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It has already been emphasized that the greatest mathematical and astronomical discoveries were made by men who were seeking cosmic design. It is quite apparent that the ancients knew about, or were seeking a design in the solar system (If they were seeking it). We do not know whether they found it, We do know that the design was there. It is possible that they may have known about it and concealed the truth in the same manner that we tried to conceal the truth about atoms. We fear that information about atoms in the wrong hands may destroy the earth. It would appear that the ancients may have had some similar fears. There was some belief that knowledge was for the chosen few. Although there is no indication that Pythagoras held such views, his followers did, and Pythagorean schools were secret schools. Those taught were sworn to secrecy. The Pythagoreans were mighty serious about this, and violations were subject to the death penalty. In the fourth century, B.C., Hippasus, a member of one of the Pythagorean societies, made a public announcement that he had discovered a solid with 12 faces (12 again). Because he offered this information to the public, the death penalty was immediately imposed. He was drowned in his bath for giving away mathematical truths. (In our own day the Rosenbergs were executed for a similar offense.) Insofar as can be determined, such a 12-face solid (with 5-sided surfaces) was unknown to Pythagoras himself, unless he, too, was holding out.
Since we must consider all possibilities, we must also consider more ancient ancients than those we know anything about may have that known far more than the particular ancients we do know something about. Knowledge may have become lost, just as a lot of people today are wishing the secrets of the atom could get lost.
However, we do have the fact that the ancients saw a significance in numbers or integers that modern mathematicians have ignored as mystic. The numbers 7 and 12 were very important to them. Later in these less6ns, we will show how, in astrological geometry, 7 becomes 12. Let us quote a paragraph from Hogbens popular, Mathematics for the Million. "When we amuse ourselves at the expense of these early societies struggling to lisp the language of number in the childhood of civilization, it behooves us to ask whether we ourselves have completely grown out of magic. Caution is all the more pertinent when were call the queer theosophical preoccupation's of Pascal and Newton, who contributed so much to the sort of' mathematics which is most useful in solving problems of measurement in the age of machinery. For European civilizations the numbers in which magical properties reside are more particularly seven and three. Theology bequeathed to us the seven golden candlesticks the seven evil spirits cast out of Magdalen, the seven sorrows, the seven deadly sins, the seven (deadlier) virtues and the sevenfold amen. The number seven has not been neglected by the unofficial theologians, more usually referred to as philosophers. In the year that Piazzi discovered Ceres (an asteroid), seven planets were known: namely, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus. In the same year the Prussian philosopher Hegel wrote upbraiding scientists for the neglect of philosophy. He illustrated his disapproval of the amount of time astronomers wasted in looking for a new planet when philosophy clearly established the only possible number as seven. Since then other planets have been discovered. Neptune followed shortly after (l876). Pluto was discovered in 1930, because stronomers are materialists so long as they remain in their observatories."
Actually, in seeking more planets, astronomers were keeping an open mind, which is very helpful to science but very rare for astronomers. Hogben himself discloses that he is locked within a frame of reference brought about by the mental limitation he imposes on himself when he defines mathematics as a mere science of measurement. What we wish to emphasize is the religious and philosophical determination to keep alive the significance of the integers 7 and 12. Without this determination, astrology would have died out completely, because the division of a circle into twelve equal parts is our most basic key. Had it been divided into 11 or 13 equal parts, everything would have been lost. We agree with Hogben that astronomers are usually materialists, but mathematics is not materialism. It is completely a study of abstractions, and because Hogben limited himself to a conception of mathematics as it might be applied to material things, his frame of reference did not permit him to view more than a very small part of the whole. Some of the greatest facts of all had to be excluded. Modern science works within a relatively narrow frame of reference which makes it necessary to constantly exclude a very large ratio of the facts. If the scientist loves his wife, and her affections are stolen by another man, he encounters what was left out of his textbook. He encounters emotion. We will find it hard to convince himself that his emotion is less real than the materials he has been measuring, but none of his formulae will help him when it comes to measuring his emotions, much less controlling them. Theologians, philosophers and astrologers have made errors, but that would appear to identify them with so-called "scientists." We will show later in these lessons there was a definite reason for keeping. alive the significance of 7 and 12, and we will show how these two numbers relate to each other.
First, let us get a picture of the solar system. We have the Sun as the center, surrounded by circles of various sizes called orbits. Although these are not really circles but ellipses, they are not too eccentric and they are almost circles. These imaginary ellipses are the paths over which the planets travel. It should be realized that they do not lie in the same plane of space. The orbit of Pluto is inclined to that of the earth by 17 degrees, that of Mercury by 7 degrees. The others are closer. The orbit of Pluto has the greatest eccentricity, that of Venus the least. In the following diagram, our relative distance between orbits is highly inaccurate, because we are only concerned with the order of the orbits.
