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 24 Feb 2008 @ 09:25
Two Conjectures concerning Fermat’s Last Theorem
For most of my life, I have been an amateur mathematician and interested in the problem called Fermat’s Last Theorem. Like most other people I was delighted when Prof. Wiles came up with his proof in 1994 and I only regretted that I was not able to understand the advanced mathematics which it contained. I have always believed that Fermat had a proof of his own and that it has to be based on the mathematics available in his time. So I continued to struggle with this problem.
My recent researches have led me to two interconnected hypotheses which, if proven, lead to a solution of this problem and which arguably could be the same approach which Fermat used.
My first conjecture concerns the equation:
X^3 + Y^3 = Z^3
If we assume that there are indeed two cubes which when added together equal a third cube then we realize that since a cube has six sides, each of which is a square, then we have the interesting fact that the first cube has a square equal to X^2, the second cube has a square equal to Y^2 and the third cube has a square equal to Z^2. This obvious fact leads me to a question which I believe is original, as I have never come across it in conversation with other mathematicians or seen it in the literature. Is it possible, I ask myself, that given the hypothetical existence of these sides x, y, and z and these squares X^2, Y^2 and Z^2, that there is a definite relationship between these three squares.
The surface area of the first cube is 6x^2, that of the second cube is 6y^2 and that of the third cube 6z^2.It is clear to me that since cubes are based on squares and squares are based on Pythagorean triangles, that it is the underlying Pythagorean triangles which make it impossible for two cubes to add to another cube or two fourth powers to add to another fourth power and so on. In fact I would say that here X^2 + Y^2 = Z^2 though this implies a contradiction.
This is paradoxical and clearly impossible. Prof. Wiles, whatever the merits or demerits of his proposed solution, does nothing to clarify the amazing contradiction at the heart of the Fermat problem.
If this is indeed so, the fact that X, Y and Z must be Pythagorean triples leads me to my next conjecture. I believe, though I cannot prove, that the same relationship between N=2 and N=3 in the Fermat equation
X^N + Y^N = Z^N
Exists between N=3 and N=4 and in general between any two consecutive powers. In other words, the values which satisfy the equation for any N must also satisfy the equation for N+1. So the solutions are like a set of Russian dolls or nested boxes in that each is contained in the previous one. Since we know that there are no solutions for N=3 then establishing these two conjectures would immediately prove Fermat’s Last Theorem.
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22 Feb 2008 @ 09:33
Edward Carpenter, Gandhi and the politics of Identity
Edward Carpenter was a Victorian writer, anarchist, socialist and spiritual adept who,famous in his own time, was forotten for most of the twentieth century and is now being rediscovered. He appears very different from Gandhi, who was famous in his own lifetime and whose reputation has continued to grow since his death, so that now he is considered one of the greatest figures of the last hundred and fifty years.
But Carpenter is comparable in many ways to Gandhi. He came from an upper middle class family as Gandhi did. He followed a conventional path and career until the chance reading of the poetry of Walt Whitman sent him on a path of simple and unalienated living in rejection of the false values of Victorian society. Gandhi went through a similar, if less dramatic, transformation through reading many deep and powerful books.
Carpenter was a mystic and had the honour of being profiled by Maurice Bucke in his classic book “Cosmic Consciousness”(1900) as a living example of the state of consciousness he terms “cosmic” and which he also ascribed to Buddha, Walt Whitman, and other historical figures such as St.John of the Cross, Jesus and Mahomet. Gandhi is known by everyone as “Mahatma” or Great Soul.
Both were visionaries and prophets. Gandhi saw that the gradual evolution of the world would lead touniversal peace and realised that the key to this was the practice of non-violence and truth. Carpenter predicted correctly many subsequent developments of society and the world.
Both had a radical view of civilization, which is a subject close to my own heart. Carpenter had a critique of civilization which is on the same level of insight as the ideas of Freud, Fourier and Marx. Gandhi used the word civilization in an ideal sense as a state of society not yet attained and famously stated that western civilization “ would be a good idea”. It is not very well known but in Chapter 6 of his 1909 book “Hind Swaraj” Gandhi wrote:
“Several English writers refuse to call that civilisation which passes under that name. Many books have been written upon that subject. Societies have been formed to cure the nation of the evils of civilisation. A great English writer has written a work called ‘Civilisation: Its Cause and Cure’. Therein he has called it a disease.”
The writer to whom Gandhi is referring is none other than Edward Carpenter.
But all this comparison of Carpenter and Gandhi would be of little point if it were not the case that Edward Carpenter has something to say to this present generation which is acutely relevant.
Carpenter was a prolific writer and dealt with themes that were taboo in Victorian times such as sexuality and homosexuality. He was one of the first to write about what we would today term “minorities” and “equal opportunities”. His own situation gave him an insight into something that is now cutting-edge and critical. He saw the wretched position of women, both poor and rich, in Victorian society. Also, the marginalisation of people seen then as deviants and criminals. All this was not alien to him and is not alien to us. And of course Gandhi was right there too. Gandhi felt passionately about the plight of Indian women, not a minority surely, but a marginalised majority. He worked hard to combat the evils of the caste system, particularly as it created the stigma of “Untouchability”. He cared greatly for the Muslim minority in India and tried to avert Partition.
