In the Time-Sliced Interstices!

The Dynamics of Change

Maths & Reality

I recently picked up a book that supposedly dealt with (among other things) the mathematics of change. The clear standpoint of the writer was the central position of mathematics in the forms and processes of living things. He contrasted mathematical formulae with genetic explanations of the structure of living things, and considered that the former explanations were largely underplayed.

The Mathematics of Change? That sounded interesting. I had to read on!

But, I must say I fell about when I got to the so-called nitty gritty. Our writer coolly talked about a parametered situation covered by some formula or another, but, merely as an aside, revealed that it was subject to external influences – forces which in a stable situation were undetectable and could be ignored, but which at certain points could overthrow the stability of the “internal” maths-controlled sub-system and destroy it. This may seem, as he obviously thought, as a normal, unavoidable situation, and so it is. But, he clearly failed to realise the significance of his admission.

When a quantitative relation is extracted from reality and fitted up with an appropriate mathematical formula, the context or ground is necessarily dumped. The whole strength of a mathematical treatment is this abstraction of an aspect of reality from the integrated, all-inclusive whole. The method allows of detailed study of a coherent fragment “outside of” the complexity and seeming incoherence of reality as a whole. It also allows the researcher to tap into a rich panoply of universal mathematical forms and techniques that are applicable in a wide range of situations. Now, as inferred above, the chosen maths form for a particular phenomenon is totally independent of the “external” context, as it must be if universal forms are to be defined for future employment. So, the chosen form can give no warnings, in itself, of the form of a catastrophic system failure. Indeed, it is NOT the sub-system that fails. For the sub-system once extracted and treated in isolation is “independent” of the original “context”. That is the power of an abstracted mathematical treatment, but, it is the extended context, including the sub-system, that becomes no longer viable, and a revolutionary change occurs. Now, many abstracted formulae DO, of themselves, give way-out results in extended circumstances. They give zeroes and infinities and similar off-scale results. So these could be said to indicate when the formulae fail. Except that many theories INCLUDE such blow-ups as being the mathematics of actually physically existing entities, such as Black Holes and many similar extrapolations from the maths into “reality”.

Now, how a mathematician can make such system-change upheavals the subject of a discussion based entirely on extracted mathematical formulae beggars belief. If the system just blows up (and remember ALL mathematics is by definition ONLY about sub-systems) then how does the sub system mathematics deal with the event that is determined externally by his own admission? Where does he get the relevant equations from?

Now, I really must not convert this paper into a full treatment of the described writer. That is NOT my purpose. It was brought in as an appropriate preface to the real subject of System Change.


System Change

Now, in this area, it seems to me that there are two distinct and equally important aspects to the area of study. Firstly, it CANNOT be mathematical formulae that deal with these events. They are too limited in scope, and at the same time too universal in applicability. They simply don’t INCLUDE the necessary factors within them. The source of answers must be in forms that DO attempt much wider syntheses. These are the methods of scientic, analogous EXPLANATIONS. The second vital consideration has to be to focus study on the detailed and compressed events that constitute the actual process of revolutionary change. We must study the narrow time slot, within which the changes first begin to appear, then form sequences of temporary intermediates, until some NEW re-organisation, coheres into a different stable system.

We must approach the problem scientifically (not mathematically) and crucially also dynamically!


A Case in Point

In almost all my personal researches over many years, these sort of dynamical overturns are evident, and yet they are generally largely unknown and unstudied.

I will now relate an appropriate case of such studies, though those who have read other papers by the author may well already be familiar with it. To them I apologize, but its inclusion is in this discussion unavoidable.

Some years ago, I was working in what has since been promoted to a full Scottish University in Glasgow. There I got to cooperating, when appropriate, with some of my colleagues in other departments. I helped when I could (mostly on computer programming and graphics isualisations) but there was little doubt as to who was doing the significant contributions (and it wasn’t me!) My colleagues in the work I am about to describe were a research chemist and an Indian mathematician. They were working together on chemical reaction fronts in liquids. I had to ask them exactly what these were, and immediately realised that these scientists were investigating just the sort of dynamic changes that I have attempted to describe above.

Instead of adding the reactive components together, stirring well, then waiting for equilibrium conditions before anything was attempted to ber measured, they instead took the greatest pains to allow of NO disturbances to the natural processes whatsoever. They spent a great deal of time finding what they considered an appropriate reaction. First, it had to be an oscillating reaction, where initially

A + B became C + D,

and then quite soon after a threshold had been passed, and the reaction REVERSED so that

C + D became A + B.

They searched, and found such a reaction, where the products at either end were clearly differently and contrastingly coloured.

So, let us see what happened.