We want to call your attention to the order of these planetary orbits. This is one thing you will want to learn, if you do not already know it. Starting at the center and going out into space it runs: Sun, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto, and whatever may exist beyond Pluto. Between the orbits of Mars and Jupiter, there are hundreds of little objects called asteroids or planetoids which also revolve around the Sun, but we know of no astrological significance they may have. The biggest would make only a good sized mountain on the earth. We will ignore them because we know nothing of any consequence about them. You don't have to ignore them, but we will for now.
The ancients made an association between the planets and the signs of the zodiac. They called the planets The rulers of the zodiacal signs. We do not know for certain how that word ruler crept in here, but let us point out that the word has a double meaning. A ruler may be a king who rules over a land, or it may be something with which you measure. If we employ the second meaning of the word it takes on an interesting significance in astrology.
Each zodiacal sign had a ruling planet. There is another object nearby that we did not mention. It is the Moon. The ancients employed the Moon as one of these rulers. Insofar as we know, the ancients knew nothing about planets beyond Saturn. Any planet beyond Saturn is invisible to the naked eye. If you are on the earth, that leaves SEVEN visible bodies: Moon, Sun, Mercury, Venus, Mars, Jupiter and Saturn. If you were on the Moon, there would still be seven visible bodies, because you would view the earth instead of the Moon. The ancients had a definite way of assigning these seven bodies to 12 zodiacal signs. The Moon was assigned to Cancer, the Sun to Leo, Mercury to both Virgo and Gemini, Venus to both Libra and Taurus, Mars to both Scorpio and Aries, Jupiter to both Sagittarius and Pisces, Saturn to both Capricorn and Aquarius. In this way, they had seven bodies ruling twelve signs. There is an odd factor here which, to our knowledge, had never been noted by modern astrologers at the time when the writer began in- vestigating astrology. Although he spotted it in 1933, he originally called attention to it in 1938 in a book entitled, A New Experiment In Astrology. The book was more or less ignored by the majority of astrologers, and reviews pictured it as claiming almost everything on earth except what it did claim. To this day, the content of the book has not been grasped. If it had been, much of astrology as it exists would be different. Elbert Benjamine, founder of a theological school of astrology, made alleged quotations from the book, and when he was asked to explain where he had found the various statements quoted, he admitted that he couldn't find them anywhere in the book. At the time when he made the quotations he had never read the book.
This is the incomplete design left to us by the ancients, and for thousands of years nobody noticed that the rest of the design could be filled in, could be completed, when the key was realized. The key is mean distance from the earth. The numbers indicate the order tin which each planet appears when mean distance of the various bodies from the earth is considered. It is known that the ancient mathematicians prepared magic squares where several numbers were purposely omitted. One person who was seeking design would immediately understand and could detect the missing factors. The above diagram carries the subtle suggestion that ancients far back may have known more about the solar system than astronomers know today. The diagram suggests the existencse of two undiscovered planets beyond the orbit of Pluto. Because people did not thin in terms of cosmic design, the significance of the above diagram remained secret for thousands of years.
If you will look at the above diagram, you will note that beginning in Cancer and running counterclockwise to Capricorn, the ancients assigned the planets IN EXACT ACCORDANCE with the bodies' mean distance from the earth. Because the Moon is nearest, we have assigned it the number I, the Sun-2, Mercury-3, Venus-4, Mars-5, etc. Mercury, Venus and Mars can be nearer to the earth than the Sun, but when we consider the average distance, the Sun is closer.
If we start in Gemini and go around the circle clockwise to Aquarius, we find the same kind of sequence The order coincides with mean distance from the earth. This gives us an interesting problem in mathematical probability. We have part of an arithmetical pattern here. What is the probability that these planets were arranged in this fashion by chance?
There are 5040 ways in which the planets could have been arranged in those signs from Cancer to Capricorn, but only two of those would have coincided with the factor of mean distance. (The other way would be to start in Capricorn and finish in Cancer, going clockwise.) Cutting 5040 in half, this makes the odds 2519 to 1 against this arrangement being due to chance.
Considering the five remaining spaces, what are the odds against those also being assigned in accord with mean distance? There are 120 ways in which 5 planets could have been arranged in 5 spaces, only 2 of which would have conformed to the pattern, making the odds 59 to I. When we consider the odds against the second arrangement applying after the first arrangement had already applied, the odds are (2520 x 60)-l to 1, or 151,199 to 1.
