The Fractal Myth of Scale Invariance
and the conclusions it reveals for Natural Law
Look carefully at the following animation and extract what you think it demonstrates.
It is in fact a movie based upon a Fractal Form resolutely chased, level-below-level, as far as you might want, which, in this delivered world, can be repeated literally forever. Can we draw any conclusions from this demonstration? Does it make us think differently about our World?
Yet, it is certainly NOT about our real World!
It is, instead, an exploration of another physically-non-existing and, indeed, a wholly non-exist-able World, which we can artificially construct, and even display dynamically, entirely from formal elements selectively extracted from our World, but, absolutely-crucially, under a set of majorly affecting constraints, and extensively carried through a range of formal changes (totally unobtainable in our world, but achievable here) to deliver this video.
It is possible in that World, allowed by such a construction - the World that we term Ideality- the World of Pure Forms alone, which is, of course, the realm of all of Mathematics!
Now, the viewer may well be wondering why I am delivering this piece: what on earth is my purpose? Surely no-one would consider that the above clip, in any way reflects Reality-as-is: it is clearly an entertaining infinite construct - a journey into a constructed world!
But, it is, nevertheless, based upon a formal equation.
And, in our world we depend, all the time, upon such formal equations as the valid embodiments of eternal Natural Laws, extracted from our world in highly constrained and controlled situations.
There can be no doubt that these too exist-as-such only in that World of Ideality. And, Reality and Ideality are very different Worlds! Though Ideality contains Forms, and Forms alone, Reality also contains Everything Else, including all the physically existing Causes for how things behave within it. So, can formal equations from Ideality alone be sufficient to predict real world developments?
The answer surely has to be a resounding ,"NO!" Yet technologists, using such equations, can make it happen!
Do they just go into the real world, get the required stuff, and apply their equations to it? Of course not - for it would always fail!
Embedded in any production process is a great deal more than a formal equation - everything else, in a series of separate processes all with the correct substances, conditions, processes and their requisite equations, must be involved in each tightly controlled stage, to finally produce something like the proginal intension.
YET, what do theorists use to extend their theories? They stand at their blackboards, or scribble on paper, using Formal Equations alone!
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Benoit Mandelbrot at the blackboard |
To explain it to you, they just give you their equations - as the Laws-determining-what-will-happen! They manipulate their Laws to predict new possible outcomes, which they could never achieve without the technicians discovering all the concrete requirements absolutely essential to RESTRICT the real world outcome to that "required theoretical objective".
But, and here is the crucial difficulty, in Sub Atomic Physics and Cosmology, the theorists have abandoned physical explanations as self-kid, and now rely solely upon their Formal Equations alone.
So, what has this done to their "Science"?
Now, these words are not those of some uninformed outsider, indulging in his profound ignorance of what the fully qualified experts can do. On the contrary. I am, primarily, a qualified physicist and mathematician. I can do all this stuff, and have been doing so for many decades.
But, my many involvements extend greatly wider than these currently severely-restricted areas, and, crucially, include significant work, in many other disciplines, where I contributed expert understanding and skills in Computer Science and Systems Analysis - finally ending up as an expert in Computers-in-Control.
To pull all this together I have spent the last decade studying and contributing to Philosophy, so rather than an uninformed outsider, I am a very well-informed insider. And, have also been involved in a trenchant, philosophical evaluation, and, indeed, criticism of my professionally qualified areas of Physics and Mathematics. And, to cap all of this I spent a very profitable time assisting the excellent mathematician Jagan Gomatam with his investigations of iterative forms of specially adapted versions of Van der Pol's Equations applied to the beating of the Human Heart, and involving the Mathematical Chaos - closely related to the Fractals at the beginning of this essay.
So, my purpose is to accurately-position scientific investigations, AND their claimed-to-be eternal Natural Laws, in their true relation to actual Reality-as-is, and how we get them to both deliver our objectives, and allow us to interpret what they deliver.
Surprisingly, we neither investigate Reality-as-is,
But, and here is the crucial difficulty, in Sub Atomic Physics and Cosmology, the theorists have abandoned physical explanations as self-kid, and now rely solely upon their Formal Equations alone.
So, what has this done to their "Science"?
Now, these words are not those of some uninformed outsider, indulging in his profound ignorance of what the fully qualified experts can do. On the contrary. I am, primarily, a qualified physicist and mathematician. I can do all this stuff, and have been doing so for many decades.
But, my many involvements extend greatly wider than these currently severely-restricted areas, and, crucially, include significant work, in many other disciplines, where I contributed expert understanding and skills in Computer Science and Systems Analysis - finally ending up as an expert in Computers-in-Control.
To pull all this together I have spent the last decade studying and contributing to Philosophy, so rather than an uninformed outsider, I am a very well-informed insider. And, have also been involved in a trenchant, philosophical evaluation, and, indeed, criticism of my professionally qualified areas of Physics and Mathematics. And, to cap all of this I spent a very profitable time assisting the excellent mathematician Jagan Gomatam with his investigations of iterative forms of specially adapted versions of Van der Pol's Equations applied to the beating of the Human Heart, and involving the Mathematical Chaos - closely related to the Fractals at the beginning of this essay.
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| Van der Pol style oscillator |
Surprisingly, we neither investigate Reality-as-is,
nor use our extracted Laws in Reality-as-is!
For, our objective is to somehow extract, from a Complex and Real World, individual, separated-out and entirely formal (i.e. quantitative) relations, and then apply them to some desired end.
And, neither of these are possible in Reality-as-is!
The relation only actually exists, as such, in Ideality- the World of Pure Form alone! So, it is clear that a location in Reality will have to be significantly transformed to become as close as possible to Ideality.
And, this is achieved by:-
This approximates that purposely-farmed-locationto what normally only occurs in Ideality, which we term - a forced conformity to the Principle of Plurality.
And, in such a situation, the relation, between the two remaining variables, is usually immediately evident, and can have a purely formal ideal relation, acquired from Mathematics, fitted-up to the obtained data set, to deliver a formal equation, designated as an eternal Natural Law!
But, there is a problem. It will never work in Reality-as-is! It can be made to work, but only if the exact conditions of its extraction are replicated for its use.
So, Fractals, and all that jazz, do not, as such, extend our reach in Reality, but only in Ideality: what they do is extend what we have in Mathematics, and are therefore merely extensions to that discipline alone. They have nothing to tell us about reality.
For, our objective is to somehow extract, from a Complex and Real World, individual, separated-out and entirely formal (i.e. quantitative) relations, and then apply them to some desired end.
And, neither of these are possible in Reality-as-is!
The relation only actually exists, as such, in Ideality- the World of Pure Form alone! So, it is clear that a location in Reality will have to be significantly transformed to become as close as possible to Ideality.
And, this is achieved by:-
- the isolation of that location,
- and the removal of as many factors as possible,
- along with the holding of certain others constant,
- while leaving only the relevant variable savailable,
- for the variation of one, and the measurement of the other.
This approximates that purposely-farmed-locationto what normally only occurs in Ideality, which we term - a forced conformity to the Principle of Plurality.
And, in such a situation, the relation, between the two remaining variables, is usually immediately evident, and can have a purely formal ideal relation, acquired from Mathematics, fitted-up to the obtained data set, to deliver a formal equation, designated as an eternal Natural Law!
But, there is a problem. It will never work in Reality-as-is! It can be made to work, but only if the exact conditions of its extraction are replicated for its use.
So, Fractals, and all that jazz, do not, as such, extend our reach in Reality, but only in Ideality: what they do is extend what we have in Mathematics, and are therefore merely extensions to that discipline alone. They have nothing to tell us about reality.
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