Hill Arches by Henry Moore |

**Quantitative and Qualitative Changes**

Though I didn’t realise during my formal education, Physics also vigorously excluded all areas involving any

*Qualitative Change.*This was obscured by the obvious meticulous attention to quantitative change, which, in fact, seemed to be its primary concern, and most experiments were attempts to distil-out the most important quantitative relations between the significant factors involved. So, though such forms of Change were easily accommodated, both on the mathematical, and the physical, models of Reality, when things changed to become something else, the system avoided them like the plague. It simply was not able to deal with such phenomena.

Ultimately, of course, a more rigorous treatment of the Nature and Weaknesses of these types of Reason had to be addressed. And, such a treatment would have to do TWO COMPLETELY opposite things. It had to explain WHY the system worked so well (as in Euclid), and yet failed so profoundly as in the Copenhagen Interpretation of Quantum Physics (for example).

Somehow, such a study would have to deal with the “truth-within-falsity”! I can express the problem in no more appropriate way!

But, there were the to-be-expected confidences of youth beginning to grasp the World for the first time. The trajectory of the studies of my maturity turned out to be long and full of necessary detours.

Such a path was unavoidable, because I insisted on a multi-discipline approach. Instead of my writings being outpourings of my specialist studies, they had to be a search in themselves, and were, therefore, no synopsis of where I was, but, on the contrary, a running commentary on how I was travelling, and what I was discovering. My chosen path regularly took me into areas that I knew little about, but were obviously crucial to my chosen task. I, therefore, regularly dedicated whole periods to subjects, in which I had no experience, and these “detours” were perhaps THE most important part of my studies and profoundly changed my conceptions.

The best example of a similar, dramatic process elsewhere that I can give for this, was embodied in the excellent BBC TV series by Aubrey Manning entitled Earth Story, in which he, a life-long biologist, had his world “illuminated” by a serious study of Modern Geology. It transformed his understanding, and changed the “tempo” of his view.

In a similar way, I, a Physicist and Mathematician, have had my theoretical foundations regularly reformulated as a consequence of serious studies in Biology, History, Palaeontology, Philosophy, Pedagogy, Art, Marxian politics, Computing and many others.

Such a width of increasing knowledge and understanding cannot but undermine your narrow, purely discipline-based conceptions of the World. You are driven to an attempted synthesis, and this brings you constantly up against your often narrowly-based and unquestioned assumptions. You “realise” the short cuts and invalid extrapolations of your cherished methodologies, and you can only end up as a generalist rather than a specialist – what can only be called a philosopher.

**The Crucial Inadequacies in Pluralist Reasoning**

Let us relate this adult stage of my investigations. After a long knowledge-gathering phase, I started on my journey with the Paradoxes of Zeno.

Initial attempts were to “solve” his presented contradictions, and my skills in Mathematics convinced me that I could “explain away” his confusing conclusions. But what I discovered were the limitations of my own techniques and the profundity of his purposes. Throughout all the time since my first finding Zeno, I have regularly returned to these Paradoxes for a reappraisal, in the light of my ever-widening other studies. For surprisingly the thoughts of this Greek who lived 2,500 years ago, I found to resonate in all areas of human study. Zeno revealed the most important weaknesses of Reason, which until his revelations, no-one had addressed.

He showed that the two most obvious principles used in dealing with Space and Time were both inadequate alone. These were the “obvious” assumptions of Continuity and Descreteness, and both could be shown to lead to contradiction.

NOTE: Though I could give chapter and verse on these many occurrences, it would interrupt the flow of my overall argument here. So, I will, at this time mention only one area where the Paradoxes of Zeno transformed the attitudes of my students. I found it essential to introduce them into my teaching of the Calculus.

NOTE: I will NOT again be drawn into the innumerable “disproofs” of Zeno’s methods using modern mathematics and “even-more-modern” philosophical positions. He, after all, lived in the sixth century BC. Reading the achievements of the past from a NOW standpoint almost always throws out the baby along with the bathwater. The constant recurrence of Zeno’s Paradoxes is due to the fact that they contain profound truths and these MUST be addressed in every context, not circumvented.

Zeno of Elea |

Not only was this work of Zeno profoundly important, but it also carried with it the opposite truth, that both these assumptions, and the Reason, based upon one or the other, could also, and did, produce profoundly true and useable extractions. Such methods were both true and yet clearly, and at the same time, also inherently flawed.

