38. A central heresy.

The formal inversion theory suggests that in due course, on the accumulating evidence, our traditional and much-cherished one-truth thinking conventions will need to be replaced by two-truth thinking conventions.

One helpful way of introducing this heretical idea is to consider the reaction of you, the reader, to the foregoing argument for the theory. When the apparently similarly structured brain forms and mind forms involved in the theory were placed before you (in a deliberately 'broad brush' introductory way) I think it highly likely, on historical evidence, that you adopted one of two main reactions, depending on which of two pivotal thought processes you prefer.

If in general you happen to be more comfortable with your breaking-down than your building-up thought, like say Aristotle, Isaac Newton and Francis Crick (as suggested by their publications) you will have probably found the theory credible or at least arguable and fairly obviously so. Further, you will probably regard it as another small contribution to our brain-based understanding of the mind. Further yet, you will probably regard the mind itself as simply the brain at work and thus as a legitimate subject for scientific study.

If however you happen to be more generally at ease with your building-up than your breaking-down thought, like say Plato, Gottfried Leibniz and David Chalmers (as suggested by their publications) then you will probably find the theory incredible and/or unarguable and fairly obviously so. Further, you will probably regard it as another small contribution to a brain-based misunderstanding of the mind. Further yet, you will probably tend to envisage the mind as involving some dimension beyond the brain at work.

The two mindsets may be used to illustrate the central heresy. The formal inversion theory suggests:

• that neither of these attitudes represents sole truth to the other's untruth,


• that both are correct in that they are natural, complementary, mutually inverted, polar products of the same brain wiring, and


• that there is abundant scientific and philosophical evidence that is compatible with such suggestions.

A recommendation that we replace our traditional one-truth thinking conventions with two-truth thinking conventions is at first sight (like all good heresies) deeply shocking -- and it gets worse. A corollary is that if such heterodoxy became orthodoxy (as heresies have a habit of doing) various famous two-way confrontations in the history of ideas would change their character. They would no longer have the status of Central Problems -- occupying some of our best thinkers in trying to decide which of the persistently double answers is the correct single answer. They would instead assume the status of Obligatory Dualities, warranting new kinds of investigation beyond their necessarily double nature.

This brings us to another intriguing aspect of the central heresy -- and one that amounts to a reinterpretation of philosophy. The formal inversion theory suggests that philosophy owes its emergence as a discipline and its broad structural features to the specific wiring patterns that have been briefly described in this introduction. The emergence of philosophy seems to have been driven by our human attempts to derive single truths from thinking equipment that appears necessarily (anatomically) double and circular -- the double cycles being mutually inverted.

One of the important issues raised by the last paragraph is why humans have continuously expected single answers to philosophical questions despite continually obtaining double ones. A suggested reason is that everyday life requires us to make firm decisions. Double answers to questions such as 'shall we have lunch?' have proved unhelpful. It seems understandable that attitudes born of such daily experience might have overlapped into philosophy. However when it comes to typical philosophical questions about value, knowledge, and existence, we appear less constrained than when arranging lunch. There seems to be no logical imperative that can insist on single answers to philosophical questions and countless double answers in the evolution of philosophy (such as the Platonic-Aristotelian described below) vividly attest to this.

Anyone who has studied Western philosophy is familiar with the double-stranded nature of its development. The contrast between the two strands is often seen as the heart of the subject and so was used by Raphael as the focus of his The School of Athens, pictured here.

One strand is epitomised by Plato (pointing upwards) who urges us to build up our thinking into ever more comprehensive and thus allegedly higher ideas.

The other strand is typified by Aristotle (gesturing downwards) who advocates that we break down our thinking into ever more fundamental and thus allegedly down-to-earth ideas.

It has long been scientifically recognised that the broadly double philosophical pattern bears a striking resemblance to the broadly double arrangement of our working brains. Although both sides of our brains are normally used in continuous combination, in the large majority of people the right brain contribution is biased towards building up or synthetically driven activity and the left towards breaking down or analytically driven activity.

All this provides yet another intriguing implication. Intellectual life has long benefited from various proposed Philosophies of Science. In contrast, the formal inversion theory suggests the beginnings of a proposed Science of Philosophy.

