These are good questions which I believe can have clear answers. However, the questions presume a misconceived understanding of the mechanism of astrology. I submit here that a big part of the explanation of the mathematics of astrology is to be found in the mechanism of wave harmonics structuring the gravitational relations between the earth and the sun and planets, and in the use of fractal geometry to model astrological rhythms.

Astrology, for the purpose of this discussion, should be restricted to the sphere of mathematical logic, ignoring speculations in the unscientific domains of spiritualism and magic, and also ignoring culturally popular forms such as newspaper horoscopes which are entertainment and not science.

I postulate that any real effects of astrology do not rely on any force other than those already known to physics but can be explained mathematically through the operation of physical mechanisms which are complex instances of the force of gravity. So to speculate about unknown forces is a blind alley. The mathematical challenge is to theorise a mechanism operating within known physical laws to explain documented astrological effects such as Gauquelin’s observation of compelling statistical correlations.

The underlying biological framework is the Darwinian mechanism of cumulative adaptation. This is explained at some length in my initial post where the basic argument is that our DNA, much of which is nearly four billion years old, has evolved in a cosmic context where its environment, properly considered, is the solar system, and where the rhythms of the seasons are deeply imbedded in all life.

The next question is why our genes should be sensitive to planetary effects. It is well known that a gene which is sensitive to an environmental reality is over time more adaptive than another gene in the same niche which is not similarly sensitive. To move beyond this general observation, we must show how the planets are an environmental reality.

As noted previously in my comparison of the solar system against the Milky Way as equivalent in ratio to a dime against the USA, the long stable isolation of our sun and its detritus justifies considering our solar system as a unit, like a vast whirlpool in space. And pace Brownlee & Ward, our hold on life is incredibly tenuous and precarious, part of a stable orbiting system in which all parts have clear rhythmic relations.

Just as a thought experiment, imagine if the Vogon blasters of Hitchhikers Guide to the Galaxy fame decided to vaporise the planet Venus. What would happen to the earth once the near-permanent 8/13 orbital relation with our hot sister was terminated? Would we drift out to collide with Mars in a few million years or fly off at some unpredictable angle? The point is that such stable relations as that between Earth and Venus are imbedded at the origin of the gravitational rhythms of our world.

In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For a sine wave, it is an integer multiple of the frequency of the wave. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc. In musical terms, harmonics are component pitches of a harmonic tone which sound at whole number multiples above the named note being played on a musical instrument. (http://en.wikipedia.org/wiki/Harmonic)

The hypothesis is that the wave relations which form musical harmony are analogous to the earth’s rhythmic relations with the sun and planets. Considering the line between earth and each planet as a vector, the vectors with any group of planets are observed by astrology to reinforce each other when they are together, and also when they are half, one third and one quarter of the way from each other around the circle, etc, in ways with different qualities (opposite, trine, square) just as different musical harmonics have different qualities (octave, fifth, third). Points around the circle which are not an even fraction are unrelated. This harmonic effect provides the underlying mathematical framework for astrology. It explains why the small variance in distance of elliptical orbits is irrelevant – the acuity of a planet’s effects on earth depend entirely on its relational position vis-à-vis other planets (and its house position), and its distance is effectively just an underlying constant.

Most recently, although not entirely rigorously, Richard Tarnas has presented a series of observations in his 2006 book Cosmos and Psyche of the combined effects of the outer planets which illustrate this harmonic principle in operation. As to the question why Uranus should be associated with innovation and Jupiter with expansion, etc, I do not know, but it is certainly an empirical observation which can be tested statistically. I believe Tarnas presents a rich vein of material for epidemiological research. For example, analysis of population statistics against birth and death dates would show if any planetary aspects affect mortality rates. Do people born when Jupiter is conjunct the Sun live longer than people born when Saturn is conjunct Pluto? Such a study would be a small desk job for an appropriate expert, but to my knowledge it has never been done because of the general odium astrology attracts. Instead, the negative studies of time twins etc are generally either looking for evidence against astrology or trying to reveal something far too ambitious, and have failed due to poor experimental design.

The mathematics of wave harmonics as applied to the astrological approach to natural cosmic patterns has an elegant fit with the axiomatic framework of fractal geometry. Fractals are complex shapes which possess the property of self-similarity at different scales. Each part of a fractal system is similar to its surrounds, reflecting the causal influence of all parts of the whole. Complex natural systems such as trees, weather systems, galaxies, rivers, etc tend to follow fractal patterns. Their irregular features tend to share a common systemic character, mirroring the patterns of the whole according to the fractal principle of self-similarity. Using fractals as a model for the geometry of nature, the question here is whether time, as a regular natural structure, has fractal patterns. In locating each process within larger patterns which share a common character, astrology views the human mind and other chaotic systems of the earth as reflective microcosms in constant fractal relation to the rhythms of the solar system, freely inclined but not compelled to have a similar character at any given moment to that exhibited by the macrocosm. This approach supports the fractal maxim ‘as above so below’ by seeing our minds and the patterns of the seasons as simultaneous expressions of the structure of time. Human beings are like leaves on the tree of the sun.

The inference can then be postulated that the sun signs are a middle level pattern within a larger galactic fractal structure. Just as the smaller branches of a tree reflect both the larger structure of its boughs and the smaller structures of its twigs and leaves, so the natural rhythm of the sun signs, defined by the seasons of the earth, should both reflect a larger whole and flow through to every sub-system. On this basis the causal theme ‘as above, so below’ should apply to the patterns of our galactic neighbourhood. Insofar as our galactic environment shares a common origin and is therefore a single system, fractal theory tells us that the natural cycles of the earth should exhibit harmonic resonance with galactic patterns at various levels.
Like whorls in a cosmic whirlpool, the rhythm of the seasons should in some natural physical way reflect the fractal whirlpool energy of our spiral galaxy. This logic of fractal reflection provides a mathematical framework to consider the observations of astrology regarding a range of observed phenomena, including signs, aspects, transits, houses, progression and precession.

Robert Tulip