They were necessary and yet incorrect!

Now, needless to say, such contradictory conclusions wedded together in the same method (that of Zeno), did not entice queues of thinkers to embrace Zeno’s ideas. They usually simply ignored his Paradoxes as clever, spoiling tactics, and continued with their very recently discovered and obviously wonderful and dependable methods, taking care to use them ONLY in amenable areas of application.

“While he’s worrying about

*That*, let us get on with the innumerable possibilities of

*This*!”, was their attitude. A thousand descrete successes were more important than a single profound but almost unintelligible error.

Returning to Euclid’s Theorems (and Mathematics in general) what were his assumptions and premises?

Euclid assumed perfectly straight lines of zero thickness. They would be conceived of on perfectly flat planes of infinite extent. Any identified position on such a plane – a point – would also be of zero extent. Parallel Lines (evidently keeping the same distance apart) were pointing in the exact same direction: they were at 0o to one another and would never cross.

Now, do these assumptions truly reflect Reality? The answer is a clear “NO!”.

Yet, the whole structure turns out to be extremely useful, and the imperatives of the methodology so persuasive, that it is clear that this obvious “fiction” somehow delivered Truth of a kind!

Now, we can easily drop into a simplistic argument as to why this was the case with Euclid’s work.

We can say that Truth “on a certain scale” was embodied in the theorems. The thickness of the lines and dots could be disregarded, when distance, shape and geometric relations were the significant elements to be considered. Euclid’s simplifying assumptions were “empowering”, in that they threw away irrelevances in the search for higher spatial relations. And, of course, all this is true!

BUT, Mankind did NOT see it that way at the time!

The general consensus, among the users of this body of Knowledge, was that the essence of geometric reality had been extracted from the mire or blurring of inconsequential everyday Reality. The process was one of revealing the Essences out of which Reality was built!

But, that was certainly NOT what had been achieved!

Even at this early stage in Mankind’s development of methods of Thought, he had, in fact, invented the idea of a Model. In order to deal with Reality, an intelligent set of simplifications were always necessary. Any old simplifications would NOT do however. The removals had to be of detachable things which were not significant in the given area of study, and the revelations of its embedded truths.

Mankind learned that the division of Reality into areas, systems and indeed Parts, was useful.

He had unconsciously "invented" Plurality – the division of anything into its supposedly-independent component Parts, in order to make any sort of sense of it. Of course as soon as any Part was isolated, even conceptually, IT had to be addressed, and then the obvious next step was to consider its components too.

But, you can’t do that willy-nilly, and tumble into a possible infinite regress!

And, crucially, Reality is NOT composed of separable Parts!

In Essence, Reality is definitely holistic and not pluralistic. All elements are inter-related, inter-dependant and indeed mutually determining in the last analysis.

The isolation of Parts to explain things is merely a useful Model.

So, Mankind’s settling on Plurality presented him with many problems as well as useful models.

For it to work, he had to constrain Reality in dramatic ways. He had to “corral the beasts” in order to tame them. Plurality only worked if the context was either naturally constrained, or purposely controlled by Man himself in deliberate and appropriate ways.

Plurality was initially quite severely restricted to those areas of Reality, which were quite naturally constrained – naturally-stable sub divisions of Reality as a whole. And this certainly kept the progress to a relatively slow pace.

But it blossomed when Mankind’s knowledge reached sufficient proportions for quite small, unnatural areas to be physically constrained in MOST of its involved variables, purposely-chosen to be fixed values, and effectively “nailed to the floor” in order to “reveal” some hinted-at regularity embedded in Reality, which normally first exposed, and then hid, its beguiling regularities.

Plurality became profoundly useful with the invention of the “experimental set up”.

Now, I have dealt with such things at great length, elsewhere, so I will not repeat it all again here. What is required, in this essay, is to clarify the methodology of Mankind in attempting to deal with a holistic Reality. To do this he constrained Reality in a series of important ways, to identify “in isolation” some of its relations. He delineated his areas of study. He made clear (at least sometimes) his assumptions and premises. He physically constrained the area with often prodigious controls. He forced a series of changes in the magnitude of various parameters, noting their consequent effects on other values, and via these results extracted a relation, which he then generalised into an abstract formal equation.

This is the main Methodology of Science, and its power has been demonstrated a million times in the achievements of centuries of Technology.

