the radius that lies outside the star. Divide the radius by the portion outside the star and the number is PHI. Measure the length of the straight line between any two points of the star. (You will notice that the line will be intersected twice by the lines going to the point adjacent to the points you are measuring.) Now measure the section of the line going from one point to the farther intersecting place from that point. The length of the whole line divided by the section equals PHI. The human body looks something like a five pointed star. Stretch out your arms straight to each side of you and have someone measure the distance from your fingertips left to right. Take this measure and divide it by the distance from on fingertip to the opposite shoulder and the result is close to PHI. Measure your height from heel to top of head. Divide this measure by the distance from heel to navel and the result is close to PHI. I say close to PHI because everybody has a unique proportion that slightly differs from person to person. Only an average of PHI is to be sought by these personal measurements. Also as mentioned earlier, the terms farther along the Fibonacci series yield results closer to PHI than those of the earlier terms of the series. In this sense we might understand that human proportions rarely go beyond the ratios represented by the first ten terms of the series.   Earth and Venus The Earth completes one orbit around the the Sun in 365 days. The orbit of the circle contains 360 degrees. The only number that will divide both 360 and 365 without leaving a remainder is 5. So the ratio of the Earth's orbit to the Earth's rotation is:   Taken at an average we can say that for every 72 degrees the Earth travels in its orbit, it will make 73 rotations on its axis relative to the sun. Thus we can say that this ratio marks out a natural pentacle in space. The synodic period of Venus, the time it takes for two consecutive inferior conjunctions with the Sun, is 584 days. Five such synodic periods of Venus is 2920 days. This is equal to eight Earth years of 365 days. Here we see the ratio 8:5 whereas 8 Earth years equal 5 synodic Venus cycles. As you look at the terms in the Fibonacci series you notice the two numbers 5 and 8. Take one synodic Venus cycle of 584 days and divide it by 8. The result is 73, the number of days it takes for the Earth to complete 1/5 of its orbit around the Sun. Incidently, it should be noted that the Mayan Calendar uses the Earth-Venus cycles as a basis for their reckoning system. PHI and the Fibonacci series keeps popping up when examining the Mayan Calendar. Sidereal Earth to Venus: 100 steps of 73 days December 4th 1950 to September 17th 1970. The above figure shows the relationship of the Earth and Venus. Viewed as above the solar system looking down on the planets with the Sun placed in the center. To the right is sidereal Aries; to the top is sidereal Cancer; to the left is sidereal Libra and to the bottom is sidereal Capricorn. Lines are drawn connecting the respective positions of Earth and Venus after every 73 Earth days in their orbits. This is repeated a hundred steps. You can see the pentagonal pattern developed by their orbits. Venus from Earth: 975 steps of 3 days, January 1st 1985 to January 1st 1993. A critic might charge that any period of orbit divided into steps that favor pentagonal patterns can be arbitrarily chosen to prove anything. To counter this charge, we will choose a number that would not normally be a pentagonal divisor of the orbiting period of either planet. In the illustration above we plot points rather than lines at the point where two consecutive lines would intersect. Points are plotted every three days for 975 steps. Even with a non-pentagonal divisor of the orbital period we can still see a five petaled flower pattern.   Jupiter and Saturn   For every complete orbit of Jupiter, Saturn will travel about 144 degree along its orbit. So after 60 years, Jupiter will have made 5 complete orbits while Saturn will have marked out five points, each 144 degrees apart. While doing so Saturn will have made two complete orbits. Here we see again the numbers 5 and 144 of the Fibonacci series. But whereas the Earth-Venus cycles contain mostly Fibonacci values, the Jupiter-Saturn relationship contains more. It has the patterns of the Fibonacci and the sexagesimal. As the pentacle was shown to have a relationship with PHI, the sexagesimal (hexagram) has a relationship to PI, that other magical number. And, as will be shown, both PHI and PI have a relationship to each other. PI is the number that represents the ratio of the diameter of a circle to its circumference. PI to four decimal places is 3.1416. PI divided by 2 represents that ratio in regard to the radius of a circle. And, as we know, the radius of a circle measured in a straight line divides a circle into six parts. Hence the hexagram. As explained in a previous article, (The Six Thousand Year Barrier), the 60 year cycle of Jupiter and Saturn gives rise to the usage of the sexagesimal system and its derivatives.   6 x 60 = 360     PI Take the reciprocal of PHI (.618) and cube it. Multiply that by 6 and divide the result by ten. Add to this 3 and you have PI to four decimal places.   In summary I will not draw any definite conclusions but instead offer suggestions. While this article may not prove to have any valuable application, it serves as an example of the insight we may get when we study the relationship between things rather than just the things themselves. Patterns of interaction and processes can be just as interesting as the things that create the patterns. Such patterns appeal to a certain symbolic part of our consciousness which creates the reality we live in. I believe that it is this usage of symbolic patterns that enabled the mystics, magicians and alchemist to practice their philosophy. And it may be argued that mathematics evolved from symbolic logic and pattern recognition. Who knows? By reading this perhaps some magick spell may work on your consciousness and bring it to another level of awareness.

