1. Preface.

Blogs normally have their newest posts first, in order to be up-to-date. The original blog on the theory is arranged in this way and can be reached by clicking here. As indicated above in the header panel, the present blog is a second version and is arranged with its oldest posts first, in order to provide an outline that can be read as a natural narrative (down the pages). The new ordering has been obtained by artificially reversing the timing of the posts. The method works well but introduces a small (easily managed) anomaly, in that the clickable phrases Newer Posts and Older Posts at the end of each page are also reversed. Please note that both blogs are outlines for ready access. Details on all topics are provided in the main publication.

The other difference between the two blogs is that this prefatory Post 1 is much shorter. Details concerning the perceived justification for blogging the theory, the broad posting policy adopted and the pre-blogging history of the topic have been omitted here and may be found in Post 1 of the original blog. All the remaining posts in the present introductory Outline are the same in both blogs.

The main messages of both versions of the blog are these. Evidence clearly compatible with the theory has been found in a large range of subjects including molecular biology, comparative and human morphology, clinical neuropsychology, philosophy, logic, mathematics, physics, cultural studies, politics, ideology, philology, computation and history. Evidence clearly incompatible with the theory has yet to be found by this writer. Despite this encouraging degree of apparent compatibility, the theory has many implications which are at first sight counter-intuitive and thus heretical. The most central of these is that if future research continues to support the theory, in due course our traditional and much-cherished one-truth (one correct perspective) thinking conventions will arguably need to be replaced by two-truth (two correct perspectives) thinking conventions. This central heresy leads to others, including the apparent 'unmasking' of the dualistic, circular, self-referential and incomplete nature of knowledge in subjects such as those listed in the header panel. Such 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. In view of all this, the author suggests that we have now reached the stage where the theory is highly arguable, even though of course it is much too early to claim that it has been 'proved'.

You are invited to join the debate.

2. Introducing the theory.

The central concept of the formal inversion theory may be stated very simply. The theory suggests that there is an apparent structural similarity between certain basic brain forms and certain basic mind forms and that the brain forms provide a credible explanation for the mind forms.

The basic brain forms are neuron wiring patterns present in the uppermost reaches of bilateral animal brains (including our own) that are characterised by left-right bicyclic inversion. By this I mean that signals in left brain cycles travel in inverse directions to signals in right brain cycles and that there are further mutually inverted cyclic paths for the exchange of signals between the two sides.

The basic mind forms are extremely pervasive human thought patterns characterised by formally inverted duality. One pole of each duality typically represents form-to-content or analytic patterns and the other pole content-to-form or synthetic patterns, each being the formal inverse of the other.

The dualities seem to match the clinically evident analytic and synthetic biases of left and right human brain/mind activities respectively.

Much of our mental life seems to involve a constant switching between analytically and synthetically biased thought, and the implied reinterpretation of philosophy and other subjects that will be discussed in later posts is apparently concerned with our brains being necessarily and inescapably wired for this constant switching process. The next post will describe some apparently obligatory features of the basic forms.

3. Obligatory features of basic forms.

The apparently obligatory features of the basic brain forms are their duality (since there are both left and right cycles), their circularity (on each side and also between the sides), their consistent self-reference (in that all three kinds of cycles 'turn back' on themselves) and their incompleteness (in that all three kinds of cycles appear endless). As we'll see, modern 'molecular clocks' indicate that these features seem to have been part of our animal brain heritage for about 1000 million years.

The arguably obligatory features of the basic mind forms are their perceived central problems of duality, circularity, self-reference and incompleteness, as epitomised for example in the famous Liar Paradox (of which more later). As we'll see, these features seem to have been part of our mind heritage for at least 42,000 years and the perceived central problems have been recognised for at least 2,600 years.

Future posts will summarise the evidence and argument for the brain forms (beginning with some introductory concepts), then for the mind forms and then for the surprising implications of the theory.

