Coherence from Incomplete Sequences: Introduction

This short paper will appear in Issue 12 of Shape Journal. It is only part of the topic of "informed speculation", which is a vital component of all scientific hypotheses, and of theorising in relatively new areas of study. It is not usually at all pluralistic, but takes reality as it is, and constructs reasonable and well informed explanations where they are sorely needed. The reason for the limited nature of the coming paper is that the more obvious elements involved are already well-covered by many previous papers.

The crucial feature of the relationship of Relative and Absolute Truth, is always treated early on in criticising any demand for Absolute Proof, beloved of all mathematicians, which is only very rarely possible in concrete Reality, so that a "lesser" demand for objective content is the proper aim of all Science. But, we must use Logic where it can be useful. Not in the Absolute Truth sense, but in the elimination of the impossible, and very unlikely scenarios to reveal the most reliable extractions and conclusions.

The paper addresses a couple of ways in which partial evidence can, none-the-less be sufficient, and how ever-available loops of correlation can home us in ever closer to the truth we seek.

Issue 12 will be published in 3 weeks time...

Issue 11 of Shape

Read it here

The Theory of Emergence - Coming Soon!

What is an Emergence? It is a special interlude of major qualitative change, in which a new level of reality is both generated and maintained. Such a Level is not a mere re-organisation, but involves wholly new entities, properties, relations and even Laws which did not exist previously. The template for such an Emergence has to be the Origin of Life on Earth. Only after the creation of the first living things did they inhabit a new Level of Reality, with its own laws. We call this collection of laws Biology, and institute a whole new science with its own scientists. But this, though without doubt the most important Emergence was certainly not the only one. Every science has had its own birth via an Emergence, and indeed from the Big Bang onwards all significant qualitative changes were created within Emergences, as have been all since that event.

As so many of my philosophical ideas revolve around this theory of Emergence, we have decided to publish a special issue of the Shape Journal, dedicated to its explanation and exploration. Watch this space...

Building A Consensus

Nice diagram from New Scientist, but I think it communicates more than the original authors intended. It demonstrates how the consensus in a particular research area is established and maintained. I'm currently writing a paper on this subject, and will post it as soon as it is ready...

Paths to Chaos or Paths to Glory: Introduction

What is the natural trajectory of change in Reality? Do we, in accordance with the Second Law of Thermodynamics, consider it to be a constant downhill descent into oblivion, or is it "built-in" that it should naturally evolve into ever-more potential-filled and richer forms? Now, for highly constrained subsets of reality, the answer is clear. They will indeed, if left to themselves, deteriorate into chaos. But what of unfettered reality as a whole, with no imposed constraints and added purposes, what will be the natural outcome there? The evidence is all around us. It will evolve!

But why does this remarkable second case happen? What is the engine of such developments, and what determines the trajectory of that process?

In order to address these questions this paper attempts to address reality as it is, without Mankind! But to do so, we must bury our usual methodology, which sees every discovery in terms of how we can exploit it for our own ends. We must instead become observers and interpreters, and never users. We must develop what we are clearly already aware of, but rarely pursue - disinterested Science.

The evidence for the evolution of Reality is undoubtedly legion, but as to what factors drive this development, we do not know. The tempo of such changes when measured with our 'clocks' seems to be zero - that reality is entirely stationary and unchanging.

Now a single tiny and isolated particle of Matter in a completely empty space cannot display, or even have, any properties at all. We have to realise that such things can only appear in aggregates. It is only when many such fragments come together that we not only get bigger pieces, but also qualities begin to be evident: the fragments relate to one another. And these qualities will be different at every stage of the enlarging aggregate. They will not only change in magnitude, but also in properties. Initially, then the property of Gravity - the mutual attraction of particles of Matter for each other, must be the initial drive. But notice, we could extrapolate all the way from the very first tiny aggregations seamlessly to a single all-consuming Black Hole into which the whole Universe could be unremittingly drawn, to vanish completely back up its own Physical Singularity! That is the simplest extrapolation of Gravity. But, of course, we know better. Vast aggregations collapse Matter into ever closer forms, until in the largest aggregations they burst into stars. Millennia of studying the Heavens have revealed a whole series of different forms of stars which clearly form a sequence of phases, and even include cataclysms such as Supernovae.

