The Metaphysical Circle

The Great Circle showing the full complexity and interdependence of all the note pitches and every interval in the twelve note scale is shown in Diagram 2 :

The lines are also lines of cause and effect in the harmonia, the scale or temperament. No note can be altered without affecting its relationship to every other note, and this affects the harmonia or temperament. The diagonals across the circle, are the tritones - the augmented fourths or diminished fifths, the diabolus in musica of early theory that was studiously avoided in practice. In modern music of course, every interval is equally acceptable including that of the diabolus in musica which simply becomes another discord that can be prepared and resolved. Nevertheless, in terms of early theory the greatest symbolic disharmony lies in the opposites. Turning the theory on its head, and looking at the circle in an unconventional way, we can see it is constructed of disharmonious opposites, arranged such that the result creates harmony along the other lines of relationship, according to the harmonia, the tuning or temperament employed. In keeping with the pre-Socratic notion, harmonia creates the harmony by fitting together the disharmonious opposites.

The whole circle represents the perfection of the unison or octaves, on which the other relationships depend, and without which the Circle would loose its meaning. The unison, the octave, the multiple octave, and the fifths, before arrangement in the Circle, are 'perfect'. But the Circle is not. As a consequence of the mathematics behind the structure it must contain the commas - 'imperfection' in the relationships is inherent in the harmonia. Some relationships may be perfect or pure, but it must always be that some will not. Perfect harmony, where it occurs, is the direct result of the harmonia, but it is not the harmonia itself. The harmonia itself, as a means of tempering, applies to the whole, and is necessary in the first instance because the whole Circle of perfect fifths in actuality cannot ever be the perfect unison or octave that it represents. Starting with C, it circulates not back to C, but to notes of actual, different pitches, B# or D double flat, depending on which way we go.

Why is there discrepancy or imperfection in the mathematical structure behind it all? It would have been very elegant of nature if twelve perfect fifths could have exactly equaled seven octaves, and very convenient if four perfect fifths could have exactly equaled two octaves and a harmonic major third. The inelegance and inconvenience is not of nature - it comes from the fact that the scale, or Circle, is not natural. Harmony, as intervals governed by integer ratios, is a part of natural phenomena, complete with its own imperfections and complications that arise when it is exhibited in physical media. Mathematically, Western harmony begins with the harmonic number series - 1,2,3,4,5,6 etc. The attempt to arrange harmony in a scale or Circle is Man's. The scale itself, if all the notes are heard simultaneously, is a cacophony. In contrast, the harmonic series itself, exhibited in say the natural behaviour of the monochord, even with all its physical imperfections, inharmonicity and complications, is unmistakably heard as both harmony and unison. The acoustical harmonic series has been called 'the chord of nature', and it occurs everywhere in nature that there is complex periodic phenomena, though not always acoustically. There is no equivalent twelve interval to the octave 'scale of nature' in natural phenomena.

The cacophony of the scale whose notes are sounded simultaneously is a reminder of the Man-made function of the scale. It is not designed (originally) to be sounded simultaneously. It is designed to diffract natural vertical harmony through time, to provide a set of acoustical reference points for the activity of extending harmony through time, in what we call music. When we study acoustical harmony in the scientific, object-orientated way, we deal with it in the context of space and time, and say it is oscillatory phenomena in time. But really, from the musical point of view, any given vertical harmony itself is not in time at all. Unlike melody, unchanging continuous harmony is not a musical function of time. From the subject-orientated position, pure unchanging continuous harmony does not have an 'objective' time element to it. Any change in it introduces time, not as the clock implies, but as persisting relationship in the awareness, of what was, to what is.

In order to 'crystallise' harmony into a set of fixtures, in order to condition it so that it can be recreated across time, a harmonia is necessary, whether deliberately 'worked out' or not. Harmonia is a static principle of the whole, that fits everything together, allowing harmony that constantly changes, in time, and necessarily includes disharmony. This much about both senses of the word harmonia is clearly present in the symbol of the Pythagorean Circle.

