A New Holistic Iterative Method?

Henry Moore in his studio. The best artists seem to use a form of Holist Iteration as an investigative method.

Prelude:

What absolutely must be included here as the basis of a determined Holistic Stance, is to replace the most often assumed yet always-significantly-misleading consequences of the usually unconscious Pluralist Stance in all our methods.

And, that inevitably means removing any assumption of eternal Natural Laws, and instead, recognising the alternative of a whole set of multiple, mutually-affecting factors, which are not only changed individually by their accompaying-context, but reciprocally by also modifying that context too.

Permanently-fixed, natural kaws were an historically- necessary simplification, in order to even begin to understand Reality. Clearly, Plurality was an attempt to adjust Reality to get a handle on it - to get approximate values, from a simplified law.

But now, we absolutely must adopt new techniques to better reflect the true interconnected nature of Reality - one of these must be Iteration.


Iterative Methods:

There is a key problem in attempting, as I do, to develop an Iterative Method, from a measured data sequence alone, especially if we attempt to do it without any assumed form of model, for a relation supposedly- connecting those data points, as has always been the case in the usually-employed iteration techniques. For, without some sort of model, there seemed to be no way of reflecting the nature of the factors that cause the trajectory revealed in those data.

Now, in dealing with this situation, it is essential that several things have to be made absolutely clear about the usual iterative methods.

They always use an Ideal Form, taken directly from Mathematics, as a basis, which had then been fitted- up to those data, by multiple substitutions of them into it, to give a set of simultaneous equations, in the constants of the general form, which can then be solved. The result is still the same general Form, but persuaded- to-approximate to Reality, BUT only within-the-range from which those data were taken.

They then “re-structure” that equation geometrically- upon-a-graph into a set of iterative-forms. Now, such a re-structuring involves a major geometrical and transformative use, because, it isn’t merely a manipulation of the ideal equation. It is actually the use of that formula in geometrically-finding a consequent set-of-forms - one for each variable, that can use a single-known-point, and substitute from it into these derived iterative forms to find another single point, and, thereafter, further points, with each one derived from its predecessor.

And, the iterative forms so derived never change!

Being based upon Geometry-in-Graphs, they are unavoidably pluralistic: for the separation of variables into distinct directional dimensions, necessarily excludes any mutual influences they might have upon one another. So these iterarive forms also perpetuate Plurality.

They are fixed, but their repeated-use always gives new points, but always some distance from the “known” point used, so that the action moves rapidly across the whole range of the “driving” function’s possibility space (along with the usual drift as with all such iterative techniques).

Remember, absolutely nothing new has been added to the original source equation, only-the-means-used to access the sequence of generated points, delivered one-at- a-time. And if, as I am convinced, that original formula is NOT the deliverer of the sequence, but a simplified and idealised approximation, then all its short-comings MUST inevitably be carried over into the iterative forms derived from it, and added to by the effects of iteration itself!

Now, the reader is certain to ask why do these forms sometimes deliver things closer to Reality than the original source formulae? It is indeed an important question!

But, as the only significant change, in the actual plotting, has been the zigzagging-about the whole range of that ideal function, then that, plus the iterative drift, must be what is adding something extra, which can reveal something that was not there in the original idealised equation.

But, that method can surely only be some sort of purely- pragmatic trick. It certainly isn’t here taking us ever- closer to a definitive set of actually occurring situations, but just others in similar-but-different positions, in well- scattered general areas. They are certainly not due to the real physical causes (which are never even mentioned, never mind considered, but only due to our chosen strictly formal methods).

Clearly, though pragmatically, it is also only when our purposes can be at least partially fulfilled by such frigs, that we will use them. But, if our purpose is instead to better understand WHY things behave as they do, then it can only mislead us away from that valid, and indeed, absolutely necessary intention.

Let me re-emphasize, there is the important point that current iterative methods are always pluralistic – just like the original equation from which the iterative forms were derived, it assumes the same additively-arrived-at formal “cause”! And, such will be, for the very same reasons, significantly misleading.

But no Real World phenomenon is driven by a single factor: the general situation will always include many different factors, and crucially, if a holist stance is taken, instead of a pluralist one, then these factors will all affect and, indeed, change, one another to some extent.

Absolutely no other factors are included in the usual iterative methodology – it uses only ONE. So, what should be down to the hidden mutual affects of all the other factors involved, is here due instead to a rigged-up version of the usual method.

And, here it isn’t the actual-contributions, but something- else that may deliver something “similar”.

The Alternative:

So, it is suggested that we address these problems, instead, through the use of Recursion, in addition to the use of real points, and absolutely none of the usual pluralist and iterative methods of the past.

With each new measurement, we start by using Difference Methods (or something similar) to reveal what powers of variables are appropriate in the most general polynomial Model. Then use our data again, but now in the usual way to find the still unknown constants of that model.

So far, this sounds like something already used in the past, but there is a significant twist! We do not stick with that form throughout.

So, instead, we now recursively do the steps all over again, including the next measurement made, and repeat the full set of processes, not only with this, but thereafter with every single new additional measurement made.

What will happen is an evolving form, changing with each new addition.

Exactly what the most general form would be, may begin with the assumption of a polynomial. But, if the evidence is against that model, we could add further non-polynomial terms. The crux of the method then becomes the comparison of a predicted location with the real measured one, and a subsequent judgement as to what changes in the adjusted general form might be required.

The original idea for this method was conceived of as the measurements being taken as the body in question was moving (as if we were the riders on a rocket in Space). But, of course, a full, extended set could be achieved, before any fitting up was attempted, and in some complex circumstances, where many dominant influences could regularly come-and-go, for then this method will come into its own.

Indeed, the processes of the method could be carried out completely after the Event, and once sufficient had been processed to get some sort of form, all subsequent positions could be associated with its own version of the form. Also, each new, as yet unprocessed position would be predicted from the current version of the form.

Studying the varying forms could tell us more about the changing-real-influences affecting an overall form, than one that is both always simplified and idealised.

Postscript:

Now, the reader must appreciate that what is being attempted here is entirely new!

First, it rejects Plurality as the current basis for such pragmatic manipulations.

Second, it is attempting to indirectly include aspects of Reality that are usually excluded.

Third, it is purposely recursive, as in the Buddhist Loka Sutta, as a means of constantly checking upon its own validity.

It will most certainly NOT be the last word in this area: it will take some time to break ourselves from “If it works, it is right!” - the credo of the farmed situations that perpetuate Pluralist Science.

This paper was published as part of Issue 62 of SHAPE Journal entitled The Whole and the Part.