Clearly, apart from the observable evidence in the sky, there is a more complex and detailed trajectory involving many other modes or phases. And what is crucial about these phases is that they change the game. These natural developments transform their own producing ground every single time! So how do such a variety of very different and indeed new forms get driven into existence merely by Gravity?

Now, one aspect of the forms involved is also crucial. There seems to be an alternation between long periods of relatively slow-moving stability, and very short interludes of radical change. Such a trajectory implies that other forces are also being generated, and grow to such a point that they always undermine, and then overthrow, the current stability, only to, at a later time, surrender to their own, different, stability-enforcing system, thus moving into a new period of stability.

If we had a mechanist, purely bottom-up Universe, such things could never happen! This evidence seems to suggest that Reality is NOT pluralistic (the bottom-up approach), but is, on the contrary, entirely holistic, involving causalities in all directions. This means that the possibilities are increased, because the ground is always changed by its own products. As soon as a product (such as free Oxygen in the Earth's atmosphere) is produced in sufficient quantities, it changes future possibilities into features that were impossible previously.

Elements of such a view are already occurring in our thinking about the world, but they are swamped by the stamp of our own purposes for USE!

This series will continue in Issue 11 of the Shape Journal. Watch this space.

Issue 10 of Shape

Read it here

Order Out of Chaos Introduction

This forthcoming series of papers (Issue 10) under the general title of Order Out of Chaos? were commenced in 2008, and bear the stamp of when they were written. They do not represent the developed, current position of the author, but nevertheless, it was decided that they must be included in the journal as a necessary preparation for the continuous stream of rapidly developing contributions that have been produced ever since. Also, it is very clear to me that this is perhaps the most important area in modern science, and will not be delivered by a single theorist, and I'm keen to see other contributions in this area.

Firstly, the erroneous claims of the mathematicians of Chaos that their new area will ultimately contain the explanations for crucial Emergences such as that of the Origin of Life on Earth, must be debunked. Formal Mathematics cannot explain anything: it merely describes, never explains, and hence can never address such an important question. Secondly, these studies must actually investigate what really happens within such events as Emergences - NOT as mathematical forms only, but as Real Science. Since when did we credit our tools with creating the masterpieces by themselves!

The question, which has motivated this author for over 15 years, is considered to be by far the most important one in Science, which is now regularly coming up against the consequences of its own basic assumptions, tenets and even "beliefs". The chaos that is today's sub-Atomic Physics, is finally heading for its ultimate demise at its own hand. The "final proofs" of its current theories expected from the experiments on the Large Hadron Collider, will not be forthcoming. Indeed, by far the most likely outcome from this mammoth experiment will be an evident failure in this regard, causing a general flight from maintaining any trust in these odd believers in Parallel Universes, Physical Singularities, Dark Matter, Dark Energy, time flowing backwards, and even colliding Branes producing our Universe out of precisely Nothing. They will finally, and justifiably, be laughed out of Court.

It was decided, therefore, to include these older papers as an introduction to the studies into Emergence by this author. For though this is an important area, it is very little supported within current research, outside of the denizens of the Santa Fe Institute, who think that Mathematical Chaos will alone provide all the answers necessary. There appear to be very few who agree with this author. Nevertheless, the line of research that will appear ONLY in the Shape Journal, has recently arrived at a new Theory of Emergences, which for the first time goes into the various phases of such an event. At the same time, such vital research cannot be a one-man show, and even hostile criticism will help refine these new ideas. Of course, even better would be the contributions of other like-minded experts, who are not merely mathematical physicists, but true explanatory scientists, who also realise that the study of Emergences is the crucial area in the absolutely imperative re-establishment of Real Science as the only sound path towards Truth.

Don't miss Issue 10 of the Shape Journal to read the first instalment of this paper.