It is reported that the Pythagoreans considered the soul to be a kind of harmonia, or an 'attunement'. It was said to be 'in' the body as the harmonia is 'in' the lyre, when the lyre is in tune. This raised questions concerning other arguments for the immortality of the soul. If a harmonia is a consequence of right relationship (proportion) between the strings, then it vanishes when the lyre is destroyed, or the strings go out of tune. Thus, by analogy the soul must be destroyed when the body, or the condition of right relationship between its vital parts or elements is destroyed, in what is called death. On the other hand, the Pythagoreans are supposed by some of their interpreters to have held there to be a mathematical Reality that is transcendental to the material world. On this basis, the harmonia survives unaffected in mathematical Reality when the lyre is detuned or destroyed, and consideration of the soul as a harmonia does not affect its immortality.

In Phaedo Socrates argues that the soul is immortal and is not a kind of harmonia. The argument rests on the notion that a lyre can be more or less in tune, and contain more or less of a harmonia, whereas a soul cannot be more or less of a soul. Also, different souls can possess different qualities of intelligence, goodness, ignorance and wickedness etc., whereas this kind of differentiation and combination of qualities does not exist between harmonias. Clearly the meaning of harmonia in the musical context here is that there is but one harmonia, one tuning.

This does not mean that Socrates did not relate the concept of harmonia to the concept of the soul. He did so but in another way. The idea of harmonia occurs in the Myth of Er related by Socrates, but here it is 'transcendental' to the material world, in that it is beyond death - it is not of this world - but rather, it is depicted as the 'harmony' of the great system in which souls are by necessity involved in the cycle of life and death. However, since it is generally not sensible to take the content of myth literally, and for other reasons, we are at liberty to say that in the Myth of Er the transmigration of the soul as a continuing entity from one incarnation to the next, is not a literal 'diagram' of the truth that the myth supposedly stands for. The actual transmigration of the soul as a continuing entity is not really what reincarnation in the Myth necessarily means. What stands unaltered from Socrates is that there is a connection between the idea of harmonia and death, and that the difference between a living body and a dead one is that there is life 'in' it. What should we say is the relationship between life, death, harmonia and 'soul'?

The source of Socrates' wisdom is not discursive thought, and his engagement in this as a means of communication is a 'top down' activity of attempting to express self-knowledge in the logical space of thinking. Whether we credit Socrates, Plato, or both for this, matters not - it is the principle that is important. Unfortunately, Plato is usually interpreted in terms of his 'theories' and 'arguments' and the tenability of the relationships between them. It seems perfectly clear that in Plato 'Reason' as practiced by the philosophers, is not merely an intellectual search for knowledge, but includes the practice of self control, self responsibility, the pursuit of self-knowledge, and ultimately is about finding the truth of death. In the arena of discursive argument Socrates utilises all kinds of ideas and pre-existent beliefs as the medium of communication. When the discussion enters the area of knowledge beyond death, the discursive method in Plato is abandoned, and communication through direct mythical discourse takes over.

In Phaedo Socrates' argument that the soul existed previously to its current incarnation stands fast in Plato's discourse, in that it is accepted by the other philosophers. Socrates' reasoned argument for the immortality of the soul also stands - but only in that the soul is 'un-dying', not in that it continues after death. The nature of 'the soul' as a continuous surviving entity that transmigrates from one incarnation to the next is still not established as a consequence of its immortality. This is never satisfactorily confirmed outside the context of mythical discourse. The reason this state of affairs is patched together by Plato's interpreters into a scenario in which Socrates is supposed to believe souls circulate intact in and out of bodies in a manner akin to taking the Myth of Er quite literally, is, I propose, a consequence of understanding Plato in an object-orientated way, that does not befit the implied subject-orientated source of Socrates' wisdom.

Now for a contemporary reflection on this. To begin with, from the subject-orientated point of view there is no meaningful object called 'the soul'. The thing called 'the soul', is a mentally postulated proposition. The 'soul' may be meaningful but if it has any subject-orientated meaning it has to be known from the subject-orientated point of view as the subject, through self-knowledge. In this case, we might as well talk about self. There are numerous different ways one could translate the contents of Plato or earlier sources into more contemporary terms for a relationship between harmonia, universe and soul. I offer one in what follows, but rather than addressing soul, what we address here is self. If anything about 'the soul' is to be known through self-knowledge, then we have to address self first.