The poet Rilke made a profound observation to the effect that “ Our deepest fears are the dragons that guard our richest teasures.” We can rephrase this to say “Over the gateway to the Free Society stands the sign of Identity”.
Ever since the first photograph of our blue planet was taken from outer space, the question of identity has grown more and more powerful. Inner space is the new frontier and has been for the last thirty years.
If we are prejudiced against Jews, or Muslims, or gay bishops or disabled black women or any other expression of the infinite variety of human diversity, then we cannot move forward through the gateway to the Free Society.
As Gandhi often pointed out, quoting the Bhagavad Gita, the real battle is the one which goes on inside ourselves, our own psyches. Gandhi and Edward Carpenter are in agreement here and this is part of their continuing relevance to the ongoing struggle for Freedom.
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19 Feb 2008 @ 09:48
Freedom and Identity
As we have seen, the most free part of us is our spirit, then out psyche. Then our economic behaviour. As we move up the levels of society, through groups to politics and finally military force, we become less and less free.
And of course, the thing about us that is free, our spirit, is characterised by individuality. And what comprises our essential unique individuality is the million and one different aspects and identities that make us what we are: the colour of our eyes or skin; our race or ethnicity or religion; our age or physical and mental (dis)abilities; our gender or sexual orientation and literally thousands more characteristics.
If our society is to attain to freedom or enlightenment and we with it, then our spirit has to be realised. And that means in the form of the celebration of great diversity in human individuality and the uniqueness of each identity. In the unfolding of this freedom and celebration it is obvious that minority groups have a huge part to play.
Conclusion: SpiritMind over Matter----- Matter Undermined
This summing-up and conclusion pertains to the whole project I undertook just before the millennium to update the views I held on the subject of alienation and civilization. Theories of civilization are not rare, even radical and deep theories. Yet to get a theory that combines depth, plus wide-ranging knowledge and erudition, plus a mystical and artistic display worthy of a master or mistress, one has to look at someone as remarkable as Edward Carpenter.
Karl Marx produced a radical if somewhat fragmentary and partial account of civilization, and even wrote poetry as a young man. Yet he was no mystic; indeed a materialist. One prejudice he shared with the vast majority of his contemporaries, will help eventually to render his theories obsolete, just as much as faulty notions of surplus-value or the State (dictatorship of the proletariat).This flaw in his theory is the lack of understanding of the importance of identity and particularly sexual identity.
Edward Carpenter, though born only 25 years after Marx, was a visionary and mystic and was indeed 100 years ahead of his time and in advance of what Marx saw. Edward Carpenter was homosexual, at a time when it was considered a heinous offence and social deviancy. Yet he realised the importance, as no other, to the freedom project of the issue of identity and particularly the centrality of sexual and gender identities. He was one of the first to write about what we would today term the minorities question.
Identity is important because it links spirituality with individuality. Yet our sexuality links our spirituality with our physical body. Spirit with Nature. It is part of our innermost, intimate identity. If spirit itself is alienated, as it always has been, in the form of our Egos thinking we are separate, lonely and cut-off “individuals”, then it was only when this alienation, or Ego, affected our relationship with surrounding Nature and our own gender and sexual identities, that society left the tribal, community path it had been on for countless millennia, and undertook the ”Great Separation”, as the Taoists call it.
This is the path of alienation and ultimately civilization on a global scale. The whole of modern history is not just the evolution of the spirit of freedom, as Hegel claims, but the reclaiming of our whole identities in all its richness and variety: our religious, racial, ethnic, gender, sexual and particularly our identities as part of Nature.
Matter is being supplanted gradually by Spirit. Matter is being interpenetrated and gradually suffused by spirit. This may be what Teilhard de Chardin termed the “Omega Point” Nobody who has witnessed the bizarre events of the last few years, such as the flooding of New Orleans, the Indian Ocean Tsunami, or the earthquake in Kashmir, can doubt that matter’s reign over the world is coming to an end. Nature, while a form of matter, is also a form of spirit.
Mindspirit over matter----matter undermined.
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19 Feb 2008 @ 09:45
Core of Civilised Society
It was the view of Marx and Engels that the core of civilized society was the state. I think that there is some truth in this, but would like to suggest that the state is the tip of a pyramid/hierarchy in the same way that the tip of an iceberg connects to a much larger pyramid. In other words it is the top section of a pyramid which is relatively small at the apex but which stretches right down to the base of society.
The main function of this pyramid is to channel resources (both human and material) from the bottom of the structure towards the top, and to channel control and coercion from the top to the bottom. I believe this is self-evidently true. The recent disasters last year in New Orleans, Indian Ocean Tsunami and Kashmir earthquake, clearly show that this pyramid/hierarchy just does not operate effectively in the opposite direction. It is almost impossible for the state to channel large amounts of resources from the top to the bottom of society. Hence the woeful inadequacies of relief in times of disasters. In ordinary times bureaucracies an barely cope with trying to provide resources from the top downwards or from the centre outwards.
