Let us apply these thoughts to the human being. Suppose we recognize that there is something in the human organization that is not at all in space but necessitates that we imagine, in a spatial way, separated line systems inherently united by another principle that is outside three-dimensional space (Figure 27). If we think of three dimensions, we can also think of subtracting these to the point that their positives become negatives—a person can have wealth but also debt and can thus be either solvent or insolvent depending upon which is the greater amount. If we apply the concept of forces moving from centripetal to centrifugal as one passes out of space, as illustrated earlier, then we can conceive of the human form somewhat as reflected in Figure 28.

To further illustrate, let us return to the Cassini curve. It has three essential forms, the ellipse, lemniscate and a third of such nature as to be a single entity from the conceptual and analytical aspect but having two branches. In the last of these, the two branches are really one curve, but in drawing it we have to go out of space and then come back in again. Steiner illustrates all three forms in Figure 29 by asking, "What will be the path of a point that, when illumined from a fixed point, appears with constant intensity when seen from another fixed point?" The answer is a Cassini curve, for it will be the locus of all points through which a point must pass while being illumined with the same intensity of light from another fixed point. It will not be hard to imagine, with respect to the ellipse, that if something shines from A to C and then by reflection from C to B, the intensity of light will be the same as if instead it is reflected from D. It will be rather more difficult to imagine the same with regard to the lemniscate, and still more difficult with the two-branched curve. In the last instance you will have to imagine as you pass from one branch to another that the light goes out of space and then shines into space again.

One must think contemplatively and meditatively upon the ideas that Steiner has been giving us here. They help us to conceive of the relationship between the conscious and unconscious parts of our earthly being, our head and nervous system on the one hand, and our metabolic and limb processes on the other, our thinking versus our willing. And they help us to see how we relate in our incarnated earthly being to our existence while in the spiritual state between incarnations. But let us also think further of how an organ in our body relates to the heavens above and is formed by or out of this relationship. In this thought process, we need to remember that the visible portions of the heavens (the Sun, Moon, planets and fixed stars) are only that and not the full scope of the force fields they represent—any more than our physical body is all there is to our more spiritual forces.

In this endeavor we have to visualize the interaction of two kinds of space. One of them with the ordinary three dimensions may be conceived as issuing radially from a central point (Figure 30); the other, which all the time annuls the first, may not be thought of as issuing from a point at all but must be thought of as emanating from some encompassing sphere infinitely far away (Figure 31). So we have to distinguish two different kinds of points: a point of zero area, which is turned outward and a point within the area of an infinite spherical surface, which is turned inward. In every instance we have to ask the question, is the point's curvature turned inward or is it turned outward? This will affect its field of influence.

And yet we must go further. It would seem permissible to see in our etheric organs (our unconscious metabolic processes) the image of forces in the heavens represented by visible bodies of our solar system and to see in our astral organs (our conscious, sensate processes) the image of zodiacal forces represented by the visible fixed stars.²³ But let us imagine that as we go farther and farther out into the universe we come at length to where we no longer find heavenly bodies—yet neither do we find a mere empty Euclidean space. There we must find something whose inherent reality obliges us to recognize its continuation at points within created space. This is simply an extension of the universal law of polarity.

Let us think of this outer inherent reality as the Father from which the Creative Word, the Son (Jn 1,1-3) went forth. ²⁴ Later in John's Gospel Christ speaks of having come from the Father and returning to the Father and drawing all persons to himself (Jn 12,32). In this, he is becoming and acting as this outer inherent reality. And we must then further think of this outer inherent reality as an awesome force of suction (negative space) that pulls the universe outward toward it. Within the universe it is represented by the stars such as our Sun. We've already seen how the suction of the stars in the universe tends to balance out matter (including the black holes).²⁵ In other words, in the creative process, the creation of light involved suction while darkness involved matter, a process of division one can readily contemplate in the study of chart I-22 so much discussed throughout this volume. This concept obviates the necessity, and thus eradicates the very basis, of the currently popular "big bang" hypothesis.

Steiner, in Lect. 17, shows how something was lost in our comprehension of the universe when the Copernican system superceded the Ptolemaic, and how calculations even today must take their start from the system of Tycho Brahe (the teacher of Johannes Kepler, whose work laid the foundation for what was to follow in the works of Copernicus and Isaac Newton, but who himself derived his knowledge from the ancient systems and comprehended relationships deeper than what was understood by his followers).

The polarities between the stars and the other "bodies" in the universe, the polarities of matter and negative matter, so to speak, are pictured by Steiner as he begins the last lecture (Lect. 18) as follows: