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.

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