In breathtakingly still conditions, the necessary components were brought into contact. The reaction started, and at first nothing could be seen. As the reaction proceeded a new colouring became evident, not everywhere, but only on the actual reaction front. A line of new colour was being laid down. Subsequently, as you have doubtless already guessed, the reaction finally passed the expected threshold, and began to reverse - this time producing the original colour again. As the process went on and reversed several times, a banded two-colour structure began to unfurl in 3D space, and its form gradually became clear. It turned out to be a Toroidal Scroll. 

NOTE: Imagine a line, becoming a sheet, which itself followed a curved trajectory gradually building up a doughnut shape – a torus composed of a scroll!

This is crucially an example of what is going on in ALL chemical reactions in liquids, but is usually invisible and also never even studied. What did they use to insist upon in my youth? “Stir well and then wait for equilibrium conditions, or your result will be chaotic and uninterpretable!”

Now such dynamical transitions are not restricted only to liquid chemical reactions or even to reactions of other diverse sorts. They occur whenever systems flip over!


Intelligent(?) Crystallisation!

My current work, of necessity, has pressed me into looking at the formation of crystalline structures from solutions or a melt, and quite apart from the obvious chemical, mathematical, and even symmetry contributions, the normal products of crystallisation are NOT predictable in detail. All sorts of aberrations, twinnings and many other “errors” certainly occur. What then is the dynamical situation at the crystallisation “front”? Why is some sort of “seed” necessary, and what ensures (if that is possible) the guaranteed production of a perfect single, coherent crystal lattice? On studying various models of crystallisation, I came across various features that had to occur in crystallisation, at least sometimes, which were, in effect, failures. Several types were revealed theoretically. First, there were the possibilities of alternate stacking forms.

[NOTE: These may not be common, or even possible, in normal inorganic crystallisation, but my work is specifically concerned with re-entrant shapes – forms which definitely are common among organic molecules. Remember even viruses can be crystallised!]

These alternatives could also be incapable of producing extended forms, that could completely and coherently fill space. They could even be only “locally” symmetrical (as in snowflakes), rather than possessing the translational symmetries essential for continuous space filling. In addition, crystallisations could start at several separated centres, and grow towards one another, and these could easily be of different types and incapable of seamlessly fitting together at the interface.

Now all of this does reflect real crystallisation processes, but surprisingly, it is not these messy situations that pose the most telling problems. It is the freak situation of the crystallisation of a large perfect single crystal!

How on earth does this happen? How can every single additional molecule march into exactly the correct place, in the most coherent and extendable way. And how are alternate sites for the commencement of srystallisation inhibited to prevent the consequent problems associated with these? These things surely cannot be wholly achieved by chance, can they?

Let us study what happens as molecules moving about randomly on solution (or the melt form) and then add on to some already existing crystal. Remember, alternative stackings are possible which in the longer run will turn out to lead to aberrations- to the wrong phase, or even in extendable forms leaving unfillable gaps. How do JUST the right options take place? Could it be that the process of crystallisation, molecule by molecule, is not a simple flip? Could it be that there is a transitional period in which the molecules (still moving independently) jostle around the already solid core, ready for integrations, effectively moving in and out from possible attachment sites, along with the other closely situated molecules, until a MINIMAL, or optimum situation is reached, when the actual connections are triggered to commence in the ideal and extendable way?


A Causal Trajectory of Change?

We would then have, once again, a process, compressed in time and space, which contained the dynamic adjustment of optimal crystallisation. Now these are only a couple of instances from my own experience, I am already convinced that such dynamical, micro-scale and short-lived transition systems DO indeed exist. Crucially, we must address the inter regnum between two stable regimes, each of which is generally dealt with by abstracted mathematical formulae, neither of which can in any way contribute to the content of such a transition process – particularly in its causal trajectory.

Analogy & Causality

In the early days of “explanation” historically, there was simply insufficient knowledge and understanding available for a meaningful causal approach. Things could be described and similarities noted, but as to a full explanation in modern causal terms, it just wasn’t possible. But, that did not mean that very useful models could be referred to, in terms of which some sense could be made out of new situations. By far the best way of doing this was to relate the phenomenon being studied to some well understood and reasonably close analogue situation with which the investigator was intimately familiar.

Thus Analogistic Explanation was the earliest sound method. There were “causal” attempts made but they tended to attribute the functioning of parts of Reality to Gods and Goblins, so were hardly either sound or useful.

