John Grieve    
 HomoRacism1 comment
category picture31 Aug 2008 @ 09:19


HomoRacism : Homophobia and Racism

I’ve never really liked the terms Islamophobia or Homophobia because people don’t take these terms very seriously, even though they reflect the truth of the problems some people have with Muslims and those of different sexuality. The public consider these terms psychobabble and have always seemed to prefer more gutsy terms like racism, fascism etc. for analogous conditions. I would like to suggest that we rename the hatred of gays as HomoRacism.
Desmond Tutu, the former Anglican Archbishop of Capetown, said a while ago in defence of gays that the hatred people showed for them was the new Apartheid and the new racism. Desmond Tutu, in my opinion, is one of the greatest men alive and a beacon to all. With religion playing such a large part in this new homoracism, it is noticeable that a large number of black people are themselves the perpetrators of this new form of racism. This seems paradoxical, and to an old-fashioned liberal a person of colour could never be a racist. But this is patently true. This fact makes us look closer into the complexities of being human, and makes us question the belief held almost as a truism that racism is the basic form of fascism. Similarly anti-racism is held to be the corner-stone of Anti-fascism. The Truth is that this view is too simplistic. Fascism is a huge problem, and always has been, with Identities and the Other.
Gays have always been persecuted, just like Jews, through-out history even in societies like the Roman Empire which was completely multicultural, and where racism was unknown. At that time it was a capital offence to be homosexual, and also the Jews were persecuted on account of their monotheistic religion, because they would not worship the emperor, and not because of their race. It is my personal view that identities based on sex are more fundamental than those based on race or religion and the modern emergence of the contradictions referred to earlier confirm this fact.  More >

 Theology of the Other13 comments
category picture27 Aug 2008 @ 08:32


Theology of the Other

It is my basic belief that the fundamental contradiction of the human condition, our basic duality, is that we are all both human and divine. We are all human but we also partake of the nature of the divine godhead. This has been known to mystics for millennia and perhaps before that to the people who shared the Perennial Philosophy as part of their indigenous culture.

It is also my belief that it is the denial of this fact that leads to the problems people have with “the Other”. It is not just minority groups or Nature itself that represent our problem with “the Other” but essentially our denial that we are divine. It is indeed ironic that traditional “civilised” accounts of the “Fall” of man and woman portray it as a result of the “hubris” of wanting to be like God. Our “hubris” consists rather in thinking we are greater than God in our isolated individuality, cut off from ourselves, each other, Nature and the Source itself. Putting our faith in this isolated individuality, and all hopes of global salvation based on it are the two main fallacies that have to be tackled by humankind. The reality is exactly the reverse. It is the Self-conscious level of awareness which cuts us off from this knowledge of the real duality of our nature. We don’t have to become like God, we have always shared in being so, and the “Fall from Grace” is a forgetting of this basic truth. Original Sin is not thinking we are Gods, but that we are greater than God/dess on account of our isolated, alienated individuality. Our extreme individuality, narcissism, is an expression of this. All the problems which are besetting the world today from racism, war, homophobia, sexism, hatred of disabled people, all sorts of scapegoating of others, and particularly climate change all stem from this crisis of identity. Everything in the world is teaching us the same lesson concerning “the Other”. God is the real Other, and our denial of all “the Others”, within us and society, is the same thing on a different scale.  More >

 Grieve''s Twin Prime Conjecture4 comments
category picture24 Aug 2008 @ 15:14


This is a restatement of the classic Twin Prime conjecture in a more particular and provocative form

If you take any prime number greater than 2 and square it then take the next prime above the original one and square that,then the intervening numbers will always contain at least two pairs of twin primes.

example: 3 squared is 9 and 5 squared is 25 and between the numbers 9 and 25 you will find two pairs of twin primes namely 11,13 and 17,19

Comments appreciated  More >

 Why is Dialectic Important8 comments
category picture4 Aug 2008 @ 09:07


Why is Dialectic Important

In an article a while ago I contrasted the Taoist approach to solving problems with the Confucianist one. Taoism tries to grasp the essence of anything it analyses or any problem it is trying to solve. Confucianism, on the other hand, seems content with looking at and considering secondary, superficial, irrelevant and numerous inessential aspects of a subject or thing. Occasionally this leads to a solution, but usually this is arrived at only after years of piecemeal efforts by different people. The Taoist approach often yields a quick answer to the solitary enquirer.