4. Introductory concepts: brain forms - A.

GENERAL EVOLUTIONARY HOMOLOGY ---- BRAIN/MIND EVOLUTIONARY HOMOLOGY

Homology. The general idea is shown on the left. An item of content in an organic form (like the thumb of a flying fox) is the homologue of an item of content in another organic form (like the thumb of a human) if some significant content-to-form relation is the same in both and both forms derive from a common ancestor.

In brain biology, this may be extended to further levels of analysis. For example, as shown on the right, items of content in bacteria like the molecular Sensors, Transmitters, Receivers and Motor units (S, T, R, M) are legitimately seen as the 'long-distance' or 'deep' molecular homologues of the neural versions in humans. [Modern bacteria and modern humans derive from a common (bacterial) ancestor. ]

5. Introductory concepts: brain forms - B.

HUMAN MOLECULAR TIMESCALE ------------- FORMAL INVERSION EXAMPLES

Human molecular timescale. As shown on the left, our forebears are thought to have emerged from an RNA-based world into a DNA-based world about 4000 million years ago and current understanding of our journey to today may be usefully divided into 1000 million year chunks.

It is now very clear, on molecular and much other evidence, that all multicellular living things (animals including humans, and plants and fungi) evolved from the same or similar single cell organisms and that descendants of stages in this evolutionary process are with us today. Our understanding of our human place amongst living things has been assembled by studying modern versions as models of the evolutionary stages. As a result, we now know that we share a small fraction of our most basic molecular make-up (our genes) with bacteria and some viruses, about a third with daffodils, about half with worms, about three-quarters with dogs and almost all (about 98.5%) with our cousins, chimpanzees.

Of the many kinds of evidence underpinning the broad concept that all our natures are one, none is more cogent than the shared strategies we have evolved for our survival. For example, we must all consume food and we must all maintain an internal physical and chemical equilibrium in our bodies despite constant change in our surroundings. Our standard answer to the equilibrium problem has been the evolution of stimulus-response devices, beginning with molecular versions and proceeding via simple to complex nervous systems.

As shown on the right, there have been numerous instances of formal inversion during human neural evolution, and the diagram shows just six of these -- 3 molecular and 3 neural.

The point of the illustration is to emphasise that formal inversion appears to have been a consistent mechanism during our animal evolution, including the evolution of stimulus-to-response flexibility for survival in the natural world.

The next post will begin to look at these specific examples in more detail.

6. Molecular formal inversion - A.

DNA. As soon as DNA was established as the Thread of Life, a formal inversion principle was firmly in place. The two strands of the sugar-phosphate backbone of DNA run in inverse chemical directions, and it is this locking nature of the arrangement that provides the relative genetic stability that DNA brings to the living world. This feature of DNA might be regarded as the Fundamental Formal Inversion, even though it is not as yet clear how (or if) this particular kind of formal inversion is translated into the others that will be mentioned.

7. Molecular formal inversion - B.

Viruses. In the virus called phage Mu, in addition to the Fundamental Formal Inversion, there are also further DNA inversions that provide it with flexible function in the interests of survival. For example, it has an invertible sequence of 3,000 base pairs called the G segment. Depending on whether the segment is in its G+ or G- orientation, the virus can attack B. coli or other host cells. Thus formal inversion was apparently an already well established principle in the molecular brain-mind homologues of viruses.

8. Molecular formal inversion - C.

Bacteria. In bacterial brain-mind homologues there are formal inversions in cell-to-cell systems rather like the virus-to-cell inversions in the previous post. One example is the fimbriae mechanism. The fimbriae are very fine hair-like protein filaments that grow out from the surface of a bacterium and enable it to adhere to other cells. The presence or absence of fimbriae on E. coli is determined by inversion of the promoter region of the gene called fim A, as shown.