Chinese Stamps for Sale

Not sure if any of my regular readers will be interested, but thought I'd mention it anyway!
I'm currently trying to sell my large collection of Chinese Stamps

Visit www.chinese-stamps.com to find out more

Issue 9 of Shape

Read it here

The Heroic Failure of Mark Rothko

 "...No figurative content is either discerned, or was intended, and though most people “see” windows and doors to somewhere (?) or even nowhere, the real content seems to reside in amazing texture and meaningful “detail”. The substance of the works seems to reside in the almost furry or “blurred” edges of his deceptively simple areas, which seem to articulate directly and sensitively into adjacent “new space”, which is itself packed full of its own colour-based activity.

We seem to be directly discerning real and complex feelings by abstract visual means alone..."

Continue reading...

A Three Dimensional Problem

Introducing the Soma Strand

These images are from a paper forthcoming to the Shape journal, as part of the "A Structure of Diagrams" series. Here diagrams and models were used to solve a complex three dimensional problem based on tessellation.

This case was to do with a self designed form which I had named the Soma Strand (after Piet Hein’s “Soma delicious Soma”).

Long before the tessellation problem outlined above, I had to design the original form. This, in itself, took a great deal of time and model making, but what finally emerged was an infinite strand, with a re-entrant form, and congruent, singly re-entrant hexagonal faces (with 90o and 270o angles only). It soon became clear (after making a bundle of these strands, that they definitely tessellated to fill three dimensional space completely.

Careful model-making had established this exciting property, but, it must be said that cardboard, glue and bits of wooden dowling (without which the strands were impossible to construct) are not the ideal materials to facilitate detailed studies in the area of volume filling stacking, particularly of such difficult (and indeed infinite) strands. Attempts at solving the problem using 3D graphics packages were soon abandoned, as these so-called tools, may deal with three dimensions, but are generally NOT designed for meaningful and revealing visualisations essential to the designer and creator of new things. You just couldn’t see what you were doing, and the figures soon became unintelligible. In addition to the complexity, that package had not helped me to adjust units effectively and lock them into the required precise positionings. Attempts at colouring to get some order out of the chaos only led to an obscuring of one part of the figure by another. I knew exactly what I wanted to do, but those facilities were simply not available.

As a last resort, I went all the way back to an ancient (and primitive) 2D drawing package that I had used for many years (De Luxe Paint 2).

Read More

Issue 8 of Shape

Read it here

Domains & Quilts

An early investigation of Man's Abstraction of Reality. See my final definitive Abstraction Diagram

The Superstructure and the Base

This philosophical area is a profoundly difficult, yet at the same time, an extremely crucial one.
It cannot be dealt with by a single paper, or even a series of them. It is about our fundamental assumptions concerning the World about us and our understanding of it. It inevitably therefore will display the unavoidable errors that will occur when one part of Reality (Mankind) attempts to explain either that all-embracing World, their own automatic origin, or finally their current place within that World. Clearly, no straight (or Royal) road to Knowledge can be viewable, or even available from within the continuing process itself. Indeed, Man has to promote himself outside of the process in the position of a God, in his attempts to address it. There is no way that the bulk of his attempts will be anything other than fictions and rationalisations. And from the exact same ground, any condemnations of Mankind’s errors in this area will involve a similarly arrogant super-promotion.
Such a trajectory was, and still is, unavoidable, and every gain made in this gigantic task will, of course, be partial and propped up with many formal inventions. How could it be otherwise?

But, that does not mean that Mankind should, “Give up now, you’ll never do it!”
On the contrary, it is the most important purpose ever generated by this evolving World.
So, any paper commencing the task of looking at our assumptions and methods will have to start somewhere, and wherever we choose will immediately and inevitable reveal contradictions. But, that is still the only way we can remedy our misconceptions and improve our attempts. What else can we do?

This author commenced writing about such questions some 14 years ago, under the title, Levels, and it is clear that the currently existing Universe is NOT a single monolithic structure. Not only is it spatially divided, but it has also generated a whole series of Levels of Existence, each with its own entities, properties, relations and even laws.
Life is just such a Level, as is Consciousness, and the real task will have to be addressing these innovatory changes of Level, as well as explaining the more mundane relations within particular Levels.

