The roots of unity and the zeroes of Space

One of the biggest myths in algebraic geometry is the concept of n orthogonal directions!

The orthogonality of space is special to the single rotation about a closed loop. Using a circle as a coordinate system orthogonal radii fall out naturally as do general orthogonal chords in the semi circle. Since orthogonality is so prevalent it is misleading to think it is of ultimate importance in referencing space. It's importance lies in the system of ratios a right triangle can be used to generate in modelling curves in space.

Thus using the cosine ratio to specify orthogonal lines is misleading. It is a known fact that the Cotes De Moivre formulae and theorem enable many roots of unity and many zeros to be generated. It is these other zero that are key to understanding n dimensional spaces!

The spiders in their webs are classic examples of ndimensional beings living in and on n ndimensional space. Our space , as Grassmann observed is not uniquely 3 dimensional. It is generally n imendional and that means fractal in its structure.
Cos ( 9@+ pi/2) will generate 9 zeroes in the course of a single rotation of @. Each of these sectors is full fractal copy of the structure on the whole circle.

What does not hold true in these other series is Pythagoras theorem! There is sn analogue which essentially is the cosine rule for triangles. This is often applied as covariant and contra variant vectors in an orthonormalisation space which does support Pythagoras.

Very simply space is created or absorbed in these vector reference frames relative to ours! What we need to apprehend is that applying conservation of space laws means this loss of space can be seen as annihilation of matter, or the gaining of space as the creation of matter. In both cases we will experience this as physical force, either of attraction or repulsion.

The space in which and of which we are is fundamentally mysterious. Our geometrical models are our best apprehension of it. How we interpret that apprehension is an individual and collective choice. As astrologers we have taken our Spaciometry to the limits. Now we must apply our models as we may to probe our fundamentally mysterious and mystical experiences.

We can measure no more than we have currently achieved. But that is no greater undertaking, astrologically than that of our great forefathers and mothers. Where we have advanced is in mechanics and technology. The experiences of this space have built skills through empirical research. But our tools of measurement have been used to advance or hinder that development. This is not due to their nature. It is due to the use to which those in power have put these tools.

At the end Plato's challenge of a world of shadows or a world of the imagination, that is : do we only rely on our senses, and thus potentially only ever see shadows, or do we rely on our imagination and see infinite potential explanations, myths as well as facts; is a playful provocation. We can have both! We do have both. It is our essential freedom to exercise both descriptions in any combination we personally feel.

The danger is that others will try to rob us of our individual freedom, and eventually even of our life.

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