In other words the pyramid is like a hoover which sucks up resources in the form of taxes and profits and channels them from the many to the few. This is the way it has always worked in civilised society, despite pious intentions to redistribute wealth to the many from the few.
Levels of Society
(1) Psycho/Spiritual
Our Psyche and Soul. Which I also equate with what Jung and Freud called the Id or Unconscious. The other psychic mechanism, the Ego, would be the equivalent to the State (in society).
Identity and individuality are key and central to this level of being. More on this later.
(2) Economics
After the personal level of psyche and spirit this is the most free level of our being and involves both personal and social aspects. Economics involves trading and production of goods and services. The alienated forms are commodities and money.
(3) Society/ Social
As we move up the levels we go from greater to less individuality. We go from individuals, to small groups and finally large groups such as classes. Basically this is about all the groups we belong to in society: Family groups based on kinship such as Tribes, clans and families. Educational groups such as schools and colleges we have attended. Occupational groups and professional ones. Finally the class we belong to or identify with. Then there are interest groups and associations based on beliefs, hobbies or identities. All these groups make up civil society.
(4) Political/The State
In a civil society the use of force or coercion is monopolised and controlled by the state. The people who control the state are termed the rulers. Politics is the competition between different groups for control of the state, which gives them the ability to make the rules which apply to the whole of society, which rules direct and control what is considered the legitimate use of force, which rules are usually termed Laws.
Naturally as we rise up the levels of the civilised society we are going from greater to less freedom. Our greatest freedom is in our own spirit, then our psyche (our personal life) then our economic relationships. As we proceed up the levels we encounter resistances to our free behaviour. In the form of prejudices, customs, rules, laws and physical coercion, repression.
(5)Military/The Army
Basically the state in civil society is based on the monopoly of the use of force or coercion. There is a contradiction here because as Gandhi said, the only truly ethical action is a voluntary one. So, by compelling others to do what we want them to do, whether for their benefit or our own, we inevitably engender corruption of ourselves and others. The state’s use of coercion is the source of vast corrupting influences, and often takes the form of rampant financial irregularities in bureaucratic and ruling (power) elites.
Civilization and Madness
It is generally recognised that tribal societies suffer less from mental illnesses than civilized societies. I will now try to briefly explain this fact. It is well known that hysteria began soon after the imposition of repressive forms of monogamous marriage on women at the beginning of civilization. Other forms of social control repressive to women only reinforced this tendency to fight back against male dominance.
It is interesting that hysteria, though it has many different forms, is basically a sort of dissociation of the personality. And dissociation is of course connected with alienation. It is not surprising that early psychiatrists were called “alienists”.
Schizophrenia, though more characteristic of capitalist societies than feudal, is also a form of dissociation. So it seems clear that mental illness is a form of alienation. More >
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19 Feb 2008 @ 09:37
This is my sixth Millennium Essay which I wrote a few years ago. I circulated it informally and this is the first time it has been published.
Essay 6: MindSpirit over Matter ----- Matter Undermined
The Crystal Palace
There is a white elephant, or a pink elephant, or any manner of unwelcome guest, which is inhabiting the magnificent crystal palace of civilization, and which everyone has long ignored or looked at with embarrassed glances and wished would just dematerialise and go away. The Crystal Palace, as you will recollect, was built in London to house the 1851 Great Exhibition, and epitomized for that generation all the magnificent achievements and promise of the nascent Victorian capitalist society. The term was also used by Dostoevsky, in his “Notes from the Underground”, in a more ironic way and counterposed to the darker, underground parts of reality and our psyches, later so well exploited by the theories of Nietzsche, Freud, the existentialists and others. The crystal palace is representative of reason, rationalism and science---while the underground is symbolic of the emotions, the unconscious (the Id) and irrationalism.
The white elephant or unwelcome guest at the table of civilization is in fact the theory of civilization: any theory of civilization which is deep and goes to the root of a contradictory and problematic phenomenon and form of society.
Of course there are experts on civilization just as there are experts on tic-tacks and asparagus tips. But the real radical theories of this subject have been consistently ignored for the past 250 years, people like Rousseau, Fourier, Edward Carpenter, Freud, Marx and Engels and more recent ones.
The Missing Link
It is my contention, that what everyone is ignoring with such nonchalant intensity, is in fact, in its radical form, the missing link which can unify and unite the many partial, different and separate facets and aspects of the world, which in their diversity and complexity so intimidate, confuse and mislead so many people at the present time.
Alienation is Separation
The reason why a radical theory of civilization can re-unite and re-integrate our understanding not only of civilization itself but also many other things, is because many theories of civilization, sometimes anarchist sometimes marxist, which go to the root of it all, point to the great separation between things (Alienation) which deeply characterises civilized society.
The fragmentary and confused state of this knowledge of our basic form of society, is itself a symptom of the alienated nature of civilization, and the fact that theories are beginning to be advanced to counter this, is a sign that the age of holism and reintegration of everything is well under way.
