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?

 

Coming soon... Natural Revolution

SHAPE Journal is collaborating with philosopher Jim Schofield and filmmaker Michael C Coldwell to make a documentary film about Marxism, Revolution, Science and Emergence

Obvious and Hidden Truths

"An Additive Mix" by Liz West. Photograph by Michael Coldwell

Both in Science and in Art

It has always puzzled me how clearly receptive literally-all artists and writers were, and still are, to the major Copenhagen retreat in Sub Atomic Physics. Approving articles appear regularly, seemingly glad to see that Physics has finally been rescued from dull, "mechanical materialism", and into the pure-light of Reason, and the beauties of Pure Form.

For, you would expect that whether you were a scientist or an artist, your clear objective would usually be to reveal that "Hidden Truth", which was, and always is, never immediately evident!

Why should this not be the case? Well, there are reasons!

Most Science is both pedestrian and pragmatic: so, the conception of it, among non-specialists in that field, is invariably closer to a technological conception, than one of "Natural Philosophy" - the original title and description for Science.

Indeed, since the heyday of the inventors, who successfully exploited any and all scientific discoveries in sellable devices, such as those by Marconi, Tesla, Bell and Edison, the ever-present demand, "What's it for?" has majorly replaced the original "Why is it so?", as the main requirement to be answered. And Understanding, as Science's major purpose, has been extensively replaced by Usability as the main aim and director of scientific investigations.

Indeed, this inversion of the usual order, in scientific investigations, has demoted Theory from being the major purpose, ground and, indeed, director of new discoveries, into becoming merely a "placeholder-explanation" of what is "already perfectly well known, and, already, most effectively used" - indeed, an afterthought!

A major principle on which current Science has been built, literally since its inception, such as Plurality, allows analysis of "extracted laws", which are then often seen as "directly-causative", as well as being, necessarily, relatively simple. And, in addition, such a stance sees what has been extracted in many different experiments, as delivering purely additive contributions: so that phenomena are conceived of with literally NO recursive effects where results actually qualitatively-change-their-causes!

Perhaps, even more restrictive than that, was the apparent basis for Copenhagen - the insisted-upon, Predominance of Form, as embodied in Formal Equations, which again arose, initially, to enhance and improve various modes of Production, based upon scientific discoveries.

So, how could its then further embodiment as "sole cause", possibly be instituted from such a beginning?

The key argument, against such "reasoning", has to be that it could never be so, when used entirely-alone. For, Form is descriptive, not explanatory: it is caused and not causing, and would always lead to contradictions and dichotomies if pushed beyond its always context-limited predictive scope! 

Anthea Hamilton, Vulcano Table (2014). Photo: Michael Coldwell

Now, such methods were relatively new to Science, though always attractive to creative artists of all kinds. For they were exclusively concerned with reflecting back to viewers, by their creations, the often unconscious, human conceptions and thinking, as directly as possible.

But, the real basis of all formulae is always Idealism - it makes the formal equations into the actual causes, and hence involves the abandonment of the materialist stance at-a-stroke.

Let us attempt to be crystal-clear!

All acquired equations from experiments, are to a significant extent, "man-made", which is both due to the necessary simplifying process of farming of the contexts of investigation, and also, thereafter, to the following essential idealisation of the products of that extraction, by the careful fitting-up of pure formulae from Mathematics to match such results, which, given an exact repeat of the same context as in extraction, enables predictable and successful use.

Such formulae do NOT exist, as such, in totally unfettered Reality: they are most carefully arranged-for by Man, and hence are man-devised reflections of only particular controlled areas of Reality. For it is this, as such, that makes them appear as eternal Natural Laws, and is, quite definitely, an idealist deformation, making the farmed-for-form the "natural cause"!

But, of course, Idealism is, certainly, not merely about the quantitative measurements alone, it is, of course, vastly wider than that.

And, it was those aspects, connected with human volition, that were the concern of artists, and made the New Physics seem so attractive to that creative group, who, in their own work, were really portraying what they considered to be the essences driving Humanity.

In addressing Humanity, artists of all kinds knew better than to be strictly analytic in delivering their subjects, because what they were really addressing was too rich and complex to be dealt with in that way. They were delighted with the move towards Idealism in basic Science. They also knew that their "means" - whatever they were portraying, were much more than what Science usually delivered.

Put as simply as possible, artists correctly see the world through Mankind's eyes-and-volitions, which they attempt to reveal to their fellow humans, whereas real scientists attempt to find the intrinsic causality of whatever they are investigating, and attempt to deliver that.

To cap it all the new physicists began to speculate in an idealist way to fill the evident cracks in the Copenhagen Interpretation.

