Sad al suud

ABAH AIEE

© ABAH AIEE

2010 All rights reserved

(ISBN 9783-940190-88-8)

(German edition)

The German edition of this book is printed in Germany All copyrights for this work are reserved. Contact: kurt-schneider@gmx.net

Conten t

The Luck of Luck 7 About the Good 9 Tune in 10 In search for the luck 16 I don´t know that much …. 19 Man is a Symbolic Being 21 Consciousness is developing in Steps 22 Every step is congruent with a Symbolic Form 23 In transition periods critical superpositions will happen 24 The road goes along from the Primitive to the Simple 25 alogoi – Numbers which cannot be spoken out 27 Man is the Measure for Everything 30 First Impulses to a New Level of Consciousness 32 From Creature to be a Creator 35 Decimal fraction and System of Coordinates 37 Nature becomes an Object of Mathematics 42 Science becomes mathematical 45 Exact Fantasy – a new symbolic power 48 Knights Jump – a symmetry breaking at the beginning of modern times 50 Conjunction of Dimensions – from Measure to Matrix 51 The scale of scales 57 I Metamorphoses 60 II Gauge 62 III Spiritus rector 63

Enlightened Consciousness of Arbitrariness 67 The Road (WEG) to Integrated Consciousness 70 I Harmonical Ratios 73 II Rhythmic Ratios 78 III Decisive Ratios 83 Translucency of the Crystal - tracks of exemption - 88 I The Gothic Project 90 II perception (wahrnehmen) 92 III cognition (erkennen) 95 IV design (gestalten) 96 V Physics of Creation 99 Yanlorum and Gizdelspil - Freedom and Form - 102 „All divine messengers must be mathematicians“ 109 („Alle göttlichen Gesandten müssen Mathematiker seyn.“) Beyond time - On the tip of Consciousness - 118 The Meash - centre and periphery - 121 I Responsibility - free energy - 122 II Autonomy - regional networking - 123 III Reason (Vernunft) - aesthetic education - 124 String of Strings – invisible centre – 126 References 130

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The Luck of Luck „Sadalsuud“ is the transcription of the arabic word used for the seemingly brightest star in the sign of Aquarius written in latin characters. „Luck of luck“ – translated to the english language – is the perfect expres-sion of the intention of this work. It does this in two ways: On one hand there is the relation to Aquarius as the determining quality of the new age which is lasting after all more than forty years. The way of realisation of this new, more than 2000 years lasting cosmic period is the number. The focus is mainly on the transition from knowledge to wisdom. Yet wisdom is not just another type of thinking in means of under-standing but it is the hearing to and the awareness of the holy number. Therefore the basic de-mand of this new age is the extension of intellect to true reason. On the other hand „Luck of luck“ as an expression is a wonderful example for the relationship of part and wholeness, to unity which always was felt as something unique. The end of the 20th century coined the term “fractal” which aptly brings the fact into one word. The perfect Unity - mathemati-cally expressed in the number one - is also a synonym for the Good, often identified with the Luck itself. At this point the wheel turns full circle.

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About the Good The farewell lecture of Plato (more than 2300 years ago) was dedicated to “The Good”. The content of this lecture was in no way about any specula-tive ethic standards or questions of moral. Rather Plato discussed questions of Number, especially the phenomenon of Unity and Variety which is a variation of the theme „The Part and the Whole“. How is it that a philoso-pher of standing like Plato says goodbye with such a topic – but above all: that the whole philosophy (according to Whitehead only footnotes to Plato anyhow) deals with it as a marginal issue? Is it because of this that we are thus far from our luck? Three hundred years ago, in the year 1707 there was born a man in Basel (Switzerland) who made fundamental contributions to the preparation of the coming age of Aquarius. His name: Leonard Euler. The greek prefix „eu“ means good, beautiful, also happy, blissful. If the latin saying “Nomen est Omen“ is true there was something to be expected from him – and Euler didn’t disappoint us. Leonard Euler not only was a great man, he also was one of the greatest mathematicians ever alive. But as usual the society only took advantage of the obvious useful and beneficial and ignored the essentials or even didn’t understand it in its depth at all till today.

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Tune in „Like the lifecycle the platonic year of the world is an astronomic-musical measure, the broadest frame for any idea of history, which always comes into our horizon in the phase of transition from one aeon to the next one as in our days in the sign of Aquarius. 1962 the point of the first day of spring-time changed to this constellation accompanied by a total solar eclipse over New-guinea – geographically the boundary of Cancer and Lion with all visible planets around 15 degrees Aquarius; a time already calculated since the ancient Greek and which coincides with the beginning of the humanistic psychology. In India it was recognized as the constellation of the battle of Kurukshetra in the Bhagavad-Gita. Many expected the end of the world and only few celebrated the transition consciously – as we did in Calcutta at four o’clock in the morning in a deserted city where the Brahmans drummed to avert a possible disaster. “ „With the time of Aquarius mankind became a community in the cosmic frame itself. Any smaller association is no loner adequate to social reality and will perish. The idea of God migrated into the sign of lion, into the paradise before the Neolithic Revolution. Therefore the Book isn’t any longer in the foreground but the direct connection with the universe, with the ghosts and beings as it prevailed in Old Stone Age. The fruit of the tree of life joins that of the tree of knowledge for those people who have the courage for the inner change.“ These both quotations (translated by AA) originate from Arnold Keyserling. Besides his travels for lectures and seminars he was a professor for philoso-phy of religions at the college for applied arts in Vienna. His teachings are summarized in the “Wheel” as an original image for integral analogue thinking and as a numerological key to world wisdom. Keyserling passed away in Matrei, Tyrol in 2005. 1962, the year of transition into the Age of Aquarius was also the year of death of Hermann Hesse. Almost only twenty years before in 1943 his no-vel “The glass bed game” (orig.: Das Glasperlenspiel) was published in Switzerland. In the introductory part we can read the following passage: „Nothing withdraws itself to the description with words more and is none-theless more necessary to make people aware of as some distinct things which have no evidence and do not have probability, but which can be brought into their existence and to the possibility of birth one step closer just because devout and conscientious people treat them as actual things.“

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Hesse himself overcame this challenge masterly and was therefore awarded with the Nobel Prize for literature 1946, just one year after the (official) end of World War II. Let’s go back another one hundred and fifty years:

„Now with the forces of the cord levitate the bell out of its grave, let it ascend into the realm of sound it should rise up into the sky. Pull, pull, lift up! It moves, it hovers. It´s a pleasure for this town, peace should be its very first sound.”

These are the last hopeful lines of the poem of Friedrich Schiller titled with “The song of the bell” published in 1800 in the “Musenalmanach”. And another three hundred years earlier:

„You do not know a part, if you do not know the whole. The whole gives us the measure for the part. Therefore, to get the knowledge of a single it will be necessary to have the knowledge of the whole and its parts before.”

„As the original image of all things is beamingly reflected in our mind as is the reality in a reproduction so our mind has something in itself to look upon and makes its judgment about the appearances accordingly.”

These sentences out of the epistemology of Nicolaus from Kues were penned down at the threshold of modern times in the 15. century.

You had much bother, I felt sorry, for nothing struggling in vain. Who wants achieve the grail by arguing, was never heard in all times

So, we cannot reach the holy grail with arguing and struggling, but through wise insight. This teaching is given to Perceval (a symbol for the alogic reasoning) by Trevrizent after the healing of Anfortas (a representative of the logic intellect). In the poetic work „Perceval“ of Wolfram von Eschen-bach, written at the beginning of the 13th century, he strikes a theme which

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is vivid as a vision since the 9th century and is to be brought into reality in our days: it is to bring our abstract intellectual mind home to the natural reasoning. Occidental man is living now since thousands of years in the prison of pure intellect. Platon made this situation an issue in his famous parable of the cave, written in the 4th century B.C.:

Bonded with the back to the entrance of the cave through which sunlight shines into the cave, man can only see the shadows of things. These shadows are the only reality for him. Once led to the bright world of the real things his eyes would hurt and he still would hold his world of shadows for the truth and the true world as something unreal. Only step by step he would be accustomed to the truth. If he then would return to the cave to release the others from there illusion they would not believe, would threaten him and maybe even kill him.

Thus far to the overall-situation man is in now for almost five thousand years. Besides the obvious meaning all of the quoted text passages also express a deep longing for liberation, for a peaceful paradise, whatever this will look like. The feeling of being separated from spirit becomes stronger more and more and so does the desire for a return into the realm of spirit, the true home of man. The age of enlightenment promised the longed-for light, one believed wrongly to be in possession of true reasoning. However, the foregoing Re-naissance was "only" the rebirth of Greek science and according to this fact spirit has difficulties to escape from the bondage of Greek philosophy. Ac-tually we have no idea what natural reasoning could be at all. Instead of the hoped enlightenment we go through the twilight of the light-bulb and the poor calculating mind gives itself airs to be the master of true reasoning. Since long time the enlightenment is uncovered as a myth itself. Because of the dominating mind atrocities have become only more merci-less. Therefore Ernst Bloch is absolutely right when he writes even two hundred years after the century of enlightenment: „Our former and still lasting technology is occupying nature like does an army the territory of its enemy and doesn't know anything about its interior.“ The contrast between our technical assets to master matter on one hand and the inaptitude to use these assets in a responsible manner, in a means of care

