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A Structure of Diagrams (Part 3) Philosophical Diagrams

SERIES: A Structure of Diagrams
AUTHOR: Jim Schofield


This rather long series of papers are actually the contents of a complete book on Diagrammatic Realisation. Indeed, by the time the whole series has been delivered a couple of years will have elapsed. Nonetheless, as the individual papers each has a clear and separate purpose, they don’t have to be seen as part of the Whole. The range of diagrams delivered in this book is vast and perhaps sometimes quite surprising. Apart from principles of design, such as need-to-know, redundancy and multipurpose forms, there are many diagrams useful in quite unusual areas. The more obviously essential and functional diagrams are those developed for use with electronic circuits, but they range far and wide via hierarchical forms used in complex situations all the way to Music and Dance. These latter forms were developed to aid in both Composition and Choreography as well as in Teaching. A series of highly structured, and carefully organised, diagrams are presented that the author used in the design and construction of a music Synthesizer/Sequencer.
In quite a different area, there are many diagrams connected with research into Tilings (tessellations), to demonstrate how these can be both analysed and created, as well as revealing ideas such as Families of Tessellations.
Perhaps the most surprising are a series of animated diagrams using simple colour cycling which can deliver otherwise impossibly complex forms for analysis and development. A whole section is dedicated to to Music, and particularly to open tunings for the guitar, but also including new notation systems for finger picking styles of playing. Finally a whole range of music aid diagrams are introduced for use in both Composition and Improvisation.

One particular chapter shows how quite difficult 3D problems in the stacking of comples, re-entrant strands to fill space were both tackled and solved. The Geography of Dance works and their dual use to also include access to multimedia resources is also fully
described. Another area connected with Dance shows the design of special Parametered , animated figures to use superimposed upon successive frames of a dance video to capture movement for future analysis and use..
Finally among these special aids, is one for superimposing sequences of position on top of a moving dance video to communicate the real dynamics of movement, via precursor and subsequent positions. Rudolf Laban’s 26 orientations in space around an individual dancer which he used both in his famed Dance Notation and in his many Scales and exercises was captured into a polyhedral aid – called a Laban Pure Form, which was produced in both a series of desktop models and even a remarkable step-inside form, which proved very effective in many alternative uses. Philosophically useful diagrams used in explaining the role of Abstractions in human Thinking are also
included, as are a series of abstract mathematical diagrams which could be used in creating useable models of aspects of Reality. Finally a chapeter considers how diagrams can help with problems of Cosmology – particularly in the modelling of the actual “progress” of the Big Bang. Even maps developed for use in directing marketing have a chapter of their own....


1.These are Philosophical Diagrams, developed by this author to aid in the communication of complex ideas, and because of this he is ideally placed to explain them.

2.They are not mere illustrations of ideas in an alternative form, but were designed as essential tools as part of a polemic against the current philosophical consensus in his area of study – Science.

3.Because they deal with Philosophy, it has been necessary to deliver, both in words and diagrams, means, which show relationships, and whereas the overwhelming tendency in this area has been to do this solely by means of Equations, a wider and better means was required.

4.The process commenced with attempts to deliver the Processes and Productions of Abstraction, and here the whole trajectory of that effort is delivered.

5.Crucially, such diagrams would have to deal with both the USE of abstractions, and their crucial role in EXPLANATION.

6.This had to be a new kind of diagram, and as this paper shows, went through a whole series of forms until an adequate solution was found. It had to include both Processes (usually as “arrowed lines”) and Products (presented as labelled circular areas)

7.The main aim of these diagrams was to identify the different processes & productions associated with Science, on the one hand, and Mathematics, on the other. It was clear from the outset that these were very different and definitely separate.

8.The basis of everything illustrated has to be Reality, as the source & confirmation of all the associated abstractions. From this starting point all conceptions had to flow and be validated by frequent returns to this primary source.

9.Categories such as Objective Relations, Models and Equations had to be related, as did processes such as The Scientific Method for confirmation, extension or rejection of the Models.

10.A clear split between Explanatory Models and purely Formal Models was evident, and the process had begun. But the first effort was clearly not good enough because it delivered only what was already known.

11.The next stage attempted to deal with repeated use of the abstraction processes, and how these allowed more general (on the one hand) and more universal (on the other) extractions from evidence in Reality. Interestingly, the term Coherence was shown to be different in Explanation from its role in universal Equations.

12.Further diagrams separated out the Scientific Method and the crucial process, which I have termed Mathematical Speculation, which centres most developments on Equations as source rather than Reality.

13.Finally, I present the culmination of these studies with a diagram in which the ground of everything – the background of the diagram, is Reality. And MAN is positioned at the centre as the source of all processes. Between that thinking initiator and Reality is a ring containing all Productions (abstractions), and between Man and these Productions via Reality are the actual Processes.

14.The success of these diagrams was not a formal solution to a problem of representation, but HOW the diagram can be used in tracing what people are doing with their thinking and arguments.

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