Analogy, on the other hand, could be very reliable, if appropriate analogies were found, so that even without any reasons for why certain behaviours occurred, the type of system which produced the rich set of factors and behaviours could be identified and a solidly familiar situation used as a guide to what was going on. Without an understanding of mechanisms and causes, the producing system type could be identified and quite detailed knowledge from a good analogue transferred to the area under study. This was not such a way out method. After all early Man was surrounded with things he didn’t understand, but he knew them very well and how they behaved. He was daily called upon to make judgements on what was likely to happen in one of these situations. He had learned to “understand” how these things acted under a wide variety of circumstances. It could be called understanding by familiarity and interaction, even though underlying causes were completely unavailable to him.

Considering this major lack of what we might call “Causal Knowledge”, this method by Analogy was highly intelligent, and when appropriately employed, very effective. Of course, to directly counter pose Analogy and Causality, as if they were fully available alternatives is very largely an oversimplification. As studies and subsequent knowledge grew, these two forms would interpenetrate and the resulting amalgam became very sophisticated, and such a simple categorisation as either one or the other became impossible.

NOTE: For example, let us consider that a certain complex situation was not only familiar but also had been carefully studied and many or even all of its components actually understood causally. If this was subsequently used as an analogue for some new area of study, the result would be extremely well founded, and considerably better than when NO causal elements were involved as in the very early cases.

But, to return to the bottom-most rungs of our ladder of technique, while analogy was dependant only on experience and could therefore be applied at a very early stage, causality was a more demanding beast. As already mentioned Man was always keen to reveal causes from the outset, but had only supernatural causes available to him. To reveal necessary causes as products of Reality itself demanded a great deal more than a seemingly appropriate Myth. The ground for causality was Man’s own capabilities. He caused things to happen everyday of his life. Without this ability to bens aspects of Reality to his needs and will, he would not have survived.

Thus, he HAD to see the world as subject to cause – his own causes in everyday life – and God’s causes when it came to things totally outside his control. But, Man did develop tools and weapons with his own hands, and began to take pride in his ability to cause! Plus his “ability to express in language” and his ”ability to form artistic images”. Such sources clearly refined his “all-powerful Deity” as” Man writ Large”

Man was built for causing and looking for causes.

While his implements were Ready-Mades, a more sophisticated attitude to cause could not develop, but from a surprisingly early stage Man began to construct original and clever implements which revealed design-for-use in himself. So, he was increasingly well equipped to look for and find causes, and the crucial stages occurred when he began to make sophisticated weapons such as Bows & Arrows. Great skill and knowledge was embedded in the construction of these weapons and “causes” were much less religious and much more functional in those sorts of endeavours.

While causes were still “bunched” together with their immediate concrete effects, no profound development was possible. They had to become causes in a wider field – that is, perceived causes in everyday activity had to be seen as applicable in a NEW way. Invention based on understanding of causality opened Mankind’s eyes to the possibilities in using causes creatively. This ultimately made possible the consciousness of sequences of causes building up to very sophisticated results. This was the birth of Reductionism.

This is usually seen “upside down”, so to speak, in that it immediately brings to mind a sort of top-down analysis. But that is typical of Man. It certainly did not arise that way round (i.e. out of analysis). That was a much later development. It MUST have been initially grasped in a “building up” way. Certain causes could be marshalled to produce situation X, and then this new set up marshalled in its turn to produce situation Y. Man began to plan a whole series of stages resulting in a final sophisticated product. In a recent TV documentary, Ray Mears and a Native American from Canada worked together to build a birch-bark canoe from original forest materials. Every stage in construction was conditioned by what was needed at each succeeding stage, so that ultimately hundreds of highly skilled sub-products had to be appropriately designed to fulfil its purpose at the next level. As Ray Mears explained, the final product was probably the finest boat ever conceived of by Man.

Just such activities laid the basis for Reductionism – levels of causes building up to complex results. Only later did it become a means of analysis – where complex situations were investigated to reveal underlying layers of contributory sub-systems – where causes had been marshalled to a complex end.

Now, Reductionism is clearly the workhorse of scientific understanding and is used everyday and in multiple circumstances to explain situations. It would be sufficient, but for one profound thing. Reality is not constructed entirely out of such pedestrian steps. Reductionism involves NO innovation – NO new levels – NO restructuring of the environment itself. Reductionism is ONLY applicable in mechanistic or single level systems – that is the steps in increasing complication are all at the same level. In Reality we have Emergence, where wholly new, never-before existed Levels emerge, which transform the forming circumstances themselves, and make possible subsequent developments that were IMPOSSIBLE before the Emergence took place. The Emergence of Life is the most important example, but such Emergences are Legion, and have occurred millions of times in the development of the Universe. But note, once a reductionist analysis arrives at such an emergent situation it fails. You cannot move through an Emergence to its original producing situation by the crude methods of Reductionism.