From Tribal Network to Civilized Hierarchy
Undifferentiated tribal society is a sort of community-based society of localised, decentralized networks. For many reasons, in the development of civilization, this became a centralised pyramidal collection of hierarchies. In these circumstances a Network of networks collapses into a Hierarchy of hierarchies.
Furthermore, the undifferentiated tribal society where everything, from politics to magic, was mixed together in a holistic mish-mash, became a highly separated, differentiated society where there are 6 or 7 distinct levels which we can schematically identify as:
Psycho/Spiritual
Economics
Social (Classes)/Civil Society
Religious/Science
Political/ (The State)
Military/ (The Army)
The Law of Analogy
It is my belief that everything is analogous. If this were not so, it would be impossible to make comparisons. It is only possible because although things are different, they are basically the same
A glass prism, for some reason, differentiates a single beam of white light into a rich, colourful beam of many hues. We are richer for those colours, beautiful though white light is. Similarly, the prism or hierarchy, of a civilised society, differentiates the mixed, holistic beam of white light of undifferentiated tribal society, into a highly complex and colourful mix of different levels comprising economics, social classes civil society, in fact all the things I’ve just outlined and more.
Because the different levels are basically analogous, it is noticeable that equivalent statements can be made about phenomena on different levels. For example (1) On the psychological level the “unit” of alienation is the EGO. (2) On the political level the “unit” of alienation is the STATE. (3) On the level of the Economy the “unit” of alienation is MONEY. It is my belief that there exists a whole multitude of equivalent statements connecting things on different levels.
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10 Feb 2008 @ 09:42
Homophobia is Destroying our Planet
All over the world the battle lines are drawing up between those who can accept themselves and others, and those who have a morbid fear of Difference, of the Other. Make no mistake, saving our planet is not about technological fixes like burying CO2 or recycling, but rather dealing with the problems of consciousness which have got us and the world into this perilous situation. The ecological crisis is primarily a crisis of a fractured consciousness, and as I will demonstrate, a crisis of our consciousness of the Other, and the Other within ourselves.
One of the first things I learnt in an advanced psychology group is that “ we relate to other people in the same way as we relate to alienated parts of ourselves”. In other words all the games, alienated transactions, processes and institutions which cause problems between people in society, have their roots in our relationship with ourselves. We relate to others in exactly the same way that we relate to ourselves. Our morbid fear of the Other; the black person, the homosexual, the muslim, the feminine woman, the disabled person are all problems we have with those parts of ourselves.
As I have demonstrated elsewhere, the soul is more or less infinite, and the human personality while finite is vastly complex and manifold. Whether one talks in terms of Jung’s archetypes or Assagioli’s subpersonalities and identities, all human life is found within each one of us. It is up to us which ones we choose to embrace and nurture, but it is definitely a huge mistake to see certain of them as “alien” and to deny and reject them in ourselves and even try to destroy them. For inevitably, as we “alienate” these identities within us, we will inevitably “alienate” ourselves from their human counterparts outside ourselves in society. The macho man’s mistreatment of women is grounded in a terror of the feminine part of himself. The homophobic woman has a terror of the bisexual or gay identity within herself. It is not for me to say which identities other people should accept and embrace, I’m just warning people of the great dangers of rejecting and alienating these parts of oneself. It will dehumanise and brutalise you and turn you into an oppressor if you can’t tolerate these parts of yourself.
It is interesting that the most repressed and rejected parts of ourselves are usually the identities connected with our sexuality. I have speculated elsewhere that our alienation from nature, surely the cause of climate change , led to man’s alienation from woman ( sexism), then other men (homophobia) and even God. In there somewhere, already alluded to, is the immense rejection of “disturbing” identities and subpersonalities within himself. Nature is a huge Other, and the insane attempts by people and society to control and dominate it, point to an incredible morbid pathology existing in them. I have speculated in some essays I wrote for the Gandhi Foundation ( of London), that our sexuality, as a part of our identity, is Nature itself within us. It’s as fundamental as that. It’s clear to me that the almost obsessive, fanatical attempts to control Nature are a direct mirror-image of similarly unhinged attempts by Church, State and Public Opinion to control our sexualities and expressions of sexual difference. Nature and sexuality are opposite sides of the same coin representing the Other.
As I said above, the battle lines are drawing up all over the world. Those who believe only in technological fixes, will only create more and similar ecological problems, whatever the outcome of their “fixes”. The solution I propose is not materialist but rather Spiritual/psychological and is one which addresses the underlying problems of the crisis of consciousness.
Traditional spirituality talks about meditation as a way of reaching enlightenment. It is the mystical union with the One, the Divine. But there may be other ways. Many people have predicted, over the centuries, the coming of what they have called Cosmic Consciousness, SuperConsciousness, Universal Enlightenment and what Teilhard de Chardin termed the Omega Point. This is the whole world attaining a new level of spirituality, a new awareness, a new consciousness.