http://www.glenn.freehomepage.com/writings/Pentacle/

Patterns in Nature

David Pratt

January 2006

Part 2 of 2

Contents

    6. Formative power of sound
    7. Planets and geometry
    8. Planetary distances
    9. Solar system harmonies
  10. Intelligent habits
  11. Sources

6. Formative power of sound

    In the late 18th century, German physicist Ernst Chladni demonstrated the organizing power of sound and vibration in a visually striking manner. He showed that when sand is scattered on metal plates, and a violin bow is drawn across them, the resulting vibrations cause the particles to move to the places where the plate is almost motionless, producing a variety of beautiful, regular, intricate patterns.*

*Joscelyn Godwin makes an interesting comment on this phenomenon: ‘Once, passing by a crowded dance hall where rock was being played, I could not help perceiving the floor of the hall in terms of a Chladni plate, and the dancers appeared for all the world like the jumping, helplessly manipulated grains of sand’ (1995, p. 246).

 

Fig. 6.1 Chladni figures. For a video, click here.

    A century after Chladni, Margaret Watts-Hughes created images by placing a powder or liquid on a disk then letting it vibrate to the sound of a sustained musical note. She experimented with several musical instruments but had most success using her voice. The particles arranged themselves into geometric shapes, flower patterns (such as pansies, primroses, geraniums, and roses), or the shape of a fern or a tree. The higher the pitch, the more complex the patterns produced; a powerful sustained note produced an imprint of a head of wheat.

Fig. 6.2 Figures generated by the voice of Margaret Watts-Hughes.

    In the 1950s the study of wave phenomena was continued by Swiss scientist and anthroposophist Hans Jenny (1904-1972), who named the field ‘cymatics’. Using crystal oscillators (which allow precise frequencies and amplitudes to be used), he vibrated various powders, pastes, and liquids, and succeeded in making visible the three-dimensional effects of sound. He produced an astonishing variety of awe-inspiring geometrical and harmonic shapes, including life-like flowing patterns, which he documented in photographs and films.

    Jenny, too, found that higher frequencies produced more complex shapes. A low frequency produced a simple central circle surrounded by rings, while a higher frequency increased the number of concentric rings. Even higher frequencies created shapes resembling petals, butterflies, or crustaceans, zebra patterns, mandala-like patterns, and images of the five platonic solids. As the frequency rises, the dissolution of one pattern may be followed by a short chaotic phase before a new, more intricate, stable structure emerges. If the amplitude is increased, the motions become all the more rapid and turbulent, sometimes producing small eruptions. Under certain conditions Jenny was able to make the shapes change continuously, despite altering neither frequency nor amplitude.

Fig. 6.3 Hexagonal pattern produced by light refracting through a small sample of water (about 1.5 cm in diameter) under the influence of vibration. The figure is in constant dynamic motion. (Jenny, 2001, p. 112; courtesy of Jeff Volk)

Fig. 6.4 A round heap of lycopodium powder (4 cm in diameter) is made to circulate by vibration. At the same time two centres of eruption rotate at diametrically opposed points. (Jenny, 2001, p. 108; courtesy of Jeff Volk)

Fig. 6.5 Jenny built a tonoscope to translate the human voice into visual patterns in sand.
Left to right: ‘oh’ sound, ‘ah’ sound, ‘oo’ sound. (Jenny, 2001, p. 65; courtesy of Jeff Volk)

    More recently, Peter Guy Manners found that an acoustic recording of the Crab Nebula caused sand to form a pattern strikingly like the nebula itself. As the near-infrasonic sound was played, the two swirling arms pulled in, forming a tight ball. Towards the end of the audiotape, the sand became very highly compacted and then suddenly exploded, throwing sand off the table.

