3) The Spider (continued)

    Occasionally we can see a sight that used to strike terror in man and animals alike, and even today is one of the most awe inspiring sights it is possible to witness. When the path of the sun co-incides with that of the moon we witness an eclipse. The sun's light is blotted out for a few minutes as the disc of the moon co-incides totally with that of the sun. For this is a great co-incidence. And it relies on some amazing facts:

1) The sun's diameter is 1,400,000 kilometres.
2) The moon's diameter is 3,500 kilometres.
3) The distance of the sun from the earth is 150,000,000 kilometres.
4) The distance of the moon from the earth is 380,000 kilometres.


    (Doesn't mean a lot does it.)

    How about expressing it another way?

    Although the sun is 400 times larger than the moon, the sun just happens to be 400 times further away. Therefore the two discs appear to us to be the same size. Sun and moon in balance. It is this amazing fact that, from our viewpoint in space, enables total eclipses to occur.
    It truly is an amazing fact, yet how many reading the true 'scientific' facts above were able to recognise the 400:1 relationship? Not many it would be imagined. How many other amazing facts would be uncovered if the scientific databases of the world were turned from decimals to fractions and looked on in terms of ratio and proportion?


c) Broadening our Horizons

    We have already seen in Section One how something that has been ignored, laughed at or even ridiculed can be used as a step towards greater understanding. Someone who experienced all these was Katherine Maltwood, who in the late 1920's discovered a terrestrial zodiac in the landscape around Glastonbury. She found that very few people were interested, despite the fact that there were many strange coincidences in this strange discovery. From the mundane - there just happened to be a rifle range on the bulls eye of Taurus, to the extraordinary - the stars corresponding to the twelve figures of the zodiac can be found lying exactly over their corresponding figures if a planisphere of the correct scale is laid over a map of the zodiac. This is extraordinary: what is above is shown below. Katherine Maltwood found the twelve figures of the zodiac, but there is evidence going back thousands of years that at one time there was a zodiac of thirteen signs.
     The zodiac is derived from the fact that, as viewed from Earth, the sun seems to travel over the same path in the sky, along with the Moon and the five visible planets, Saturn, Jupiter, Mars, Venus and Mercury. The path seen every night in the sky is an arc, a section of a vast circle that seems to hold the seven major bodies on an unchanging route across the backdrop of the star constellations. It is the circle of constellations through which the sun travels that we call the zodiac - our star signs.     We see a section of the arc every night, and if we made careful notes every night, after several years we would have a very good idea of the path of the moon and the planets. The sun unfailingly rises every morning, although each morning it rises at a slightly different place on the horizon. Again, if records were kept, maybe using some kind of sight against the horizon; a large stone for instance, it would be noticed that after a period of time the sun will rise in (almost) the same place as it did on the first sighting. It is this period of time that defines the year.

    The night sky has always held a fascination for man and over the years we have given names to the patterns we have seen. We call the circle through which the sun travels the plane of the ecliptic, and the star constellations through which the sun travels, the zodiac. One would assume that there are twelve constellations through which the sun travels during the course of the year, but in fact there are thirteen. Ophiochus 'the serpent holder' is omitted from our sun signs.
     Thirteen has always been a number associated with the moon. If we had recorded the movement of the moon through the plane of the ecliptic over the course of the same 'sun' year we would have noticed that the moon moves just over thirteen times as fast as the sun; 13.368 being the precise figure. No doubt we would also have noticed that there were actually less than thirteen full moons in a year and may have wondered precisely how many. There is an easy way to find out precisely how many, and you do not even need a telescope. Rather, the tools required are set square, ruler and compass.
    By drawing a right angled triangle with sides of ratio 12:13:5 and then drawing another line from the corner where the 12:13 sides meet, to 3/5ths of the way up the 5 unit side we can measure the new line in the same units of measure we have chosen for the main triangle and just call the units lunar months. This is because the length of the line we have drawn to split the '5' side in the ratio 3 parts to 2 just happens to have a length of 12.369. The exact (computer accurate) number of times we see a full moon in the space of a solar year is 12.368, so getting it right to 1 part in 12,000 is not bad going; or maybe it is just coincidence.