Now, surprisingly, you may think, analogy copes very well with Emergence – because it is not attempting to reveal quantitative formulae, but instead copes with explaining the situation by finding similar analogistic forms and processes elsewhere. It takes things as given in real analogies and reapplies the features of a whole system to obviously similar sets of processes in other circumstances. Where formulae blow up when presented with the simplest of Changes of State, for example from solid to liquid, analogies sail through both in verbal explanation and in physical modelling.

New Special Issue: The Loka Sutta

The writer of these papers is not a Buddhist. He is, however, a holistic philosopher, who sees his ancestry as stretching from the Buddha and Zeno of Elea in the ancient world, through Hegel and Marx in the 19th century, to his own attempt to carry the gains made by these great thinkers towards a wholly new form of Science.

This has not been an easy task !

In spite of a commitment to this basic position for almost all of his adult life, the task he set himself constantly generated other more urgent, more basic tasks, and in the end required the fullest possible investigation of the holist position in Philosophy, and the attempt to reclaim Science for this standpoint by a thorough understanding of just how such an all-embracing position could deliver an affective methodology.

It has demanded a series of prepatory works including a new Theory of Emergence, a substantial period of work on Iterative Techniques and Chaos in Mathematics, and finally a return to the Buddha’s Loka Sutta, his foundation for what individuals conceived of as “The World”.

What follows are my first real attempts to reconcile my own philosophical theories with those of that original and great holistic thinker.

Read the issue

New Special Issue: Wave Particle Integration

The idea of Wave/Particle Duality is much more complex than the nature of an electron or of a photon, for in its very conception it localises phenomena that are not actually local.

We are always happier with individual entities, carrying with them their unique load of properties, and interacting with one another, due to both these properties and to “prescribed” Laws of Nature. Any holistic mish-mash of an alternative, with things being changed, or even determined, by their vast range of possible contexts and contributions, confuses us, and is widely condemned as unsolvable obscurantism. So, in spite of evidence to the contrary, we stick-like-glue to our naming, defining and studying of particular entities, and their properties and relations.

But, what if Empty Space were not actually empty at all?

Read the issue here

Supporting Videos:

What Next For Turkey?

Yet another country in the Islamic world is in crisis. Perhaps the biggest country in the Middle East - Turkey - has also toppled into a state of crisis, seemingly over a park being earmarked for development into some sort of mall. Yet, of course, it is much more than that.

The discontent is country-wide, and the usual tactic of the ruling class, a turn to an Islamic state, is again coming to the fore. But though the peasants feel it will help them, the city-dwellers are sure it will take away what they have gained, and instead of the future they envisaged, there could be a retreat to a deprived past. Turkey is truly at a crossroads.

The dictatorial and religious tendencies of the current Prime Minister, Recep Tayyip Erdogan, are clearly opposed by the rising middle class, educated workers and city-dwellers generally, and it looks like another pulse in the so-called Arab Spring - the general move towards revolution for an entire civilization.

Listening to the various political commentators, even those on Middle Eastern TV stations such as Al Jazeera, you would think that the threatened uprising could never happen. Turkey is a democracy, we are told. Half the population are rural peasants that back the Islamist Prime Minister, we are assured, while the other (roughly) 50% live in cities, the workers and the middle class, who are lead by disaffected students, who know what they want, and it isn't an Islamic State! This impasse cannot be traversed! This is what we are told, but, of course, they are mistaken.

A Revolution is always an alliance of differing groups who come together with a unifying common purpose. The red flags in evidence at these various demonstrations are not all Turkish flags, some are emblems of the socialists and communists - the appearance of 'hammers and sickles' proved it. Clearly there is some culture of socialist ideas evident within Turkish society, and hence there may be real revolutionaries amongst them, who can correctly interpret what is emerging on a national scale. 

In Russia in 1917, with a successful defeat of the 1905 revolution behind them, the general consensus seemed to be that with the forced abdication of the Czar, enough was enough, and the vast preponderance of peasants would ensure that no social revolution could occur to take things further. Yet, the Russian revolutionaries knew what was necessary, and they knew that they must win the peasants to their cause, by including their most heartfelt demand in their battle cries. The demand became "Peace, Bread and Land!" - wedded to the demands of the working class there would be a turning over of private farmland into the hands of those that worked it - the peasants. They would own their own plots, and the vast majority of the national army were peasants - they not only were for peace, but would own their own land, and had the arms-in-hand to achieve it.

The leadership of the Turkish people must be won by those who understand revolution, and can present the appropriate demands to unify the peasants, workers and middle class to eject the reactionary government, for a just society.

Victory to the Turkish People!