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for and promotion of life on the other hand, is one of the characteristic and at the same time perilous signs in our time. In 869 the catholic Christian was finally cut from his spiritual roots on the Council of Constantinople (today Istanbul), he is not thought of to be a spiritual being any longer. With the introduction of "zero" in the 13th cen-tury the door was unlocked for arbitrariness. The final opening happened three hundred years later, when the calculation with decimals was launched. With the raise of Algebra, originally the theory of solving equations, on a new level another 300 years later man was finally brought up into the state of the self-opinionated creator. Theoretical physics was possible and with it all those things, events and facts which are known as blessing and curse of the 20th century. Mathematics has become a tool in the hand of barbarians. Has there any-thing went wrong, may there be a better way? – a way to happiness, maybe the way to the luck of luck, to Sadalsuud? We all know (or at least could know), that ethics of whatever kind will not help. All plea and pious hopes will serve at best to take away basic rights from those who are in good faith and leave them doze in their believe in the good whereas those who rise the bids and laws for improvement and an-nounce them in the name of the ideals of enlightenment known as "freedom – equality – fraternity" will live a carefree life at the expense of their sheep or better slaves until further notice. As long as faulty developments led to local and temporarily catastrophes only and as long as one could comfort himself with the proverb that time will heal all wounds one could live well - more or less - with the division in technical development to control the earth on one side and ethic-psycholo-gical refinement to control people on the other side. The single person at least had a real chance to escape. Indeed on a globe which is completely overdrawn with the electronic dataweb and where every conflict in the end may lead to the extinction of all higher living there is no escape and there are also no wounds, here un-derstood as limited injuries, to be healed. Besides that we should not forget that this development is not any longer performing in centuries but in ever shorter cycles, meanwhile in the beat of decades or even years. So – when neither ethics nor escape nor the patience of a saint gives us a real perspective for a bearable, maybe even a peaceful life, there is time to

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ask if there might be something wrong in the basic structures, in the utmost underlying fundament. Technics is the issue what modern times are all about. The core of it is phy-sics. But the hard core of physics is mathematics. Mathematics is the very fundament of modern times. The superficial materialistic success is in fa-vour for the stability of this fundament and nobody dares, and just the lay-men, to analyze this grail of the very truth. Here we shall end this unfortu-nate tradition. What were the milestones on the way to modern mathematics from their beginning in the 13th century? Are these cornerstones put in this building maybe in a wrong way? Mathematics developed in no way independent from the dominating philosophical streams and styles of thinking. Therefore we shall also touch them in our search for possible mistakes in the funda-ment of mathematics. In the end on one hand we shall come across the venerable logos from the age before metaphysics and on the other hand we shall find out, that the diversion through philosophy with logic, metaphysics and ethics gave us a new capacity, which is actually still to be brought into our consciousness. It's about a new grade of symbolic power and here we find that the Brand-New is touching the Age-Old. Now it is exactly this point where we are in a dangerous dilemma: we have to say that we as a contemporary species by and large have lost every sense for the essence of symbolic forms. On one hand we do not understand the Old any longer and on the other hand we don´t yet understand the New and there is a latent threat to be overpowered by this situation. Erich Neumann phrases it optimistic: „Mankind reduces slowly but continuously the psychological projections like the hierarchy of gods and spirits, heavens and hells which helped us to decorate the emp-tyness of the world, thereby experiencing with astonishment the creative wealth of our own spiritual fundaments.“ This happens to express what Keyserling called „the direct connection with the universe, with the ghosts and beings as it prevailed in Old Stone Age.” Of course it is out of question that mankind will give up the achievements of modern times in favour of a primitive Idolatry – a risk which is absolutely real in view of the cult of stars and political leaders – but it is about to recognize the quality of num-ber in its genuine substance and to distinguish them in their different func-tions with absolute clarity. This is the only way to ground the building of mathematics and therefore also physics and technics.

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Whereas reductionary science, detached from any spirit, collected a vast amount of knowledge in a short time it lost the actual human being as well as the world and tied up itself to matter only. But this devouration by earth is something completely different from grounding in a means of combina-tion with the earth. All we need is not another kind of ethics but it will be crucial to get a new understanding of the connection between the creative forces and the timeless reality which can be grasped by man only in a sym-bolic way. A living connection between a clear mind and the creative forces of the subconscious will enable the further development of our conscious-ness which further on will lead us to our luck. Why not finally use our intel-ligence? The root of „intelligence“ is the latin „intus legere“ and means to „read the divine characters in nature“. The famous German writer Goethe uttered with striking words to his secre-tary what we as mankind will be faced with: „Behind us is the civil revolu-tion. What we are experiencing now is the beginning of the revolution of the machinery. But there will be the great revolution which will clear up the whole silliness of our creature – the absolute revolution of consciousness.” One of the most magnificent and maybe also most important tasks was and will be in the future to impart to our descendants the interaction of freedom and form in a way which does not occupy there fantasy from the very be-ginning as restriction and to be free of it but in positive means. The basis of the education of personalities is the imparting of mathematical and aesthetic principles which allows the young man to acquire the original strength of the creative design. Identification with the creative forces involves earthing and measure and out of this will grow the respect for life so mankind will no longer abuse its creative assets for barbarian destruction. The Age of Aquarius is the age of number where life is not labour any longer but will pass easily and in a creative manner. A changed understand-ing for numbers and forms will open the doors to Amension and lead us again on the pathway of luck – maybe even into the luck of luck: Sadalsuud, the seemingly brightest star in the sign of Aquarius.

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Before we start on our road to luck we want to get a short orientation about our destination: what luck actually is – or at least could be. „To act in harmonic manner, this means luck.“ These are the words in the translation of Richard Wilhelm for the 16th sign from "I Ging", the chinese book of change. „All those who are unlucky are so because they are pursuing their own luck of life only. All those who are lucky are so because the luck of others is laying at their heart.“ Shantideva Friedrich Nietzsche observed: „All the loud noise results in putting luck into silence and faraway places.“ But not only noise, it's also the restlessness of time which hampers us from happiness. Hermann Hesse wrote: „To witness the luck it needs the inde-pendence from time which is also independence from fear and hope. The meaning of life is to intuit the unity of the manifold or at least the ability of mind to suspect the clutter and huddle of the world as Unity and harmony. “ What a difference to completely flabbergasted writers in the 20th century: "Luck – this is simply good health and a bad remembrance." this are the words of Ernest Hemingway. Some more cynic is Gottfried Benn: „To be stupid and have a job, that is luck!“ Peter Sloterdijk quotes this sentence as a phrase of the century for cynism. Such a conception of luck we find at the end of a development where man defines his place in universe himself and therefore also the measure for his life. „The modern Cynic is an integrated antisocial man who copes easily with every hippie when it comes to subtle loss of illusion." and further on "to act against a better knowledge is the global superstructure of today." diagnosed Sloterdijk in 1983. How could we come to such a nihilistic-cynical, existentialistic-dismal, miserable affectivity? The principle situation of man did not change after the turn of the millennium. Mankind as a whole is still on the rocks – today possibly the whole living nature. Everyone can feel the symptoms, the diagnoses are clear and there is no doubt in distinctness. There is also no lack of accurate analysis. Though in almost all cases they do not reach the central question one tends to take the next best action because of the obvious and acute threat – and will find that the new situation is even worse than before.

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The quickest and least painful way to react is to change our methods which is our practices on encounter with the environment. Methods can be chan-ged relatively easy and give us the feeling of relief. This is the level where we can find almost all political magazines, news, blogs or talk shows. There is pro and con for every question and an excellent field for arguing. As long as structures are not touched every compromise is even good or bad. The main thing is that something is done, even when the result is not necessarily what we expected it to be. It is much more difficult for us as a community or society (and even as world-society) when it comes to change organizational structures. At a first glance this seems to be contradictory to the facts. Actually we are witness-ing immense radical changes on a global level and we allow them to happen more or less uncomplainingly. All these structural changes (accomplished in the pretext of security – whose security?) are serving exclusively the pre-vailing structures which are really hardy and robust, the actual status quo to be transformed from the national level to a global scale. The basically out-moded but still existing patterns, thousands of years old, are projected glob-ally and are able to establish their supremacy and influence in fact only because they are supported by peoples even though with reluctance and perhaps unconsciously. We allegedly enlightened ignore our personal re-sponsibility and are to idle to drain the swamp, to cut the energy sources for the apparatus. Unflustered and in good faith we go for voting, pay taxes, send our children to school, entrust our health to hospitals (german: Kranken-haus! which means house of/for illness) and consume all the mass-media. Such a primitive-egoistic attitude gives an easy job for despots with their obsessions for power. Strictly speaking what matters is that we as the people start to form a network, organize us on our own behalf (which is the opposite of divide and rule), take responsibility for ourselves and develop structures for self-governance which are appropriate for man. This does not exclude global teamwork wherever necessary. As much as necessary and as little as possible. Confidence is the key. The ones however which proof to have the highest steadyness are the men-tal conceptions of the world. They are deeply embedded in the souls of peoples as religions and philosophies and a change on this level is taken literally as the end of the world. This is exactly the situation we are facing in our days. On this extremely immaterial level which is not perceptible by the senses we find the works of Oswald Spengler „Untergang des Abend-landes“ or Friedrich Nietzsche „Zarathustra“ with the Superman. In view of the depth or height respectively on which these and other thinkers are re-

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flecting they are either understood not at all or completely misunderstood by most of all people who are used to think on the level of methods, at best on the level of structures. The issues which are discussed by these philosophers seem to be unworldly, abstract and theoretical to many contemporary. In fact they undertake what is imperative: it is about the exchange of our basis in the ongoing opera-tions, the basis on which we are moving with almost no consciousness and on which we don’t care about in our everyday business – and this is just in a situation where nothing would be more necessary than a steady fundament. But this is a characteristic sign of fundamental changes: we only recognize their necessity when they can be done successfully only with the utmost effort. This is the epochal dilemma where we find the reason for the fear of real freedom which is equally the fear of luck. We can and will reach it only when we finally take away this only seemingly robust ground and learn to live in and with a new and till now unfamiliar consciousness. We can see the external messengers of this change in the courageous jumps of the hang-gliders across the rockledges, the daredevil capers of snow-boarders or the breathtaking actions of freeclimbers. These physical limit- experiences these persons are facing are first and foremost on the agenda in the realm of mind. However, the spiritual adventure seems to be much more dangerous to almost all people than to risk ones life in sports or get high, drunken, stoned or whatsoever with drugs. Metaphorical spoken the lively methodologists are acting on the level of the fashion designer, or expressed with a more indigenous word: on the level of the tailor. He though needs fabric for his ideas. This is produced on a level below in the weaving shops. The weavers can be seen as the organizing structuralists who are literally pulling the strings. Therewith we got the catchword for those whose place of work is even one level deeper: the spin-ning rooms are below the weaving rooms. It is here with the spinners where the threads itself are twisted, down to these places it is where we have to descend today if we even want to get the tang of a chance to rescue the world for ourselves and the coming life on this planet. The thread itself is to be spun in a complete new way.