The Confucianist way is analytical but reductionist, it splits things into a myriad of incoherent aspects that seem to lack a connecting thread. This is the method of traditional science. It is also very anxious to eradicate qualitative aspects of the matter in favour of purely quantitative ones. As part of this it gets rid of any analysis of the problem into complementary opposites or dialectical categories.

One can say that there is almost a phobia, as yet unnamed, which people have when dealing with qualitative and dialectical angles of the problem or idea. And I will tell you why. This fear, almost pathological, of qualities and opposites is very similar to the fear of intimacy which you find in a neurotic person, usually men. Because dialectical analysis, literally, is a way into the heart or Essence of a thing. And just as many people shun intimacy, likewise many people feel very uncomfortable with the essence of anything, preferring instead all sorts of distractions, secondary aspects and irrelevancies.

The analysis of anything in terms of its opposites and contradictions is a time-honoured method of getting to the heart or essence of it, and has been part of the Perennial Philosophy for thousands of years.

Some people think that the Taoist way of solving problems always involves an incredible “Eureka” moment, akin to a moment of mystical Enlightenment, which relies on the complete grasping in one stroke, of something’s essence. It does sometimes happen like that, but often it involves the hard work of thoroughly analysing and understanding the opposites and contradictions in the thing and their mutual connections.






 More >

 Phi, the Pentagon and Self-Similarity2 comments
category picture3 Jun 2008 @ 09:12
Phi, The Pentagon and Self-Similarity

It is my contention that there is just one unified knowledge, there is just one mathematics, not straight mathematics versus “mystical” mathematics, or straight geometry versus “sacred” geometry, just one science which is the union of the strong points of mysticism with the strong points of quantitative science.

To this end I am putting forward the assertion that Phi (1.61803….) is the constant of Self-similarity and that they are always found together.

I have previously shown this to be the case where we have the Fibonacci sequence and also the Pythagorean theorem ( through the use of self-similar right-angled triangles). Now I will add to this by demonstrating that the so-called “mystical” pentagon exhibits self-similarity, and that the well-known prevalence of Phi in anything connected with pentagons, pentacles or pentagrams is connected with this fact and not anything other-worldly.

Phi (1.61803…..) is a very unusual ratio and is demonstrated by Euclid in his Elements where he calls it division “in the extreme and mean ratio”. What this means is that in any straight line, if you cut it at a certain point where the ratio of the whole to the greater part is exactly the same as the ratio of the greater part to the smaller part, that ratio will be the irrational number Phi, approximately 1.61803989. Then Euclid goes on to use this line to construct a regular pentagon and the regular solids based on it. All the remarkable properties of pentagons are based on the fact that the diagonals of a pentagon cut each other in this ratio of Phi. What has been overlooked in all this is that if you draw all the diagonals of such a pentagon, then they cut each other in this ratio and they create in the middle of the previous pentagon an exactly self-similar pentagon, rotated 180 degrees, whose sides are smaller than the larger pentagon by a factor of Phi squared. This is well-known but its significance seems to be ignored. Clearly if we construct diagonals of this smaller pentagon we create a smaller one and so on ad infinitum. This is clearly a case of self-similarity as I have sought to demonstrate as the basis of Phi. I would also speculate, though this is unproven, that the expression for Phi =(1 + SquareRoot(5)) / 2 is but a specific example of a general formula which links the number of sides of a polygon, in this case 5, to the ratio of the intersecting diagonals of that polygon, whether it has 5, 6, 7 or more sides. In other words this remarkable ratio is produced by ordinary mathematical processes, which need to be explained and clarified and not mystified. The real deep mysteries in all this are self-similarity,fractals, chaos and complexity theory which as yet are imperfectly understood.  More >

