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Docta Ignorantia XXVII Ratio and Integer 'Irrational numbers' is a post-Cartesian concept. Euclid/Geometry -- which is Theology -- does not have the concept of irrationality. Rather, the concept is 'proportion' or 'relationship' or 'ratio.' This is important to grasp. Irrationality is a foreign experience in religion. The 'irrational' numbers (actually called indeterminate numbers), such as pi and especially phi, are not numbers, they are ratios. They only get to be 'irrational' when one takes the ratio (e.g., 89/144 in the case of phi) for a division problem. Purely speaking, the ratio should not be expressed in integers. It should be expressed in figures: circles, lines and planes. In other words, number itself must be taken as structure, as syntax, not as semantics. This, perhaps, is several steps of logic in advance of where you are wanting to be at this time, but it is true. Today, the 'irrational numbers' you mean, such as pi and phi, are called transcendental numbers, which is a decorous nomenclature. Problems occur when these are expressed with integers (arithmetic.) rather than with figures (geometry). Integers are very delusive things because they seem to stand alone, than which nothing is more impossible or risible because nothing ever can or does stand alone. Universe is integral. There is no indivisible particle other than Universe, Itself. This is why Greeks Theologians stuck with figures and relationships (ratios) between elements of figures. They maintained this way the constant sense of relatedness, which it is essential to maintain if one is to be realistic. They wanted to be realistic, and so they were. Of course, male and female are inseparable, not divisible. Universe is actually female in nature. God is the only male principle. This is what Vedas declare, consistently. But this is not to say one is one and other is other. Each is both. Or better, a distinction between them cannot be made. 'Male' and 'Female' are merely descriptive terms for indicating different aspects of the same thing, aspects which are integral and, therefore, inseparable. 'Physicists' foolishly look for an indivisible particle. Their aim is a contradiction in terms, a logical howler. The entire universe is indivisible, but they think they have to and can find indivisibility in a single particle -- when there can be no 'single' particle because there is no independent system.
God is One without a second. I know your plate is full and so I make this reference reluctantly, but, if you would like a pleasurable and fairly rapid and not expensive and classic entree into the realm of number/elegance/beauty, then this comes to mind as the best I know of short of Euclid's Elements, which would be burdensome for you: *The Divine Proportion: A Study in Mathematical Beauty,* H. E. Huntley, Dover Publications, available anywhere. In print for many many years and will be as long as Euclid is, I suppose. Probably you know that the second most published book in the world, after the Bible, is Euclid's Elements. Anyhow, Huntley is it.
Adwaitha Hermitage
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