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I don´t know that much, but it's something not known by many others.

(Pico de Mirandola) Do you have a favourite place? A place which is not known by anybody else, a place where you go to if you want to be alone with yourself or with a beloved person? Of course you never would disclose such a place to anybody else. Soon it would become an insiders' tip and in an even shorter time a rubbish dump but definitely no longer a place to feel comfortable. It is exactly such a place to which I invite everybody right now. YOU are also invited for a stroll in the garden of a queen. I'd like to show you my favourite place. If it is really our new paradise – who knows? Anyway it cannot be hogged by anybody. Everyone can go there and one has in no way to be afraid to tread on each others feet. On a first glance the garden to which I invite you shows comparatively little attraction in todays circumstances. Effects are not obvious offhand, but in return they are all the more sustainable once you realized it. For a due appreciation of what we shall see in this garden first we shall go a piece of way. This is: we shall not beam ourselves into the garden with superluminal speed but choose the (mental) pathway which is still appropri-ate even for nowadays man. There is lot of effect when we get suddenly into an attraction but in general it's without persistent impact and soon we shall find ourselves in search for even stronger effects. In case of recurrence this leads into addiction as is well known with all the unpleasant and perhaps even painful consequences of an extreme and exorbitant up and down. Gimmickry becomes a self pur-pose and will end in self-destruction – without having grasped even the cusp of luck, not to speak of enjoying the luck of luck.

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Coloured Windows

Did you see at the cathedral, Stained glass scattered in grey lead, High above the hustle and bustle Panes stay bleary in the sun? However, all the colours will be glowing, Once you enter to contemplate – Look at a masters marvel building, how it's adorned with a burst of beams!

Karl Berner We, who burnt the candle at both ends, who yield the temptations of the glaring neon signs again and again, isn't it that we are also got grey inside ourselves? Therefore outside it cannot be colourful enough. On the first part of our way we may miss the external colours. To one or two our way may appear as grey and bleary just like the panes at the cathe-dral from outside. This should be the way to a colourful garden of paradise? Well – it's like on the pathways in the mountains: the efforts will be re-warded with a splendid view. As it is all about a fundamental question of human existence (as said: the thread has to be spun in a new way), there is no avoiding to begin with Adam and Eve. But we shall make progress swiftly. To succeed on this way some retrospective aspects are summarized in the fashion of theses. We cannot and we don't want unroll the whole development of mans mind but emphasize some few relevant viewpoints. Are you ready? – so lets start!

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Man is a Symbolic Being Everything that is, is what it is only because it is able to hold steady in com-petition with others. The persistency of a mineral is granted because of its crystalline shaping. In the case of plants and animals the ability of survival is based on a wide variety of specialized functions. With the first there are maybe the ingenious chemical actions, refined phyllotaxis or their shapes to maximize the light yield, tantalising attractants for insects etc. With an animal it is possibly its pure strength, especially refined senses, highly spe-cialized catching-techniques or deception maneuver. Here we can see al-ready time as a factor of capability in form of remembrance. Man has not such a specialized ability or function as mentioned above. His strength is his distinct ability for recognition beyond all measure. Additional to his memory he has intuition and sudden insights, the ability for arrange-ment and combination, and: he is able to anticipate coming events in his mind. He knows about his abilities for perception, cognition and design (german: Wahrnehmung, Erkenntnis, Gestaltung). This is his way (WEG) and we call it consciousness (german: bewußt-Sein) or "Vernunft". However, consciousness has a conjoined twin. It’s the ability for symbolic communication which is the development of symbols for the depiction of imperceptible things. This initial unimposing ability to organize events and objects by distinction and especially the symbolic representation with icons made man the being that he is today: the greatest power and therefore also the greatest hazard for and on this planet. We can assume that ordinal numbers were part of the very first set of icons of man at all. Depth psychology considers them as preconscious which is: archetypal dispositions of structure. Shiv Charang Singh says: Numbers are primary intelligence. Within archaic cultures the „Numerator“ as the one who can deal with numbers was held in high esteem ever since. He was and is the magician who honours the Divine. For all pagans all over the world the inner order in all things, rhythm and harmony were self-evident.

Ordinals

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Consciousness is developing in Steps As a part of dealing with numbers we can assume that the ability to desig-nate the size of a group or a set was developed very soon. That is one has detected the counting functionality as a property of the number, one has learned to count, to operate with the number. Until this point numbers might have been tightly connected with the object which was arranged or counted, for example a group of people or a set of apples. However, at some time one got the insight that one can take away a count from an existing group. But more than this – depending on the size one could deduct the group multiple times by the same number, and: the same procedure works independent of the chosen set. Therefore it doesn’t matter if I deduct a group of people multiple times by four persons or exe-cute the equivalent procedure out of a herd of animals. This is a considerable accomplishment in means of abstraction. Numbers become independent from the counted object and beyond that they can be moved. What we call a difference nowadays is a number in itself: the so called cardinal numbers are born. A number can be added or subtracted. The difference as a multiple of the Unit does not change. Whilst such an insight is an abrupt step for the individual person – when the famous penny dropped – such a change in gradation takes a long time for a group of people or even mankind as such. We may see it as an incubation period till the recognition comes to a breakthrough in full size. Once such an insight is there in the world as an approved knowledge it will be impossible to make it undone. The transition is irreversible, in contempo-rary words it is a break of symmetry. Breaking of symmetry means an in-crease of order as well as of complexity. Thus we have more options for design and at the same time the execution requires a higher level in preci-sion. The more elements are correlated to each other the more precisely the interplay must work. The additional freedom in design requires a more in depth understanding of the laws given by nature.

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Every step is congruent with a Symbolic Form With the insight in the entity of the difference the unity of number and ob-ject was suspended. In reverse the independence of the number from the object made another abstraction necessary: the counted object has to be designated independent from the number. As a result we see the symbol free of numbers, the icon which points to a concrete thing for example a person or a sheep. We may state as a peripheral remark that the symbol itself passes a development from a vividly three dimensional to a pictoral two dimensional stadium and will finally end in the completely abstract signa-ture. The development of cardinal numbers on one side and the development of symbols on the other side mark with no doubt a new step in the develop-ment of consciousness of man. Both, cardinal numbers as well as symbols share the property of independence from the actual real object. The meaning of this fact is that we can share or communicate a real thing which actually does not exist but only in our minds. The manner of communication, its form is changing with every new step in the development of consciousness. The legacy symbolic forms experience enrichment with every new form. Therefore we also experience a change in our way of perception of our world and thus as a consequence of our behav-iour in and our relationship to this world. A more and more differentiated ability for speaking acts as a mirror image of the gradually extending sym-bolic forms.

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In transition periods critical superpositions will happen

When new knowledge is spreading out, at first it may be captured by the legacy consciousness which is superior. As a result the New will be inter-preted against the background of traditional knowledge and experiences therefore a deformation. As a consequence the (misconceived) new knowl-edge is brought into discredit to some degree. On the other hand the legacy consciousness in reverse experiences interference, which shows it in review as a deficient form. Transitions are always phases of uncertainty. In such a way magic which obtains its power out of its saturation of experi-ence happened to become depraved to humbug and disintegrating supersti-tion in the transition from the magic to the mythic state of consciousness. The multilayered and deep-grounding myths used to become transfiguring fairy tales and exaggerated hero tales with the transition to the mental age. On this way the actual content of rites, myths and wisdom is almost lost because of those forces of all things which want to conserve them. It hap-pens because they clinch with all of their force with the tradition and can see the New only through their old glasses. Such a fundamental transition is always a transition by hook or crook. The newly acquired symbolic capability is used to reproduce the previous steps of consciousness in a new way – and with the utmost throughput of energy until total exhaustion. Old power and new expedients result in a highly volatile mixture which carries every society to its border of existence. In order that the new level forces through permanently all available mental and spiritual resources are required. Certainly they are then not supposed to fight the legacy level. That would mean to support it with new energy. Much more the New is supposed to prevail because of its superficiality above the Legacy. This superficiality will only become obvious with the active and consequent penetration down to the entity of the new forms by ongoing critical pursuit and practicing.