    John’s Gospel begins: ‘In the beginning was the Word, and the Word was with God, and the Word was God.’ The Egyptian Book of the Dead, contains a parallel passage: ‘I am the Eternal, I am Ra ... I am that which created the Word ... I am the Word ...’ The Hindu tradition teaches that ‘Nada Brahma’ (the world is sound). The underlying idea is that everything we see is a divine word – or vibration – that has solidified and become manifest, the vibrations originating in the inner, more ethereal realms. All of nature is essentially rhythmic vibration. Everything from subatomic particles to the most intricate lifeforms, from planets to galaxies, comprises resonating fields of pulsating energy in constant interaction. In the poetic words of Cathie Guzzetta:

The forms of snowflakes and faces of flowers may take on their shape because they are responding to some sounds in nature. Likewise, it is possible that crystals, plants, and human beings may be, in some way, music that has taken on visible form. (D. Campbell, ed., Music: Physician for times to come, Quest, 1991, p. 149)

7. Planets and geometry

    If we draw a circle representing the earth – which has a mean radius (in round numbers) of 3960 miles – and then draw a square around it, the square will have a perimeter equivalent to 31,680 miles. If we then draw a second circle with a circumference equal to the perimeter of the square, its radius will be 5040 miles (using 22/7 as a good approximation to pi (π), as the ancients often did) – or 1080 miles more than the smaller circle. Just as 3960 miles is the radius of the earth, 1080 miles is the radius of the moon. In other words, the relative dimensions of the earth and moon square the circle!

Fig. 7.1 Earth and moon square the circle. Note that 5040 (the radius of the outer circle) = 1x2x3x4x5x6x7 (known as ‘factorial 7’, also written: 7!) = 7x8x9x10 (or 10!/6!). A quarter of its circumference (also equal to the diameter of the earth-circle) = 7920 = 8x9x10x11 (or 11!/7!), and the area of each semicircle = 11!.

    Exactly the same proportions and digits (expressed in feet rather than miles) can be found at Stonehenge (see Michell, 1995, 2001). The outer (sarsen) circle has a mean radius of 50.4 ft and a circumference of 316.8 ft. This is equal to the perimeter of a square drawn round the smaller (bluestone) circle, which has a radius of 39.6 ft. This radius is also equal to the diameter of the circle defined by the inner U-shaped structure. This is clear evidence that the ‘English’ foot and mile are at least as ancient as Stonehenge and, like many other ancient systems of measures, are closely related to the dimensions of earth, moon, and sun.

Fig. 7.2 Ground plan of Stonehenge. The lintels on top of the stones of the outer (sarsen) circle were mortised to the uprights and jointed at their ends, forming what was once a precision-made, perfectly level platform.

Fig. 7.3 Given its slope angle of 51.83°, the Great Pyramid, too, squares the circle. The length of each base side divided by the height equals π/2. In addition, the apothem divided by half the base side equals φ.

Fig. 7.4

    If a tetrahedron is inscribed in a sphere with the apex placed at either pole, the three corners of the base will touch the sphere at a latitude of 19.47 degrees in the opposite hemisphere. This latitude marks the approximate location of major vorticular upwellings of planetary and solar energy. The primary focus of sunspot activity is about 19.5° N and S. On Venus, there are volcanic regions at 19.5° N and 25.0° S. Mauna Loa and Kilauea (Hawaii), Earth’s largest volcanoes, are located at 19.5° and 19.4° N respectively. On the moon there is a mare-like lava extrusion at 19.6° S. On Mars, Olympus Mons, possibly the largest volcano in the solar system, is located at 19.3° N. The Great Red Spot of Jupiter is located at 21.0° S. On Saturn there are storm belts at 20.0° N and S. On Uranus, there are upwellings causing cooler temperatures at 20.0° N and S, and a dark spot at about 22.5° S. The Great Dark Spot of Neptune, photographed by Voyager 2 in 1989, was located at 20.0° S, but when the Hubble Space Telescope viewed the planet in 1994, the spot had vanished – only to be replaced by a dark spot at a similar location in the northern hemisphere.

