A glimpse into the cyclic movement of Nature brings the greatest encouragement. Without such understanding one is easily led to feel that we follow a path which at the best would be endless repetition, getting us nowhere. But when we learn that cycles are not mere repetition, but a majestic pathway, forever going forward and forever expanding, a new hope and courage are given to life.
As the law of cycles goes to the very heart of Nature, we find countless examples in the natural phenomena around us. Of especial interest is the method of the growth of plants and of all kinds of organisms. One of the best examples is the plan of growth in sea shells. Here we have a beautiful example of the working out of a law of cycles, which is not much written about, but which is full of inspiration for us as evolving entities. There is tremendous significance in the fact that this growth, this evolving, takes place with nearly mathematical precision, and that the ratio of growth is always almost exactly the same, and follows the course of a rapidly expanding spiral. It is not a matter of addition, but is a ratio of expansion known to mathematicians as the Pythagorean Golden Section, and can be easily demonstrated by geometry. The chambered nautilus shows the proportions perfectly. Innumerable other things in nature develop according to the same plan. The spider uses it in building her web, the palm tree in the growth of its trunk, and the development of the nodes on the stalks of growing plants are other examples.
The ancients knew this law well, which is indicated in much of their art work and architecture. The proportions of the Golden Section set the keynote for the design of the finest Greek pottery, the volute capitals of the Ionic columns, and especially for the design and ornamentation of temples and buildings held sacred. The Egyptians used it in their bas-reliefs and it is also found in a special angle of the great pyramid. It is exemplified in the proportions of the five pointed star. It was well known to be one of the proportions of all rectangles excepting the square. Early writers have referred to it also as the "Divine Proportion," "Sectio Divina" and "Proportio Divina." (Kepler, Fra Luca Pacioli and others.)
The Egyptians worked out a primitive scheme of surveying about 4000 b.c. which required only a length of rope and two men to operate. Because of the periodical overflowing of the Nile, all boundaries of land were washed away, and it was necessary to reestablish property lines after each seasonal flood. The rope was knotted at intervals to form twelve units. The right angle was determined by laying out the rope in a triangular form on the ground, four units forming one side, three the other, and five the hypothenuse. This was the origin of the historic "cording of the temple" and is a method still used today. From the knowledge of ratio relationship which was gained from the right angle in surveying and laying out rectangular floor plans it was only natural that they should carry it farther, in working out architectural design and ornamentation.
In a method worked out by Girard of expressing the ratio of segments of a line cut according to the Golden Section he takes the sequence, 0, 1, 1, 2, 3, 5, 8, 13, 21, etc., every turn of which after the second equals the sum of the two turns that precede it; thus 5 is to 8, as 8 is to 13, 13 is to 21, as 21 is to 34, and so on, or 1/1, 1/2, 2/3,3/5, 5/8, 8/13 — etc. nearly expresses the segments of a line cut in Golden Section. However the exact proportions are to be found in the numbers 0.3181966 over 0.618034, then this denominator 0.618034 becomes the numerator, and so on in the series. A simple diagram of a parallelogram shows this ratio, and the rapidly expanding spiral which follows its course, and which many sea shells follow as a plan of growth. Neike defined the term Golden Section as applied to different units such as areas and volume and not alone line segments, as a ratio where the smaller part is to the larger, as the larger is to the whole.
In his book Dynamic Symmetry — The Greek Vase, Jay Hambidge points out that there are two kinds of symmetry expressed both in nature and in art, one of which he calls dynamic symmetry, and the other static symmetry. Dynamic symmetry is expressed in the rapidly expanding spiral, as described above, and is developed from the application of the Pythagorean Golden Section. It has qualities of activity and in art it is considered the most beautiful, the most subtil. In modern times it has been entirely lost sight of by artists, but the Greeks and the Egyptians had it worked out to perfection. Static symmetry is in a state of passivity, and all artists follow this naturally, because there could be no proportion without it, unless the dynamic symmetry were used. Nature gives us examples of it in certain crystal forms, diatoms, radiolaria, etc. All this implies two kinds of cycles. It would seem that all cyclic movement which is continuous repetition, such as day and night, the seasons following each other with such regularity, the tides, and many others might be placed in such a classification. But we must not lose sight of the fact that all cycles, no matter how often repeated are never exactly the same, and that they are contained within larger cycles, that are all following a pathway of growth and expansion. Scientists today are using such terms as "our expanding universe."
What a thrill and inspiration came with the knowledge of this law, and what it can mean as applied to our lives. It opened up avenues of thought and speculation as to how it works out for humanity. When did humanity begin to take the great step forward which would be indicated by the outward swing of the expanding spiral? It must have been with the coming of the Manasaputras, when mind and light began to work in our unfolding. We know that as individuals we spend aeons of time in countless numbers of incarnations, making only little progress, even sometimes going backwards, and this would be very discouraging if we did not know that when we begin to apply will and effort we can begin to take this mighty swing of the spiral, which is Nature's plan for us. We need not remain in a passive or static condition of endless cyclic repetition.
We might wonder why the plan works out so perfectly in the sea shell, and why our own growth does not go ahead in the same way. With a little thought, however, we can realize that the shell, the plant and all the less evolved things of nature do not put any resistance in the way of Nature's plan working out perfectly, while we with our wills and desires, our minds and our power of choice are constantly blocking the Divine plan for our evolving. When we begin to work with Nature, and not against her, to take down all barriers to our growth and development, we make possible our own rapid evolution. When we realize that it is Divinity back of this great law, that the Divine Spark is in every living entity, we begin to glimpse the glorious pathway that lies ahead of us, to have vision and strength to go ahead, and to allow nothing to interfere with our progress along this golden path.