1. Precession of the equinox presents a cosmological framework with significant resonance to a weak but real harmonic structure produced by the earth’s annual cycle.
2. Scientific cosmology operates at such big and long scales that human magnitudes seem vanishingly small. There are the equivalent of 500 million human generations since the big bang, and three million million million earth equators to the furthest visible object. Against this context, there is value in also studying cosmological structures of more comprehensible scale than the whole universe, with a view to finding intermediate scales of time and space that have cosmological significance.
3. Precession of the earth’s equinox, the ~25,800 year periodic wobble of the planetary axis, provides such an intermediate cosmological structure. Measurement of precession is a mainstream topic in astronomy, as explained at http://en.wikipedia.org/wiki/Precess..._the_equinoxes. My approach studies precession from a geocentric harmonic perspective. I argue this provides a fruitful scientific cosmology based on resonance between precessional cycles and the earth’s annual cycle.
4. ‘Geocentric’ is used here in a legitimate scientific sense to recognise that all human thought is a product of terrestrial evolution, that all our knowledge occurs within a terrestrial perspective, and most importantly, that simple temporal wave structures observed from and defined by earth are real. We look at the universe from our planet, for both objective science and for everyday markers of ordinary time such as sunrise and sunset. The structure of time is geocentric in its basic levels of measurement, and this basic measure has an important place within a coherent scientific framework. Not only are geocentric rhythms such as the day and year physically real, but they have wave structures that resonate at multiple levels.
5. Each day, we can observe the ‘rotation’ of the galaxy about our seemingly fixed point. The daily rhythm of sun and stars structures ordinary time, producing illusions such as ‘sunset’ and ‘sunrise’. The next levels of ordinary time are the week and month marked by the phases of the moon, and the year, marked by the apparent movement of the sun around the cycle of the equinoxes and solstices. Looking at cosmic time from this human framework, precession of the equinox, the slow shift of the seasons against the stars of the zodiac, is a next order of magnitude after the day and the year, structuring terrestrial time.
6. The framework explained here is grounded in pure mathematics, starting from the rhythm of the year. The zodiac star chart at Attachment 1 illustrates the annual sine wave movement of the sun as seen from earth. The structure of the seasons causes annual sinusoidal oscillation in both the length of the day and the position of the sun in relation to the celestial equator. On the chart, the solstices are the stationary points of this sine wave and the equinoxes are its points of inflection. Another way of mapping this sine wave is by charting the length of the day. http://www.bautforum.com/attachments...conds-2007.jpg illustrates a stationary point of the day length curve at the December solstice. Earth’s annual rhythm has four points of change, traditionally accepted as the first dates of each temperate season at about the 21st day of March, June, September and December. Geometrically, the earth’s orbit is a near-circular ellipse divided by these four points of change.
7. Drawing the orbit of the earth in simplified terms as a circle in space, lines can be drawn through the sun to connect the positions of the earth at solstice and equinox points, making a cross in space. These four points have existed physically for billions of years, and are imbedded in the adaptive ecology of the earth, structuring annual cycles of plants and animals. A harmonic geometry with real cosmological significance can be derived from these four points.
8. The picture at Attachment 2 is a purely scientific derivation of the twelve signs of the tropical zodiac from this mathematical foundation. The circle is the earth’s annual orbit, and the central cross connects the solstices and equinoxes. The step required to derive the signs applies harmonic theory, taking the first three harmonics of the circle to inscribe four equilateral triangles in the circle based on the four turning points of the year. The claim is that each of the four turning points exhibits harmonic resonance with the two points on the orbit which are equilateral to it. These four triangles divide the circle into twelve equal segments and define the physics of the twelve signs of the tropical zodiac.
9. The musical analogy of a guitar string provides an explanatory image for this harmonic theory. The open string or first harmonic represents the whole orbit, the second harmonic at the bisect point of the string represents the opposite point of the orbit, and the third harmonics, at the two points one and two thirds along the string, represent the points one and two thirds of the way around earth’s orbit from each of the four turning points. Higher harmonics also exist, but are much weaker, and are not considered further for the purpose of this analysis.
10. Whether or not this depiction has any effect beyond this mathematical structure, these twelve points of the orbit are imbedded in the empirical temporal framework of the earth and have been basically unchanged since the dawn of life. This physics demonstrates that the tropical signs are not ‘emanations from the stars’ as depicted in some folk traditions and in claims that precession refutes astrology, but are pure mathematical products of the annual relation between the earth and the sun. This is a useful piece of information in itself, given the common error (recently repeated here http://www.bautforum.com/1116991-post125.html at Baut) where scientists suggest that precession of the equinox refutes sign theory.