There is a connection here with the discussion above. It is possible that by accepting and integrating within ourselves the manifold identities contained in each one of us, particularly the common identity of sharing in the Godhead, that universality will ensue. Certainly, this is the purpose of Psychosynthesis, Assagioli’s form of psychotherapy, at the level of the individual. In his teaching, the individual becomes a whole person by integrating into a synthesis, these sub-personalities and identities.
This is one possibility, there are many others. Whatever happens, it will be our consciousness being healed, our willingness to love ourselves and everything else, particularly the Other, which will play a major part.
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27 Jan 2008 @ 09:37
On Creating and Resolving Contradictions on the ChessBoard : Part I
Introduction
One of the great arts of wisdom is the study of opposites or contradictions, known as dialectics. This is the knowledge of the observation, analysis, creation (where appropriate) and resolution of contradictions in any of a large number of fields ranging from logical debate to mathematics and, as in the present case, even board games like chess. The Perennial Philosophy, in its many different versions, affirms that the universe has a dual nature, everything being composed of pairs of opposites. When we come to practical action of any sort it is possible to take this fact into account. Socrates did, in ancient Athens, and he and his followers applied Dialectics to the practical task of drawing out the contradictions, inconsistencies and confusions in the customary arguments of their fellow citizens, and in this process uncovered the foundations of logical debate and a grand philosophical theory which came to fruition in Plato’s system of Forms.
Many mathematicians were also dialecticians but the example I have in mind is the little known case of Pierre de Fermat who, in 17th century France, laid the foundations of number theory and modern mathematics. In doing so he invented a wonderful technique called “the method of infinite descent” which is in reality a sophisticated dialectical handling of algebraic forms to arrive at a contradiction and thus prove different mathematical theorems. After Fermat’s death his techniques gradually fell into disuse and science, not just mathematics, turned its back and reacted against this knowledge of contradictions.
In the late 18th century philosophy was reinvigorated by the theories of opposites inherent in the work of Kant and Hegel. Unfortunately, following on from this, attempts to change society which came with Karl Marx’s adoption of dialectics, led to another reaction against it which has lasted ‘til the present day.
Now this knowledge is ready for a rebirth, and I present the following simple account of its application to the game of chess, as an attempt to de-mystify something which is really very simple to understand but very difficult to practise well. Indeed it is not called an art of wisdom for no reason. It is the art of mastery or mistressy.
Chess
In everyday life a double-bind is usually something that cannot be beaten. In a game that proceeds one move at a time, like chess, if you can create double or multiple threats with one move, the equivalent of a double-bind, then your opponent is usually in trouble.
There are many ways to win at chess, but as you improve and so do your opponents, it becomes impossible to rely on people making mistakes or blunders. One can’t even rely on an overwhelming powerful attack to win, brute force, because to every move you make there is a counter-move your opponent makes that neutralizes or otherwise gets them out of the trouble your move has created for them.
As a game proceeds, both players move their pieces into what are often, chaotic and disorganised formations. The original, undifferentiated position which exists at the start, gradually becomes more complex, interpenetrated and differentiated and, despite every effort to maintain organised, strong and harmonious formations, certain awkwardnesses and weaknesses are created in both positions.
These are what I call the “contradictions” on the chessboard. There are well-known and obvious weaknesses which can be exploited by pins, forks, checks, discovered checks, double checks etc. This leads to the possibility of skilful moves, employing subtle threats and tempo gains, either separately or in combination, in order to derive an advantage, whether of material or position.
Indeed, this finding and working on a contradiction and finally resolving it, is often the course followed in a game. One side, will bring pressure to bear on weak-points, and as each move is met by a counter-move, a position is finally reached where one player is able to get a double-bind and thus win.
In the next part of this article I will look at creating contradictions on the chessboard in more detail.
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7 Jan 2008 @ 09:41
On the Dual Nature of the Universe Part II
Elsewhere I have referred to the fusing of opposites, and a new possibility of science and mysticism coming together. If spirit and matter are indeed fusing, and in Hegel’s formulation, presenting a synthesis in the form of ‘Mind’, and in my words, also as ‘Information’, then after this period of alienation a new Oneness, a new Monism, a new Monad is emerging. What is this.
In my Millennium essays of a decade ago, I put forward a view, new to conventional ideas if not mysticism, that the personality was like one side of a coin, the other side of which was the Soul. I will now expand and develop this.
In the Buddhist/Hindu tradition the personality is compared to a jewel of myriad facets, each one reflecting an innumerable number of other faces, like a hall of receding mirrors. Depth upon depth, image upon image. The personality, or Self, if not actually infinite, is manifold and complex. In literature we have the remarkable view presented by Hermann Hesse in Steppenwolf. He first mentions that his protagonist, Harry, is both a man and also a wolf of the steppes ( a ‘steppenwolf ‘) not surprising, when we consider the title of the book. Then he proceeds to say that Harry’s personality is much more complex than this simple schema suggests, and is in fact manifold and practically infinite, divided into different sub-personalities and identities. Later on, in the surrealist/hallucinogenic episode where Harry is in a theatre, strangely reminiscent of a renaissance Memory Theatre, he can go into different rooms with titles on the doors referring to his past, and which are filled with mirrors, images and crystals, where he encounters more sub-personalities and identities.