Self and thinking are related. For thinking to take place there has to be a self. The first thing to be said is that the knowledge beyond death mentioned above is observed by Socrates in the intellect, but unlike everything else, it evidently will not lend itself to demonstration in dialogue with the other philosophers, through the apparent process of reasoned deduction. The scenario for the truth of death Plato indicates, especially in the Myth of Er, certainly does not pass the test of Occam's Razor - for example as a 'logical' extension of what is otherwise established by the philosophers in so-called Reason, we do not need the harmonia between the Fates and the implications about planets and planetary characteristics. This is an unnecessary proliferation of entities. At the same time, it would be wholly out of character for Socrates to have merely accepted these details from pre-existing beliefs as correct. He soon rejected the popular belief that the soul is like a harmonia!

The 'logical space' of the developing dialogue is, in effect, the employed 'logical space' of thinking. Plato is implying that not everything that can be observed in the intellect can be arrived at through the 'logical space' of thinking, although it can be expressed in the logical space of thinking, once observed. In dialogue, the other philosophers test what Socrates says against experience and the intellect, approached through the logical space of thinking in which the dialogue takes place. Why does Socrates see more readily solutions in the intellect than the other philosophers?

If Socrates has a superior intellect, why does he say that he alone knows he knows nothing? If what he sees is only of his intellect, why do the other philosophers come to agree with him? Presumably because they share the same 'logical space' of thinking as Socrates, and agree what he says makes sense in the 'logical space' of thinking.

What follows requires abandoning the mental association of the concepts 'logical space of thinking' and 'the intellect', with individual, organic animal brains. Rather, we have to consider something more universal, at least at the scale of the species that we constitute. We must see that the philosophers share the same intellect as Socrates. If we feel an immediate objection to this it is because we consider the intellect to be an individual faculty of thinking in 'logical space' (the space of thinking in which things 'make sense'). The truth remains that things can be observed in the intellect that cannot be approached through the 'logical space' of thinking. In this sense the intellect is not itself the faculty of thinking in 'logical space'. The idea that there is one intellect is not so far removed from the idea that there is only one logical space for the behaviour of natural phenomena, or only one species that we can be.

However, if the philosophers share the same intellect, as just proposed, why is Socrates more able than the others? The answer is twofold. Firstly the ability to think in 'logical space' of any kind is individual, and the intellect is, in the case of evolutionary self, normally approached through thinking. Secondly, the intellect can be 'looked into' directly without the need of thinking in 'logical space', and the impediment to this is actually the action of evolutionary self thinking. Socrates knows he knows nothing, yet he is the wisest man in Greece. This does not just mean he alone has sufficient self-knowledge to know his own ignorance. It means he has the power to know nothing - which is the power to look into the intellect without the impediment of evolutionary self, and its need of evolutionary thinking and knowing, based on the evolutionary self/not-self duality. This is where Socrates, with his immediate self-knowledge of The One, or Being, differs from the other philosophers. Plato does not indicate this power comes from cogitation. It comes from the practice of 'philosophy', which is not to be confused with the discussion of philosophy or the discursive arguments for what it reveals, as it occurs in Socratic dialogue. The power is distilled from the reducing need of experience in, and reducing attachment to the material world. This is participation in a process in which already nothing survives, and it correlates to the reducing need to fear evolutionary death - the end of involvement in the material world - self in form. It is no wonder Socrates has no fear of death - he already knows his self, the world in form, and knowing it, with sufficient self-knowledge to know the truth of it, he sees through it. He sees through his evolutionary self, through the evolutionary world, and through evolutionary death. The intellect provides the ability to perceive the truth of the universe through whatever impeding medium evolutionary intelligence provides. The result does not approach the truth of the universe or knowledge of the intellect itself, until the impeding medium is sufficiently aligned with the intellect, sufficiently ready to transcend its own evolutionary position and see through itself, and through time. We can say the intellect does not 'belong' to Socrates, to any of the other philosophers, or to the reader of these words - it is free of human self, it 'belongs' to humanity, or if we like, the universe. We are in fact saying again now what has been said before and after Plato, that the intellect is the one Seraphic intellect described by Fludd and other neo-Platonists, it is the super-celestial fire of Pico, and it is the 'glassy object' of the Pythagorean Philolaus, through which the Real Sun is transmitted to us 'through certain pores', to become the symbol of the Sire of the Earth Thought, the visible 'reflection of a reflection' in the heavens that we call the sun.

