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Before man’s supersensible part enters into a physical body there is no means of conveying to it experiences other than those of levity, and this condition prevails right through embryonic development. For while the body floats in the mother’s foetal fluid it is virtually exempt from the influence of the earth’s field of gravity.
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Since Point and Plane represent in the realm of geometrical concepts what in outer nature we find in the form of the gravity-levity polarity, we may expect to meet Radius and Sphere as actual formative elements in nature, wherever gravity and levity interact in one way or another. A few observations may suffice to give the necessary evidence. Further confirmation will be furnished by the ensuing chapters.
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It is clear that, in order to become familiar with this aspect of geometry, one must grow together in inward activity with the happening which is contained in the above description. What we therefore intend by giving such a description is to provide an opportunity for a particular mental exercise, just as when we introduced Goethe’s botany by describing a number of successive leaf-formations. Here, as much as there, it is the act of ‘re-creating’ that matters.
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History has given us a source of information from these early periods of man’s existence in Traherne’s recollections of the time when his soul was still in the state of cosmic consciousness. Among his descriptions we may therefore expect to find a picture of levity-space which will confirm through immediate experience what we have arrived at along the lines of realistic mathematical reasoning. Among poems quoted earlier, his The Praeparative and My Spirit do indeed convey this picture in the clearest possible way. The following are relevant passages from these two poems.
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The Radius-Sphere antithesis appears most obviously in the human body, the radial element being represented by the limbs, the spherical by the skull. The limbs thus become the hieroglyph of a dynamic directed from the Point to the Plane, and the skull of the opposite. This indeed is in accord with the distribution in the organism of the sulphur-salt polarity, as we learnt from our physiological and psychological studies. Inner processes and outer form thus reveal the same distribution of poles.
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The following exercise will help us towards further clarity concerning the nature of geometrical infinity.
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In the first we read:
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In the plant the same polarity appears in stalk and leaf. Obviously the stalk represents the radial pole. The connexion between leaf and sphere is not so clear: in order to recognize it we must appreciate that the single plant is not a self-contained entity to the same degree as is the human being. The equivalent of the single man is the entire vegetable covering of the earth. In man there is an individual centre round which the bones of his skull are curved; in the plant world the equivalent is the centre of the earth. It is in relation to this that we must conceive of the single leaves as parts of a greater sphere.
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We imagine ourselves in the centre of a sphere which we allow to expand uniformly on all sides. Whilst the inner wall of this sphere withdraws from us into ever greater distances, it grows flatter and flatter until, on reaching infinite distance, it turns into a plane. We thus find ourselves surrounded everywhere by a surface which, in the strict mathematical sense, is a plane, and is yet one and the same surface on all sides. This leads us to the conception of the plane at infinity as a self-contained entity although it expands infinitely in all directions.
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‘Then was my Soul my only All to me,
A living endless Ey,
Scarce bounded with the Sky
Whose Power, and Act, and Essence was to see:
I was an inward Sphere of Light,
Or an interminable Orb of Sight,
Exceeding that which makes the Days . . .’