 Pascal's Triangle, Self-similarity and Phi11 comments
category picture23 Apr 2008 @ 09:25

Pascal’s Triangle, Self-Similarity and Phi

In maths the simple operation of adding two consecutive elements in a sequence and then iterating, which process is well-known to us in the Fibonacci sequence, leads to many of the more remarkable properties we come across in nature and mathematics. The Fibonacci sequence, as I pointed out in my last article, is based on self-similarity and exhibits the mystical number and proportion called the “Sacred Ratio”, approximately 1.618… which is an irrational number.

Now something very similar occurs in that very famous table of numbers, known to the ancient Chinese, but known to us as Pascal’s Triangle. This is a symmetrical table, with ones at the apex and at each edge, with the intervening numbers created by adding together the two numbers directly above and to either side. Pascal’s triangle has a multitude, maybe indeed an infinite number of remarkable properties. Every interesting thing in mathematics more or less, can be found in different ways in this pyramid. Fibonacci itself, can be found in sequence if you add the short diagonals. This of course yields Phi, the Golden Proportion. However, this is a bit misleading, because Phi is conspicuously absent from the other patterns you will find in this triangle. This is because if you divide any two of the numbers in the table they will be a rational fraction, not irrational. Adding different numbers together, as in the Fibonacci example, is the only way to get a sequence which gives Phi. The whole structure is based on the iterative technique mentioned above, and I suspect that this technique is a cornerstone of self-similarity, though I can’t demonstrate it as convincingly here as I did in my previous article on Fibonacci.

I believe, since Nature produces Phi all over the place, and Fibonacci sequences in the number of petals of flowers and the spirals of shells, that at an early stage in the evolution of life, in plant RNA and animal DNA, the simple iterative technique I refer to, was encoded and passed down to following generations. Thus we find Phi everywhere in Nature. Why it leads to very remarkable properties in mathematics is another issue and one I will address in a later article.  More >

 Phi is the constant of Self-Similarity8 comments
category picture13 Apr 2008 @ 09:47


Mysticism and Science: A new Union

1. Phi is the constant of self-similarity

It is my belief that the way forward involves the coming together of mysticism and science, to give a new holistic discipline which will combine the quantitative strengths of science with the holistic and qualitative strengths of mysticism.

What I am writing is not “sacred geometry” or “sacred mathematics”, but just plain true knowledge. My first assertion is that the number or ratio Phi, known from antiquity, is the constant of self-similarity. Let me illustrate this with a simple numerical example. Take the Fibonacci sequence

1 1 2 3 5 8 13 21 34 55 89 144 … … …

each number is the sum of the previous two terms, thus 8 = 5 + 3. It is very significant that if you divide any term by the immediately preceding term you derive a fraction which is alternately greater then less than Phi, and which quickly closely approximates its value of 1.618…. For example 89 divided by 55 is 1.61818, whereas 55 divided by 34 ( the preceding number) is 1.617647058

Now, the next thing to observe is that this sequence is self-similar:

1 1 2 3 5 8 13 21 34 55 89 144

0 1 1 2 3 5 8 13 21
taking away each previous term, in sequence leaves a sequence which is identical to the original one. The whole thing appears to be nested and self-similar, and this process can be repeated ad infinitum.

Now let us look at the famous right-angled triangle and Pythagoras’ theorem. There are, it seems, hundreds of valid proofs of the theorem that the square on the hypoteneuse is equal to the sum of the squares on the other two sides. One of the least well-known of these proofs is the one which uses the fact that the two small right-angled triangles formed when you drop a perpendicular from the original right-angle to the opposite hypoteneuse, are similar to each other and to the larger triangle. In other words this is another example of self-similarity. It is possible to construct spirals ad infinitum around the vertices of the ensuing smaller and smaller right-angled triangles which you can construct within these two triangles. And where you find equiangular spirals you will always find the ratio Phi, approximately 1.618

There are many other sequences e.g. the Lucas sequence, which like the Fibonacci show the Phi ratio, and they always display a form of self-similarity. I will leave it to you to investigate.