Fig. 7.5 Jupiter’s Great Red Spot.

8. Planetary distances

    Are the planets of our solar system located at random distances from the sun? The Titius-Bode law, discovered 1766, suggests they are not. The law is obtained by writing down first 0, then 3, and then doubling the previous number: 6, 12, 24, etc. If 4 is added to each number and the sum divided by 10, the resulting numbers give the mean distances of the orbits of the planets in astronomical units (1 AU = the earth’s mean distance from the sun). Uranus, discovered in 1781, fitted the law, as did Ceres, the largest asteroid between Mars and Jupiter, discovered in 1801. However, the law breaks down completely for Neptune and Pluto, which were discovered later. Various efforts have been made to modify the Titius-Bode law to make it more accurate.*

*William R. Corliss, The Sun and Solar System Debris, Sourcebook Project, 1986, pp. 34-42.

    What the Titius-Bode law essentially means is that planetary orbits become progressively greater by a ratio of approximately 2:1 (the ratio of the octave) with increasing distance from sun. This is brought out in columns 3 and 4 of the table below, in which half the distance between Mercury and Earth is taken as the unit of measurement. Uranus and Pluto have mean orbits close to the exact distances necessary to complete two further octaves. Neptune is located almost exactly half-way between Uranus and Pluto, as though to fill in the half-octave position. This may indicate that it was not an original member of the solar system (theosophy says it was captured from outside our solar system). Likewise, the Titius-Bode law works for Pluto if we ignore Neptune.

    Due to its ad-hoc nature, the Titius-Bode law is usually dismissed as a numerical coincidence that has no physical basis. However, the fact that the planets’ distances from the sun follow a pattern can easily be demonstrated by plotting the logarithm of the mean distance of the planets (including the asteroid belt) against their sequential number (1 to 10). The fact that all the points lie very nearly on a straight line proves that gravitation is ‘quantized’. However, there is currently no detailed mainstream theory that explains how gravity works and why it should be quantized. The orbits of satellites around moons show the same quantized spacing, as do the orbits of electrons around an atomic nucleus (in the Bohr model of the atom).

Fig. 8.1
Figs. 8.1 to 8.6 courtesy of John Martineau (A Little Book of Coincidence, Wooden Books, 2001)

http://davidpratt.info/pattern2.htm

    The spacing of the planets shows many geometrical regularities. For example:

Fig. 8.2 Three circles touching: if Mercury’s mean orbit passes through the centres of the three circles, Venus’ orbit encloses the figure (99.86% accuracy).

 

Fig. 8.3 Left: The mean orbits of Mars and Jupiter can be drawn from four touching circles or a square (99.995%). Right: A related pattern spaces Earth’s and Mars’ orbits (99.8%).

 

Fig. 8.4 In this diagram, the smaller and larger circles represent not only the relative sizes but also the orbits of Mercury and Earth; they are related by a pentagram (99.1%).

Fig. 8.5 This diagram shows Earth’s and Saturn’s relative sizes and orbits;
they are related by a 15-pointed star (99.3%).

 

Fig. 8.6 Earth’s and Jupiter’s mean orbits can be created by spherically nesting three cubes, or three octahedra, or any threefold combination of them (99.89%).

9. Solar system harmonies

    The 17th-century astronomer Johannes Kepler discovered a remarkable relationship between a planet’s mean distance from the sun and the time it takes to orbit the sun: the ratio of the square of a planet’s period of revolution (T) to the cube of its mean distance (r) from the sun is always the same number (T²/r³ = constant). For instance, measuring T in earth-years and r in astronomical units, we get:

    Orthodox science has no real explanation for this, or for the many ‘resonances’ in solar system dynamics. For instance, the periods of Jupiter and Saturn show a 2:5 ratio. The periods of Uranus, Neptune, and Pluto stand in a 1:2:3 ratio. Mars and Jupiter are locked into a 1:12 resonance, Saturn and Uranus are in a 3:1 resonance, and there is a 2:3 resonance between Mercury’s rotational and orbital periods.