Death and the Intellect

In subject-orientation the experience of life is as self. We know that the evolutionary survival principle out of which the brain-body system arises, requires instinctual 'drives' for self survival at the individual animal level - survival and protection of the body - as a pre-requisite at least for a time, before other mechanisms such as self sacrifice for the propagation of the species could possibly take place. The survival instinct transposed up into self-consciousness becomes the urge for self survival, but self in this case is now no longer just the body. It is a psycho-emotional entity also. Nevertheless, it is identified with the animal body.

The human self does not just see other human bodies - it sees other human selfs like itself. If it does not question its own reality, it sees the death of other bodies as the death of other selfs, and the threat of death to its own body, as the threat of self-annihilation. Apart from possibly the fear of existing without a body, it is not really the death of body that self fears, but rather it is a) the annihilation of itself, and b) the loss of the world. The two amount to the same thing from the subject-orientated position, but self, thinking in 'logical space' often denies that it fears its own death, whilst it still fears anything that threatens the end of the world. Hence the concept of 'the end of the world' has about it a ring of ultimate doom to be avoided at all costs, whilst death, which is known to be unavoidable, is conceptualised as a different matter. This is the taking of an evolutionary position, it is a lack of knowledge of self beyond its evolutionary position in time.

This situation creates the psychological and emotional need of the idea of survival of self beyond physical death. But in humans, it is not just fear of self annihilation that creates this need, or this need of belief in endless self survival. It is also the unconscious knowledge that the appearance of the necessary, evolutionary event of annihilation by death, is actually, like the appearance of every person, part of an illusion. This knowledge comes from unconscious but direct, natural contact with the intellect, in which it is possible to see that evolutionary self is entirely illusory, and that therefore death of evolutionary self is possible without annihilation of the consciousness on which it depends. However, consciousness as evolutionary self experiences it, is obviously not what consciousness is, without evolutionary self.

The attempt to escape self-death by inventing in thinking, self-survival after death, is not necessary, because the death we are trying to escape only relates to the evolutionary scenario of psychical and physical survival of the person, which is not real anyway. This thinking obscures the naturally available intellect, which is outside time and evolution, and it prevents consciousness of the process in which such survival considerations are completely unnecessary, within total surrender to the process.

That death of self is annihilation, is a 'lower state' deduction in the (self-conscious) evolutionary logical space of thinking in evolutionary self-consciousness. It is not a part of self-knowledge. The object-orientated thinking processes are movement and activity that tend to obscure the subject-orientated potential to observe in the intellect, that even in living, in time, death of self already happens by degrees, especially when the subject consciously and willingly participates in surrender to a greater process in which self need not survive. When self is involved in a process in which it is constantly transmuting by not surviving (which is of course paradoxical), then it is seen that the burden of trying to ensure survival of self is actually not necessary, because there is no 'annihilation of life' to avoid - there are only physical processes of living and dying, and the greater process in which self does not need to survive - the process of coming to be. This is seen using the intellect. At the same time it is seen that the intellect on which all thinking relies is not a consequence of self thinking, but is transcendental to thought.

The content of Plato's Myth of Er can be related in the following way. Like all Myths, the Myth of Er can be considered as an example of what Schopenhauer called a 'comprehensible substitute for the truth'. Every element in the story is a mythical symbol. In particular, the myth as Socrates tells it appears to be a scenario of metempsychosis - the transmigration of the 'soul' from incarnation, through a process between incarnations, and back again into incarnation. Thus, in the scenario as it appears, there is a self-entity, the 'soul' that survives throughout the process. The elements of the story dealing with this correspond with the general principle of the Buddhist and Hindu religions, in which life and death are cyclic. The doctrine of reincarnation as it is widely understood allows for this survival of self as 'soul', the form of each life being determined by the actions in the previous life.