11. Science has of course not found any demonstrable physical influence from these four equilateral triangles defining the signs. Certainly, if there is any influence it is very weak as it has not to date been proven empirically despite popular use in horoscopes. It is still however an open question whether proof of such a weak effect could be obtained from large scale statistical studies.
12. These four triangles are part of a stable rhythmic wave pattern with the same duration as the earth-moon system. Considered as four factors which form the annual cycle, they can be visualized as demonstrating the physics of the four ‘elements’ of fire, earth, air and water, not in any metaphysical or alchemical sense, but as simple mathematics, with the permanent rhythm involving monthly succession of these four ‘elements’ in this same order. As well, each season has three signs, producing a threefold rhythm or triplicity, traditionally known as cardinal, fixed and mutable. The cardinal signs are the first of each season, the fixed signs are at the middle of each season, and the mutable signs are the last of each season. This triplicity interacts with the fourfold ‘elemental’ rhythm to produce twelve unique combinations each year. So Aries is defined mathematically as the combination of fire and cardinality, Pisces as mutable water, Aquarius as fixed air, etc.
13. In the rhythm of the year, the four-fold division of solstices and equinoxes is obvious, but the claimed further division in three to produce twelve signs is a mathematical observation of uncertain effect. The cusp of Pisces to Aries is the inflection point in March of the curves mapping the length of the day and the movement of the sun from south to north across the celestial equator, but the next cusp, of Aries to Taurus, is simply the point equilateral to both the stationary point between Sagittarius and Capricorn at the December solstice and to the cusp of Leo to Virgo.
14. Whatever its empirical influence, this twelve fold annual cycle has happened with clockwork regularity more than four billion times, producing a stable law-like rhythm within which all life on earth has evolved. My key argument here is that this rhythm produces a weak but real harmonic structure, and that this harmonic structure can be mapped on to the apparent precession of the sun around this cycle vis-à-vis the fixed zodiacal stars of the galaxy. The precessional cycle has happened more than 150,000 times (4 billion/25,800 years), and this long stability gives grounds to explore how it may be imbedded in deep biological rhythms. Traditionally, the precessional cycle is known as the Great Year, while the one twelfth divisions of this period, each about 2152 years, are known as Ages, or Cosmic Months.
15. In claiming that a precessional cosmology is meaningful, I argue that each of the >150,000 cycles since the birth of earth has reinforced the ‘mapping’ of terrestrial genes onto an underlying rhythmic niche by resonance with the stable wave structure of the year. Just as the sun has traveled around the zodiac four billion times, so it has also traversed the same path much more slowly 150,000 times due to precession. My hypothesis suggests that, like all chaotic natural systems, these cosmic structures have a unique directionality established at their origin, and flowing through to all levels, and that this directionality suggests the precessional cycle is mapped in a real physical sense to the annual cycle. These long precessional cycles, with each wave period of 26,000 years containing movement of the equinoctial point through all twelve sidereal signs, each also contain 26,000 instances of the annual solar cycle through the signs. Based on the physics of harmonic resonance, notably in music, these two main temporal cycles of the earth and sun against the galaxy would resonate, with the precessional cycle functioning like a deep ‘overtone’ of the annual cycle, just as all harmonic divisions of a musical note are physically and mathematically present in the sound waves produced. Such a linkage would require a directionality, with the great year of precession divided into twelve ages which correspond to the twelve signs.
16. Hence we have a cosmology which is large, encompassing the history of the earth, and scientifically coherent, but not so immense that it cannot be related to history. This historic linkage means that considering the possible meaning of each 2152 year period against events is a productive project. The natural start and end point of the annual cycle is the end of winter and the start of spring, i.e. in the Northern Hemisphere the cusp of Pisces to Aries. Similarly, my hypothesis suggests that the directional structure of the Great Year maps on to the annual cycle. The question is how to discern this directionality, i.e. how to tell when the natural start of the Great Year occurs. Traditionally, this point is understood as the moment between BCE and CE dates 2007 years ago. There are a number of religious images which have an elegant fit with this cosmology (eg Jesus Christ as the Alpha and Omega), but their use to illustrate it may be outside of the scope of this board. I would, however, like to note the elegant fit of this cosmology with the theory of the Age of Aquarius. Assuming the BCE/CE point as the beginning and end of the Great Year, the March equinox has since been precessing through Pisces and will arrive in Aquarius in about 2152 CE. Interestingly, tradition ascribes to Pisces the theme of belief and to Aquarius the theme of knowledge.
17. Hence, in conclusion, precessional cosmology suggests we are coming towards the end of an age of belief (ie where belief is the ruling principle of the world) and towards the start of a new age of knowledge, which could be interpreted as a coming time when scientific understanding will be decisive in public policy.