Nevertheless, we must make a start, and perhaps the best issue, which cannot but expose the essentials of such a World, must be that of The Superstructure and The Base. The main criticism of Marxism by its conservative opponents was that they could not even explain their own existence, never mind that of the rest of Reality.
So we will start there!

In this current period SHAPE is involved in publishing a series of papers addressing these and related issues. They include:-

The Second Law of Thermodynamics
Formalising the Heavens
Truly Natural Selection
The Superstructure and the Base
Order Out of Chaos
Paths to Chaos or Paths to Glory?

These papers were either purposely selected, or specially written, for this period in the establishment of SHAPE as a new kind of Journal.
It will NOT be re-hashing old ideas, but on the contrary making original contributions on all the questions that it addresses. It will, therefore, seek to represent the cutting edge of research, and though most of the early contributions will be from the pen of Jim Schofield, the whole idea is to generate a whole school of contributors keen to tackle these crucial questions.
Instead of playing the role of a conduit for the publishing of all and any papers on these issues, it is intended to deliver coherent, comprehensive and new contributions to a 21st century view of the World!

Mankind's Bubble of Abstraction

Enlarge Diagram

The Processes And Productions of Abstraction

The version of the diagram that is shown here did not finally reach the state you see until about four years

ago, but it has ever since allowed me to pursue all other studies from an objective standpoint.

It is, of course, by no means the last word on this area, but it has most certainly been for me the first and

dependable one.

To trace the increasingly important sub-processes involved in Mankind’s abstractions, we must start at

Process I (observing Reality) to Production 1 (observations), as on the diagram, and then continuing anticlockwise

around the circle...

Continue Reading

Diagram by Jim Schofield

Graphic Design Mick Schofield

(Belated) Issue 7 of Shape

Read it here

Issue 6 of Shape

Read it here

Eureka! It's Populist Science

"...On reading the current issue [Eureka Magazine, The Times, Nov 5 2009] from cover to cover, I was surprised to find that really nothing new was presented there at all. It reminded me of New Scientist, but whereas that journal is aimed at “scientists” (supposedly), this one is certainly aimed at the “interested layman” in mind instead. And one of the characteristics of such disseminations is that they are totally subservient to the “experts”.

No longer do we have hostile antagonisms by arts-types and other non-believers, but in the new attitude of embracing Science in all its current glory, all the participants merely swell the ranks of the consensus merchants, who “wonder” at the might and power of Big Science as propagated by its producers. This removes that absolutely vital criticism which Science has always needed to continue to progress, and which is now, more than ever absolutely essential, as its ageing philosophy and consequent methodology becomes increasingly inadequate to cope with the major unanswered questions that are daily arriving at the top of every agenda..."

Read the rest of this article

The Fruits of Asymmetry

Coxeter - 'n' dimensional tilings - assuming maximum symmetry

A Penrose Tiling - concerned with near symmetry cases

Tessellation utilising re-entrant polygons
(in this case using a singly re-entrant asymmetric hexagon - or "L tile")

"...What was evident to me was that the essential component in these formal investigations was Symmetry! While my colleagues in Physics were totally wedded to complete maximal Symmetry (and indeed Super Symmetry), I was finding that instead of the limited numbers of tilings and crystal forms that were available to them, I was finding (in 2D at least) a seeming infinite complexity of Forms. With maximally symmetric units, these all funnelled down into a minimal set, but with re-entrant forms (the first deviation from maximal symmetry), and various regular asymmetries, the possibilities were vastly increased.

Indeed, from monolithic tilings (using a single basic unit in a single way) there occurred a wide range of hierarchical forms, which could be different or mathematically similar at each succeeding level."

To read the rest of this paper, click here

Diagrams on the Science of Music

One of my many music theory diagrams - this one showing the family of C tunings on the guitar. More images and possibly some papers to come...