    In ancient times the year was split into 13 'moon' months of 28 days (our word month coming from the word moon) with an extra day added to keep in step with the solar 'sun' year, thereby keeping a balance in their calendar between the lunar and solar forces. We keep a 12 month calendar with no thought of the moon's travels, though if we look in the sky we can still see the natural rhythm. For instance, we can see why we have a leap year every four years, when to account for the fact that the year is actually 365.242 years long, we insert an extra day into the fourth year. We can see this for ourselves by using the method described above, when we can see the sun rise almost behind the same marker every year, its inaccuracy reducing, until after four years it does very nearly align with its original marker. But for an exact rising behind the same point one must wait thirty three years, and for millennia the number 33 has held great significance for societies, religions and secret organisations as a number of perfection.

    At one time, astrologers used to draw diagrams of the heavens which are laughed at these days. The dance of the heavens was known as the music of the spheres, and in the drawing below of our triangle described above we have also described music.

    When we listen to music we know that we find some note combinations harmonious and some discordant. The musical scales are based on harmonious combinations and the notes themselves are arranged at intervals that are chosen to be as harmonious as possible when played in combination. The octaves are the most harmonious division - two As or two Cs from adjacent octaves when played together will always sound the most harmonious. They sound harmonious because there is a simple relationship between the rates of vibration, or 'frequency', of the two notes. In the case of the octave the relationship is 2:1. For instance, if one violin plays a C and at the same time another violin plays a C an octave higher, the string on the second violin would vibrate twice as fast as the string on the first, giving the 2:1 relationship; and the two vibrations would combine to give a very pleasant sound.
    The other vibrations that sound harmonious to us also have simple numerical relationships. The most harmonious after the 2:1 frequency ratio of the octave is the 3:2 ratio known as the perfect fifth. We can hear it if one violin plays a C while at the same time another plays a G. By a strange co-incidence we have already seen the 'perfect fifth' in action, showing the number of lunations in a year. When the same diagram is redrawn below to show the relationship of the perfect fifth to the octave, only the labelling changes.

The Perfect Fifth

    It is strange that the note combinations we find the least harmonious are not those that are mid way between the most harmonious combinations, but are the vibrations that are just 'off' from the most harmonious. These discordant combinations happen to be the ones with the most complex numerical relationships. This is illustrated in the diagram below.


A c' is held on one violin while another glides through two octaves. The harmonies are recorded.
The more harmonious the note, the nearer to the line it is; the less harmonious, the further away.
Diagram originally published in 'The Physics of Music', Methuen, 1944.
Based on research by H. Helmholtz.

    In the diagram above we can clearly see the most harmonic notes, bounded on each side by the discordant shoulders forming humps, seemingly there to keep the harmonious grooves in place. Surely this is a feeling we have all felt: of being 'in the groove', of doing something that feels 'just right'. It is certainly a feeling common to writers, poets, musicians and artists: they have described it many times. Is this Jung's synchronicity, the state of being when coincidences 'just happen'? Surely this is the state that Robert Graves was in when he wrote the bulk of 'The White Goddess' in three weeks of fevered writing and which he descrbes most eloquently in an appendix to the book. At its most extreme could this be the explanation for religious ecstasy, when direct communication with 'something' is felt?
    Could this also work the other way? Could cosmic harmony touch us? When it is necessary might strange things happen? Might prophets appear as divine messengers? Might children receive divine visions? Might angels appear in the middle of battle? Indeed, might we outline strange things in the landscape? - or is the world like that anyway?

    Mankind has always been fascinated with questions like those above. Pythagoras (572-497 B.C.) is famous for his pioneering work in the fields of number and trigonometry, but less well known as a musician and astrologer (used here in its true sense as 'one who studies the stars'). In fact it is Pythagoras who is credited with being the first to investigate the relationship between one musical note and another - it was he who discovered the perfect fifth, as well as the square root rules linking the lengths of the sides of a right angled triangle.
     These things and more were discussed in the Pythagorean mystery schools. Nowadays we have made tremendous advances in all scientific fields. Yet maybe modern science has got so complex that we can no longer see the trees for the wood.

    Fortunately the old ways of thinking are being continued. People like Richard and Robin Heath, together with John Michel, continue to look at our planet and the cosmos through the eyes of ratio and proportion - and continue to make amazing discoveries.

    There is also a series of little books available that form a first rate introduction to ratio, proportion, ancient astrology and associated topics.

    So, if Nature was to pluck a string somewhere in the cosmos.......

    In fact there is one creature on Earth that plucks a string when she vibrates the first filament of her web to allow natural resonance to space the markers around which she builds the rest of her creation....... Wisdom indeed!