MATHEMATICS: the symbolic expressions of the logical implications of existential simplifications

Mathematics is the creation and development of hypothetical symbolic structures of relationships, for the eventual purpose of manipulating simplified patterns in numerical and spatial data, in order to be able to predict, control, and understand existential phenomena.

Awarenesses, and the human mind in particular, abstract and simplify patterns from the complex chaotic interchange of energy forms that is the universe. The sun and the full moon, wheels, craters and river-worn stones can be characterized as being 'round' for the purposes of general communication and thereby augment language with a richness that enables useful information to be shared. When such broad concepts are further constrained by uncompromising precision, the symbolic expression of those concepts is what is described as 'mathematics'. The 'sphere', for example, is constrained in the mind to be a round shape such that its surface has no thickness and is everywhere equidistant from a single fixed point which occupies no space. Such entities do not and cannot occupy reality, but exist only in so far as individuals agree to cooperate and mutually entertain their description. It may be convenient to describe the sun, a cannonball, a Moeraki boulder or an airborne bubble as being 'spherical', but such objects are rarely even remotely approximate to the mathematical abstraction. The supposition that nature is somehow 'mathematical' because some aspects approximate idealised forms and patterns is confusing and unhelpful nonsense. As well as various shapes like circles and ellipses being rigorous simplifications of existential phenomena, other aspects of reality, like distance and duration and weight, appear to be measurable and as a consequence can be added and subtracted. This gives rise to a class of concepts like space and time and mass which are generalizations of those measurable quantities. Symbols are allocated to each of the generalised concepts of the measurable universal features and the language which then evolved to logically manipulate those symbols is also called 'mathematics'.

It is nature that is the immediate stimulus and motivation for the creation of various conceptual-mathematical relationships. The circular and exponential functions for example, arose from attempts to model oscillation and growth-decay patterns. Probability functions were devised as a means of modelling those aspects of nature where the causal process seemed to have a specific set of a several outcomes... as is the case when a die is thrown or a coin is tossed. If any observed general changes in the chaos of nature can be simplified, the devised mathematical patterns can be used to predict the course of the perceived natural pattern.

Once attention is turned to the numbers themselves, which are used in the measuring processes, increasingly creative and complex computations of addition and subtraction result in the recurrence of specific patterns. Some numeric sequences have proved to be of such practical use that specific symbols like 'π', 'e', and 'δ' for example, are allocated to them. That is all they are. They are just specific numeric sequences resulting from tightly defined computation rules. They are not ephemeral entities occupying some sort of virtual reality. Yet mathematicians continue to talk of 'discovering' a new number, as if it was just waiting out there hidden somewhere under a rotting log or a potting-shed bench.

It can be quite tempting to suppose that some mathematical concepts are so pure and unchangeable that they can somehow be time independent entities. It may be claimed for instance that the concept of a triangle does not change with time and is thus a time independent concept. Firstly, this is to pretend that when a concept is contemplated time does not pass and memory is not an intrinsic element in the contemplation process. Secondly, even the meaning of the concept itself is not immutable... as is the case when we define a triangle to be formed by the intersection of 3 straight lines, and we are not at all sure what the meaning of 'straight' is.

Some individuals of a hypothetical inclination continue to be persuaded by the remote ramifications of their symbolism. They assume that the manner by which their thought patterns have been conditioned by their language and their culture is irrelevant to the objectivity of their thought. They presume a cosmic generality pervades their thinking. But when an ordinary gardener enquires as to the relevance of any of their initial assumptions, their ability to use ordinary language evaporates and they can only resort to an intricate display of their arcane symbolism. '...if only you simple plant nurturers could understand the power of the mathematics, and the implications of possible solutions to the matrix of nth order differential equations, then everything would become clear'...

Nature then is not mathematical. Symbolic patterns of measurable quantities are devised to simplify observable phenomena. To suppose that there are mathematical 'laws' which somehow control and guide the processes of nature and that they can be discovered, is quite mistaken. All such mathematical concepts exist only in the domain of an awareness. They do not have any form of existence as some sort of independent intrinsic property of nature. Mathematics only exists as a temporal sequence in the memory of an awareness. The assumption that mathematics can be 'pure' and independent of reality is only made by those who have lost touch with their origins. The concepts and creative explorations in any field of symbolic manipulation are only possible using the mental processes that are formed and biased and conditioned by the way that nature works. Supposing that thoughts and thinking can be independent of the thinker presumes a spirituality that pragmatists have yet to bottle.