The Five Dimensions:
The Third Dimension is the SOLID, such as a cube. It contains an infinite number of planes or squares. Temporally, the Third Dimension represent the Past. The disc of the Second Dimension (Present) turns one half time around its axis and fills out the sphere of the past.
The third dimension brings out the Real numbers. Real numbers start from zero and connect fractions of the same numerical value, leading to the proportions and functions.
The proportions are the basis of continuity and harmony. They connect fractions of the same value to zero. The functions are the basis of discontinuity. They connect products by which bodies are in relation, as for instance in the atom, where the distances of the electron shells follow the numbers of the central diagonal 1 - 4 - 9 - 16, and the possible number of electrons in each shell, the capacity, follow the diagonal 2 - 8 - 18 - 32. The rational numbers of the second dimension, and the whole and natural numbers of the first and zero dimension, all have a fixed place on the number line. The real numbers in the third dimension are, however, fundamentally different; although they are located somewhere on the number line, they have no fixed place there. To the ancient Greeks who first developed mathematics to a high art in the West, all numbers had to have a fixed location somewhere on the number line. The existence of the Real numbers, with no fixed location, was known only to a few high initiates in the Pythagorean brotherhood who swore to keep it secret. It can be easily understood today by way of the Pythagorean theorem:
The Pythagorean Theorem exemplifies the rational numbers. But what happens if A and B both equal 1? In this case C must equal the square root of 2. But the square root of two is an irrational Real Number. It is a number which goes on and on with no repetition into infinity. 1.41421... . It is a never ending number and has no fixed place on the number line. Unlike an infinite rational number which goes on and on, but repeats, such as a third (.3333333...), where we can know the exact location on the number line, with a Real Number, we can only know its approximate location. There are other examples of Real Numbers, such as Pi (the ratio of a circumference of a circle to its diameter), the square root of any prime number, e, etc. These Real Numbers never end and never repeat.