Clearly, there is a profound view that the human personality is complex and deeply-nested with sub-personalities, identities and characteristics which reach off into infinity.
Building on this view, I add a passing comment on Eric Berne’s theory of Games and Transactional Analysis. Berne’s whole approach is built around just three archetypes, namely the Parent, Adult and the Child. Using this template he creates a rich analysis of society and psychology featuring as a key aspect alienated psycho-social behaviour which he calls “ games”. All this can be done employing just three archetypes ( Jung’s term), so demonstrating the amazing power which is inherent in these archetypes, sub-personalities and identities.
However, there is more to this. Some people believe that the psyche is physically based, in our genes and also in our brains. That is, that it has material aspects and foundations. Also, that while manifold and complex, it is not actually infinite. Furthermore, each of us being a unique individual, it is discrete, in the same way that an individual particle is. Also, all theories of the personality agree that it is highly structured. In Freud we have Ego and Super-ego and also Id. In Jung we have archetypes, Collective Unconscious, Animus and Anima. In Assagioli we have sub-personalities and identities. All this suggests that the individual human personality is an aspect, at the material end of a pole of a contradiction, as I put forward in part I of this piece.
The infinitude of the personality, referred to earlier in those accounts, is by no means certain for the simple reason that there has always been ambiguity, and even confusion, in most traditions when discussing these three things : the personality, the Self and the Soul. It is my belief that the central thing is the Self, of which the material aspect is the personality and the spiritual aspect is the soul.
We are treading upon sacred ground here and must proceed with caution. According to Kant, in his 1781 book ‘ The Critique of Pure Reason’ there are things which are inherently unknowable, things he averred belonged to the noumenal world of “things in themselves” or essences. The Soul belongs among them. Among other things in that remarkable book, Kant reintroduced antimonies or opposites into philosophical thought which were to achieve a pinnacle a few years later in Hegel’s theory of contradictions, known as dialectics. By the way, Hegel did not share Kant’s view about things being unknowable. Even essences, he believed, were knowable.
Much has been written about the soul but it remains a misty area of vague notions and speculations. I am not conversant with the opinions of Church Fathers or theologians but I believe my opinion will merit consideration.
I believe in an inherent duality of all things in the universe, based on a prime duality of Spirit/Matter which together make up the Monad, which is One, but not a monolithic One. More on this later.
In this view, the soul is the spiritual aspect or half of the Self. It is infinite, continuous just like a waveform of light, and contrary to the discreteness of the personality, its continuity provides a bridge to all the other souls that exist. All these souls are part of the Monad, the World Soul or Self, which together connect and interconnect everything and thereby provide the universal web, which mysticism/perennial philosophy asserts as one of its basic beliefs.
Science and mysticism
As I demonstrated in Part I science is the product of a succession of alienations and of the most alienated society in the history of civilization (capitalist). Yet we must not thereby conclude that it is worthless or negative. Alienation is not necessarily a bad thing. Each of us has to separate from our parents, particularly our mother, during adolescence in order to become individuals and find our true identities. This is clearly a process of alienation. Similarly, as put forward by Hegel, Spirit undergoes a process of alienation when it becomes a myriad of individual, material things. Science has achieved many remarkable things. Particularly, in recent years with its growing fusion with mysticism in the form of quantum physics and Chaos theory it has produced some remarkable results. James Gleick in his book “ Chaos: the Making of a New Science” demonstrates some amazing mathematical objects and ideas. One in particular seems to tower above others and I believe people don’t really understand what it is.
First I will describe a traditional representation of the monad: the Yin/Yang symbol. A pair of interlocking spirals which together form a perfect circle but each half of which is of a different colour( polarity) and facing in opposite directions. This elegant, beautiful object is considered a perfect representation of the One and is a central icon of Taoism. I believe that Chaos theory provides another, similar icon
which is practically identical to this yin/yang symbol but different in informative ways. I am referring to that weird mathematical object known as a Strange Attractor (or Lorenz attractor). I will not baffle the non-scientific reader with overly technical details except to say that this “attractor” represents physical processes or qualities. It has two wings, like a butterfly, and is as beautiful in its own way as the yin/yang symbol. It is completely continuous with no breaks. When the “action” or “locus” of a moving point moves from one wing of the butterfly to the other, it represents either a reversal of direction of a physical system ( such as a pendulum) or the change of polarity from one quality to its opposite. Gleick comments that this mathematical object has strange properties and is almost mystical and similar to classical spirals. One strange property is that it is an infinite object in a finite space. The continuous lines that make up this unique object, upon closer and closer examination, keep splitting into two parts, which then split into two again, and so on infinitely.
We see then that opposites and polarities and contradictions and the number 2 are not just the preserve of philosophers. I believe that this mathematical object is another icon of the Monad equally as valid as the Yin/Yang symbol. It has been produced, quite independently, by scientists, many of whom have no interest in, or knowledge of mysticism.