There is another kind of bacterial formal inversion switch that works on larger protein outgrowths called flagella. For example, as in the sketch shown in post 4, a flagellum (or motor unit) of E. coli works by rotating clockwise or anticlockwise. When the bacterium detects an attractant chemical, the molecular brain-mind homologue of the cell signals the 5 to 10 flagella to rotate anticlockwise and collect into a sort of pony-tail that drives the cell in a 'run' towards the chemical. When a repellent chemical is detected, the flagella rotate clockwise and fly apart so that the cell is said to 'tumble' at an angle to the run and away from the chemical. The run and tumble effect is yet another example of the formal inversion principle being deployed in the interests of survival.

9. Formal inversion in a Radiata model.

We have been edging our way from molecular stimulus-response systems and brain-mind homologues towards the emergence of their neural counterparts, which first appeared in the Radiata. A standard laboratory model for these typically jar-shaped, blind-gutted, radially symmetric animals is the freshwater Hydra. The hydra polyp is attached by its base (B) and has an upward pointing mouth/anus (MA) surrounded by a zone of tentacles (T).

The nervous system of a hydra is a body-wide nerve net (NN) via which any stimulus anywhere provokes a full body response. The key structure for our purpose is the nerve ring, which is a thick neuron bundle running round the circumference of the animal between the mouth/anus and the tentacles. Its key developmental feature is its stability. Whereas the rest of the hydra nervous system undergoes constant cell replenishment, the nerve ring does not. The nerve ring is thus a highly credible candidate for a simple brain.

The Radiata represent the most likely evolutionary stage at which the circularity factor became an integral part of our own brain heritage (some 1300 million years ago according to modern 'molecular clocks'). There are at least six arguable theories as to how Radiata nervous systems became Bilateria nervous systems (like those of humans) and one of these is simplistically shown. The main point for the present argument is that at this stage, before the advent of bilaterality and forward foraging, all brains were unicyclic.

When the nerve ring is examined closely, as schematised in the lower diagrams, it is seen to be made of chains of individual neurons in which signals from any stimulus travel in both (mutually inverted) directions round the ring.

10. Formal inversion in C. elegans - A.

We have now arrived at the famous Minimal Bilateria Model of animal life called C. elegans (in the upper diagram). This tiny (1 mm long) creature is the most completely understood multicellular animal in science. It was the first to have its genome sequenced and thus provided central lessons for the human genome project.

It also has the only nervous system in a multicellular animal for which we have an essentially complete wiring diagram, including that of a Minimal Model Brain, represented by the contents of the box in the diagram. Here the black dots represent neuron cell bodies and the nerve ring is the probable homologue of the nerve ring of the hydra. This magnificent neuroscientific resource (the wiring diagram) was provided in 1986, after seventeen years of intricate electron microscopy and painstaking reconstruction, by the Cambridge team of John White, Eileen Southgate, Nichol Thomson and Sydney Brenner *. [The upper diagram and several diagrams in following posts were developed from data published in their now classic report].

The brain of C. elegans is capable of such fundamental activities as taste, smell, touch sensation and heat sensation, all of which are also central to our own lives. The mind (or working brain) of 'the worm', as it is known to its devotees, is also capable of learning, memory and thus primitive knowledge. Crucially for science however, the worm brain/mind achieves all these functions with about 180 neurons and about 4000 interconnections -- an entirely tractable conceptual challenge compared with the enormous complexity of human brains. We are thus able to begin to learn about the basic workings of brains while it is still possible to study them neuron by neuron and connection by connection.

In the next post we shall begin to look 'inside the box' at the brain of the worm.

* White J. G., Southgate E., Thomson J. N., Brenner S. (1986). The structure of the nervous system of the nematode Caenorhabditis elegans. Phil. Trans. R. Soc. London. B314, 1-340. [Also accessible on the Web at www.wormbase.org Click on The Mind of a Worm (White et al. 1986).

11. Formal inversion in C. elegans - B.

A Minimal Model Bilateria Brain. Each black blob here represents the cell body of a neuron. The nerve ring of cell fibres and its extension into the belly of the worm is shown in yellow. The main brain circuitry for our current 'broad brush' purposes is the amphid complex, which includes circuits for taste, smell, touch and heat sensation -- all of which have evolved equivalents in our own brains and some of which are already known to be involved in learning and memory in the worm.