The above contradictions to prevailing paradigms appear to be suitable heresies for our modern age, because they represent scientific challenges to truth concepts at the heart of the aspiring authority of science itself -- hence the title of the main publication mentioned in the side-bar.

This completes the 'broad brush' introduction to the theory.

37. A General Convention for Form - B.

A GENERAL CONVENTION FOR FORM is a suggested practical solution to the many problems emanating from our apparent anatomical obligation to use left-right bicyclic formal inversion as a central neural-mental principle.

The convention is an independent reference frame for thought, in which the general universe of forms (1) is subdivided in two ways.

In the trefoil device, the three great scholarly traditions of philosophy (2), logic (3) and mathematics (4) show overlapping borderlands (5, 6, 7) and share a central area of maximum overlap (8).

In the distracted gradient device, an analytically driven or clockwise reading is that the general universe (1) contains the physical universe (9) which contains the organic universe (10) which contains the human universe (11) -- the brains/minds of which contain the general universe -- which brings us back to (1) again.

A synthetically driven or anticlockwise reading is the inverse of the above.

The apparent evolutionary obligation of our brain wiring patterns to involve left-right bicyclic formal inversion implies new interpretations of many established ideas, some of which seem particularly heretical. Perhaps the most central heresy is described in the next post.

36. A General Convention for Form - A.

DERIVATION. Having looked at the apparently structurally similar brain forms and mind forms of the formal inversion theory, a natural question is, of course -- what next?

It is suggested that scientists and philosophers and others interested in the brain/mind should attempt to develop an independent and neutral reference frame for thought. A proposed first draft for the purpose has been derived by combining the previously explained distracted gradient device (shown top left) and the trefoil device (shown top right) into the device shown below them.

The result is shown in more detail in the next post.

35. Mind forms in human communities - D.

HISTORY. One way to represent the story of Western understanding over the last 3,000 years is to map the apparent balances and imbalances between analytic and synthetic drives against a time-scale, as shown.

A main feature of the map seems to be that for most of the three millennia the story has been dominated by synthetic drives. Arguably the only periods of balance between the drives occurred during the classical Greek Age (say the 6th to 4th centuries BC) and in recent times (say the 17th to the 21st centuries AD).

The reason for the historical synthetic dominance seems to lie in basic differences between the drives. There is strong clinical evidence that right-brain-biased processes meet our immediate needs more readily than left-brain-biased processes. They appear to be our first instinctive responses to the constant stream of new data that our brains receive every day. For these immediate imperatives, our automatic ordering seems to be synthesis first and analysis later --or building-up before breaking-down.


Before leaving mind forms in human communities, it should be noted that this introduction has provided only a few samples. For further examples in subjects such as philology, quantum physics, computer science and various typical mind debates the reader might wish to consult Chapter 9 of the main publication.

34. Mind forms in human communities - C.

IDEOLOGIES. Other formally inverted dualities occur when human beings seek some 'everything' to justify belief. The main traditions seem grounded in the usual formal drives -- either analytically or synthetically driven.

For analytically driven people this 'everything' has typically been some ultimate content, in which the human, organic or physical universes have been broken down into perceived essentials -- as for example in humanism, organicism and physicalism.

For synthetically driven people the everything has been some all-embracing form, in which the general universe has been envisaged as being built up into perceived systems -- as in various Western and Eastern religions.


Readers requiring more details might wish to consult pages 192-193 of the main publication.

33. Mind forms in human communities - B.

POLITICS. One formally inverted duality of politics is that the left wing variety (epitomised in the famous battle-cry 'liberty, equality, fraternity' with its perceived overarching theme of rationality) appears to have the main features of left brain drives whereas the right wing variety (based on such watchwords as 'authority, hierarchy, property' with its perceived overarching theme of conservation) seems to show the main features of right brain drives.

Readers requiring more details on the apparent political implications of the formal inversion theory might wish to consult pages 186-191 in the main publication.

32. Mind forms in human communities - A.

CULTURES. There are various formally inverted dualities that may be termed cultural (including the political and ideological dualities to be mentioned shortly) but one obvious example is the perceived separation between the Arts and the Sciences, which was epitomised in the famous Two Cultures debate of the 1950s.