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The road goes along from the Primitive via the Complicated to the Simple

or: bring your mind back to reason It is such a transition we are actually going through since the beginning of modern times which is about the beginning of the 15th century. All progress and especially technics as its medium till today is primarily determined by a metaphysical manner of thinking. After all the most inner entity of the something which enables modern technics is still unconscious in general. The core of our technics is physics, the very core of physics itself is mathe-matics – today much more than ever. It is mathematics where the new sym-bolic power is expressed. This potential is equivalent with the potential of communication and organization of a society and it designates eventually the horizon of development for a society. It is not enough to have the expe-dient at hand. And its not mathematics as such which makes our technics and our societies that much complicated. This is much more the result of a minor insight into mathematics real entity. We have learnt to describe structures and their changes. At the same time our consciousness is moving still in the rigid forms of a mind which is fixed with static terms. To reach a consciousness which is appropriate to the new potential means to bring the thinking which is stoned by terms into a flow. It is exactly this for which Max Born, one of the fathers of quantum physics, won the Nobel Prize 1954 after a long delay. We are on the way. Only when mind has taken back its original role, which is to serve the reason which itself is listening to the flow of life we shall again become aware of the simplicity of life. Charcoal or the likewise black mineral oil are the obvious signatures of a inhuman and unnatural technology. Actually we are witnesses of a critical point of transition where the black amorphous charcoal is transmuted into the stadium of the clear transparent diamond by immense pressure – or it will be powdered to dust. We may take the newly discovered modification of carbon, the fulleranes or football-carbons as a clue for the ongoing change of the aggregate state in our consciousness. There are four real great works in the intellectual history in my mind which have foreseen, attended or participated as well this development in a sur-passing manner. At the very beginning it is the „Perceval“-poetry of Wolf-ram von Eschenbach in the year 1200. It was three hundred years later at the

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beginning of the 16th century when Albrecht Dürer created one of those copperplates which is one of the most often reproduced: „Melancholy“. The novel „Wilhelm Meister's Years of Travel“ of the German writer Johann Wolfgang von Goethe originated another 300 years later and finally the already mentioned novel "The Glass Bed Game" of Hermann Hesse was published in 1943. It is the precise and equally ludic simplicity of our world which is not ap-parent to our one-sided complicated logic. Maybe the scientific develop-ments of the second half of the 20th century can help us to start off into a new way and therefore new world of awareness.

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alogoi – Numbers which cannot be spoken out or: the art of measuring

In the everyday language „logical“ and „rational“ have almost the same meaning. Whilst the first one is more correlated to the thinking in terms and its consistent order the second one is merely focused on calculability. Our view of the world is ascertained in a very high grade by this mind-oriented mode of cognition. Everything which cannot be categorized in this scheme is deemed to be irrational and is not really taken serious by the guardians of this view. To develop this way of thinking without disturbance it was basically neces-sary to ban the unpredictable energies or gods. In a first step they were put into the ban-circle of the magicians and in the second step they wandered into the templum of the priests. Referring to our scheme of consciousness we started above we call this new level according to Jean Gebser the mental consciousness. For the understanding of numbers the step onto this level is equivalent to the recognition that if we compare cardinals among themselves which is to proportion then we obtain a characteristic new value which is independent from the original variables. For example: the ratio of 15 by 5 is the same as 6 by 2 or 9 by 3. This becomes obvious in the well-known abstract geomet-ric figures, where equal ratios produce similar figures which is: figures with precisely equal angles. The recognition of proportions or equations of ratios may have happened in the transition from hunters and gatherers to farmers and stockbreeders. We call this period at around the 4th millennium B.C. the Neolithic Revolution. The centre of this development is seen in the cultures of Sumer and Babylon in Mesopotamia. Babylonians already had a powerful mathematical set of tools to their dis-posal. They used simple trigonometric methods for astronomical time-calculations and figures for the measurement of the surface of the earth as well which is what we call geo-metry since the time of the ancient Greeks. At least since the Egyptian culture which followed the Babylonian culture the theorem of Pythagoras is well known and therefore also the phenome-non of incommensurable lines. Once they are translated into measures we are talking about irrational numbers. The diameter of a circle as well as diagonals of regular figures of an intersected circle, for example a triangle or a square cannot be depicted as plain ratios to the circumference or the sides respectively.

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These numbers which cannot be spoken out are ubiquitous and Egyptians had a distinct awareness of them. Therefore they attributed them as divine, likewise the phenomenon of time-cycles which are connected inseparable to the course of the stars. According to Albert von Thimus there is much to be said that the holy Egyptian sign Ankh had the same meaning as the sign for the square root we are using today. For Egyptians the Unit, symbolized by the figure 1 which means as ordinal the First and the Highest in ranking, was of particular importance. All mea-sures were written by Egyptians as basic fractions or sums of numbers and basic fractions respectively (with the exception of 2/3 where the numerator is 2). Inevitably we shall face the infinitesimal if we try to approximate the incommensurable in a methodological manner by fractions for practical purposes. The unsolved problem of the infinite turned out to be one of the driving forces in mathematics - and it is like this even in our days. From the Greek philosopher Protagoras we got the quote: „Man is the mea-sure for everything.“. This is the famous „homo-mensura“ phrase. In his time, after Pythagoras and before Plato, One as the measure was still valid and one respected the individual measure of everything. Mathematicians in this time were fully aware of the fact that space could be measured almost precisely with the available instruments of mind for practical purposes but that there is no methodological way for an absolute precise measuring. Therefore Protagoras didn´t talk at all about the full power of man over matter by subduing them under his own arbitrary measure but his focus was on the limit of human cognition. In general the birth of occidental science is credited to the Greek. Its starting point is basically geometry which is the science of space as it was set up by Babylonians an Egyptians. However we can read in Plato´s writings that it is ridiculous to believe that geometry has to do anything with the measure-ment of earth. Rather the art of measuring is the knowledge of the everlast-ing things. Again, here we have once more an incisive act of abstraction: in the same way as the cardinal number was separated as difference from the counted object we can now observe the separation of the measure as an independent ratio from the figure. For Pythagoras who was educated in Egyptian traditions numbers and ratios were immanent divine arch-principles of the cosmos. With Plato they became otherworldly ideas, ab-stract cosmic principles of order independent of anything which are now available for formal mathematical operations.

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Aristotle who was basically oriented on practical experience and therefore his followers in Greek science as well was interested only in natural num-bers and their ratios. These were available for ordinary calculation and fit perfect in the Aristotelian logic of distinct terms. The incommensurable ratios however, the irrational numbers as well as time were kept in ban in the heaven of gods. This realm, later on called metaphysics, which is ulti-mately the measure for all energetic phenomena, the cognition of the ever-lasting things was left to the platonic philosophers and traditional priest-hood. Eventually heaven was captured by the main book-religions. So it is not by chance that in all the holy books specific numbers and intricately examples of calculation appear at various quarters.

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Man is the Measure for Everything or: The Loss of measure

At the threshold to modern times science and art were tightly interwoven, often within a single person. The Renaissance yielded creative fellows. Mathematics was basically integrated into traditional ideas of numbers and geometry was founded on the obvious shapes of things. The divine creator in heaven was an unquestionable fact although the Catholic Church began to lose her central position in correlation to the loss of the central position of the earth in the universe in the mind of man. This revolution in minds is owed arguably to the unique impetus of that time: the individuation of the single person. The mind-driven aspect eventually became the centre of man. The man of renaissance understood himself throughout still as part of a major whole which was in god's good hands. However, he became aware of his unique value as this specific part in the major whole and asserted this value. This is the true sense of the name „Perceval“ which is the title of the poetry of Wolfram von Eschenbach in the 13th century. It was in this time when the uprising cathedrals were built and many cities were founded. As a result we see the separation of agricultural and urban population as well as a distinct division of labour within the society. From now on the individual was mainly exposed by his specific profession which also gave him a dedi-cated role and his name. With the invention of the mechanical watch around 1300 A.C. the periodic cycling time slowly becomes independent from the revolving movement in the sky and undergoes a transition into the linear beat of the clockwork. Till that point the continuous time was the paragon of the irrational, divine, celestial. Now it becomes divided into particles of seconds by the escape-ment mechanism and is therefore available for the counting principle. This time of emergence also brought the letterpress, progress in navigational methods and thanks to the protestant spirit of Martin Luther a direct access to God himself. From now on not only space but also time has become disposable in princi-ple. With such a new self-confidence man of renaissance began to master the problem of the incommensurables and thus the problem of the infini-tesimal as well. He is successful just because he inverted the original mean-ing of the theorem of Protagoras, the "hom-mensura"-phrase. The Faustian man of modern times unsheated to put his own measure on all the things. In the short run he was really successful and won tremendous power over

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nature surrounding him. It is not that the limits of his capabilities of cogni-tion have changed basically but he reduced nature to its obvious measurable sizes which is: to its quantitative aspects by throwing the net of the coordi-nate-system over it and operate with it in an analytical manner. However, above measuring the knowledge on measure and number was lost. Wants woke up which knocked over into measureless greediness and today we recognize that the disregard of natural given relations of measure inevitable drive into self-destruction. It is one of our main problems if not t h e Problem that we have no idea at all what measure and number means. Measure is what cannot be measured itself. It is outside the realm of our mind and likewise the number. With his awkwardness the occidental man basically fall back behind Egyp-tian consciousness. This splendid achievement of the previous level of con-sciousness – the knowledge about measure and number – is lost, a substan-tial part of our ability for distinction and therefore recognition is equalized. This situation is aptly shown in Dürer´s image of thinking (Denkbild) „Me-lancholy“. Dürer himself as a man of the renaissance and therefore on the threshold between medieval and modern times was still a master of the art of measuring of the traditional art as well as of the new discovered perspec-tive. He positioned the compass as a symbol of measure and the hour glass as a symbol of the continuous celestial time on the central axis in his pic-ture. The human figure in this copperplate, “Melancholy”, may consider if it will be possible to get back the lost measure in a new way. The phenomenon of the Renaissance, which means the renaissance of the ancient world, did not show up at once but is the result of a developing pro-cess. It was initiated through some previous steps. On the following pages we may have a short look to some of these steps and shall than study the really revolutionary discovery of the decimal numbers.