Phi is indeed the constant of self-similarity.  More >

 Taoism and Confucianism : Part II7 comments
category picture3 Mar 2008 @ 12:50

Problem 3: How to bring fresh water from a nearby river to a small Chinese town.
This example is given by Joseph Needham in his book Science and Civilization in China as illustrating the main differences between Confucianist and Taoist approaches to doing things. The problem is how to provide fresh water to a small town from a nearby river. The Confucianist approach would be to divert water from the river at a convenient point well below the town and then use much man-power, mechanical devices and expense to lift it up again to the level of the town and so distribute it. This will solve the problem while generating employment, circulating money, aiding the invention and perfection of mechanical devices and generally keeping everybody busy. The Taoist approach would be to divert the water at a convenient point above the level of the town and using the natural tendency of water to find its own level, that is to run downwards, create an aqueduct to lead the water to the village or town and so distribute it. This method uses nature’s properties to move the water rather than human effort, creates much less employment (a one-off aqueduct rather than constant lifting of water), circulates less money and does not need inventions or mechanical devices.

This example clearly reveals that Confucianism is a social philosophy, and its solutions to problems are designed to benefit society in creating wealth, employment and invention. The Taoist method is one which is based on the individual, addresses the essence of the problem rather than appearances, and is in tune with nature. Instead of expending effort in lifting water upwards after we have allowed it to run downwards, we just divert it at the right point to run by its own momentum (with gravity’s help) into the town.


Conclusion
Clearly, there are simple, easy ways to solve problems and there are difficult, tedious ways. It seems very much the case that civilized society, with its obsession with externals, appearances and irrelevant details prefers the difficult way to do things. This is in keeping with its greatly over-yang nature. Over-Yang means giant, mechanical, crude, external, superficial and so on but most importantly, over-masculine. There is a clear link between the problems in our society and problems in our psyches concerning sexuality and gender. The solution must be to redress the balance and level-off with an equal emphasis on Yang and Yin values. Yin, after all, represents the small, the inner, the subtle, the essence and naturally, the feminine. If we are in harmony then society is in harmony.

It is my belief that every problem, whether it is Fermat’s Last Theorem, or CERN’s accelerator, or getting cheap energy through FUSION, has a simple solution as well as a difficult, complicated one. But our society’s obsession with doing things the Confucianist way, in order to create wealth and employment and inventions, means that people have forgotten, to a large extent, the ancient Taoist (and universal) approach that seeks simple, easy and cost-effective solutions to difficult problems. People just don’t believe that there are simple solutions to many of these problems. If the experts can’t solve them then they must be impossible, they think. But maybe the experts are looking in the wrong place, and the wrong way, and from the wrong perspective.

I am not asking people to abandon completely the Confucianist approach, which is so engrained in all of us, particularly men, by our upbringing and education. All I ask is for the imbalance to be less completely one-sided and total.

Ideally we should use both techniques to solve difficult problems, both the Yin and the Yang, both the ‘left brain’ and the ‘right brain’, both Taoist and Confucianist.  More >

 Taoism And Confucianism: Part I2 comments
category picture3 Mar 2008 @ 12:47

Taoism and Confucianism

Confucianism and Taoism are seemingly opposite but also complementary ways of approaching life and solving its problems. They are world-views which originated in China but that are both universal. Confucianism is named after the Chinese Sage Confucius (Kung Fu Tse) who incidentally was not a Confucianist, and developed a moral and ethical philosophy, six centuries before Christ. Taoism is the nature mysticism local to China and is far more aimed at individual development and enlightenment than social. Both are universal in that Confucianism is a way of doing things which comes naturally to civilized, organised, bureaucratised and conformist (official) societies world-wide, while Taoism is part of the perennial philosophy and is the personal ideology of the individual, the lover, the eccentric, the spiritual searcher after truth, the rebel and the seeker of simple solutions to life’s problems and union with Nature.

