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.