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Fixed and variable relationships
As we have seen, in analogical thinking there is no cause or effect, nor a time lapse for events to occur. It simply names the similarity in nature of correlations between existing sets of phenomena and describes these correlations as a law. Now, the mental framework of analogical thinking enables us to not only describe fixed relationships, such as that between an apple and its tree, but also variable relationships.
Gnomon of Pythagoras
A good example of a variable relationship is that between an object and its shadow. Pythagoras called such an object a gnomon. The shadow of a house, for example, will change in the course of a day, while the dimensions and form of the house do not. The size and form of the house’s shadow will also vary continuously in the course of a year, due to the sunrays’ changing angle of incidence. Still, the house always retains its inseparable relationship with its shadow. In other words, within an analogical correlation, any shape-shifting is included in its equation.
So in a gnomon equation, at any time in the day and throughout the year, it is true that:
a house : its shadow = a tree: its shadow
The equivalence sign (=) in this statement is based on the sunlight’s identical angle of incidence at the time of observation, while the gnomon is perpendicular to the plane the shadow is projected on.
So in analogical correlations, too, time is involved as a contributing factor. In this case, however, ‘time’ does not refer to the time lapse between cause and effect, but to the fact that the shape-shifting relationship is exclusively valid for a specific moment of observation.
For our thinking about astrology, horoscopy and transits, this moment-related connection between the shape-shifting of shadow forms and their fixed, underlying gnomon is of key importance.
Measuring the immeasurable
The fixed position of a tree or a house enables us, via their shadows, to determine the local angle of incidence of the sunrays. By comparing several shadow forms cast by the same tree at different moments during the year, we are able to calculate the Sun’s yearly orbit. In this manner, the analogical correlation makes the immeasurable measurable.
As mentioned above, analogical thinking does not work with quantitative or absolute values, but with relative, interconnected values. Any form of manifestation is being described as a function of another form of manifestation: So in analogical thinking no form is isolated or separate, but is regarded as related to an other form. The form of a shadow, for example, is inextricably bound up with something else, its gnomon.
In case of a horoscope, as another form of manifestation, we do not know its underlying gnomon. However, due to the relationship of this form of manifestation with its gnomon, we are still able to approach it and put it to use, at least in a qualitative sense. But for this to work, we do need to know the nature of the relationship. Once we know this nature, we can describe, through analogical thinking, the identity of the form of manifestation as a derivative of its gnomon.
(Please note that the root ‘gno-‘ in the word ‘gnomon’ also appears in the ancient aphorism "Gnothi Seauton", “Know Thyself”, which was inscribed above the entrance to the Temple of Delphi. It is also found in the word ‘gnosis’, which means ‘hidden knowledge’.)
As we saw (1.4) astrology works with this type of transferals. For example, when we look at the transferal of the Tropical Zodiac to the framework of the Houses, we see an identical division of the circle in relation to its center.
From the perspective of that center, we can say that:
the Zodiac : the Earth = the framework of the Houses : a human being
And from the perspective of the passing of time, we can say:
the Spring Equinox Point : the Zodiac = the Ascendant Point : the framework of the Houses
All qualifiers are relative
So within analogical thinking, we can assign an identity to a value-free astronomical fact by considering its function within the system in which it has a function. In a different system, the same value-free fact may play a different role, and therefore represent a different quality of identity.
As such astrologers use them.