Although the hexagon is the most economical means of building these cells, we can hardly visualize each hive of bees employing intellectual bees who labor over a drawing board computing the mathematics of what shaped room would require the least wall space to house the greatest content. Neither can we say that snowflakes cause bees to build six-sided cells. Nor can we say that snowflakes freeze in six-sided fashion because they are copying the bees.
Yet a hexagon room enclosed by 60 feet of wall will contain over square feet of floor area, while a square room enclosed by the same amount of wall will contain but square feet of floor space. A room shaped as an equilateral triangle with 60 feet of wall will contain only square feet of area. Of course, a circular room would contain a greater ratio of area to enclosure, but you can't fit circular rooms together. The more equal sides a room has, the greater the floor area, but if a room has more than six sides, you can't fit the rooms together.
Among polygons of equal sides you can fit together only hexagons, squares and triangles. Mathematically, the bee would appear further advanced than Man. He builds warehouses out of hexagonal shaped rooms while Man builds warehouses out of square or rectangular rooms. We find a strange parallel in the fact that the ancient astrologers regarded planetary aspects based on parts of hexagons as harmonious and aspects based on parts of squares as discordant. The sextile aspect is merely one side of a hexagon, while a trine aspect is one side of an equilateral triangle or two sides of a hexagon.
An opposition aspect can be considered as either two squares or three sides of a hexagon, and oddly, astrologers have disagreed as to whether the opposition aspect is harmonious or discordant. It has been our experience that the aspect brings tension, problems and worries while forming, but produces CHANGE that solves the problems and gives re-lief while separating.
If there is any astrological symbolism behind the six-pointed star of the Jewish church and the four-point cross of the Christian church, then one would appear to Indicate harmony and the other discord. Yet, the advanced astrologer realizes that the l, 10, 7, 4 House Cross Leo, Scorpio, Aquarius, Taurus is something that can be transcended through understanding and higher knowledge or wisdom, while those astrologers who look upon the story of Christ as symbolism see Christ, not as a man but as an abstract principle.
To them, it is the rise of the individual above materialism and into the abstract realms. Whether Christ ever lived as a man is beside the point.
The principle is the same. Just as astrology is concerned with geometrical and therefore mathematical figures, we find these figures throughout the mineral world. Different minerals are made up of crystals of different geometrical patterns.
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Not all minerals follow the hexagonal pattern. Salt crystals form the square or degree angle. This is true of other minerals, but the hexagonal pattern is quite common. The crystal mines of Arkansas seem to show everything in accord with the hexagonal principle. Where erosion had washed away a patch of a lava bed at the floor of the Grand Canyon, we found petrified wood covered by hexagonal crystals.
At the Spring Creek Ranch in the Texas Panhandle are found strange objects composed of calcite an inch thick and two inches in diameter that are in the form of a perfect hexagon.
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They are said to be a hang over from the Triassic Age, which was the earliest period of the Mesozoic Era. By careful selection,you could pave a bathroom floor with these strange objects, but most of them have other hexagons growing out of them at various angles. A geode is a strange object of nature that looks like an egg and is shaped like an egg.
Their is a location near Mammouth Arizona, where these eggs lying on top of the ground in quantity over an area of ten or more square miles. These are agate geodes. They are white on the outside like an egg. Originally, they appear to have been mere shells, but from the inner surface grow crystals until the object finally becomes a solid.
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A hollow ultimately becomes a solid. Where does the material come from? Or does material need to come from some place? When it is ready to appear it seems to appear. Astronomers are trying to learn how matter appears or forms in space. How does it appear or form in the hollow of these geodes? An astrological aspect is merely an abstract geometrical measurement.
True, it is sometimes a measurement between two material objects, but this need not be true. It can be a measurement between a planet and a mathematical point, or a measurement between two mathematical points where there is nothing whatsoever of a material nature. It can still have its counterpart in human affairs. Because the planetary nodes are even more important than the planets themselves, it is important that you understand what a planetary node is.
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Remember that we used imaginary embroidery hoops to illustrate two planes of space. Put one hoop inside the other, twist one so that one hoop crosses the other at two points. Look at the hoops from above that point where they cross and you see an X. The point where the two hoops cross is the node.
The other point where they cross is also a node. It is customary to call one point the north node, the other point the south node. What we call the north node of a planet is that point where the orbit of a planet crosses the plane of the earth's orbit as the planet goes north. The south node is the other point, and when the planet crosses the south node, it is traveling southerly. Actually, no planet ever crosses the earth's orbit. It crosses the plane of the earth's orbit, Therefore it is not strictly true to consider these factors as mathematical points.
When referring to a node, an astronomer means that mathematical point where the plane of a planet cuts the earth's orbit, but we could as well consider the node that mathematical point where the plane of the earth's orbit cuts the planetary orbit. These two points would not be the same in space.
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One would be at the orbit of the earth while the other would be at the orbit of the planet. However, if we draw a straight line from the Sun to the mathematical point that is furthest away from the Sun, it would of necessity have to pass through the other mathematical point. Thus, the important factor with which we deal becomes not a mathematical point, but a mathematical line drawn from the Sun in opposite directions to infinity. The plane of the earth's orbit and the plane of the planetary orbit join all the way along the line. As computed today, the planetary nodes are considered as heliocentric, those points where the above described line crosses the earth's orbit.
However, if we use these points as if they were geocentric, they appear to work. This is easy to understand if we consider that we are dealing with mathematical lines instead of mathematical points. Now, we can draw a new set of lines with the earth as the center to those points where the line above described reaches infinity and their direction must be exactly the same as the direction from the Sun. Such a conception justifies us in using the planetary nodes in our zodiac just as they are given in heliocentric longitude.
This view might also completely justify Hugh MacCraig and others who are employing heliocentric positions in the earth zodiac. We know from experience that when the nodes are employed in this fashion they function. We do not know whether they will also function when located by Iines from the earth as a center to those points where the nodal line crosses the earth's orbit, for these points have never been calculated and published.
A student well schooled in mathematics is now calculating these positions, however, and we hope it will ultimately be possible to publish them for experimental purposes. It becomes vital to know the zodiacal position of the planetary nodes. The position of the north lunar node is given in the ephemeris.