    What is the nature of such ‘resonances’? Abstract mathematical concepts such as ‘curved spacetime’ shed no light on the matter. A concrete explanation must be sought in the behaviour of the dynamic ether filling space, whose vorticular motions cause the planets and stars to rotate and carry them along in their respective orbits. According to the ether-science model known as aetherometry, T²/r³ is a constant for all the planets because it refers to the constant flux of energy that the solar system as a whole extracts by its primary gravitational interaction with the ether, entailing a nearly constant energy supply for each of its members.

    The speeds of the planets in their orbits represent their pitch-frequencies. Cosmic ‘chords’ are produced when planets come into conjunction (or ‘kiss’), i.e. stand in a straight line with the earth and sun. A certain number of regular planetary conjunctions occur over particular periods of time, and the ratios between these numbers reflect with considerable accuracy the length ratios necessary to produce the diatonic notes of an octave, i.e. the seven notes of a musical scale.

Fig. 9.1 Planetary conjunctions as ‘chords’ (Tame, 1984, p. 239).
The line in this diagram represents an octave, divided into seven intervals by eight notes. The line could represent the string of a one-stringed musical instrument. The numbers above the line are the numbers of conjunctions of each planet with the sun and earth, and those below the line are the numbers of years involved.

    The planets’ orbits are ellipses with the sun at one of their foci. Their speeds are therefore variable: they speed up as they approach perihelion (the point in their orbit nearest the sun) and slow down as they approach aphelion (their greatest distance from the sun). Following Kepler, Francis Warrain expressed the ratio between the minimum and maximum speeds of one planet and those of different planets as a musical interval. The results (only those for the inner planets are given below) rule out chance altogether, and constitute ‘a powerful argument for the harmonic arrangement of the solar system’ (Godwin, 1995, pp. 132-6). Of 74 tones, as many as 58 belong to the major triad CEG.

    The time taken by Venus to seemingly orbit the Earth (i.e. a Venus synod) is currently 584 days, so that 5 Venus synods are equivalent to 8 ‘practical’ earth-years (of 365 days). Venus has a sidereal orbital period of 225 days, and 13 of these periods equal 8 practical earth-years. In both cases, the numbers composing these ratios are consecutive Fibonacci numbers, and therefore give approximations to the golden section: 8/5 = 1.6, and 13/8 = 1.625. Venus rotates extremely slowly on its axis: its day lasts 243 earth-days, or 2/3 of an earth-year (the same ratio as a musical fifth). Every time Venus and earth ‘kiss’, Venus does so with the same face looking at earth. Over the 8 years of the 5 kisses, Venus will have spun on its own axis 12 times in 13 of its years.

    Thus, in 8 years Venus has 5 inferior conjunctions (when it lies between earth and sun) and 5 superior conjunctions (when it lies on the opposite side of the sun). Plotting either of these sets of 5 conjunctions in relation to the zodiac produces a five-pointed star or pentagram, the segments of the constituent lines being related according to the golden section. There is a slight irregularity, for the pentagram is not completely closed, there being a difference of two days at the top. This irregularity generates a further cycle, as it means that the pentagram will rotate through the whole zodiac in a period of about 1200 years. It is interesting to note that the pentagram was associated with the Babylonian goddess Ishtar-Venus, and that depictions of Venus as a five-pointed star have also been found at Teotihuacan in Mexico. In theosophy, Venus is said to be closely connected with our higher mind (manas), the fifth principle of the septenary human constitution.

Fig. 9.2 Teotihuacan: stellar symbol of Venus dispensing its influence
downwards towards the earth.

Fig. 9.3 The Venus pentagram.

    According to theosophy, the key numbers to the solar system lie in a combination of the year of Saturn and the year of Jupiter, expressed in earth-years (Purucker, 1973, pp. 3-15). About 12 earth-years (11.86) make 1 year of Jupiter, and about 30 earth-years (29.46) make 1 year of Saturn: 12 x 30 = 360, the number of degrees in a circle and the number of days in an ideal earth-year. (Theosophy says that an earth-year oscillates above and below 360 days over very long periods of time.)

