The Death of Mathematics

The Future of Science and Philosophy

Following the Demise of Mathematics

as

The Lingua Franca of Reality

I have been a Scientist and Philosopher for sixty years now - but I fell-out with my primary subjects and evident mathematical abilities when I was just 18 years old, in my very first term at University (studying for a degree in Modern Physics). And that was already the second profound setback in my, by then, very short life.

I had first, while still at School, settled upon Mathematics, as the key to Understanding the World, as I turned out to be a natural in seeing and using its Theorems and Proofs, and was always top of my A stream Classes in the Grammar School that I then attended, from my prior Elementary School. For I alone, had managed to pass my Scholarship to enable me to attend - which surprised everybody, both in my family of unskilled labourers, the teachers at my initial school, and even those I was taught by at the Grammar School. In spite of being top of my classes throughout my whole education there, and ultimately obtaining a record 7 "A" and "S" Level Passes by the age of 18. Indeed, the one constant comment upon every single one of my School Reports was "promising". And, having been pressed to take those 7 Sixth-Form courses and exams, my achieved marks were not what I would have achieved, if I had taken just 3, as did everyone else.

But though while still at school I was initially-at-least satisfied with Mathematics as a general Lingua Franca, it was very soon found wanting in my increasing commitment to Physics, because instead of merely formal relations to phenomena, Physics also delivered Explanations for them, too - it was possible to also understand Why things behaved as they did, and luckily all my Science teachers thought the same.

So, though I continued to excel in Mathematics, it was Physics that held the promise of a continuing expansion of my understanding of the world! So, I only applied to take a Physics degree at the Universities I applied to, in the late 1950s. 

Hence, I was devastated when in my very first term at University, literally no explanations were forthcoming whatsoever: the sole purpose of study was to arrive at a mathematical formula that fitted the acquired evidence.

And questions weren't allowed: it was assumed that if you asked for an explanation, you couldn't follow the Maths!

So, the only access to staff that was available, were the postgraduate demonstrators who helped with experiments, but they were the worst, and would get angry at my insistence upon explanations. They were all involved in the NEW Physics, a subject totally dominated by Mathematics - explanation was banned!

Clearly because of my abilities in Mathematics I could do what was increasingly demanded, just as my educators were less and less competent at the explanatory side! I who, contradictory to my tutors probably the best at handling their version of Mathematics, was also the most critical of the way they were doing it.

I had taken up Painting, when I was 16, so I joined the University Art Society, and by the end of the Academic year I was running it as its secretary. But I couldn't be satisfied with what I was doing in Physics at all, so, I spent a great deal of time in the magnificent Brotherton Library within Leeds University, seeking an alternative to what I was being given within my course. I found nothing at first, until I slightly widened my criteria, after which I found a book entitled Materialism and Empirio Criticism- which was a trenchant philosophical critique of Henri Poinaré and Ernst Mach - who originally developed the Positivist Empirio Criticism, which later became the Basis for Modern Physics!

The book answered their mistakes philosophically, but not physically, so I decided to trace his sources - the writer of the book was Vladimir Iliych Ulianov (more commonly known as Lenin - the Marxist who later was to lead the successful Russian Revolution in 1917). The philosophic stance involved followed Karl Marx's criticisms of Pluralist Philosophy within Social Phenomena (usually termed Marxism, but more properly termed Dialectical Materialism).

But neither Marx, nor anyone else, had ever applied the new philosophic stance comprehensively to The Sciences! I knew what had to be done: I had to undertake that task, but aged just 19, I simply did not even know how to start - so I joined the Communist Party and afterwards a series of other purportedly Marxist Parties, but I never found a single person who could help.

I turned to other things over the years, becoming first a Sculptor, and then a System Software Expert, and in that capacity finally returning to Higher Education, with a series of posts in three countries - but it was in my expertise in designing tailor-made Software Aids to High Level Researchers, followed by a final career as a Writer, that I finally knew sufficient to do the job myself!

It certainly wasn't straightforward, though, as a universally-subscribed-to major limitation upon all experimental investigations, permanently terminated the study of Reality-as-is, for, instead, the major distortion of only ever taking data from entirely artificially-produced Pluralist Contexts, and also, over two millennia, finding it imperative to have to implement diverse tricks and workarounds, to try and circumvent the unavoidable short-comings of maintaining such an entirely and mistaken and consequently strictly Pluralist approach, especially when it came to using the inevitably distorted Laws, in every single form of consequent Production.

For, in making successfull the pragmatic production of particular outcomes, meant that what had to be arranged-for, and carried through successfully, was NOT involving Reality-as-is, but instead entirely by achieving predictable outcomes within an artficially-constructed-and-maintained Pluralistic Context! While those arrangements did deliver what was required, it was absolutely always achieved entirely within separate unique, artificial situations, that were always different in each and every case.

And this made it impossible to get Generally True Laws, as each-  and every one only worked in its own tailor-made Pluralist situation.

Consequently, NO Everywhere-Applicable-Law was available: and, in addition, NO purely-manipulative-substitutions between different laws were possible! Indeed, the whole set of Formal manipulations - the mathematical transformations of supposedly Scientific Formulae were totally illegitimate, as being the case in Reality-as-is. Consequently, the whole usual systems were illegitimate, and all purely on-paper manipulations were simply wrong!

In actual Real World production, every Law was forced to have its own tailor-made artificial context (technology): and complex situations had to be transformed into a series of entirely separate experiments to even be able to achieve a required overall result. Hence, all cerebral investigations were impossible to he legitimately carried out, and Real Theory was impossible!

And, the reason, for all this, was the Pluralist Myth of Stability as the Natural State, which was always, in fact, an unnaturally-maintained "Stability"! For, in Holistic Reality-as-is, all stabilities are naturally-and temporarily-maintained, as "Balanced Stabilities". So, the Pluralist assumptions are never true and actual "Balanced Stabilities" turn out to be naturally-selected bundles, consisting of balanced-diametrically-opposite processes, so selected for as to be self-maintaining, by means of equal and opposite processes in the bundle, one of which, that with anotherhaving the same external initiator, will always counter the errant process. And then, to compound the overall Effect, the various bundles involved perform, in the same way, by their mixes of cancelling opposites.

As soon as the artificially Fixed World and the Fixed Laws of Plurality are replaced by a multiply-simultaneous factor Holist World, the evident Interludes of apparently stable natures of the natural stabilities of Plurality cease to exist, and Hierarchies of Systems and Subsystems governed by opposites come into the reckoning in far more complex ways. This is why a dialectical logic is needed rather than a formal one.

Now, in such a short paper as this, a comprehensive set of explanations is, of course, impossible! The very fact that it hasn't been attempted in two and a half millennia illustrates the difficulties involved. But this work  is now, finally, securely underway,  and will indeed result in an even larger Intellectual Revolution than did the Greek contribution in the 5th century BC. 

But if Mathematics can no longer be seen as the language of nature, how should we approach it going forward, and what will ultimately replace it as our primary means of understanding?