In this paper I will briefly outline a few problems of a simple kind and present Confucianist and Taoist treatments of their solutions.

Problem 1: Opening a vacuum-held jar lid.
The Confucianist approach to getting a top off from a jar, held tight by a vacuum, is primarily to apply brute force externally to the lid and force it off. This is done with either the hands or a mechanical device, a lever. With small jars this is a practical technique but with larger and larger jars and lids, it becomes exceedingly difficult and tedious.

The Taoist technique is to release the vacuum. This addresses the essence, not the externals of the problem – because inside, the lid is held on by the power of vacuum in the top of the jar. The vacuum is released by inserting a wedge – sort of object, it could be a spoon or other strong object, between the side edge of the lid and the jar top. Applying a small amount of pressure causes the two to separate allowing air into the top of the jar. The lid then unscrews with the minimum of effort.

Comparing the two techniques, it is clear that the Confucianist method uses a cumbersome, mechanical approach which does not address the essence of the problem. With large jars it would be completely inappropriate and impractical. On the other hand the Taoist method is quick, simple, costs nothing and is exactly the same whether you are dealing with a tiny jar or a large one. The Taoist technique is geared to the inner essence of the problem which the Confucianist method ignores, looking only at external superficial appearances in trying to deal with the problem.

The second problem 2: Calculating the number of games played in a knock-out tournament.
This simple mathematical problem is given by Edward de Bono in his book on lateral thinking as an illustration not of Confucianism and Taoism but of his technique at lateral thinking. A teacher wants to keep a class busy for half-an-hour with a simple, mechanical but tedious sequence of calculations that lead to the desired answer. However, one bright student, using ‘lateral thinking’ solves the problem in a matter of seconds. What is the problem? Imagine a football or chess tournament which has 16 teams or players in it. How many individual games need to be played before a winner emerges? The Confucianist technique is to calculate the number of games piecemeal. First there are 8 pairs of teams, then when the winners go through this becomes 4 pairs, then 2 pairs and finally one pair in the final. The total number of games then becomes (for a tournament comprising 16 teams), 8 + 4 + 2 + 1 = 15. So the answer is 15.

The lateral thinker or Taoist uses a different approach. Instead of concentrating on games won he or she looks at the opposite, that is games lost. With clear intuition he realises that in the tournament all teams or players will lose a game except the final winner. So the number of games lost is the same as the number of games won, except it is much easier to calculate. If there are 16 teams in the tournament then 15 losses occur = 16 – 1. Both techniques arrive at the same answer but one is much more simple and quick than the other. The Taoist technique takes seconds and it doesn’t matter whether there are 16 teams in the tournament or 256. The method is essentially the same. If there were 256 teams in the tournament the number of games played (lost) would be 256 – 1 = 255. Using the Confucianist technique to calculate the numbers at each stage of the tournament piecemeal would take hours in this case.

So in this example, we see slightly different aspects of the difference between the two techniques. The Confucianist method is slow, laborious and we suspect, primarily designed, in this case, to keep a class busy and out of mischief for half an hour. The Taoist method goes straight to the heart of the problem and instead of being misled by society’s obsession with ‘winning’ it solves the riddle by looking at the key to the problem which is that the number of games lost is equal to the number of games played. All that can be said in favour of the Confucianist approach is that it is useful to society and in generating the result generates additional statistics and data about the different stages of the tournament and finally suggests a mathematical relationship between the sums at the powers of 2 (8 + 4 + 2 + 1 = 2^4 – 1).  More >

 Homophobia is Destroying Your Planet7 comments
category picture10 Feb 2008 @ 09:42
Homophobia is Destroying Your 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.


 More >



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