    The whole process of evolution can be summed up as a descent of divine consciousness-centres or monads into matter, and their subsequent re-ascent to spirit, enriched by the experience gained on their aeons-long evolutionary journey. This process can be symbolized by two interlaced triangles, known as Solomon’s seal or the sign of Vishnu, the upward-pointing triangle representing spirit, and the downward-pointing triangle representing matter. Significantly, as Saturn and Jupiter revolve around the sun, they mark out two interlaced triangles around us every 60 years! The upward triangle is formed by their conjunctions and the downward triangle by their oppositions. Once again, there is a slight irregularity: after 60 years the conjunction does not take place at exactly the same point; there is a gap of 8 degrees, so that the interlaced triangles slowly rotate through the entire zodiac in a period of 2640 years. There are 432 of these 60-year Jupiter/Saturn cycles in a precessional cycle of 25,920 years.

Fig. 9.4 Conjunctions and oppositions of Jupiter and Saturn.

    The sun is the heart and brain of the solar kingdom and the regular sunspot cycle is akin to a solar heartbeat. The sunspot cycle has a major impact on earth, especially terrestrial magnetism and the climate. Over the past 250 years its length has varied irregularly between 9 and 14 years, averaging 11.05 years. Sunspots peak shortly after Jupiter passes the point in its orbit closest to the sun. (The ‘ideal’ sunspot cycle is said in theosophy to be 12 years, so there would be one such cycle for each year of Jupiter.) The sunspot maximum does not occur exactly in the middle of the sunspot cycle. The ascending part of the cycle has a mean length of 4.3 years – very close to the figure of 4.22 years that would divide the 11.05-year cycle exactly according to the golden section.*

*Theodor Landscheidt, ‘Solar activity: a dominant factor in climate dynamics’, www.john-daly.com/solar/solar.htm.

10. Intelligent habits

    To attribute the order, harmonious proportions, and marvellous recurring patterns in nature to pure chance is absurd. The pagan philosopher Cicero wrote:

If anyone cannot feel the power of God when he looks upon the stars, then I doubt whether he is capable of feeling at all. From the enduring wonder of the heavens flows all grace and power. If anyone thinks it is mindless then he himself must be out of his mind. (On the Nature of the Gods, Penguin Classics, 1972, 2.55)

    However, the traditional theological picture of ‘God’ as a supreme selfconscious being who thinks, plans, and creates – even managing to make the entire universe out of nothing – is untenable. If ‘he’ is a being, he must be finite and limited, and have a relative beginning and end. Whereas if the divine is infinite, it cannot be a thinking being, separate from the universe, but must be one with it, as taught by pantheism. The divine essence would then be synonymous with boundless space, or infinite consciousness-life-substance. And since nothing can come from nothing, it must always have existed.

    Materialistic scientists prefer to attribute the patterned order of the cosmos to ‘laws of nature’, with new ones emerging ‘spontaneously’ as evolution proceeds. But this explains nothing, for the word ‘law’ simply denotes the regular operations of nature – the very regularities that the term is supposed to explain! Patterns in the living world are sometimes attributed to genetic programmes, but this is merely a declaration of faith, since all that genes are known to do is provide the code for making proteins – not for arranging them into complex structures. Moreover, it is hard to swallow the conventional claim that genetic programmes themselves originated by chance.

    If some patterns arose through random genetic mutations and natural selection, it would mean, for example, that the reason the golden angle is widely found in leaf arrangements throughout the plant kingdom is because it contributed to their survival. This implies that at one time most plant species did not embody the golden angle – but such a claim can never be tested. What we do know is that life emerged on earth incredibly quickly, that new and fully functional types of organisms have tended to appear on earth incredibly quickly, and that there is no evidence whatsoever for vast periods of trial-and-error experimentation along darwinian lines.

    The theosophic tradition, or ancient wisdom, teaches that nature’s patterns and regularities are better seen as habits, an expression of its ingrained instinctual behaviour, of the tendency for natural processes to follow grooves of action carved in countless past cycles of evolution. For it teaches that all worlds, on every conceivable scale, reembody again and again. And behind these habits lies an all-pervading consciousness, the universe being composed of interworking hierarchies of intelligent and semi-intelligent ‘beings’ or energy-forms, from elemental to relatively divine. The order of nature also reflects the essential interconnectedness of all things, and the fact that the same basic patterns and processes recur on widely different scales.

