What exactly is Mathematics?

Mirror mirror on the wall, who is the purest of them all?

Mathematics isn't what people think it is. 

Even its greatest exponents have little idea what their discipline is and where it came from. 

In again watching Leonard Susskind's continuing Lecture Series from Stanford University on Quantum Mechanics; he spends most of a particularly intensive Lecture upon Pure Mathematics, establishing Complex Numbers as "Descriptors of Reality".

But what they really are, as he effectively demonstrates, (though that is most certainly NOT his intention!) are pure Abstractions from Reality. And most certainly NOT a "full & comprehensive reflection (with nothing omitted & nothing added) of Reality", but instead a:-

Mirror-like reflection

- losing most of what is intrinsically involved, in order to deliver a dramatically simplified version, which both merely and exclusively deliver a virtuality, totally without its actual determining causal content, and as such conforming ONLY to a set of Rules (as in a Game), which make what it does deliver mutually consistent with one another , BUT NOT for any intrinsic causality, but instead due to that set of Rules, independent of the Reality that was the real Causal Origin.

Now as a highly competent Mathematician, myself, I, long ago switched my allegiances to Physics, for its very different Basis as a Science of Reality-as-is! It (historically, at least) always attempted to explain things as well as describing them; and in so doing was regularly forced to correct and even extend its concrete premises, in order to remain subject to its key purposes.

But what is it about Mathematics that makes it inadequate in actually explaining Reality fully? And how does it' universal utilisation in the Sciences, distort our view of the Universe?

It was discovered in the Greek Intellectual Revolution of the 5th century BC by assuming all relations between Forms to be permanently FIXED (as they must be to enable a Formal Mathematical Rationality possible) - and this was much later embodied in the Principle of Plurality in which all such concepts are necessarily permanently fixed, for, by doing so, a fairly easily achieved self-consistent Logic as its main means could be guaranteed.

And this very first Intellectual Discipline of Mankind was so successful within Mathematics, that it was also illegitimately exported, wholesale, to both General Reasoning and all the emerging Sciences, crippling both of their attempted applications to a Clearly Evolving Reality.

Susskind constantly confirms my definition of mathematical Rationality both regularly and clearly throughout this lecture, as he extends the idea of Complex Numbers, entirely, exclusively and openly in this very way. But mentions NO actual Physics whatsoever.

Having seen many of his other Youtube Lectures, it is clear that Susskind's unifying basis for Everything he is concerned with is Mathematics: it alone Drives the World! And, he regularly sails well beyond the Three Dimensional Limits of Reality, legitimately with Time, but thereafter totally illegitimately with everything else. As long as the Determining Integrity of the reasoning is maintained, in the mathematical way, all can be stuffed into this same model!

And, of course, once everything becomes symbols on the page, related solely via Mathematical Logic, the concrete aspects fade into insignificance, enabling all sorts of Physically illegitimate reasons to justify wholly Pluralist so-called "Theories"!

Now this transformation of Physics is absolutely crucial, because the essential policemen of that Science, The Theorists, had always been absolutely essential to keep the pragmatic Technologists in their midst, in check via the physical Causality of their Theories. But, with the increasing triumph of the Mathematicians within those theorists, the whole approach in Theory was converted to wholly Pluralistic Mathematical Formulae.

Physics is being totally castrated by these changes!

And in a career-long struggle to reverse this tendency, this committed theorist had to spend the rest of his career, fighting these major inadequacies via extensive diversions into Philosophy, both of Mathematics itself, and of Physics, Chemistry and Biology, in order to find the answers, which only finally came to fruition in 2019 after many different research projects: 

The Processes and Productions of Abstraction,

The Philosophy of Mathematics,

Truly Natural Selection,

The Theory of Emergences,

Substrate Theory

and finally the Critique of the Copenhagen Interpretation of Quantum Theory, which took a considerable amount of time, and which have all been published in SHAPE Journal over the last 10 years, and are available for anyone to read for free.

But when will other Scientists have this same realisation about Mathematics?