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First Impulses to a New Level of Consciousness Imagine: on our way to the promised garden we are now walking along the shoreline of the sea. The Old, the stronghold is awashed by the Transient, Liquid. On one side the water penetrates the stronghold and softens it – from the other point of view the stronghold sucks up the liquid. This is less noticeable at the sandy shore as at the cliffs of the steep coast. This is a picture to illustrate the inter-relation of the superposition during the transi-tion to the new level of consciousness. The Arabization of Spain was a first wave borne by the Islamic expansion. On this route ancient Greek (and therefore heathen) knowledge came to the southern occident via the diversion of Gondishapur. In a second impetus the dominant Catholic Church sound the bell for its own decline when it denied the spirituality of human beings at the council of Constantinople in the year 869. Thus from now on man was merely only a being of matter and soul. This was the signal for the mind to take command within man. Whereas Aristotle despite of its logical thinking stuck with the sensual in-tuition at least with regard to mathematics the man of the occident was now prepared to follow pure formal considerations even in practical mathemat-ics. The formal correct become the primacy above the obvious truth. At this point the way was paved for a successful introduction of the Arabic digits by Leonardo of Pisa, also known as Fibonacci, at the beginning of the 13th century. From now on especially zero became a calculable valid figure. At first written after the figure 9 within 200 years it captured the place be-fore the figure 1. The figure Zero was well known since the Babylonians – rather not as a number like the others but as a placeholder which marked empty slots in the representation of bigger numbers. In such a meaning Zero was also known by ancient Greeks who wrote them as the small letter “omikron” in their calendar tablets. At the times of Renaissance Zero was ultimately accepted as a number. Originally Zero was invented in parallel at around 7th century A.C. as a calculable number by Chinese mathematicians as well as by Indian mathe-maticians to whom we also owe the so-called Arabic digits. Because of their religious attitudes they were not that much interested in this-worldly matters which are seen by them as pretence and for them it was a pure intellectual enjoyment to deal with numbers. This is as well the reason why we owe them algebra which means the calculating with formulas without any bond

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to any sensual imagination. For them it was no problem at all to reduce for example four by seven. Therefore they attained on one hand the concept of the number line which goes to the infinite on both ends and on the other hand they also yielded the negative numbers inclusive Zero which had its place between one and minus one. Now we mentioned a second crucial building brick for the new mathemat-ics: the negative numbers. Because of formal correctness one not only al-leges the real existence of zero but beyond this the real existence of nega-tive numbers in the series of numbers. Taken numbers as representatives of the real world this is complete nonsense and this is why it lasted several centuries until the negative numbers became full citizens in occidental mathematics. For the commercialefficient merchants of India as well as in the empire of the Hohenstaufen dynasty the sense was clear at one go (and this is how the negative numbers were invented): negative numbers mean dept. So it hap-pened that something which originally belongs to the realm of spirit is trans-ferred into the realm of matter and therefore the whole cosmos was turned upside down. Everything else is the well known history of the capital which obtained a spiritual fundament with the Calvinistic shaped Protestantism. However, Fibonacci not only brought the Arabic numbers to the occident. It was also him who resolved the legacy equation of ratios, always written in four parts, into a three-parted equation. Fibonacci sharpened the mind for something which was arguably seen before him by many others but they never took it into account as a valid operation because for them it must have been pure blasphemy: it is that the One as denominator can be omitted! The One sank literally into the fundament of mathematics which depraved more and more into pure formal calculating methods. This step from the four-parted proportion to the three-parted equation was the preparation of the transition from the discrete ratio to the continuous function. The right side of the equation is not any longer a distinct ratio or measure but as a digital fixed value it represents the whole series of conceivable equivalents (Analoga) of the single specific ratio on the left side of the equal sign. As an abstract representative the single number is absolutely independent of any image in mind or even of a material equivalent. With this step the loss of consciousness for measure becomes obvious in full clearness: The harmony of the world relies on the integrity of its several parts which are determined by form in their entity. Form is a result of the

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relationship between an item or a single entity as a part respectively and the bigger wholeness, the unit to which it belongs. The proportion documents this aspect of form in the things, their nature as scaled beings. In a ratio, written as a fraction of integers, we can always see in a specific example the universal harmony of the things which finally completed their becoming. This coherence, the sense for the whole, integral, the sense for order, the in-form-ation is lost with the reduction to the three-parted equation. After the Council deprived the occidental Christian man his universal spiritual home officially in 869, the self-confident man of the Renaissance decoupled him-self from his personal measure, his generator of rhythm, his individual pulse of life as soon as he accepted the profanation of One, which therefore be-came an equalized number within the series of numbers. This is the Faustian theme where man aspiring after the infinite sells his soul to Mephistopheles. Man becomes admittedly creative, but he is unable to bear a real creation without an appropriate consciousness of measure. He is biased in measure-less constructions. By the way: this aspect of the One as a reference, as a non-number is de-picted in Dürers „Melancholy“ in the correct and full title of the work: „Melencolia I“. Peter-Klaus Schuster has shown how the „I“ in the title completely conforms with the Greek reading of One, in particular as the symbol for the measure of all numbers and therefore for the principle of mathematics in its original meaning as such.

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From Creature to be a Creator - Impact of Reason -

Whereas Plato still had an essential consciousness of measure, which out-lasted in a more or less shadowed shape until the Renaissance, the same person founded a theory of ideas (eidos). This theory teaches the separation of idea and a specific instance and is therefore indirect the basis for a way of thinking which came to its culmination in the so-called Nominalism. It was already around 1000 A.C. in the Chartres School when monks began to explain God on a basis of reason (actually this is a revival of Origenes at-tempts 800 years earlier). Till then the certainty of every being was authen-tic by its divine substance which is its connection with its individual idea. But this concept was not taken for granted any longer. Things were not any longer seen as soulful and therefore the relationship to the symbol was cut. So what remains is the nominalistic certainty of mans own thoughts which is formulated by Rene Descartes in his famous theorem „cogito ergo sum“. According to this all our terms for the items in this world, their nouns are products of our minds and the so-called entity as the preceding idea and therefore the true reality is a fantasy. This should also be valid for numbers. The term is therefore no longer something which follows the things but it becomes independent from them. From now on it is even possible that the term is there before the thing. The promethean man, the one who is thinking ahead becomes the one who is seizing ahead. However the meaning of this is that the heretofore planning man becomes creative, becomes a poet, a literal producer. As a consequence we observe how language, even better: the single letter takes precedence above the numerals. The primacy of language above num-bers was already denounced by Plato and was then fixed eventually in the "artes liberales", the educational curriculum of late medieval times. Further on nominalistic thinking led to the separation of syntax and semantics: The sign or term respectively becomes moveable against its meaning so we may freely operate with it. The mathematical counterpart is the calculation with letters which was invented in the 16th century by the French mathematician Viete. Herewith the still somewhat number-related form is finally resolved into the pure formula without any number. In reverse to the basic thought of Aristotle now, after the exposure of the principle structure, we can build a complete new tangible, sensual compre-hensible construction, an artefact can be constructed in a purposeful manner

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and be realized in material or later on as a virtual existence in a digital ma-chine. According to this way of thinking man assumes that God has built the world as a Unity but within this system everything is correlated to every other thing in a lawful way. The Method, also the title of the famous writing of Rene Descartes, is therefore nothing more and not less than science as such and its duty is to unveil all this single dependencies and to make it mathematically explicit. The original individual-divine relationship of each single thing is now replaced by one single and magnificent systemic con-text, world has become a machine, represented by a myriad of functions. Once we are able to see through it we are also able to add our own crea-tions. Given this circumstances “Part and Wholeness“ has no longer any meaning in the traditional sense – now there are only parts and construc-tions which are themselves part of an even bigger construction. Man becomes a creator and the one who gives names – without having any inkling of measure. The platonic eidos, the idea is reduced to its construc-tive aspect. This is also valid for numbers and especially for One. Once things are got rid from their substance or entity their representational signs loose their meaning as well and degenerate to pure calculable values. The case of One has shown us already how it sank from the decisive unit to the equalized freely movable number. The new elements of mathematics like zero, minus or square root are not apprehended with their true meaning but integrated in the only formal logic of mind as pure operational signs or numbers respectively. Within the hori-zon of the mental consciousness we cannot expect anything else. Mathesis is degraded to a servant for calculation. Thus the nominalistic understanding of „term“ becomes the starting point for completely new things which did not exist before. In the context with time which has become linear and man got a grip on it likewise as on space modern times and progress become synonyms. Within this context freedom is misconceived as self-righteousness and form is apprehended only as limit which has to be overcome. Both are understood only in their negative as-pects. The admonition of Friedrich Schiller addressed to the artists therefore is not just by chance but has to be taken serious: "The dignity of mankind is given into your hands." The question of Friedrich Nietzsche: „Who gave us the sponge to erase the whole horizon?” we may answer like this: Nominalism is the impact which rips open the horizon out of which emerges a new symbolic power and therefore eventually a new consciousness. Now it is up to us to define the new horizon (if the term „horizon“ further on makes sense at all!).

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Decimal fraction and System of Coordinates - two ingenious superpositions -

I Making the irrational rational With the depiction of numbers as decimal fractions the old dream seems to be fulfilled which is the mastering of the irrational, the comparison of the incomparable.