Here is one of the most extraordinary facts of astrology that has been overlooked and ignored for the last 2500 years. An astronomer can ignore a fact of this kind, but a mathematician cannot. However, this is but a tiny part of the coincidence. Even greater odds are involved. The symmetry, the mathematical design, does not stop here. It continues. You will note that by putting Mars in both Scorpio and Aries, the ancients were associating what we have described as the FAMILY SURVIVAL DYNAMIC with the FAMILY REFORM DYNAMIC.
By associating Jupiter with both Pisces and Sagittarius, they were associating the SOCIAL SURVIVAL DYNAMIC with the SOCIAL REFORM DYNAMIC
By placing Saturn in both Capricorn and Aquarius, they associated the INDIVIDUAL SURVIVAL DYNAMIC REACTOR with the INDIVIDUAL REFORM DYNAMIC GUIDE.
By placing Mercury in both Virgo and Gemini, they associated the SOCIAL SURVIVAL DYNAMIC REACTOR with the SOCIAL REFORM DYNAMIC GUIDE.
They neglected to put the Sun or Moon in both Cancer and Leo, which was the only necessary step left to complete this particular symmetry. Then they would have associated the INDIVIDUAL SURVIVAL DYNAMIC with the INDIVIDUAL REFORM DYNAMIC. We have not reached the end of the design.
When Uranus was discovered, the materialists accepted the event with great glee. This, the astronomers told us, disproved astrology. Instead of seven Solar Bodies, there were eight. The magic qualities of 7 were disproved, or so they thought. There was a bit of confusion in the world of astrology also. This did not appear to upset things, but unlike the astronomers who are supposed to make so many millions of observations but yet fail to observe, the astrologers began making observations, and in time, they came up with a conclusion. It had been a mistake to put Saturn in Aquarius. It belonged to Capricorn. Uranus was the ruler of Aquarius. Strange as it may seem. all astrologers soon agreed on this. In studying Uranus, they found the same qualities that they found in studying Aquarius. Still unconscious of the factor of mean distance, they had placed an 8 in Aquarius and thus continued the sequence. This increased the odds against the first part of the pattern being due to chance to 20,159 to 1.
In time, Neptune was discovered, and after some years of observations, the astrologers agreed that Neptune and not Jupiter belonged in Pisces. Still unconscious of the factor of mean distance, they had again continued the sequence and had placed 9 in Pisces, and this time they increased the odds to 181,339 to 1.
In 1930, Pluto was discovered. This time, there was some disagreement. Some astrologers placed Pluto in Scorpio, others in Aries. Placing it in Aries conformed to the pattern again, and drove the odds to 1,814,399 to 1. Oddly, placing it in Scorpio also conformed from the other point of view. When you count the other way, 10 falls in Scorpio.
Even more strange is the fact that the astrologers who identified Pluto with Scorpio were an occult group and their conclusions came out of study of Greek mytho1ogy. Even these methods brought about an unconscious conformance with the arithmetical pattern that was piecing itself together.
The writer first observed that this connection between planets and zodiacal signs conformed to the mean distance in late September 1933, and from that time on assigned Pluto to Aries. The student may later find it of interest to note that Jupiter, Mercury and Sun were in Libra at that time, the sign that we identify with an understanding of mathematics More interesting might be the fact that the whole idea just popped into the writer's head while in bed, dozing off to sleep. He suddenly saw the pattern of the whole, and forced himself out of bed to write it down, in fear that he might not remember it the following morning.
The pattern is not yet complete, but only two pieces are missing from the jigsaw puzzle, and we know what they are like and where they belong. To complete the pattern, there we must be two more planets outside the orbit of Pluto, and the first must be assigned to Taurus, the last to Gemini.
The zodiac is an abstract mathematical pattern. It is divided into l2 equal parts. The association of planets with abstract signs of the zodiac implies there are 12 objects other than the earth in the solar system when the Noon is counted. On another planet, our Moon would have no significance, and the number of signs of the zodiac for another planet like Jupiter which has its own 12 (at least) moons, could vary, just as the number of electrons in atoms of different metals vary. Thus life on another planet could be expected to be quite different from life on earth.
For the benefit of the mathematically minded, we would like to explain the computation of odds referred to above. The astrologers have unconsciously fitted ten planets into ten spaces in one of only two ways that would conform to the mean distance of the bodies from the earth. The number of ways that ten numbers can be arranged in ten spaces will be 10! or factorial 10, which means (10 X 9 X 8 x 7 X 6 x 5 x 4 x 3 X 2 X 1).
