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part of one whole. The ancients regarded mathematics and geom- etry as the tools to understand patterns in Nature and in the Uni- verse. The religious leaders of old, who were also the scientists and mathematicians, did not make our mistake of putting differ- ent phenomena in separate compartments. To them, the world of matter and reason and the world of spirit and the awareness of God were all one. In the context of myth and symbol, they used numbers and forms in a way that would satisfy the spiritual sense of meaning and the scientific need for structure and reason. Out of this process arose the traditions of numerology and sacred geometry. In all the ancient cultures, the square symbolized the Earth of matter and rationalization, and the circle the encompassing world of spirit and feeling. How to bring them into balance was called 'squaring the circle' and was the pursuit both of architecture and philosophy. The sum of the sides of the square was equal to the cir- cumference of the circle, so they come into harmony by enclosing the same area. This is sometimes used as a metaphor for the bal- anced personality. So 'circling the square' indicates someone whose rationality is greater than his/her sense of feeling. As with other problems in sacred geometry, though it is not possible to draw this relationship by simple measurement, because it is part of the natural order, that is where the solution is to be found — in fact in the relationship of the size of the Moon to the size of the Earth.12 You draw a square around the circle of the Earth (each side of which will equal the Earth's diameter). Then you draw the Moon on the same scale, sitting on top of the Earth. A circle with its centre as the centre of the Earth, and its cir- cumference passing through the centre of the Moon will have a circumference equal to the sum of the sides of the square enclos- ing the Earth. Fig. 4.2 also contains the 3-4-5 Pythagorean triangle which connects the corners of the Earth and Moon squares. It was from such relationships that the 'Pythagorean canon of proportions' was created. The basics of musical harmony depend on intervals created by these divine proportions. There were canons of architecture, of painting and of musical harmony taught in the medieval mystery schools, and partly revived in the Renaissance. Fig. 4.2. Squaring the circle. Sacred geometry is based on observations of cosmic relationship. The Great Pyramid's base straddles the Earth's equatorial diameter; its apex is at the centre of the Moon, which is in true proportion to the Earth, and held to the square by a Pythagorean 3-4-5 right-angled triangle. 4. NATURE'S PATTERNS AND SHAPESPDF Image | Hidden Nature Insights Viktor Schauberger
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