    All monads, or units of consciousness, are said to progress through a series of kingdoms towards a state of relative perfection in the system of worlds in which they are then evolving, before passing, after a long rest, into other world systems, on other planes. Humans, in their present stage of rebellious selfconsciousness, often succumb to the temptation to misuse their free will for selfish and shortsighted ends, creating discord and suffering. But it lies within our power to attune ourselves to the fundamental harmony of our inner, spiritual selves – sparks of the universal ‘Self’ – and to become voluntary coworkers with nature in the great cosmic adventure of evolution.

11. Sources

• Blavatsky, H.P., The Secret Doctrine, Pasadena, Theosophical University Press, 1977 (1888)
• Cunningham, Bailey, Mandala: Journey to the center, New York, DK Publishing, 2002
• Doczi, György, The Power of Limits: Proportional harmonies in nature, art, and architecture, Boston, Shambhala, 1994
• Ghyka, Matila, The Geometry of Art and Life, New York, Dover, 1977 (1946)
• Godwin, Joscelyn, Harmonies of Heaven and Earth: Mysticism in music from antiquity to the avant-garde, Rochester, Inner Traditions, 1995
• GoldenNumber.Net, http://goldennumber.net
• Heath, Richard, Matrix of Creation: Sacred geometry in the realm of the planets, Rochester, Inner Traditions, 2nd ed., 2004
• Heath, Robin, Sun, Moon, & Earth, Yew York, Walker & Company, 1999
• Jenny, Hans, Cymatics: A study of wave phenomena and vibration, Newmarket, MACROmedia Publishing, 2001 (original 2 volumes published in 1967 and 1974)
• Knott, R., ‘Fibonacci numbers and nature’, www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html
• Knott, R., ‘The golden section ratio: phi’, www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phi.html
• Lawlor, Robert, Sacred Geometry: Philosophy and practice, London, Thames and Hudson, 1997 (1982)
• Livio, Mario, The Golden Ratio: The story of phi, the world’s most astonishing number, New York, Broadway Books, 2002
• Lundy, Miranda, Sacred Geometry, Cascob, Wooden Books, 2nd ed., 2002
• Martineau, John, A Little Book of Coincidence, Cascob, Wooden Books, 2001
• Michell, John, The New View over Atlantis, London, Thames and Hudson, 1995 (1983)
• Michell, John, The Dimensions of Paradise: The proportions and symbolic numbers of ancient cosmology, Kempton, Adventures Unlimited, 2001
• Murchie, Guy, The Seven Mysteries of Life: An exploration of science and philosophy, Boston, Mariner Books, 1999 (1978)
• Pennick, Nigel, Sacred Geometry, Symbolism and purpose in religious structures, Chieveley, Capall Bann Publishing, 1994
• Plummer, L. Gordon, By the Holy Tetraktys! Symbol and reality in man and universe, San Diego, Point Loma Publications, 1982
• Plummer, L. Gordon, Three Steps to Infinity, San Diego, Point Loma Publications, 1993
• Plummer, L. Gordon, The Mathematics of the Cosmic Mind: A study in mathematical symbolism, Wheaton, Theosophical Publishing House, 1982
• Purucker, G. de, Studies in Occult Philosophy, Pasadena, Theosophical University Press, 1973
• Purucker, G. de, Fountain-Source of Occultism, Pasadena, Theosophical University Press, 1974
• Schneider, Michael S., A Beginner’s Guide to Constructing the Universe: The mathematical archetypes of nature, art, and science, New York, HarperPerennial, 1995
• Schwaller de Lubicz, R.A., The Temple of Man, Rochester, Inner Traditions, 1998
• Stewart, Ian, and Golubitsky, Martin, Fearful Symmetry: Is God a geometer?, Oxford, Blackwell, 1992
• Stewart, Ian, Nature’s Numbers: Discovering order and pattern in the universe, London, Weidenfeld & Nicolson, 1995
• Sutton, Daud, Platonic & Archimedean Solids: The geometry of space, New York, Walker & Company, 2002
• Tame, David, The Secret Power of Music: The transformation of self and society through musical energy, Rochester, Destiny Books, 1984
• Thompson, D’Arcy Wentworth, On Growth and Form, New York, Dover Publications, 1992 (1942)
• Volk, Jeff, ‘Sound insights’, Kindred Spirit, issue 60, autumn 2002, www.cymaticsource.com/KindredArticle.pdf

Golden ratio in the planets

From CreationWiki, the encyclopedia of creation science

The Golden ratio in the planets shows that the planets are engineered around the same golden ratio as innumerable other objects including the human body, dolphins, and the Parthenon.