You should now imagine that you are looking at the worm brain from above and behind as indicated by the yellow arrow -- and that you can see four neurons, as in the next picture.

[Diagram developed from data published by White et al. (1986)].

12. Formal inversion in C. elegans - C.

Diagram developed from data published by White et al. (1986).

The four neurons have been artificially separated. To envisage the natural state, imagine the nearly circular parts superimposed on one another. These nearly circular parts contribute to the nerve ring -- the 'highest' structure in the worm brain and the homologue of our own cerebral cortex. Expressed simplistically, the homologous structures are the sites where the respective animals (representing minimal and maximal Bilateria) do the most sophisticated 'thinking' of which they are capable.

The black dots connected by coloured lines are sample connections between neurons.

• Green(ish) lines represent connections on the same side of the animal,
• Red(ish) lines between the two sides and different neuron pairs, and
• Blue lines between two sides and within a neuron pair.

[the 'ish' of the green and red lines refers to the fact that the scanning method has lost some of the colour of the original artwork. I shall hope to improve these colours in due course.]

In evolutionary terms, the green connections will eventually become the critically important association fibres and the red and blue connections the critically important commissural fibres in our own brains -- so that the scientific value of the minimal model brain in beginning to understand our own thinking processes can hardly be overstated.

Two other important points about this stage of Minimal Bilateria neural evolution should be appreciated. First, neurons were already manifest as three broad types: cells to receive stimuli (sensory neurons), cells to trigger responses (motor neurons) and cells to connect the two (interneurons) -- the basic arrangement that continues in all subsequent Bilateria including humans. In later animals, the three neuron types were to become increasingly structurally complex but whereas the sensory and motor neurons also increased their number in each circuit to a relatively small degree, the interneuron parts of circuits were to expand hugely to produce more and more powerful brains.

Second, connections between neurons were already of the two main types that occur in all later animals (chemical and electrical) but such connections were made via relatively simple 'touching points' between adjacent neuron processes -- a situation best imagined by the superimposition mentioned above. Such en passant connections were the earliest kind of neuron linkage in bilateral animals. In later animals such direct links were generally replaced by much more complex devices.

Because the worm brain has only about 180 neurons and only around 4000 such connections, it is possible to work out various basic circuits, as in the example in the next post.

13. Formal inversion in C. elegans - D.

A CIRCUIT FOR A 'MINIMAL MODEL THOUGHT' CONCERNING TASTE

[Diagram developed from data published by White et al. (1986).]

The circuit illustrates some of the fundamental workings of the worm homologue of our human cerebral cortex. As an informal description of the circuit's activity, the worm in the diagram may be envisaged as having a 'minimal model thought' concerning taste.

Two main sensory cells for taste (at the top of the figure) are called ASE. The left is ASEL and the right ASER. When the worm detects certain chemicals in the outside world, signals flow in the direction of the arrows.

The sensory neurons connect with interneurons called AIB (left and right again). Note that at this stage the signals change direction. The previously clockwise left signals now travel anticlockwise, and the inverse is the case on the other side. Note also that in making the connections at this level, the ASEL-AIBR connections are one-way and that the ASER-AIBL connections are two-way or circular. The latter pattern is emphasised in the upper right dotted yellow box.

How have these patterns been revealed? By use of a newly developed technique called a connectogram, which will be illustrated in the next picture.

14. Formal inversion in C. elegans - E.

Connectogram for amphid

SENSORY NEURONS and INTERNEURONS

All the sensory neurons are listed in rows and all the interneurons in columns. Each dot represents a chemical connection site identified by White et al. (1986) on a sensory neuron and each small square surrounding a dot represents a corresponding connection site similarly identified on an interneuron.

The small diagram on the left shows the plotting key: TO the left and TO the right in upper quadrants and FROM the left and FROM the right in lower quadrants.

If you now look at the two yellow squares, where the taste circuitry begins, you will see that the two (red) connections from the left sensory neuron to the right interneuron are one-way and that the opposite connection (from the right sensory neuron to the left interneuron) is two-way or circular.

