Monday, September 9, 2013

On the Incoherency of Mathematics, A Primer on Dimensional Mathematics

Part I.

I have acknowledged for some years a stipulation of my studies of philosophy, which is the following:

Systems must be dynamic or they involve work. There are two choices: mechanics or a labor-intensive project. This insight was first introduced by the late philosopher Alfred North Whitehead, who was the progenitor of process philosophy. However, he did not introduce a dynamic system in a coherent sense. That would involve the insight that Aristotle had no exclusive proofs, and that exclusive proofs required the Cartesian Coordinate system, which supposedly only came later.

Anyway, the theory that the choice is between mechanics and labor-intensiveness comes about by considering the alternatives. Those two are really just neutral categories. But, I think, only so many neutrals are possible in extant reasoning. For example, easiness or laziness is one alternate neutral category, and reduces to semantics. (Mechanical easiness is determinism, which reduces to semantics). The strong categories which are non-neutrals are absoluteness or pure energy, which when combined with labor is also a form of semantics, that is, relative effort, which must be concluded to be either labor or non-labor, but cannot be both. The other non-neutral category is passivity, which is not really a principle at all in most views. Combining passivity with mechanics yields dysfunction, rather than an alternative. In most views this is not open to interpretation. Another option for neutrals in the context of passivity and energy is magic, but that has been discarded in prior history. Some, anyway, would consider it to be a form of mechanics, or to involve labor. So the circuit of the diagram looks like this: [Energy] [Magic] Mechanics [Passivity] Labor [Laziness]. All the terms in brackets have been eliminated.

In conclusion, the two options remain mechanics or labor-intensiveness in any system. And labor-intensiveness has many forms, whereas mechanics is the efficiency of these forms, and it is always dynamic. Consider for instance Pascal's Numbers, or E = MC^2. They derive their value from dynamic operation, which is only possible when they involve dynamic organization. And that is not to say that they are prime examples of this phenomenon, in terms of pure theory. They may not be.

Part II.

Cartesianism, in dimensional terms, that is, "axiometric" terms, is a two-variable calculus (meaning calculus in a simple sense). It takes two operators, plus and minus, which express the single dimensional axis running diagonally. If it had four variables (as mathematicians evidently unconsciously assume), then multiplication and division would not be capable of being expressed in terms of addition and subtraction. But they are expressible in those terms. Indeed, a chart in which multiplication and division were a separate opposite comparison from addition and subtraction would be ridiculous, because it would be at least partially redundant. The only conclusion is that, in the simple terms of the original intentions of the Cartesian Coordinate System, it is a two variable calculus, that is, we can treat multiplication and division instead as simple functions acting on a single diagonal axis of comparison. See the following diagram for reference:

Part III.

What is the conclusion?

Math that does not state the problem of dynamics / labor-intensiveness in an obvious way runs a serious risk of being systemically incoherent. Accepting labor-intensiveness is not a good alternative. So the only option is to express systems at the functions level. When these systems are not coherent, the result is incoherence. According to this observation, much of math as we know it today has made a fatal error---very likely the types of errors which are now deemed to be mathematical knowledge, but which according to my system are no more than semantic references to the prior failure of mathematics. Math is possible. But it is really proto-math. Just like meta- (after) physics is the only study of reality.

Cite Nathan Coppedge if using this material, as a novelty or otherwise. I welcome inclusion of my ideas in student papers.

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