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 NOVA: Intelligent Design on Trial 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.
Robert Tulip

Attached Images

	Ecliptic Wave.JPG (117.2 KB, 21 views)
	Physics of the Signs.JPG (47.1 KB, 126 views)

Can you show us some quantitative support for your ideas, whatever they might be?

Thank you for your question. My opening post presents claims about the astrophysics of the tropical zodiac based on the two attached diagrams which are purely empirical.

The first diagram (Diagram One – Ecliptic Wave) shows the ecliptic, the celestial equator and background stars to illustrate the sun–earth wave function operating at frequencies of both one cycle per year and one cycle per great year. These wave lengths are well known. For the wavelength one cycle per year, the stationary points of the sine curve are the solstices and the inflection points are the equinoxes. For wavelength one cycle per great year, the corresponding turning points are not known with certainty. My post introduces this as a problem in cosmology to explore how the great year may be considered as a directional structure of the galaxy. I note possible ideas about the dates of these turning points based on inductive cultural correlations but they are far from proven.

Diagram Two (Physics of the Signs) is a simple mathematical extrapolation from Diagram One, taking the four turning points of the sine curve in diagram one as the four points where the cross intersects the circle. I have included pictures of the earth at each of these four points, taken from http://en.wikipedia.org/wiki/Image:North_season.jpg, to illustrate the angle of the planetary axis at the equinoxes and solstices.

To help visualize the quantification of my previous comments about celestial harmonics, consider the operation of harmonic resonance in an acoustic structure such as a cathedral. For example, if a loud organ note is played at wavelength one cycle per second (one hertz), this sub-sonic noise will resonate through all objects in the space. People can feel it but not hear it. The 1Hz wavelength also produces overtones at all whole multiples, 2, 3, 4, …n. The overtones diminish in strength as n increases, but overtones which are regular powers of small primes are stronger than large primes. For example 256Hz = 2 to the power of 8 = the note C, and is an overtone of all smaller frequencies which are also powers of 2. So the C string of a cello would sound in resonant sympathetic vibration in the presence of the subsonic note 1Hz.

My mathematical hypothesis is that the four turning points of the day length wave produced by the earth’s orbit can be similarly considered as producing resonant wavelength overtones analogous to a subsonic organ note, but with much slower frequencies, and at planetary scale. The full frequency length (one year or one great year) equates to the fundamental tone or first harmonic, where the natural cycle returns to the same point (eg solstice). At the annual level, in the cycles of the earth this wavelength is observed in all natural annual patterns of life and climate. The second harmonic, with wavelength six months, indicates the relation between the two opposite solstices or equinoxes. The third harmonic, with wavelength four months, dividing the year in precisely three, produces the physics of the tropical signs as explained in my opening post.

Astronomers already know the Earth goes round the Sun, and about the ecliptic and precession, or so I believe; what effects do you think these 'harmonics' are having in the real world?

And could they be demonstrated? And more importantly could they be falsified, if by any unfortunate chance, there was no effect?

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That may have been true a long time ago, and historically, but no longer. The basic measure of time is the second, which has no connection to terrestrial events, in the way that you are referring to terrestrial events.
While it is certainly true that the earth's orbit is nearly circular (it deviates from a circular path by not much more than its diameter if I recall), but the center of that circle is offset from the sun by over a million miles, some six times the distance to the moon. That causes the earth to speed and slow in its orbit as it gets closer to and farther from the sun. Because of the reason mentioned above, there is not really that nice of a symmetry.
Some people are just ignerint.
From the studies, we can say that it is weak enough that any predictive power it has is completely swamped by the astrological noise.
In other words, you're simply re-naming "three" as "air" or something? If there is no metaphysical or alchemical sense to it, it seems to be just adding to the astrological confusion.As I mentioned earlier, the offset of the sun from the center of the circle causes a deviation from the regularity such that if you had a timepiece with that "clockwork regularity" you'd have tossed it to the street with the trash.

Another astrology thread???

No need to waste my time here...

It's really something about the number of words that can be used to describe nothing.

Meanwhile, to fold the subject in upon itself, there's only one sign that properly describes astrology. It's found between the ram and the twins.

Now back to the science threads.

Bye.

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Great remark, Maksutov. I almost split a gut laughing.

Back to Off-Topic Babbling is more like it.

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Gee, Mak...what did you do to Warren?...kill his puppy or something?

Doggone it!