I have asserted that music is ultimately part of a process of which survival is not the point. Thus, it could be argued that this is fundamentally at variance with the account of the music of the spheres encapsulated in the Myth of Er, which depicts continual survival through reincarnation. My answer to this, is that as Schopenhauer perceptively recognised, the notion of ultimate self survival in the doctrine of reincarnation, is itself, like any doctrine, also supposed to be a comprehensible substitute for the truth, all the more appealing because it promises self survival. The Myth of Er is in the class of the general doctrine of reincarnation, which Schopenhauer adequately addresses. The doctrine of reincarnation as the transmigration of a surviving self from one incarnation to the next, can be understood as merely a simple conceptual representation of a process in which reincarnation, as Schopenhauer puts it, is really through a psychical version of palengenisis. In biological palengenisis no individual self survives - the species which we say survives, is a concept whose reality in matter at any time is only through the physical individual members who ultimately do not survive. The reality of 'the species' outside material form, is abstract. Only in as much as a member's identity is with the abstract thing called the species does that member 'survive'. No individual member passes from death to birth, but births continue to arise. By analogy, in reincarnation, only in as much as the identity of a 'soul' is not with a given 'incarnation', but with the great process in which nothing 'survives', governed by harmonia and the Fates, does the notion of 'survival' in continual incarnations, have any meaning. To put it another way, only when a soul enjoys a state of consciousness in which nothing survives, and in which reincarnation is obvious, but an illusion, does reincarnation have any truth in it. Where there is no such consciousness, there is only the notion of survival from one birth to the next, and no truth in it.

The nature of the Pythagorean Circle and its relationship to harmony can be used as a symbol in a more extended context than that related to musical scales. Each element round this circle in diagram 3 now represents a concept in thought. Everything round the circle is related to everything else, either round the circle or along the straight lines of connection. Like the Great Circle of fifths, it is a diagram of a harmonia, in the sense that something fits it all together, but here, the harmonia fits together the concepts in thinking. It is a harmonia of thought - of understanding in human thought. The diagram could equally well have had any number of elements. The twelve it has are not special. The diagonals connect conceptual pairs or opposites, as I have presented them here, but this is not especially important.

The harmonia the circle represents can be whatever 'temperament', that is, theory, science or philosophy, that thinking applies to the conceptual elements - it depends on the philosopher, the scientific theories, or the chosen arguments. All kinds of conceptual equivalents of 'commas' may be introduced as a result of the way the concepts relate, sometimes confirmed by observation of natural phenomena - all kinds of puzzles, paradoxes and problems - but that part of the universe itself, the part the Circle purports to represent, like the natural harmonic series, has, so to speak, no 'problem' or 'puzzle' in itself.

The whole thing is a diagram of thinking relationships between the elements. We can say it is the human brain that does this thinking - but we can also view that as only one of many working hypotheses, given the complexity and variety of object-orientated theoretical possibilities for explaining things like consciousness, human intelligence and thought. We can just as validly say, from the subject-orientated point of view, that it is self that thinks.

So the whole thing is a diagram of something self does. It is a diagram of all the elements, the relationship between the concepts, from the point of view of self. What I said above could 'not be drawn' - the absence of self - could be diagrammatically 'drawn' as the disappearance of this diagram. This might seem rather Zen, but it is not Zen, because unlike Zen I have more to say about what it means, but it certainly shares with Zen a relationship to what is intelligible, but unapproachable through rational thinking.