You can multiply these out if you choose. The answer is 3,628,800. Since two of these ways would conform to the pattern, one counting Clockwise, the other counterclockwise the chances are 2 in 3,628,800 or 1 chance in 1,814,400. This gives odds of 1,814,399 to 1 against this pattern having been an accident. With the discovery of two more planets the pattern will be complete. However, we are already close enough to visualize the complete design, and that means close enough to give the astrological characteristics of the two missing planets. The first planet beyond Pluto must have the same characteristics as. Taurus, while the last planet Out must have the same characteristics as Gemini.
Just as there are seven visible bodies in the solar system, as viewed by Man on the earth, there are seven white keys in an octave on a piano. Just as there are five black keys in the octave, there would appear to be five planets invisible to Man's naked eye. This does not mean that the planets cause the keys on the piano or that the keys on the piano cause the planets. It merely illustrates an a causal relationship in the coincidence, the same mathematical design.
We offer another diagram above showing the planets and their numbers going around the circle both ways, starting from Leo and going clockwise, starting from Cancer and going counterclockwise. This is a perfectly symmetrical pattern. It is a mathematical design. In all of their associations of planets with zodiacal signs, the astrologers of all known times have unconsciously conformed to this design. We have added two theoretical planets and have called them "Y" and "Z".
Now let us look at the above diagram . Here we have merely drawn lines to connect the numbers in the clockwise, count with the numbers in the counterclockwise count. We get an interesting design. It is a design that closely resembles that of a magnetic field. That does not mean that it IS a magnetic field any more than the solar system is a piano. If you study this design, you will find that a SURVIVAL DYNAMIC is always connected with a corresponding REFORM DYNAMIC, and a SURVIVAL REACTOR is always connected with a corresponding REFORM GUIDE. An INDIVIDUAL factor is connected with an INDIVIDUAL factor. A FAMILY factor is connected with a FAMILY factor. There are no exceptions to the rule. The pattern is complete symmetry. There are no missing pieces. The jigsaw puzzle has been put together. As you grow more familiar with the pattern, it will become simplicity itself. It is nothing but an abstract mathematical figure, but the only such figure that has ever caused us to find a connection between distance from a center and divisions of a circle into twelve equal parts. These two factors appear to involve a factor of coincidence, but it may be only the a causal coincidence that we find connecting a piano and the solar system. We can employ white keys to represent visible planets, the black keys to represent invisible planets. As you will later see, both counts, the clockwise and the counterclockwise, have a very definite significance, and each is to be employed under different circumstances.
We will not need to devote much space to an explanation of what the planets mean, for the simple reason that they mean the same thing that is meant by .the signs of the zodiac The same twelve basic principles expressed in the zodiacal signs are expressed in the planets. Just as you have lined a basic principle with a particular zodiacal sign, you will now link the same principle with a planet. The following table will show the manner in which this applies.
The numbers at the right side of the page are the same numbers that appear in our diagrams. The first column of figures represents mean distance from the earth insofar as the named planet is concerned. The figures in the second column represent the count the other way around the zodiacal circle. In this way, 1 is joined with 2, 3 with 12, 4 with 11, 5 with 10, 6 with 9, and 7 with 8. It will be necessary to retain both of these counts as we will later see. Each has a significance. If you omit one and substitute 13 (for the 1 would become 13 if you continue counting), the two integers joined each time will always total 15.
We have shown that there is only 1 chance in 1,814,400 of the counterclockwise count of the planets in the zodiacal signs being due to chance. We have also shown that there was 1 chance in 60 of the as astrologers hitting the target five consecutive times relative to the clockwise. count, but the target was hit again when the occult group associated Pluto with Scorpio. There are 720 ways in which 6 planets can be arranged in 6 spaces (6 x S X 4 X 3 X 2 X 1), only 2 of which would conform to the mean distance, meaning that there is 1 chance in 360 that these selections were due to chance alone.
Now, to determine the probability that the entire mathematical pattern was a matter of chance, we can say there is one chance in 360 x 1,814,400 or 1 chance in 653,184,000. The mathematical odds against the possibility that the astrologers were deceiving themselves are 653,183,000 to 1. In
Lesson Four, we presented a diagram identifying time with the signs of the zodiac. This was a pattern. Patterns are not due to chance. They involve abstract laws. They are called natural laws because we find them in nature, but what we find in nature is not the mold. The mold is the abstract law itself. In nature, we find only what has been formed by the mold. However, by making the identification of planets with signs of the zodiac as we have done in this Lesson, we encounter a new association, because we can now associate time with the planets in the same manner as we have done with the zodiacal signs Certain solar bodies are related to the perpetuation of forms of the past, while other bodies are to be identified with destroying the form of the past that the pattern of the future may come into being. So, if we arrange the solar bodies in the order of their mean distance from the earth and relate them to past and future, we will come up with the following table.