Definitions

Sidereal years

The sidereal years and synodics of all planets until Uranus are related by the Golden ratio to a statistical significance of over 99%.

Mercury's sidereal year is 88 days. The Mercury-Venus synodic is 144.5255474 days. 88x1.61803 = 142.387, which is within 2 percent of the Mercury-Venus synodic.

The Mercury-Venus synodic is 144.5255474 days. Venus's sidereal year is 225 days. 144.5255x1.61803 = 233.84, which is within 4% of Venus's sidereal year

Venus's sidereal year is 225 days. Earth's sidereal orbit is 365.24 days. 225x1.61803 = 364.05, which is within .3% of Earth's sidereal orbit;

Earth's sidereal orbit is 365.24 days. Mars's sidereal orbit is 686.9601. 365.24x1.61803=590.969, which is within 13% of Mars's sideral orbit.

Mars's sidereal orbit is 686.9601 days. The Mars-Ceres synodic is 1161.588 days. 365.24x1.618=1111.4, within 4% of the Mars-Ceres synodic.

The Mars-Ceres synodic is 1161.588 days. The orbit of Ceres is 1681.24 days. 1161.588x1.618=1879.4, within 10% of the orbit of Ceres.

Ceres's orbit is 1681.24 days. Jupiter's orbit is 2746.223 days. 1681.24 daysx1.618 = 2720, within 1% of the orbit of Jupiter.

Jupiter's orbit is 2746.223 days. The Jupiter-Saturn synodic is 3687.59 days. 2746.223x1.618= 4443, within 17% of the Jupiter-Saturn synodic.

The Jupiter-Saturn synodic is 7261.85 days. The orbit of Saturn is 10757.73 days. 7261.85*1.6180339887=11,748, within 8% of the orbit of Saturn.

The orbit of Saturn is 10,757.73 days. The Saturn-Uranus synodic is 16,558.56 days. 10,757.73x1.61803=17,406.3, within 5% of the Saturn-Uranus synodic.

The Saturn-Uranus synodic is 16,558.56 days. The orbit of Uranus is 30,708.16 days. 16,58.56x1.61803 = 26792, within 12% of the orbit of Uranus.

The orbit of Uranus synodic is 30,708.16 days. The Uranus-Pluto synodic is 46,449.19781. 30,708.16x1.61803 = 49686.46524, within 7% of the Uranus-Pluto synodic.

The Uranus-Pluto synodic is 46449.19781 days. The orbit of Pluto is 90,613.31 days. 90,613.31x1.61803 = 75156.19554, within 17% of the orbit of Uranus.

Deviations

The deviations are minute, in comparison to the similarities. In fact, the planets deviate from the series less than 1/1000 of one percent. Yet why are there deviations at all?

• Orbital variation over time;
• Equinox precession: If the sun is moving as argued by the binar theory, then the tropical year, rather than the sideral year is the true year. The tropical year, while close to the sidereal year, differs somewhat.
• Imprecision in measurements;

Also, Neptune does not fit into the pattern. Why?

• Perhaps a more complex pattern exists that incorporates those two;
• Perhaps Neptune was not included in the pattern.
• Perhaps some cataclysmic events knocked Neptune out of its proper orbit.

Implications

The correlation with the golden ratio is obvious. The only remaining issue is, is this a function of chance and natural law, or of engineering?

• No naturalistic explanation has been proposed to explain the above facts.
• Creationists, on the other hand, point out that in order for this to take place, all of the planets had to be a particular mass in order to move at a particular period at a particular distance. If any of them had been smaller than they are, the pattern would not exist. If any of them had been bigger than they are, the pattern would not exist. Thus there is evidence that the size of the planets was deliberately chosen to make the planets move in a particular and aesthetic harmony. To creationists, it is no surprise to find harmony engineered into the planets by the Great Engineer.