The disappearance of the diagram would not necessarily mean the disappearance of self, but it would represent the disappearance of the self thinking. The disappearance of the diagram would represent the disappearance of the elements as concepts, like the disappearance of the implied scale design and its notes from a vanishing Great Circle. The harmonic series behind the notes of a scale still remains in nature as a natural 'structure' when all scales and Circles made in human thought vanish, but this remaining 'structure' is not the same thing as the notes of any scale or temperament - it is just the natural harmonic series. If we now, metaphorically speaking, jump to the next octave, the 'structure' I am proposing to which the concepts round the circle actually correlate, still remains when the diagram vanishes and the thinking stops. But this 'structure', again, is not 'made' of the concepts, just as at the lower metaphorical octave the natural harmonic series is not made from the temperament or scale. The structure the circle represents is not necessarily an objective thing, but we objectify it in thinking, because we necessarily make it a concept-structure in order to think about it.

Let us say that in principle we could put round the circle all the concepts we need to map out the entire universe conceptually. It would have to include things like mind, consciousness, gravity, self, life, quantum, love, matter, death etc, and unless the harmonia, so to speak, really was a 'theory of life the universe and everything' we would expect some connecting lines to have zero 'knowability'. Again, this would be a concept-structure, but one that is supported never more than a part at a time by actual observation. The whole conceptualised universe, is never observable at once.

The very term 'whole universe', meaning absolutely and completely everything, is a presumption in the first instance. It begins as a concept in thought, and then ends as a concept in thought. In between, it is partially supported by observations of the behaviour of parts, but the conviction that there is such a thing and that we should gather data on the basis of this presumption is only psychological in the first instance - the object in thought named 'the universe' as implying the inclusion of the unobserved, the possibly unobservable, the unknown, and the possibly unknowable, is a proposition, not a fact. It is felt to be the 'logical' extension of the immediate world perceived by self-consciousness occupying a world of not-self, but it can only be only presumed in thought, that such a thing is either known now, or remotely knowable.

The word 'universe', as we know, means everything turned into one, and in object-orientated thinking this is a thought, a concept, named 'the universe', that is equivalent to E, the Universal Set, the concept in mathematical thinking. (The blue symbol may not appear correctly on your browser - if so, this is of no consequence). The whole process works as follows:

We can observe the mind in action, that is, in the action of object-orientated thinking. Consider the Russell paradox itself. We define an R set as a set of sets that includes itself. For example, the set of all objects describable in exactly eleven English words is an R set. Now we define a set M as the set of all possible sets except the R sets. Now we ask is M an R set?

It is not the paradox that is important here, it is the observation of what the mind does as it attempts to 'work out' the answer to that last question, and the quicker it answers, the quicker one has to be to see it in action. I am assuming one tackles the problem as one of 'intuitive logic' and not as one of mere algebraic operation. Even if one already knows the answer, it is necessary to actually watch what the mind does in checking out the answer again. The action of the logical process in the thinking, takes place in a pre-existing 'logical space' in this part of the human mind, in which this kind of thinking logic 'makes sense'. One needs to watch it. Once observed in action, the process could almost be called mechanical.

The process of creating the concept 'the universe' to mean absolutely everything (rather than just the observable cosmos), is observable as another process, but one that happens in the same, or similar 'logical space', with a similar mechanicalness. This logical space is in the mind, determining 'reason' and 'what makes sense', in the current field of thought-objects. The mind, connected with the brain, connected with the physical senses, connected with the animal, evolutionary body, is connected with existence and survival in the sense-perceived physical world, and so there is a certain correlation between the 'rules' of this logical space and the 'rules' of local phenomena in the sense-perceived physical world. This logical space we can observe in consciousness, is part of self. The sense-perceived physical world for the survival purposes of the evolutionary animal is not-self. The experience of this state of affairs in human self-consciousness is a duality between self thinking in logical space, and the sense-perceived physical world of not-self.

Human enquiry into natural phenomena is a process that uses experiment, study, education and learning. Through these we change our concept structures and thinking methods in logical space, and attempt to improve their correlation with natural phenomena. Study, education and learning shortcuts the need to repeat the experience that produced the information now available for learning. At the same time this has been a process towards emphasis on object-orientation, and elimination of self from the enquiry. This has the effect of putting an increasing psychical distance between logical space and other aspects of self, so that conscious attention can generally only be in one or the other. Thus mathematical thought appears abstract and 'objective', and not related to say, emotional self and thinking consideration in this area. This is an illusion due to this psychical distance, because emotions, emotional thinking and syllogistic logical thinking are all proximate in self, all being part of self's activity. Nevertheless mathematical thinking does take place in logical space remote from the space pertaining to say, emotional thinking.

