The relationship between chord and radius
Extracting the square root
If we want to retreat from this outer expansion and return to the original line segment, we will need to apply the opposite operation, which is extracting the square root. Through this operation, we fold up the successive dimensions one by one. The cube becomes a plane, the plane becomes a line, and if we continue further, the length of the line segment is collected into a point. In that point, the world no longer reveals itself outside of us. Our observation of the world ceases to exist.
And although here, too, we are not able to imagine any realms smaller than a point, in an arithmetical sense, we can still simply continue our extraction of roots. We then leave the physical world and pull our attention through the zero point into our inner realms of existence. We have already given some attention to those realms and the forces that are at play there. In addition to that, in our contemplative moments we all acquire some personal experience with this inward-pulling movement. In those moments, we enter our own inner world. This world may be subjective, but that doesn’t make it any less real, in the sense of operative (25.2).
So we see that the operation of extracting the root will fold up some dimensions, but open up other dimensions on the other side, making them accessible (25.7.a).
The horoscope, too, is such a root. It literally is the radix or root that we extract. This radix, the horoscope, reveals reality not in its physical appearance, but as related to the underlying realms of reality; the horoscope reveals the essence in which all phenomena are rooted.
This essence can be expressed on various levels. In this relationship, the subsequent realms are perpendicular to one another.
So the chord and the radius belong to different realms of power, and each derives its own potential from the root essence, the Center. Their degree of power, or root, determines their capacity for expression. These distinct potentials exert their influence in the horoscope in an integrated way through the aspects between the planets.
Now, experience shows that some time before the aspect becomes ‘full’ or exact, the influence of the reciprocal resonance of the two planets involved can already be perceived. Apparently, the aspect already begins to exert its influence even when the exact aspect angle has not yet been fully reached. There seems to be a warming-up period before as well as a cooling-down period after the ‘full’ aspect. This trajectory of increasing and decreasing influence is known as the orb. Traditionally, an orb of 7,5° on either side of the full aspect is allowed.
This deviation from the exact point turns out to be correlated to the point where the aspect begins and the point to which it returns. These are nearly the same, but not exactly the same.
Circle and ellipse
For the sake of simplicity, up till now we have spoken of a centered, dimension-less Self standing in the midpoint of the circle and casting out around itself a perfect circle. Meanwhile, we have seen that the reciprocity of the centripetal aspects plays a central role in the awakening of consciousness in the Center.
But actually, Earth’s orbit is not a perfect circle, but to be more exact, an ellipse. And an ellipse does not have one, but two midpoints. The inherent quality of the second midpoint has already been described in the addendum about Christmas (15.2.a).
This implies that there are also two radiuses. These do not have the same distance to the circumference, but complement each other in such a way that the sum of both radiuses will always remain the same. In other words, they are attuned to each other, which amounts to a qualitative relationship.