13.072 13072 .13072 Now I just assume that you can simply denominate the difference of these series of signs. If you have to explain how you got this result most probably you may talk about groups of one, ten, hundred etc., because the value of a single figure in a positional notation system is determined by its position in the sequence. The pure principle of this kind of representation was inciden-tally known before Christ by the Mayan, Chinese and Babylonian people as well. This is the reason why the Babylonians were forced to invent a place-holder, the symbol of Zero. So far, so good. What would you tell if there is written

13.0728 130728 .130728 Now - to put it in a nutshell: I would like to direct your attention to the fact that there is more behind the decimal fractions (with its basis of 10) as we are used to think of usually. But above all they are internalised by us in such a strong way that not only few people (including academics) believe that this system is virtually given by nature. So we can read in the volume for mathematics of a lexicon for high-school graduates from the year 1968: „Calculating with the logarithms of ten is especially convenient, because the logarithms of the powers of ten with whole exponents are integers.“ Besides the platitude of the sentence we may notice that if we exchange the word “ten” in every position with any other number the truth of the sentence will not change. At least from the point of view of number theory there is just nothing which marks out the number “ten” before any other with regard to its representation. Even – who tells us that these groups of figures are three numbers? Actu-ally we can read each of these expressions as a number only when there is also given a logarithmic basis. So, as we can see there are several prerequi-

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sites when a price board shows „gas 152.9“ and I should interpret it in the right way. The calculation with decimal fractions as they are known by us assumes all the elements we named thus far as impulses: Zero, negative numbers, the three-parted equation. Besides them we have to consider the rules for the calculation with powers. The brilliance especially of this numbering system is mainly based on the fact that we have ten fingers and therefore the system is the spitting image of an intuitive numbering system in which units and superior groups of units are added (for example the Roman numerals). As a result the whole mathe-matical background is covered up elegantly and a correlation with the real world is suggested. Actually the representation of numbers with decimal fractions fulfils the nominalistic „term“ in a high degree: pure formalism, absolute abstraction from the real world and therefore complete non-vividness. The essence of a given number, its structure of divisibility, which shows the complex relation of a given issue and therefore a correlation with the real world is completely blurred by a positional notation system. The decimal system is a very powerful instrument in our hands which al-lows us to act without thinking about the essential numbers. The autono-mous figures allow constructions according to formulas without form and therefore we manipulate the inaccessible full-scale without a real knowl-edge of what we are actually doing. “... because they are not aware of what they are doing!” With a decimal fraction every number can be depicted with the precision of an arbitrary number of decimal places. The problem of infinity seems to be finished once and for all. It is significant that this scheme of representation was consequently used first in trigonometric and logarithmic tables if we think back to the trigonometric calculations (actually calendar tasks) of Babylonian astronomers which originally evoked the problem. It was only in the age of ancient Greeks when trigonometric insights became an instru-ment for the calculation of space based on the heroic act of Euklid who virtually brought down the divine right angle from heaven to earth. Here we also find the explanation for the fact that angles of geometry till today are divided in minutes and seconds.

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Actually the term "an arbitrary number of places" is a pure theoretical statement. As soon as we cut the sequence at any point the precise infinity is over. The contradiction of abstract cognitive faculty and straight view can-not be eliminated even with decimal fractions. Absolute precision is a fic-tion and in practical calculation we must live with the precise approxima-tion and rational values. The Faustian man wants to usurp all issues in the structures of life and death as well by all available means. But in his flush of formalism he forgets the actual fuzziness. Despite all perfection the always and everywhere emerging chaos indicates that the constructive core of our creations is eventually overgrown by the seemingly subdued irrational. Ultimately all the uncer-tainties and vagueness are due to our numerical illiteracy. Although almost everybody is able to juggle with all possible figures more or less successful almost all of them finally have no inkling what numbers actually are or mean. This ignorance is concealed overly successful with the decimal numbers. We can calculate everything but anyway we remain in the purely quantita-tive. Therefore it is not surprising that mathematics in general is seen as the science of sizes. II Fasconti - fascinosum continuum When Rene Descartes invented the system of coordinates (which was a right angled system only later on) he provided a geometric, hence a vivid interpretation of the mastering of the irrational. Actually the display of cor-relations in a right angled scheme is nothing new. The initial innovation is to be seen in the continuation of the number line. The arrangement of numbers on a straight line was already accomplished around 1560. But it was only about seventy years later when Descartes took the liberty to declare this line, which till then was nothing more than a gap-less arrangement of discrete points, by means of the irrational decimal num-bers as the continuous number line. With the decimals he putted a continu-ous continuum underneath the line of discrete numbers and ratios. From now on the difference of measure and size is also flattened in view and hence at the same time an essential means of cognition is dimmed out. On the continuous line of real numbers every physical value is assigned a real number. As the axis is apprehended as a pure value of numbers which

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is: the multiple of an arbitrary unit of length, the mathematical operation is separated and hence free from any view. This is now also valid for time. Since time is captured and measured with the mechanical watch in absolute consistent sections of hours, minutes and seconds it has its place on the pictorial line of numbers as directed time likewise the spatial extension. Hence time not only has become a vivid issue but has become mathematically operational as well. Consequently the second step goes beyond the line and entails first to sub-ject the plane and afterwards the whole Euclidian space to the continuum of numbers. In this concept each single point of space is represented by a real number. Hence every point, every figure, every curve, every solid in space is independent from any vividness and accessible by calculation. Absolute space and absolute time are seen as homogeneous indifference. The Euclidian ideal of continuous space is extended by the continuum of time which now is thought of to be absolute. The basis of this concept is the fiction of a precise capture of the infinite, here of the infinitesimal small. We have to think of it as a point which then is expressed as a numerical value and therefore becomes mathematical operable. The mental corset of an absolute space, in which our mind is moving around all the time since Euclid is now extended by Descartes onto the layer of numbers. Model or idea respectively and reality were put into one by Euclid. The confusion of both is perfect and is now continued on the layer of numbers. Geometry becomes accessible for the rules of arithmetic and algebra and can therefore be resolved completely into abstract symbolic formulas. With the idea of Descartes the principle of division is interwoven into the vivid or intuitive continuum respectively and in reverse the principle of divisibility includes the continuum. All physical values including space and time can be dimensionalized which is they can be transformed into mathe-matical expressions and in reverse mathematical values can be interpreted as vivid sizes. Sense and mind are melted further on in a fruitful way. (ger-man: fruchtbar oder furchtbar? sic!) The superposition of the Old above the New is presented here in a perfect way. With regard to the basis of the numbering system we still stick with the tangible consciousness which is we rely to the ten fingers. When it comes to the choice of expedients all available possibilities of the new looming consciousness are used. As a result we observe seemingly absolute

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creational freedom without respect to any form. This is only felt sometimes to be a nasty limitation. The mathematical space of the system of coordi-nates on the other side perpetuates the prison of the fiction of an absolute space and therefore the transition or passage respectively into the immanent realm of information (Amension) is prevented. In such a way the legacy is extended with the aspect of time and newly wrapped with new means. Indeed Leibniz already criticised the system of coordinates with its arbitrary chosen origin as an essentially improper aspect of analytical geometry and although Desargues as a friend of Descartes explained his ideas of a projec-tive geometry to Descartes – all this objections had no impact at all. Ana-lytical geometry with all its extensions and refinements is the prevailing concept which lies under our ideas of space and time. Dedekind constructed (and therefore justified) the irrational numbers with the help of Zero – as far as I understand this is a classic circular argument. Until today the essence of numbers und of ratios is veiled because of the actual monopole of the deci-mal fraction in the representation of numbers, actually it is made invisible. The representation of ratios as decimal numbers has stunt the sense for order. Numbers are degenerated to vacuous sequences of numerals. The age of rationalism, of mind is completely built on irrationals which are used arbitrarily. As we have seen actually they are rationals for practical pur-poses anyway but science and hence all of us are trapped in the (irrational) believe we are dealing with the infinite. Although this delusion is heavily jolted with the progress in physics from electrodynamics via thermodyna-mics to quantum physics till today it is not really overcome. Nevertheless we have to recognize that the reduction of the original divine to the tangible and direct measurable without respect to the true essence of numbers them-selves turns out more and more to be self-destructive.

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Nature becomes an Object of Mathematics - From Proportion to Function -

A preliminary culmination of the superposition is reached with the term “function”. Function is the new ideal of any scientific term and is contrary to the formal logic of the Aristotelian schemes of terms. The formula as a mathematical term is opposed to the ontological term as it is given in words. The function is the contemporary adaption of an idea which was shaped about two hundred years before by the German cardinal Nicholas of Cusa. In his writings about the “Coincidence of opposites” (lat. Coincidentia op-positorum) he assumes that the One and the Many or the Infinite and the Finite are in a relationship of mutual dependency. Each single One as a part of the big wholeness is always aimed to another single One. World is a functional coherence which conveys between its parts and the whole as well as among the parts themselves according to defined rules. According to Cusanus in such a context there are no longer any static things but condi-tions only, momentarily captures of knots in an ongoing moving and trans-forming network of relationships. This far reaching idea is realized at the beginning of the 17th century in the horizon of the mental consciousness with the mobilisation of all disposable new achievements as there are: time which is reduced to duration, decimal numbers, system of coordinates with all its premises and the calculation with letters. A function is the description of a lawful dependency of rela-tions written as a mathematical formula wherein instead of definite single properties variables are shown as placeholders for varying values. Whereas the variables pass through a continuous series of values the formula as a general term includes actually all thinkable and therefore also all special cases. As a dependency of relations we may understand the transition of a value in its relation to an independent value in its neighbourhood. In means of formal logic tangible attributes and moments of relationship are indiscriminated mingled. However it is the basic idea of a function to dis-sect the generating rule for the ongoing lawful changes in relationships. Therefore it is not a general reproduction of a mental concept, of an idea but a rule of series which describes the emergence of one condition out of an-other one. This is the feature which gives its imprint to the term „function“. Change once was thought of as movement in space. This coincides with a duration, with a progress of time. The usurpation of the only shortly mas-