This psychical distance is necessary. Without a good psychical distance between logical space and the rest of self, logical space becomes easily infected by other aspects of self, especially emotion. So without this distance, the rational and reasonable nature of logical space becomes corrupted by active emotions, and the capacity to think rationally and reasonably is lost. Perhaps because of a survival advantage offered by the capacity to think rationally and reasonably despite emotional activity, the potential in us to increase this psychical distance through applied effort, exists in us in the first instance.

Homo sapiens, the physical animal with the amazing brain, the vehicle of self-conscious self, is itself, brain and all, a part of the sense-perceived physical world from which, so to speak, it is actually made. There is only one physical system, one set of matter, one set of natural phenomena, but there is duality of self and not self, from the subject-orientated position. From the point of view of the universe, there is no such duality.

Logical space can be explored away from the physical senses, 'in the abstract', which really means in thinking. Thinking is not really abstract at all, we only think it is. Thinking takes place in self (which is not 'abstract' at all) including this kind of thinking in logical space that instantiates objects of thinking, and assists the thinking processes by using symbols to stand for the objects, as in mathematics. The 'rules' of logical space then become 'externalised' in symbols, and logical space can be explored beyond its natural presentation in sensory experience. So it is we can explore things like the topological properties of 'exotic spheres' with multiple dimensions, that we have never experienced except in remote logical space. It seems that the contents of this part of logical space are 'abstract', - that we discover them outside self, through this tool called mathematics that is outside self, that deals with what some mathematicians think of as an abstract 'Platonic Reality' (Plato never said Reality was mathematical, or abstract. What he said was that Reality is Being).

What we actually do is externalise or 'discover' what is inherently already present, but unrealised, in unbounded logical space in the mind. Because what we learn, has been externalised through the process of accumulative objectification (mathematical and conceptual 'discovery' over thousands of years), we first consciously encounter it in the objectified external form, usually expressed in object-symbols like those of mathematics, and think it is absolutely not-self. The truth is, that as long as we understand it, it is just as much self as it is not-self. Otherwise it is nothing more than a lot of meaningless symbols.

Now the 'universe' that my Circle of concepts, or any nexus of concepts represents, consists of facts and relationships in logical space, but this logical space is as much a part of self as a part of not-self. Neither exotic spheres or quantum phenomena 'break the rules' of logical space, which is well separated from the rest of self. They are both logically sound. Quantum phenomena is perfectly consistent with mathematical logic. But this logic is the logic of remote logical space, space well psychically distanced from the rest of self. Exotic spheres in logical space do not (as far as I know at the time of writing) correlate to physical phenomena, but at some time they may, because logical space and physical phenomena are all part of the same, single system, and there are many examples of esoteric areas of pure mathematics subsequently finding application in physical science and thus becoming better known. Quantum theory however does correlate to quantum phenomena. Quantum phenomena is observable by self, as a part of not-self, but not directly through the senses. It is observable in phenomena through its effects, through apparatus, which is in correlation with thinking in lower (not remote) logical space, space that correlates well to everyday phenomena in the world of animal survival. Exactly the same thing can be said of Relativity Theory, which occupies a different part of remote logical space. Quanta, large gravitational fields, and things moving close to light velocity, have not been pertinent in the scenario of sense-perception and animal evolution. This is something to which only lower logical space is required to correlate. The so-called 'collapse of the wave function' in relation to quantum theory is actually a 'quantum jump' from remote logical space to lower logical space.