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These are good questions. I hope my attempt at answer will make sense to you. This is a complicated and unusual claim, so please let me know if I use terms in ways that are not clear (as per my comments on time and the elements in response to hhEb09'1 below). I thank anyone with the patience and interest to keep with me on this discussion as it opens an area of theory that has not been pursued rigorously to date.

My intention is to produce a falsifiable case for these effects. Initially I am trying to present a mathematical case for their possibility, both to show in principle that such natural rhythms could in fact exist, and to show that the annual natural rhythm is built into the longer rhythm of precession. There is an element here of cleaning out cultural debris, especially since this area of study is beset by folk tradition and false belief.

Working out how to apply falsifiability in this area is quite complicated. For example, Phil Plait at http://www.badastronomy.com/bad/misc/zodiac.html and http://www.badastronomy.com/bad/misc/astrology.html has disproved the theory that astrology is caused by the stars by pointing out, inter alia, that the constellation of Ophiuchus crosses the zodiac. The apparent constellations have no internal organic connection, so the traditional naïve image of the signs as ‘caused’ by the stars is false. I argue that no such disproof of my claims is possible because I think my claims are scientifically coherent and true. Of course I would welcome analytic debate on this. The issue regarding falsification is whether any possible evidence would disprove my claims. (A flippant example using your comment is that the earth careering towards Mars would falsify current laws of physics. We 'know' this won’t happen but it is a logical possibility of how a theory might be falsified). Most traditional astrology is of course not falsifiable which is why it is not science. I am arguing that a regular change in the cycle of the year (something like a shudder?) occurs at the four natural turning points, and that the mathematical harmonics of this effect produce the signs, as observed and elaborated in the folk traditions, and that this effect produces a longer deep cycle of Ages structured by precession. A gradual shift of world politics over the next two centuries from a basis in belief to a basis in knowledge would provide inductive support for my precessional claim, but establishing whether it is falsifiable will be quite complicated. The models of ball and cross below expand on this response.

Regarding your question on demonstration, my view is that empirical proof of a harmonic sign theory will require large datasets, as these effects, despite their permanence, are extremely weak and are generally swamped by terrestrial factors. Gunther Sachs in The Astrology File presents the only argument I have seen claiming statistical verification of tropical signs, but his methods are disputed. Michel Gauquelin found extensive statistical planetary effects but no sun sign effects, and his planetary findings were replicated under hostile peer review. I am confident that well constructed studies would demonstrate correlations between, for example, period of the moon and rain data, plant growth rates against moon sign and phase, and population health indicators against a range of cosmic cycles. None of these studies have been done to my knowledge. The examples cited by Phil Plait show the incompetence of astrologers under laboratory conditions, but these tests have sought to measure very complicated psychological effects and I do not agree that they disprove an underlying cosmic rhythm. Large scale simple statistical studies such as those I suggest here would verify (or falsify?) the hypothesis that planetary rhythms produce significant ecological effects corresponding to the tropical signs.

Consider the following model. A spinning ball in a pool of water, powered to maintain constant velocity, is analogous to our planet earth held in position in space by solar gravity. Assuming some surface perturbation and friction, the ball’s rotation will produce a regular wave in the surrounding liquid with frequency based on the speed of spin. For this model the spin is considered as analogous to the year rather than the day. A constant regular wobble of the ball’s axis, akin to precession, will produce a regular secondary wave motion in the surrounding liquid. For any life that evolves on the ball, these wave motions in the surrounding water will be environmental constants, just as temperature, air pressure and atmospheric composition are, but with cycles that are much more regular, large, weak and deep. By the logic of evolution, assuming the pool is a closed system of long duration, all these constant factors will be built in to the replication structure (DNA) of any life on the ball. Over 100 generations the difference between entities existing at the trough and peak of the precessional wave will be negligible. Over 1.5 trillion generations (~daily algal production since dawn of life), it is conceivable that cumulative adaptation to this very weak environmental signal will become measurable. The annual spin will produce waves with frequency that are a constant multiple of the waves produced by the wobble, especially if the spin is a tiny fraction of the wobble period (eg 1/25,800). I argue that the annual wave function will map on to the slower wave produced by the precessional wobble.

