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.