But not everything is amenable to such forms of study. Once more, the methodology limited those areas to be studied to those that could be so constrained.

Science became not only a method, but also a defined area, wherein such a method could be applied. The Method could not but actually define its areas of application. And, where such physical controls were not possible, these methods could NOT be used. In addition, these same methods of scientific investigation ALSO defined those areas wherein its achievements could NOT be used.

Now, before I go any further, I cannot continue without making clear that the vast majority of human concerns were necessarily-omitted from this area of feasible investigation and use. Most things could NOT be treated in this way and so were not addressed by the scientists.

An equation may seem to relate two clear things in isolation, but that does not mean that, with it, we have in our hands one of the many “components” of Reality. To think that assumes that Reality is composed of separate Parts that exist independently of one another, and can be brought together to reproduce some area of the Whole. And that is certainly NOT true!

To use such equations (necessarily isolated, extracted and abstracted from a constrained piece of Reality), the EXACT SAME conditions must also be constructed for its effective and predictable USE! The equation would only be true with those precise defined conditions – defined on extraction.

So, every equation has its own Domain of Applicability, and if that Domain is not adequately delivered and maintained, the equation will FAIL. So, if we use the equation within that Domain it will work, but if those conditions are NOT in place, or if they change during use, for whatever reason, the equation will give increasingly more and more incorrect predictions until they are completely wrong!

Ask any school student of Science and he will be guaranteed to confirm this point. It’s why most of his experiments gave the wrong answers!

So, in applying our logical methods we have to clearly delineate our areas of application. We have to limit, in some way, our theatre of operations – either physically or conceptually, or most likely in both of these ways.

Even Reason is predicated upon a defined area with defined assumptions and premises, and Euclid’s Theorems are a perfect model of the method.

NOTE: The assumption that these extracted “truths” are eternal, and can be “summed” in some way to reproduce phenomena in Reality, first in Parts, and subsequently “as a Whole” is, of course, NOT PROVEN.

So, Man, via Control, found a way of bending certain constructed situations to producing predicted outcomes, and being both intelligent and flexible, as he undoubtedly is, he made them serve his needs (as well as fitting his conceived of "needs" to only he could deliver).

Surely, such a methodology is remarkable?

Well, yes it is, and is universally applauded as the solution to ALL problems in the modern world, where it is called “Science”, but is more accurately termed Technology!

And, could not this be considered as wholly sufficient?

The answer has to be a resounding, “NO!”.

An equation may seem to relate two clear things in isolation, but that does not mean that, with it, we have in our hands one of the many “components” of Reality. To think that assumes that Reality is composed of separate Parts that exist independently of one another, and can be brought together to reproduce some area of the Whole. And that is certainly NOT true!

To use such equations (necessarily isolated, extracted and abstracted from a constrained piece of Reality), the EXACT SAME conditions must also be constructed for its effective and predictable USE! The equation would only be true with those precise defined conditions – defined on extraction.

So, every equation has its own Domain of Applicability, and if that Domain is not adequately delivered and maintained, the equation will FAIL. So, if we use the equation within that Domain it will work, but if those conditions are NOT in place, or if they change during use, for whatever reason, the equation will give increasingly more and more incorrect predictions until they are completely wrong!

Ask any school student of Science and he will be guaranteed to confirm this point. It’s why most of his experiments gave the wrong answers!

So, in applying our logical methods we have to clearly delineate our areas of application. We have to limit, in some way, our theatre of operations – either physically or conceptually, or most likely in both of these ways.

Even Reason is predicated upon a defined area with defined assumptions and premises, and Euclid’s Theorems are a perfect model of the method.

NOTE: The assumption that these extracted “truths” are eternal, and can be “summed” in some way to reproduce phenomena in Reality, first in Parts, and subsequently “as a Whole” is, of course, NOT PROVEN.

So, Man, via Control, found a way of bending certain constructed situations to producing predicted outcomes, and being both intelligent and flexible, as he undoubtedly is, he made them serve his needs (as well as fitting his conceived of "needs" to only he could deliver).

Surely, such a methodology is remarkable?

Well, yes it is, and is universally applauded as the solution to ALL problems in the modern world, where it is called “Science”, but is more accurately termed Technology!

And, could not this be considered as wholly sufficient?

The answer has to be a resounding, “NO!”.