In thinking this through to respond to your question, I have prepared the attached diagram, with the earth depicted as a cross orbiting the sun. Assume for the purpose of this model that the cross does not itself spin on its axis, but presents one of its beams perpendicular to the direction of orbit at each of the four marked turning points. In the diagram, the orange beams produce the two solsticial waves and the blue beams produce the two equinoctial waves. As per the previous ball model, setting this up in a pool of water will produce waves which are strongest at each of the turning points, as shown, with the crossbeams operating as ‘paddles’ with precisely three months between strokes. After long constant circulation (say 4.6 billion rotations) the wave produced at each turning point would be deeply imbedded within all complex features of the system. My claim regarding the harmonics of this model is that each of the four turning points would produce a wave with one cycle per orbit. These waves can be considered as natural harmonics, which produce overtones (waves of whole multiple frequency). The first overtone of this cosmic wave that does not map directly on to the other turning points is the wave with triple frequency. As explained previously, the four triple frequency waves generated by the four turning points of the earth produce the cusps of the signs.

Attached Images

Seasonal Planet Waves.JPG (42.2 KB, 8 views)

This comment opens up the definition of time, ie whether time is inherent in nature or is solely a function of human knowledge. By ‘basic’ I did not mean ‘scientifically precise and constant’ but ‘underlying source’. The second is a scientifically precise human construct, whereas the sign, the year and the great year are natural cycles of time imbedded in all complex systems of earth. The second derives from division of the day by 86,400, even if for modern physics it has been decoupled from its natural origin because the variance within the day length does not serve the needs of science for precision. For the scales and rhythms I am discussing the exact precision of the caesium second is not relevant.
This oscillation in planetary velocity would not affect the existence of a wave structure produced by the seasonal turning points of the orbit. It might cause a small variance in the period of the signs (eg a solstice may be 3.01 months after the preceeding equinox rather than exactly 3 months). This effect should be factored in to the exact determination of sign cusp time. In any case, each secondary cusp (ie the eight of the twelve that are not at one of the four seasonal points) is produced by resonance to one of the turning points, not to two or more.
This is a simplified schematic model produced for purpose of illustrating a theory. Of course the actual elliptical reality requires adjustment.
The attached diagram shows the interaction of elemental and seasonal zodiacal wave functions to produce the signs. My suggestion regarding the 'elements' is to visualise the rhythms of the year as sine waves with one cycle per four months, interpreted as harmonic products of the annual waves based on the four turning points. A sine curve has four phases. In order these are: ascending positive, descending positive, descending negative and ascending negative. Historically the sign mapping of these phases, within this new scheme I am presenting, is identified with the four alchemical elements, fire, earth, air and water. Of course you are right that this would be an obsolete identification to argue in physical terms. I want to avoid the cultural debris of obsolete ideas while remaining open to the possibility they may have some meaning. At this stage I am using the four elements and seasonal triplicity for ease of reference and imagery – ie Gemini is defined as mutable air. An alternative suggested by your comment is to define Gemini as (33) where the two numbers represent the position of the sign within the triple and quadruple divisions of the year. Using this latter method, which may be more scientifically congenial, we would have the following pattern of twelve unique combinations from Aries (11) to Pisces (34): 11, 22, 33, 14, 21, 32, 13, 24, 31, 12, 23, 34, repeated annually with constant regularity. The corresponding codes on the attached are: CF, FE, MA, CW, FF, ME, CA, FW, MF, CE, FA, MW.
Sure, having a clock that goes fast and slow depending on the velocity of the earth would be quite inconvenient for our daily human use, but, in a sense I am arguing that just such a clock has been dealt to us by nature, so it is useful to try to understand it. As I noted above, if ellipticity causes less than a few hours difference in the length of time between the four turning points of the year, and these differences are entirely predictable and regular, that still counts as clockwork for these purposes.

Attached Images

Zodiac Sine Waves.JPG (102.2 KB, 7 views)

I was responding to your comment "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." That may be your thesis, but so far it is not established. As I pointed out (and you agreed there), the basis for our measure of time has not been geocentric for a long time.
I'm behind your investigations 100 percent, but I don't think you should assert your thesis before it is proved, that's all. We haven't seen much support for the geocentric measure of time, as you seem to mean it, having "an important place within a coherent scientific framework." I'm not sure what exactly 3 months would be (what is an exact month? ), but looking at my starware ephemeris, it says that the next solstice is followed by the next equinox very close to 89 days later. However, the solstice after that waits over 93 and a half days for the next equinox. That's a difference of a bit more than 0.01 month--more than 0.15 month, probably.That's what I want to do As I said, it seems to be a few days, rather than a few hours.