Many idealist concepts transferred from Pure Mathematics, such as what became known as Singularities, began to move to central positions - with Big Bang Origins and Black Hole Demises for everything in the Universe, not to mention multiple Dimensions, above the natural three of the Real World, which appeared in order to "explain" the stances in many anomalous phenomena.

But, I would not equate the artists' stance totally with that of the new physicists.

The former were attempting to be true to a human experience of reality, and in that they are more true to an important part of it than the new physicists ever could be, but their common stance of Idealism, would not, alone, deliver what either group were really seeking - Truth!

"Reciprocal Spaces" by Shelley James and Scott McLaughlin. Photo: Michael Coldwell

Correction:

Perhaps much earlier, in this account, I should have explained Postmodernism. For this is the contemporary philosophical excuse for Pragmatism - and the regular switching between contradictory alternatives apparent in all logical impasses in reasoning. Artists loved this because that "kind of Truth" was better than just one or the other of the contradictory alternative being solely correct.

And, you cannot do that without discovering the reasons for the generation of such a dichotomy.

Instead, they considered, keeping all options was better, and this is borne out by the success of such pragmatic switching - you certainly didn't understand why, but nevertheless, "picking the right one", by chance or trial-and-error, in a given situation, did indeed work!

Artistic ambiguity played a similar role, but also, in the hands of a great artist, could indicate something of true, but not completely known, circumstances.

That is why truly great art always includes such profoundly directed and revealing ambiguity.

It is nothing like the crude methods of the new physicists, which actually do the opposite, and not only hide the real causes, but actually BAN all attempts to uncover them.

To this degenerate group "The World simply obeys statistical probabilities" - which is simply not true!

The artists' generally were aghast at the prior Mechanical Materialism, which to them was like dissecting dead Life, it lacked the impulse for Change evident in the Real World, so they mistakenly gave unwarranted support for these new idealist physicists...

New Blog Series

Man & Reality - now available on the Shape Journal

The Man & Reality blog series is now available in full, in a new issue (40) of Shape Journal. Click the cover above to read the PDF. Our new policy of serialising older unpublished work seems to be working, as it provides a good introduction to the broad philosophical stance of this theorist, without the necessary layers of added complexity present in later works.

While Man & Reality offered a robust philosophical criticism of Mathematics from a Marxist standpoint, so our new series does the same for Science.

What is to be Done?

Developing Marxism Today; Introduction

Our new 12 part series was written as a single, 15.000-word paper back in 2008, and preceded literally all the later significant theoretical developments by this Marxist theorist.

Nevertheless, it was, and still is, an attempt to deliver a comprehensive approach, by a modern-day Marxist, to the significant problems that were then considered to be still outstanding in both Philosophy and Science.

The credentials of this writer, that you may consider are appropriate to the task are that I am a professional scientist, in fact, a retired Professor from London University, and a lifelong, active revolutionary socialist. So, the subject will be treated professionally, and its validity will be proved by the analytical power revealed by its wholly new contributions.

It will not be an historical narrative, but a current, urgent development of Marxist Theory!

The paper was always an important attempt, in spite of its evident omissions, because, nevertheless, its completion went a long way to defining, "What is to be Done!" But, of course, it will only be by the subsequent successes of the new approach that it will, and should, be judged.

For the author's Theory of Emergences was only formulated two years after the completion of this paper. And the scientifically significant Theory of the Double Slit Experiments in Sub Atomic Physics was also only begun during the writing of this paper, and finally formulated the following year.

So, why not just deliver those completed theories?

Well, they certainly require some sort of grounding, without which they will not inform and empower the reader. This chosen paper is being serialised here, because of what it does achieve in establishing the necessary agenda and ground. The intention was not to merely add the current “Works of the Masters”, but to encourage potential Marxists to actually join the fray. For the task, being applied to a living, changing World, is clearly never ending!

The contents of the new series are as follows. The aim is to publish one a week for the next 12 weeks.

What is to be Done

CONTENTS

Introduction

I. Epiphany, Activism, Election and Expulsion

II. Political Stance, Campaigns and Theory

III. Philosophy, Researches & Zeno

IV. Inter-disciplinary Studies, Dichotomies & Eye-Brain Interpretations

V. Technology, Science’s Source & Method, Plurality and Holism

VI. Hegel, Contradiction and Abstraction

VII. Explanation-or-Use, The Crisis in Physics, Reality Evolves

VIII. Revolutionary Change, Marx & Hegelian Dialectics

IX. Outstanding Tasks, The Holist Stance

X. Emergences, Breaking from Old Ideas, Tackling the Problems

XI. Universally Applicable Theory, Science, Explanation above all

XII. The Fight Back, a Physical Ground

Part I will be published here on Monday. This body of work is AVAILABLE NOW as a Special Issue. Read it all here!