The symbols "Y" and "Z" represent two hypothetical planets out beyond the orbit of Pluto. We have never seen these planets. Their existence is merely a matter of calculation. Neither have we seen an atom. Its existence is merely a matter of calculation. However, we have demonstrated that the probability of those planets being there is 653,183,999 to 1. The astrological pattern is not complete until these two missing pieces of the jigsaw puzzle are added.
It is extremely diffIcult for the writer to visualize how the whole superstructure of astrology could have been discovered by Man except in the same manner that the atom was discovered, by calculation. If the original knowledge came from the calculations of super- mathematicians, who were they? Surely, no one that history can tell us anything about. If these super-mathematics knew from their own astrology that civilization was to go into a decline for thousands of years, it might account for much that was done. Why do we dig up the twelve symbols of the signs of the zodiac carved on stone throughout the world? The conception that the great pyramid was a tomb motivated by a king 5 vanity is childish when we consider that it is a mathematical figure involving facts of astronomy. When we pat ourselves on the back while observing the great structures, buildings and dams we have constructed, we ignore the fact that no modern structure compares in cubic yards with the wall that surrounded the ancient city of Babylon. The ancients left behind them their messages in the form of design and symbols which have remained uninterpreted for thousands of years. After the tremendous amount of labor that was employed in carving the Aztec Calendar Stone, what was done with it? It was hidden. It was buried in the ground where it was not discovered until more than a century after Cortez entered Mexico City. The diameter of the large circle is 12 feet. (Do not place significance on 12 here because the foot is an arbitrary measurement.) The stone is three feet thick, and its weight is over 20 tons In the center of the circle is the symbol of the Sun (not the earth). Around it are the symbols of FIRE, AIR, EARTH and WATER. Other markings represent such cycles as days, weeks and months in the Aztec calendar system. At the time it was found, it was a more perfect calendar than any that had been designed by astronomers of the time. Interesting is the fact that after the stone was found by the Spaniards, it was hidden again by the church, in the fear that knowledge of the symbols and the story told by the stone might cause people to abandon the church. It was buried by the theologists for another 150 years.
What Hogben describes as the cradle of civilization may actually have been the tomb of a former civilization. Of course there are legends about Atlantis and Lemuria, sunken continents which supposedly held more advanced civilizations than ours. We are not authorities on Atlantis and Leniuria, but speculations on the possible existence of such civilizations are interesting, and even if these speculations contain a vast amount of false information, they should be combed for any few threads of fact which may possibly exist. One such speculation contained the claim that the Lemurians colonized the east coast of Asia and the west coast of South America before the continent sank into the Pacific, and that after the disaster, those on the coast of Asia thereafter bowed to the east to the former motherland in their religious cults. This conforms to the curious fact that the religious cults of South America bowed, not to the east, but to the west, in their religious ceremonies.
The ancients have been described as being superstitious by some of the moderns, but they could have described our moderns as being superstitious. The nebular hypothesis and many so-called scientific theories are actually superstitions. The astronomers are busy making observations. They are busy counting the number of stars in the heavens, and they might as well count the grains of sand on the earth.
We associate the survival factors with stability, the non-survival factors with instability. Oddly, the stability of an atom is said to have a relationship with whether the number of electrons is odd or even.
It will help your astrology if you begin early to think of astrology as a science of design rather than a science of cause and effect. It is a science of design in the same way that mathematics is a science of design. Your personality and your character is a design. It is actually different in some respect from the design of another person. The design of the solar system at this particular moment is also the design of whatever is born at this particular moment. In astrology, you are always comparing the design of one moment with the design of another moment Two moments of time can be harmonious or discordant to each other. In that respect some days may appear harmonious or discordant for you. That which may appear discordant may be more harmonious when you understand it. It is necessary for you to become familiar with your own design.
Much of your own character is invisible to you. There are parts of your nature that may never have had an opportunity of expressing themselves. Some hidden part of your nature may suddenly be stirred tomorrow, because the design of tomorrow attunes to the design of your birth. in a way that has not previously occurred. All astrological designs resemble dials, and you can think of the dials on your radio or television sets. A slight twist of the dial may tune out Kansas City and tune in Chicago. The astrological dial is more complicated. It is constantly turning. It is ever tuning things in and tuning other things out. That is why your interests shift from year to year, from day to day, from minute to minute. We are always comparing designs, one with another. The man who experiences a sudden sweep of popularity has merely run into design that allows his own personal design to express itself.
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