Note that such circular left/right connection patterns (red sites, one above the other and within the same grid square) occur in four places in key circuits.

Two of these are concerned with the main taste circuit initiated by the ASE neurons: the above-mentioned yellow square (ASER-AIBL) example and another at ASER-AIAL.

Another is concerned with the main smell circuit initiated by the AWC neurons: namely at AWCR-AIYL.

The other is concerned with the main thermosensation circuit initiated by the AFD neurons: at AFDL-AINR.

Newcomers to C. elegans data will by now have begun to appreciate the value of the Minimal Model Brain (and its Minimal Model 'Thoughts') at this very early stage in our quest to understand the many mysteries of our own brains and minds. In the next post we shall return to the main demonstration taste circuit.

15. Formal inversion in C. elegans - F.

On returning to our demonstration taste circuit, we can confirm that the specific anatomical sites [identified by White et al. (1986)] of the one-way connections between ASEL and AIBR and the circular connections between ASER and AIBL conform to the plots that we noted on the connectogram.

At the next stage in the circuit the AIB interneurons make connections with motor neurons called RIM (left and right again). Note now that the signals change direction yet again -- from clockwise to anticlockwise on one side of the circuit and from anticlockwise to clockwise (i.e. the formal inverse) on the other side.

Also note that once again there is a one-way connection and a two-way or circular connection but that the positioning of these is the inverse of the connections noted at the level above.

How have these patterns been elucidated? Via another connectogram, as shown in the next post.

16. Formal inversion in C. elegans - G.

Connectogram for amphid
INTERNEURONS and MOTOR NEURONS

This time the plotting is between interneurons in rows and motor neurons in columns.

Looking at the yellow squares again, it can be seen that the interlateral (red) connections between the right interneuron and the left motor neuron are one-way and that the corresponding connections for the left interneuron are two-way or circular.

This may now be checked again on the circuit sketch (as in the next post).

17. Formal inversion in C. elegans - H.

Here it can be seen that the information from the last diagram conforms to the details on the demonstration taste circuit.

Finally note that in the last stage of the circuit, the motor neurons connect with muscles (via similar connections to those between neurons), so that the worm may respond to the original taste stimulus -- by moving towards it or away from it.

The small diagram at the bottom is a mnemonic summary. The Minimal Model Thought circuit is one of left-right bicyclic inversion. Signals in left brain cycles travel in inverse directions to signals in right brain cycles and there are further mutually inverted cyclic paths for the exchange of signals between the two sides.

This demonstration circuit has been concerned with taste but as indicated earlier there are similar Minimal Model Thought circuits for smell and thermosensation.

We should now look at an overview of Minimal Model Brain activity -- as in the next figure.

18. Formal inversion in C. elegans - I.

OVERVIEW OF MINIMAL MODEL BRAIN ACTIVITY

We have been looking at one example of a neural pathway -- via which a taste stimulus (S) is converted into an appropriate response (R) -- as in (say) the upper path shown.

As previously noted, there are other instances of such wiring -- via which, for example smell or thermosensation stimuli (S) are converted into responses (R) -- as in (say) the lower path shown.

In addition, there are multiple connections across the grain of the S-R circuitry -- connecting sensory neurons with sensory neurons, interneurons with interneurons and motor neurons with motor neurons -- as shown.

The point of the illustration is to emphasise that all of the connections have the same basic form -- and that is the form of left-right bicyclic inversion. Readers requiring further details of these connections, both along and across the grain of worm brain circuitry, might wish to consult the main publication on the subject mentioned in the side bar.

19. Formal inversion in C. elegans - J.

MINIMAL/MAXIMAL BRAIN HOMOLOGY

The formal inversion theory suggests that the Minimal Model Brain activity of the last figure (here repeated in the lower diagram) is an entirely credible stripped-down-to-the-essentials version of what is going on in our own minds at this very moment -- and that organic evolution has seen to it that our own Maximal Model Brains are massively multiplied versions of the minimal model case.