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tered time by the mental oriented consciousness reached its preliminary culmination with classic experimental physics. The variable number on the line of numbers was the crucial tool for the analysis of physical processes in the hands of the first physicists of modern times, the congenial scientists like Galilei, Bacon or Kepler. The key to make nature an object of mathematics is measuring. Physical phenomena, first defined as terms, are translated into numbers which then can be operated mathematically. Actually measuring is not to measure the object itself but its relationship to its surrounding. However, the basis for the comparison of measuring results is a homogeneous context of condi-tions. In case of complex investigations we therefore come up inevitably with arbitrarily abstract gauges or comparing units respectively. The well-known experiments of classic mechanics show how the movement of a object, thought of as to be invariable in itself, in space (a sphere for exam-ple) is measured relative to its static surrounding (for example an inclined track on which the sphere is rolling down). The system of coordinates is the perfect mathematical counterpart to the laboratories of the researchers. The movement or change in the real space can be described as an ideal process mathematically in the system of fixed coordinates with the graph of a function as well as with the function for-mula itself. As the term of the number interpenetrates with the term of the function every possible form of lawful dependency of values can be de-picted. Especially because of the extension of the idea of the function to the analytical calculus each single moment can be fixed. Every such a discrete point within a movement, which itself is thought of to be continuously, is called a limit. Actually a true mathematical point is inconceivable. „Point“ always means a sensual extension even if it is itsy-bitsy. Again we reach the problem of the irrational. With the fixing of a limit in our thoughts we still stick frantic with an object as a thing. But this is: we suspend the achievement of the idea of the function. The object of a function is the rule which defines a relation. As long as we think in rigid static terms we restrict ourselves. When we fix the value of a function as size mathematics capsizes into magic, becomes measureless formalism. It is at this point when the word of Spengler becomes true which denounces function as the Faustian number. The settled man is programmed to possession. Once mind takes command with its formal logic first we can see the development of an addiction for

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surveillance and eventually an unconditional claim to power. Mind´s atti-tude never is like to accept things in their authenticity. It wants to have them at its disposal and arrogates to constrain them under its own measure. It is in these different attitudes with regard to nature where we also find the core of the famous controversy of colour recognition as it is given by Goethe and Newton. The idea of the function as shaped by Cusanus is realized by Descartes through an admirably sophisticated mathematical toolset. However, it is characterized by a pure tangible oriented mind. Besides this massive superposition we may state a second overlay: the over-lay by language. We are simply missing the words, an adequate capability for expression. Our languages are centred about nouns and are static ori-ented. There are no appropriate constructive elements in our languages available which allow us to express the dynamics in the ubiquitous proc-esses of movements in a suitable manner. Max Bense phrases the situation as follows: „When language becomes insufficient it becomes obvious that the things to be expressed exist on another ontological level as the things on which the actual language itself was formed.” It is this deficiency which shows us that a new symbolic power is necessary now.

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Science becomes mathematical - From Term to Formula -

„The bird struggles itself out of the egg. The egg is the world. The one who wants to be borne must destroy a world. The bird flies to god. The god's name is Abraxas.“ These are the words in the development novel „Demian“ of Hermann Hesse at the beginning of the protagonist´s path to himself. On our pathway to the promised garden it is now also only a short distance. At first we shall observe the hatching of the butterfly out of its cocoon. The crucial moment of superposition is given in the reification, the seem-ingly fixing of the irrational as a manageable value. However, with this mental materialisation the core of the idea of the function actually becomes crippled. Although Descartes in his concept of dimensions employed intensely subtle considerations when it comes to the accurate description of things and their interfaces or overlays and therefore their limits in a system, he finally failed in the face of the inquisitorial verdict against Galilei to overcome the tangi-ble minded thinking in such a way to think the relationship of an object with its surrounding without space at all. So we observe Descartes moving in the tangible Euclidian world which is mapped by him completely as a func-tional system. The pivotal turnaround for the coverage of the pure coherence of relations forthcomes only with a generation change. When Rene Descartes ceased to be in 1650 Gottfried Wilhelm Leibniz was just four years of age. Blaise Pascal, an important bridge between the two, was borne 1623 and died al-most only forty years old, the year in which Leibniz with sixteen years of age just finished his first year as a law student. For Pascal every dimension (he calls it "Order") of a cause represents a separate view to this same cause. Various dimensions represent the same cause independently in various modes. Although the orders in a way inter-penetrate each other each of them is invisible to all the others. In this cohe-rence of different orders Pascal detected what is known as transcendental difference, a term coined by the German philosopher Kant. The model of order of Pascal indeed includes hierarchical structures whereas the superior can "see" the inferior, however all orderlevels are subjected by the regulari-ties of an overall order themselves.

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The formal mastering of the problem was then accomplished ultimately by Leibniz who extended the space-allocated „mathesis universalis“ of Rene Descartes to the „scientia generalis“. He considers pure relations which are no sensual conceivable substances at all but act as actual phenomena, as distinct elements to be treated like objects which are determined among themselves by their mutual position in a comprehensive order just like their tangible cousins. For Leibniz the realm of the natural numbers is the pre-figuration of such a comprehensive order of positioning. Therefore every concrete nexus of clearly defined relations can be mapped to an order of numbers and therefore also to numbers itself. Once formalised in such a way every correlation is accessible for the mathematical calculus. Leibniz had the view for the essence of mathematics and was clearly con-scious about symbolic mathematics. He combined his own insights and the mathematical elements of his direct predecessors Fermat, Pascal and Des-cartes to a scheme which he called „ars combinatoria“. For him it looks like that with this scheme man actually attained a new intellectual organ. He was confident about that it „would increase the intellectual capability much more than the optical instruments can increase the visual abilities of the eyes.” Out of the combination of elementary terms we may obtain all possi-ble cognisance. His alphabet of thoughts, the so called „characteristica uni-versalis“ becomes an art of detection by the principles of combinatorics, it opens a plethora of possibilities of conjunctions. From this point of view the „mathesis uninversalis“ of Descartes is a kind of science of a consistent order of a specific system. However the „scientia generalis“ of Leibniz is an order of orders. That is: it describes a structure. It does not describe the coherence of objects in a formal way but the lawful coherence of relations is formulated mathematically. The emerging limits in a sense of transformation- or transitorial phases are not values to be fixed any longer but can be put into and handled in the calculus as if they are values. In the model of Leibniz things no longer stay or move in coherences but they are emerging out of the coherence of an absolutely consistent unity. This fundamental unity of all being – as a single whole as such as well as a part of the bigger whole – is finally based on the principle of the infinite. This principle states that a value of an order can show up as a limit in an order which is of a different quality. Herein it is ruled by the other order but its property as a limit is not fixed as a value within this other order.

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It is already in the writings of Descartes where we find as an example for this connection the geometric fact of a length which belongs to the first dimension if we look at it as a definite part of a straight line but as a diago-nal the same length also can be part of a plane and therefore belongs to the second dimension. The calculus derived from these basics, the „ars combinatoria“, is a basis for the mathematical logic. As a result we observe the development in which science as such becomes mathematical (the cartesian function made nature an object of mathematics). However, they were also these insights which enabled a widely branched algebra and therefore the whole symbolic mathe-matics. The whole age of industrial revolution until to the atom bomb, which means mainly the development of energy based engines, accomplished almost completely in the mathematical baroque. That means in the horizon of the term of function as it was originally defined by Descartes. However the insights and ideas of Pascal and Leibniz took effect in full size only with the computer revolution in the 20th century. No longer is it the replacement of muscle power but the removal of intellectual attainments which can be formalised through machines is now in the focus. This development finally owes to the world-shaking insight of Gottfried Wilhelm Leibniz which says: „The fundament of truth lies in the conjunction.“ The Leibniz calculus founded the structural science. By them a whole series of philosophical problems are lifted onto a mathematical level and therefore at the same time the province of man is newly staked out. However, the hatched butterfly is unable to fly as long as its mind persuades it of being a caterpillar and it has to creep on the surface of the leave. Intellectual eager-beaverness just does not mean new consciousness at all.