If this is true it suggests some important conclusions. Dualities emanate from the Monad because it is by nature “One-Composed-of-Two”. It is not a monolith. It is actually composed of an infinite pair of opposites, joined together into one like the two wings of the butterfly, which can split into two ad infinitum. This is what they do as they emanate from the Monad. This scientific icon confirms the wisdom and correctness of the ancients, and demonstrates the unity of science and mysticism and points to the possibility that this observed fusing of opposites in the world of politics, media, economics etc. is just the monad calling us all back to Itself. More >
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30 Dec 2007 @ 09:43
On The Dual Nature of the Universe Part 1
Everything in the phenomenal world has a dual nature. This has long been known to mystics but has only in recent years begun seeping into general awareness. It was considered weird and paradoxical when the wave/particle duality of light was revealed to the world of science a hundred years ago. And also that matter and energy were two different aspects of the same thing associated with the theories of Einstein and nuclear physics.
In truth, everything shares this feature of a dual nature. The only exception is the Source ( sometimes termed God/dess) which is believed to be One, and therefore a Monism. The Source has all these dualities emanating from it and is thus the creator of the phenomenal world which we term reality.
If we enquire further we can see that the dualities are the same thing over and over again. The basic duality is Spirit/Matter which then takes on many different guises and suggests some interesting implications if we follow it through.
A particle (for example of light) is finite, discrete and material whereas the other aspect of light, the wave-form, is continuous, non-material and possibly infinite. I am suggesting here that the Source can be represented as a form of energy and that energy is a spiritual thing. Similarly, Einstein’s theory that matter and energy can be transformed into each other suggests the same thing that energy is a spiritual form and that matter is a non-spiritual form of God that we term material.
In Part II of this piece I will assert and try to demonstrate a further example of this basic duality which I think will surprise you, namely, that the human personality, Psyche, is a discrete, structured, almost material aspect of something, the other aspect of which we call the Soul. In the same way that matter and energy are equivalent so, I contend, are Psyche and Soul. This is not new to the science of mysticism but is relatively unknown to the materialistic, quantitative science of modern society.
This prompts me to look at, by way of introduction, what we mean by mysticism, religion, philosophy and (modern) science.
Mysticism, as I see it, consists of the common ground between all the different versions of the Perennial Philosophy. Mysticisms vary, and so do the different forms of indigenous wisdom which people call variously, perennial philosophy, wisdom teachings, first nation teachings etc. I believe they are all saying the same thing in slightly different ways, and the version I particularly follow is Taoism, which was originally native to China.
The basic idea of mysticism is that everything is One and that all the parts of that One are completely interconnected. It is a theory of Identity and also communication and intercommunication. There is a web that fills the whole universe. Everything is interconnected and alive, pulsating with energy. It is a profoundly vibrant and loving conception of the world.
I will briefly describe the ‘progress’of modes of knowledge. Thirty years ago I wrote a book and commented there that I agreed with Auguste Comte’s view of the ‘progress’of forms of knowledge via religion, philosophy and Science. I will now add to that comment and conception. I believe that the perennial philosophy/mysticism is the original template for all knowledge and that the succeeding forms are in fact only described as ‘progress’ in a qualified way, being indeed alienated steps away from the original wisdom. Religion follows mysticism and is one degree of separation or alienation from it. In religion we find many of the same things as in mysticism, but in a strange, alienated way. It does not talk about the wonders of the Universe and its oneness, but is obsessed with deities or gods. This inevitably leads through time and development to a monoculture represented by monotheism or the belief in One, all-powerful, all-knowing God.
The next form of knowledge, both historically and logically, is philosophy which is one step of separation or alienation further on. It is really an abstraction of religion; religion in a completely abstract and de-mythologised form. It tries to prove the existence of God, it does not assume it. Volumes could be written on this subject so I will not attempt to say any thing further here.
Science, the next form of knowledge in Comte’s trilogy, and according to his view and that of his contemporaries the highest form possible, is one stage of separation and alienation further on. In this version the alienation becomes unbearable. The Universe is a cold dead place, everything is separated , nothing is connected, there is no God, only cold, lifeless matter. Qualities are disregarded. Only Quantities are thought relevant and important. The most alienated society in the history of civilization produced this kind of knowledge, and used it to subjugate nature and the whole world.