The upper diagram of the six basic layers of our human left and right cerebral cortices shows just one of the very many ways in which the principle of left-right bicyclic inversion might be realised in our own brains. We do not yet know which of the many possibilities is the correct one but at least the theory provides one highly credible pattern for which we should be looking.

In broad outline, in mammalian (including human) cerebral cortices, intrinsic cells of layers 3 and 4 are the main receivers of subcortical and cortical input and are here represented by cells in layer 4. Layers 2 and 3 provide the main outputs to cortical destinations and are here represented by cells in layer 3. Layers 5 and 6 provide the main outputs to subcortical destinations and are here represented by cells in layer 5. The connections shown between cells are standard and profuse in life.

In keeping with the 'broad brush' nature of this introduction, we shall next look at one brief 'snapshot' of how simple bilateral brains become complex bilateral brains -- by considering the chordates.

20. Chordate neural evolution.

Chordates are animals named after a stiffening rod (the notochord) that appears in their bodies at some time during development.

Chordate neural evolution may be schematised as shown. Looking at the left diagram first -- the central nervous system arises as a groove along the back of the organism, which then sinks into the body as in 1. Along most of the the groove the lips come together to form a tube as in 2 but in part of its length it remains open so that it looks V-shaped as in 3.

Different parts of the groove develop different functions. The main division is into Input or Afferent pathways marked A and Output or Efferent pathways marked E.

As shown in the right diagram, the Input and Output parts of the groove gradually evolve into more and more complex versions of four main types of circuit -- Visceral, Branchial, Somatic and Special Somatic.

The evolution of mammalian (including human) branchial circuits has been emphasised with a yellow border because this circuitry is homologous with the demonstration worm taste circuit that we looked at earlier. We shall look at our human version of the worm taste circuit in the next picture.

21. Maximal model taste circuit (human).

The general arrangement of our human neural groove/tube is the same as in all chordates. It is shown in cross-section in the upper half of the diagram and in frontal and side views in the lower half.

Although the basic taste circuit has become much more elaborate than in the worm, it still serves the same purpose, has the same major components (sensory neurons, interneurons, motor neurons), makes the same kinds of connections (chemical and electrical) and, according to the formal inversion theory, employs multiples of the same kinds of circuitry (left-right bicyclic inversion).

The examples of first and last neurons shown are those concerned with selection or rejection in feeding and breathing. Taste at the back of the tongue for example is sensed by the ninth cranial nerve (marked IX) and the muscles responsible for guarding the feeding and breathing portals by reacting to such stimuli are partly supplied by the same nerve as shown.

Other details of the diagram are not required for this introduction but are described in the main publication.

Taste is of course just one of the many ways in which chordates (and worms) convert energy from the outside world into neural energy inside their bodies, a process that we shall begin to generalise for human brains in the next post.

22. Human neural energy transfer - A.

The diagram shows the pathways for neural energy transfer on ONE SIDE of the brain. Energy in the external environment is converted into neural energy in humans in three basic ways.

Electromagnetic energy is sensed as sights and temperatures via eye and skin receptors. Chemical energy is sensed as smells and tastes via nose and tongue receptors. Physical energy is sensed as sounds and pressures via ear and skin receptors.

(Our continuing taste example is highlighted in yellow.)

All types of energy in the internal environment (inside the body) are sensed by receptors in vessels, viscera and glands -- marked VVG.

A further type of transduction is that of positional sense or proprioception (marked PR), mediated via the labyrinth of the ear and receptors in muscles, joints and tendons.

We respond to all these stimuli via either our somatic (SM), branchial (BM) or visceral muscles and the energy transfer cycle is completed by heat loss at body surfaces and in excretions.

23. Human neural energy transfer - B.

This diagram generalises our human neural energy system 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 simplistically, left cortical activity has been shown to be dominant in analysis and language and right cortical activity 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 and knowledge. 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.

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.

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 example to be described next) 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.