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Jan 25, 1994 07:27 PM

by John Mead

> There is considerable philosophy in even simple mathematics, and with > a little thought we can find great truths in it, throught the law of > analogy. Mathematics is one of the keys to the Mysteries, and as a > key, it does not necessarily give specific numbers to cycles as much > as it reveals deep philosophical truths. > > Consider the natural numbers, 1, 2, 3, ..., on to infinity. They > represent a quantity of some type of thing, of some object. Natural > numbers give us a count of group membership, but only deal with > quantity when they deal with something that can only be measured in > whole units. > > Quantity implies more than one of a certain type of being, or object. > We have, for instance, three chairs in the room. To have more than one > of anything, the objects need to share in a particular quality, to > have a quality in common. In this case, the three wooden chairs all > share in the nature of "chairness", they are prototypes of the > archetype of a chair. Group membership, or influence, is represented, > then, by natural numbers. I prefer to say that the concept of a unit is independent of position, space, and time. Hence it is a transcendent concept. > Coming to the number zero, we don't have a quantity, but a lack of > existence. We can have zero of any possible or impossible thing. To > take on an attribute of zero imples going into non-existence. disagree... zero is VERY different from NULL or NOTHING. It has to do with additive identity. zero is definitely NOT nothing, but a concept which preserves units under very specific operations. > This non-existence need only go as far as the realm of thought. When > we say, for instance, that we have zero tables, we need the thought > of the table's absence, and the thought of what a table is, in order > to say that we have zero of them. Our thought gives the absence of > the table a limited sort of reality. It is non-physical, but patterned > after what we consider a table to look like. That thought may be > lacking in some detail, but there is something to it. actually, the Hindu's first understood zero. it is invaluably used with powers, logarithms, and is extremely important when considering the technique of expressing numbers in exponential notation. > When we talk about quantity and measure, we are really talking about > attributes of the manifest world. this is why I decided that measure theory held keys to the differences between the physical plane and mental plane... > Consider a triangle. A triangle does not exist, but is real in its own > sense. to say that a triangle does not exist is like saying that the concept of metaphysical trinity does not exist. I disagree. > After rational numbers, we come to the irrational. These numbers are > magical in a sense. They are not based upon the ratio of any two > integers, but can only be derrived by mathematical means, and never > exactly. The numbers can only be approximated, but never fully > expressed except in symbolic form. > Consider the square root of -1. When we compute a square root, we are > asking the question, what number, when multiplied by itself, gives > the number we are considering. For 4, we would say that its square > root is 2, for 2 times itself is 4. > > But we know that two negative numbers, when multiplied together, give > us a positive number (like -2 * -2 is +4) and two positive numbers, > when multiplied together, give us a positive number (+2 * +2 is +4). > > So how do we come up with the square root of a negative number like > -4? We would treat it as a complex number, with a real and imaginary > part, > and say what other complex number, multiplied by itself, gives > us this complex number. We'd say that 2i * 2i = -4. > > In other words, we have a non-manifest, karmic potential of two, times > itself, giving us the manifest, active negation of four. The meaning > of this is something to puzzle over, and we'll have to come back to > it. We need to consider what a negative number means, what an > imaginary number refers to, and what is implied by a multiplication. it is interesting that modern physics *has* to use imaginary numbers. This says a lot about their reality. peace -- John Mead

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