It is my belief that this development of knowledge through increasingly alienated modes can be salvaged and turned into something positive. If one-sided modern science can be fused with the deep qualitative truths of mysticism, which in fact does seem to be already happening, it will produce a mystical science and a scientific mysticism and open the road to real knowledge. Not just superficial knowledge which comes from the head, the intellect, but a deep knowledge of essences, which is achieved by integration of the head and the heart, and which is truly wisdom. More >
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17 Dec 2007 @ 09:59
Superconsciousness
In this new period, post millennium, post modernist, 21st Century, all distinctions seem to be gradually disappearing. Only a few weeks ago Tony Blair, in a farewell speech, complained that in the media’s treatment of news stories the old distinctions between values and facts were becoming blurred. What we are in fact witnessing, in this and other areas, is the fusing of opposites that were once considered distinct and indeed often irreconcilable. Other examples include the public/private dichotomy which is being seriously affected by new means of communicating such as mobile phones/ internet. Most relevant to our discussion is the blurring that is happening between matter and spirit, to which I have alluded elsewhere. Material things seem to be becoming less “massy”, and indeed “material”, they are becoming etherealised, digitalised even spiritualised. If opposites are indeed in the process of undergoing fusion, then this raises some very intriguing possibilities. In the area of theory, a fusion of Idealism (as in Hegel) and of Materialism (as in Marx) would lead to a supertheory, which we could provisionally call “IdeoMaterialism”(IM) which would be a monism of a new kind. The old dualism of matter and spirit would be in a new relationship, and when I give some examples I think you will agree, a more harmonious relationship. In other areas the fusing of opposites promises radical if not utopian possibilities. The fusion of mind/ body in the Cartesian sense would promise a new and holistic science, while the fusion of Id and Ego, long mooted by utopian psychologists, would usher in a new era of enlightenment.
To return to our monistic “IdeoMaterialism”, I will present some of my ideas in this new light. I believe in three stages of human consciousness, two of which have long existed and the third of which is gradually emerging globally right now. The first level is what we would call “Animal “ consciousness, and is that level of consciousness and awareness that existed right through our process of evolution through primate and human groups of varying complexity, up to the lower/middle stages of Barbarism, associated with tribal/clan society. As the name suggests this level is typical of animals and does not imply real individuality or self-awareness. The knowledge of Good and Evil, presented in the Bible myth of the Garden of Eden, along with an awareness of nakedness and shame, is ushered in by the next level of consciousness, which is commonly called “Self-Consciousness”. This leads to great individualism and even narcissism, and indeed rapidly transforms and destroys the old society of clans, tribes, kinship, family and undifferentiated solidarity. The conventional materialist theory such as Marx’s, portrays these events as caused by money and other forms of wealth, brought about by improvements in technology and production techniques. But that is only half the truth. In reality, it was the new Individualism, the new consciousness, that created the conditions for these developments. It’s not that materialism is wrong, it’s that it only tells part of the story.
This brings us to the present time and the next level of consciousness which some call “Superconsciousness”, others like Bucke and Edward Carpenter term “Cosmic Consciousness”, and more recently people have started to refer to as “Universal Mind” and “Universal Consciousness”. This level of awareness and consciousness is well known and its coming long predicted by spiritual adepts and enlightened mystics. Basically it is an awareness of the cosmic connectedness of everything, a wholistic awareness that gets beyond the limitations of separation, individual egos and alienation. Just as “self-consciousness” gave the rationale to the sort of society known as civilization, so “Superconsciousness will give, and is now giving, rise to a particular and unique form of society. Whether this coming society will be called “SuperCivilization” or indeed “The Kingdom of God on Earth” we cannot yet be sure, but undoubtedly it will be characterised by some amazing and almost unbelievable things.
I will now present a further example of a subject which can be illuminated by this fusion of Idealism and Materialism. This look at the phenomenon of Fascism is no idle exercise, and i believe and hope to demonstrate, that it is one of the biggest threats to our common survival and achievement of “Superconsciousness”. Many different perspectives exist on the subject of fascism. It has been analysed from the viewpoint of economics, politics, society, mass and individual psychology, all more or less materialistically and, i’m sure, relevantly. It may surprise you that I am analysing it as a misguided form of mysticism, and as an infantile attempt to go back to the “animal” stage of consciousness, instead of forward to the higher stage of “Cosmic Consciousness”. A few commentators have already noted mystical elements in fascist themes of “the totality”, “the Folk” “union with Nature” etc. but I fear they do not see its true essence. In Fascism, people seek to follow seemingly powerful, Big Daddy, Big Brother leaders who will answer every question with certainty and make all decisions for their followers. These people are giving up their role of autonomous, responsible adults and seeking, in an infantile way, to revert to a “golden age” of childhood dependency and irresponsibility. They seek mystical union with a “whole”, whatever it is, whether their local football team, their nation, their state, and try to give up the pains and tribulations that come with self-awareness and adulthood. They want themselves and society to return to the preceding stage of “animal” awareness and their football team is a substitute for the tribe and the clan. There are great dangers in identifying something which is only partial as a totality, whether it be a football team or even a state, or a great talent like being a musician or artist. We are called to be whole people. The only totality is the Universe, The Absolute, The Source, God. To erect anything else as a totality is to worship false idols and we know what danger there is in making a great leader or state into an idol.
There are great dangers of these kinds facing the world today. Fundamentalism of any sort is similar to this wish to revert to a simpler, more primitive, infantile state of certainty and dependency and is potentially fascistic. This inevitably gives power to those who are unworthy of it.
No, forwards is the only way. Towards greater awareness, responsibility, superconsciousness and the recognition that the only totality, the real mysticism, is of the universal. Not one tribe but all tribes. All creation, All the Universe.
More >
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