For the present introductory purposes it is sufficient to remind the reader that the Arts appear synthetically driven or right brain biased and the Sciences analytically driven or left brain biased. For a fuller discussion see pp. 184-5 of the main publication.

31. Mind forms in human individuals - F.

THE TREFOIL CORE. We should now return to the perceived trefoil pattern, and look at the centre of all the overlaps -- the trefoil core (marked 1) -- where the ideas appear common to all three of the great traditions. As most readers will know, the ideas are often called elements (2), sets (3) and relations between elements and between sets (4 and 5) -- ideas that are considered in much more detail in the main publication.

For the purposes of this brief introduction however, we should concentrate on the proposed core of the core. The formal inversion theory suggests that the concept of form itself is a strong candidate for the most central idea in human abstraction. The proposal is of course not new -- it has been previously proposed in various ways by various people including Plato and Aristotle. What is new is that the proposal is backed by arguably strong physical evidence concerning all brains including our own.

The distinction between a set and a form is best demonstrated with an example. The diagram marked 6 shows a set of elements that are not recognisably related. The diagram marked 7 shows a set of the same elements that are recognisably related. Diagram 6 represents a set. In diagram 7 it has become a form.

Form seems to be the characteristic that the brain adds to a set when its elements (be they elements of sight, sound, smell, taste, touch or whatever) become recognisably related.

Having looked briefly at some putative mind forms in individuals, we should next look at them in communities.

30. Mind forms in human individuals - E.

PHILOSOPHY. In philosophy, the most wide-ranging of the great trefoil traditions, yet another formally inverted duality has long been evident.

Analytic philosophy (which today is often seen as typically anglophone) appears to be left-brain-driven.

Synthetic philosophy (which today is often seen as typically 'continental') appears to be right-brain-driven.

We shall return to the important subject of philosophy (and the potential synergy of its two main divisions via A General Convention for Form) towards the end of this 'broad brush' introduction. At that point I shall try to explain why I think that, whereas intellectual life has long benefited from various proposed Philosophies of Science, in contrast, the formal inversion theory suggests the beginnings of a proposed Science of Philosophy.

29. Mind forms in human individuals - D.

LOGIC. Since ancient times there has been a broad, formally inverted duality in reasoning.

The version of the subject called induction appears to be left-brain-biased logic, in that it begins by noting particular characteristics of forms and reasoning proceeds from such particulars to general conclusions. Because each dog we know swims we conclude that all dogs swim. It is the dominant kind of reasoning in the sciences. Its strength is that new understanding is accumulating. Its weakness is that the new insights can only refer to probability.

The version of the subject called deduction appears to be right-brain-biased logic, in that it begins by noting general characteristics of forms and reasoning proceeds by applying these generalities to particular cases. All dogs swim -- Patch is a dog -- therefore Patch swims. It is the dominant kind of logic in pure mathematics. Its strength is the security of the conclusions. Its weakness is that no new understanding is obtained because the derived conclusion is part of the earlier understanding.

We appear to await the blending of the two arguably half-brain-biased logics into a synergic logic that will complete our human quest for increased information with certainty.

28. Mind forms in human individuals - C.

MATHEMATICS. From prehistoric times until today, arguably the most fundamental duality of abstraction has been represented by the formally inverted concepts now called shape and number.

It seems that while studies of shape (geometries) are essentially building-up, apparently right-brain-biased, synthetically-driven notions, so studies of number (arithmetics) are basically breaking-down, apparently left-brain-biased, analytically-driven notions. Human efforts to make the two kinds of mathematics work together have had three main phases.

The Greek desire to unify the ideas necessitated a crucial choice -- between shaping number and numbering shape. They chose to shape number, creating synthetic geometry, the right brain biased mathematics that was dominant in the West for 2000 years.

In the 17th century Descartes (and arguably Fermat) reversed the Greek option and chose to number shape by inventing analytic geometry. Up to this point, human attempts at mathematical synergy seem to have reflected large scale brain forms -- at the left-right brain level.

The 18th century saw the beginning of another kind of synergy -- a search for fundamentals -- in a phase called set theory. In broad terms, set theory deals with elements of thought, sets of the elements and relations between elements and between sets. The ideas are basic to all mathematical abstraction and thus arguably to all thought. It is suspected that in due course set theory will be seen to reflect small-scale brain forms such as neurons and their sets just as earlier theories reflected large-scale brain forms.