The lower 'logical space' correlates to the world as presented through the animal senses but with no appreciable psychical separation from the rest of self-space. Its 'logic', the 'logic' of thinking in it, correlates to the logic of local natural phenomena, but it is also the native space of the 'logic' of the self to not-self relationship. This 'logic' is mutable, depending on the emotional and psychological condition of self. This is a most unreliable space, in which even the perception of the nature of natural phenomena is easily distorted. Only to the degree to which the 'logic' of the self to not-self relationship is distanced or absent does thinking in logical space become less troublesome, tricky, and liable to mislead. The greatest distancing is achieved by thinking in remote logical space, and externalising the 'logic' in algebraic symbols. However, this all still takes place in logical space, which is still in self. The whole scenario, the whole 'world' that is being 'understood' is a 'universe' of logical space accessible only in the evolutionary mind, and natural physical phenomena.

This is not yet everything, because there is also the rest of psychical space, in self. In a sense, if we want to say that animals think, then we can say they do so in a 'logical space' that pertains to the 'logic' of animal behaviour, survival, etc. This psychical space exists as an underlying area in our own psyche to the extent to which the human brain includes the animal past in its structure. However, because we humans have self-consciousness, we also have the area of psychical space pertaining to our own 'self-logic', the 'logic' of self-conscious self that the animals do not have. This is the 'logic' of human psychical self, the 'logic' of the world of persons. 'Person' is our rational word for human psychical self. The 'logical space' of the person is at its base, the 'logic' of animal self in the world of survival 'projected' or raised into the higher psychical space created by our ability for self-reflection - the space of self-consciousness. Its principles are an 'image' of those in the lower logical space that serve the world of animal survival. One of the effects of this is that all kinds of scenarios and behaviours that occur in the world of animal competition for survival, now occur again in the uniquely human world of persons. However, here it is no longer just the survival of the animal that is being served, but the survival of the person, the human psychical self. The world of persons is operating on a bed of principles derived from those pertaining to the survival of animals in the wild, but it becomes complicated by self-consciousness and our ability to think in higher logical spaces. This thinking is often used as a tool in the struggle for survival of the person, against the competition of other persons, as quite distinct from survival of the body. This might manifest climactically as what is colloquially called a battle of egos, but really, ego, literally meaning the individual 'I' that functions for the survival of the body, is not the cause. The cause is self.

Not all of these logical spaces are remote like the logical space of mathematics. There is, for example, the 'logic of law', not the laws of natural phenomena, which pertain to a more remote logical space, but human laws, both unwritten sociological 'laws' and formal statutes. The 'logic' of the nature of this space is of course related to higher logical space, but at the same time its nature is so different to that of remote 'logical space' in which we think about pure mathematical problems, that it can hardly be called 'logical' at all. It is the 'logic' of the collective world relative to self-reference, self interest and self protection. In it, the 'logical' relationship of self and not-self is highly pertinent.

Then there is the 'logic' of dreamstuff - only very partially does it correlate to natural physical phenomena, and sometimes not at all. Deeper down even all concepts and objects disappear, and there are only presences or 'energies', the stuff of nightmares or ecstasies. In object-orientation we would call this deep brain phenomena, the phenomena of the subconscious or id. From the subject-orientated position, it is just what it is experienced to be. In here, the 'psychical distance' from lower self we achieved in remote logical space is lost, although the 'dream' image of it can remain - we can do algebra in a dream but the results may not correlate so well. We are now immersed in self. All this, from the very remote to the unconscious id is the only 'universe' we can conceive and think about. Even the conception of God or any 'other world', or the thinking about it, is all in this 'universe', this 'set of everything'.

Diagram 3 is an object in logical space. The form of my diagram may not truly represent how the concepts of the nexus would be related for describing a given aspect of the universe. However, we could say the general form of the diagram is F. F may even be non-integral, unrepresentable or unknown or unknowable, for we do not necessarily know in thought the form or complexity of our own concept-structures and mechanisms of thinking. The 'Real' 'structure' that lies behind F, the 'structure' that is independent of F, and that F supposed to represent, is a part of whatever it is that we give the object name 'the universe'. We could 'object-orientate' it, objectify it, give it a symbol, and call it U_p. U_p does not 'exist in logical space', or include things like Euclidean space, Hilbert space or Relativistic space-time, because these are all parts of the object-orientated concept-structure F. It does not exist in any kind of mathematical space which makes sense in the processes of thinking, but rather, 'contains' or causes all this.