27. Mind forms in human individuals - B.

[5] A FORMAL DRIVE pattern is a fifth suggestion for a generally recognisable mind form. Although all humans seem to make continuous use of their zigzagging arcs of thought, relatively few people appear equally at ease with their zigs and their zags. Most of us seem to prefer one or the other. This seems to have the effect of driving our individual trains of thought in our preferred direction --- either an analytically driven or a synthetically driven direction.

[6] In addition to the gradient and the distracted gradient patterns, humans have also evolved another pattern for dealing with the 'whole' general universe (the universe that combines abstract and physical complexity). This is the TREFOIL pattern, based on the three great scholarly traditions that include abstract forms in their deliberations, namely philosophy, logic and mathematics (marked P, L and M). The approaches typically show overlapping Borderlands in pairs and all three traditions and their borderlands also share a Trefoil Core of maximal overlap (marked C) where the ideas are common to all such approaches.

We shall next take a quick look at each of the great traditions.

26. Mind forms in human individuals - A.

Opinions will of course differ as to which mind forms genuinely exist, but it is suggested that there are certain generally recognisable patterns, the most evident being our habit of switching between synthesis and analysis and various elaborations of this habit. The suggestions are as follows.

[1] A FORMAL ZIGZAG pattern representing our (arguably) most basic habit.

[2] A FORMAL GRADIENT pattern - an elaboration in which for example we 'break down' the general universe into a contained physical universe that contains an organic universe that contains a human universe that in turn contains the concept of a general universe again --- or we 'build up' a human universe that is contained in an organic universe that is contained in a physical universe that is contained in a general universe that is a contained concept in the human universe again.

[3] A FORMAL CIRCULARITY pattern - an elaboration in which we emphasise the two-way circularity of the preceding pattern by separating out the various universes into a distracted gradient --- physical from general, organic from physical and so on. This pattern will be used later as a basis for a suggested General Reference Frame for Thought.

[4] A FORMAL ARC PATTERN pattern - which may be thought of as combining our typical zigzag and two-way circularity patterns into one pattern. The result is a pattern of zigzagging arcs. Each zig or zag arc is envisaged as a segment of a process that is apparently ultimately circular.

The next suggestion for an individual mind pattern takes the elaboration of the synthesis-analysis pattern a stage further.

25. Associated clinical evidence - B.

There is much published evidence (detailed for example in the main publication mentioned in the side-bar) of LEFT cortical analytic bias and RIGHT cortical synthetic bias in studies of:

• General Vision and Reading Vision anomalies focused on the Occipital lobes (marked O),

• Audition and Olfaction anomalies focused on the Temporal lobes (marked T),

• Proto-abstraction anomalies focused on the Parietal lobes (marked P), and

• Planning, problem-solving and language anomalies focused on the Frontal lobes (marked F).

Having looked at an introduction to the evidence concerning BRAIN forms, we shall now look at some of the evidence for putative MIND forms.

24. Associated clinical evidence - A.

Via functional brain imaging, humans have been shown to 'light up' different parts of their brain wiring in dealing with parts and wholes of forms.

• When subjects concentrate their attention on a part such as the letter F in the diagram, an area of the LEFT brain lights up.

• When subjects concentrate their attention on the whole large letter S, a region of the RIGHT brain lights up.

In addition to this kind of evidence in the normal brain, which is now much repeated, there is also an associated large literature on studies of brain disease which reinforce the results, as in the next diagram.

23. Human neural energy transfer - B.

This diagram generalises human neural evolution yet further, by schematising BOTH SIDES of the brain working together. Our right and left brains together engage in both visceral mental activity which is largely unconscious and somato-branchial activity which is largely conscious.

The concept of essential symmetry in neural activity began to be modified in the early 19th century and since then clear evidence of major differences of emphasis between the activities of our left and right brain hemispheres has been recognised.

Very broadly, the left cortex has been shown to be dominant in analysis and language and the right in synthesis and emotion. This laterality has been shown to occur in a large selection of other animals and so now is seen as an evolved pattern.

Again, the pattern has been frequently clinically confirmed, as illustrated in the next two diagrams.