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E x a c t F a n t a s y - a new symbolic power -

The Leibniz calculus transforms the thinking in terms to an operation with meaningless signatures which are separated from any things. For so called Leibniz-languages the formal rigour is crucial. The formalism for combina-torics was prepared among others by Diophant, Raimundus Lullus, Francois Viete and Blaise Pascal. Incidentally the potential for order as it is gathered in the so called Pascal triangle is age-old knowledge which was only redis-covered by Pascal. However, when it is said that the figures in the calculus are meaningless this is true only from the point of view of the metaphysical imprinted tangible oriented mind. For it the calculus represents a completely independent appa-ratus of rules. Actually the calculus depicts the once incomprehensible great diversity of possible conjunctions in a system. This is given in the scheme of a matrix as well as in the formulas of the infinitesimal-calculus. (Seen through the eyes of Leibniz the rules for the differential- and integral-calculation are simply applications of the ars combinatoria applied to the analytical geometry of Descartes.) The lawful inner coherence is given by the principle of the infinite. Within this coherence unfolds the infinite re-fracted inner horizon of a network of relations, in which the structure (mor-phé) of an integral whole is grounded. The type of God which is thought of to be a mechanic is suspended. With him man stuck to the metaphysical dualism of heaven and earth, spirit and matter. However, even Leibniz has not overcome the need for a numinous background and so God as a watchmaker is transformed into a God which is to be thought of as a gardener. The causal system of facts as it was shaped by Descartes evolves into a synchrotopic structure of possibilities. Out of a germ compressed in a smallest thinkable space in a shortest think-able moment a something, a salient point unfolds an uncountable number of theoretical possibilities, a well ordered, manifold changing shape. Its never-theless incomparable character is owed to the invisible and unchangeable form, which is constituted in the moment of in-form-ation, which is: the selection out of the abundance of possibilities. „Scientia generalis“ no longer embraces the one big system of a world. With the transition to formal symbolism particular solutions, and even the most complex ones, are replaced by universal methods of solutions. These

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are applicable for the big whole as well as for the smallest integral whole. Independent of its size every single integral becomes an independent cos-mion which lives its individual metamorphoses according to its Eigenzeit and its structural dispositions. According to Leibniz every possibility demands its realization. Possible means it can be realised in principle because there is no inner contradiction. However, besides the thinkable contradiction there is obviously a principle of choice which dissects the actual out of the abundance of the possible. Leibniz formulated this principle in his „Theodizee“ in a philosophical or theological way as the best of possible worlds, mathematically as the prin-ciple of extremes and physically as the principle of least action. This is at the same time the foundation of theoretical physics. The character of the new symbolic power has the distinction that we are enabled by the calculus to analyze existing orders as well as – and espe-cially – to join such invisible orders to new ordering-structures in a purpose-ful manner. We can describe these structures in a formal way with the help of mathematical structures and hence they also can be calculated. This act of creativity basically performs in the realm of ratios. The process which projects a new structure into the tangible world and hence makes it a reality (in metaphysical categories) is called information. With this new power man who was a creature up to date only, with the abil-ity to plan, finally has become a creative being. However, creation is pre-ceded by perception and cognition. The appropriate perception of order, mathematically apprehended as systems und structures, needs an exact fan-tasy. The (thus far so-called) spiritual is living invisible, but nevertheless it is accessible for visual thinking. With regard to this power of perception which is an old one in its essence but new in its today's form we are largely still in the state of an embryo. This fact causes the demand to educate people in an appropriate capability of perception. Such a capability is the prerequisite for a contemporary power of expression and design. The lack of this capability in a technical world which is based on calculus in such a high degree with no doubt will once result in the discharge of brute force.

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Knights Jump - A Symmetry Breaking at the Beginning of Modern Times -

In the chess game the knight is the symbol for the awakened. Nothing else can show our situation better: as mankind we attained a new figure for our game of life: the knight. It changes around systematically amongst the white and black squares, between heart and mind. The conjunction, the transition between space and form, across and over is defined as a rule!

However, we still move with this figure in a way as we are used to do with other figures: straight or diagonal. Although we obtained the creative poten-tial with the knight we play the game according to our self-made rules or the legacy scheme respectively. The handling of the knight requires a structural change in our perception, our ways of thinking and acting – just only new thinking is insufficient: that means to carry on within the system. No: our own structure has changed! The conditions of our existence have changed. Right now we believe the king is mate because he is threatened by our knight, at least according to our (mis-) understanding. What seems to be intermingled, obscure and complicated on lower levels in fact follows simple laws on higher levels. On a playboard shaped as a Moe-bius-area knight's jumps become simple as well. However, we are still play-ing in our world of three dimensions. „Royal art consists in ruling the world according to its own laws. This art demands the wisdom which consists in the recognition of the possibilities.“ (Titus Burckhardt) The calculus opens up the possibilities, however a new consciousness is necessary to bring the best possible of them into reality.

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Conjuction of Dimensions - From Measure to Matrix -

There are good news for you: we reached the garden. However, it is not possible to step in offhand. Like all precious objects this garden is accessi-ble only over staircases, bridges and through gates. Now we are standing in front of the gate and this is protected twice. Hence we need another two keys. The first one is needed to decipher the conjunctions themselves.

On our last piece of way we already heard about orders and their conjunc-tions. What is it all about with conjunctions? (german: Ver-schränk-ung) In german language the word “Schranke” appears in bar in the court (Gerichts-schranke), bars in front of the chancel in cathedrals (Chorschranke) and in needlework there are “verschränkte Maschen” (conjoined stiches). To set a saw is “schränken”, means to askew its teeth. Originally court bars looked about like the above shown door to the garden with skew crossed bars, maybe not that much high. What has that got to do with the key for the door of the garden of mathemat-ics? Well, mathematics means to arrange, has to do with cognition. Cogni-tion means to distinguish one something from another something. We al-ready observed this process in the chapters about the stepwise development of consciousness. There we become acquainted with the cardinal figures as virtually independent „differences“ which actually means „distinctions“. It is absolutely evident that we can reduce a finite set only finite times by a given difference. The result after each single operation is a definite count or ultimately nothing.

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In search for the first impulses for the ongoing transition of consciousness we encountered zero and the negative numbers. These were accepted as such famously only after a great deal of hesitation. Against any reason we accepted to reduce a set with more than what is in existence at all. And if we reduce the resulting negative number again – from which nobody has any idea about its meaning – we obtain even more of the unknown. The "less" is summed up. On the number line we may interpret the reduction as progress in direction of "less". In calculations we have to pay attention if the minus-sign is used as an operator or as a sign of a number. At the latest now it is the time we should ask if there is literally something going wrong which is: the contrary of right and therefore the invisible "mi-nus" or "less". Actually with the minus-sign we are already entering the realm of ratios. Something relates to another something – however in the same category. In the simplest case we refer to it as a distinction as seen above, however in general today a relation is expressed as a fraction. Thereby we distinguish improper fractions (the calculated result is greater than one) and proper fractions (the result is smaller than one). What has this got to do with negative numbers? The simplest proper fractions are the basic fractions: A unit, a cake e.g., is fairly apportioned in that many parts as there are hungry yaps. If there are four children sitting around the table every one gets 1/4, decimal written as 0.25. A rather uncommon spelling would be 4 -1. Oops! Here we see appear-ing a negative number – however as an exponent. We are used to see expo-nents only with powers. What is their meaning in this context? An exponent is a calculation specification, hence an operator like +, -, x or /. In distinc-tion from those here we have an operator which contains a value. Besides the raised position we give advice for the rate how often the so-called basis should be multiplied by itself. A raised negative number has to do with division. On the number line this means also less, now however not any longer beyond zero but between one and zero. The result is a real usable value even if it is very, very small that is: almost just zero. Therefore raising to higher power with negative expo-nents is an ongoing division with the same divisor. Raising to higher power with positive exponents can be reduced always to the operation of multipli-cation and this again to the operation of addition. If we have a negative exponent there is a division behind it, the reverse multiplication. Finally we may state that every exponent, if positive or negative, is an operator which contains a value.

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In case the exponent is 2 we are speaking of squaring. For the one or two may come into mind thereby the square-root which he learnt as the reverse operation of raising to higher powers. This reversal means nothing else than that the operator itself is a fractioned number. It is now at this point where we obviously blunder into the realm of the conjunction of orders. Let us study this situation at a geometric-visible case of the conjunction of dimen-sions. As far back as the age of Babylonians one has extracted square-roots from powers – provided the power (formal: radicand) was a square-number or the square of a simple ratio. As we remember: the art of measure deals with the division of areas. In contrast to a simple division where a linear value is divided in equal parts, here we need a (linear) scale to dissect nonrectangu-lar areas in equal parts by calculation. As we can see, here the first dimen-sion of a length, generally spoken: a linear value is conjoined with the two-dimensional area. Let us take the simple case of square-root out of 16. We may write the expression as follows:

216

or this way:

16

1

2 ..... and this is equal to 16

21

Now we are surprisingly at a point in which the exponent – remember: an operator – is raised to a higher power itself in fact with a negative exponent. Whilst the fraction describes a conjunction within the same category of order as we can see in the simple negative exponent, the square-root is rather the formal expression of an interdimensional conjunction. This con-junction among different orders has the distinction of an exponent which is raised to a higher power itself with a negative exponent. When man usurped the art of measure in times of the Neolithic revolution of course there was not only the ideal of square radicands. In that time the problem of extraction of roots was solved by refined formulas of approxi-mation. We already heard about the divine Ankh-Symbol of ancient Egypt which possibly is an equivalent of our root-symbol. This indicates the im-portance that was attached to this knowledge.

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On this occasion we also encountered the Alogoi, the numbers which cannot be spoken out. These irrational results indicate clearly another quality of numbers. In case of roots it is not only to reverse a manifold multiplication. Consider how to extract a simple root without knowing the times table up to 100 and some squares of fractions by heart? Not everybody is a Leonard Euler. We can state that with the conjunction among different ordering-schemes we basically always obtain irrational values. This can be seen sim-ply and in a vivid manner in geometry: In a square the ratio of baseline and diagonal is irrational. The diagonal line is a characteristic length in a square and as such a one-dimensional element within the two-dimensional area. For all we already know this diagonal line is a limit but not a measurable size. However the baseline is a limitation of the square and as a border ele-ment of it it is a size within and part of the two-dimensional area.

characteristicline (limit)1-dim. side-line

element of2-dim area

From this considerations about the conjunction of orders for Leibniz finally emerged the integral calculus. As an example you may take the fact that we obtain the function for the circular area immediately from the integral of the circumference of a circle. Within the context of area calculations we inevitably encounter the right angle as well as the theorem of Pythagoras and the trigonometric functions. Trigonometric functions actually are already defined as ratios and are there-fore in a close connection with the conjunction of orders. This is the expla-nation for the appearance of typical square-root values in a series of distin-guished angles. Famously for the right angle the cosine value is 0. This means that order-schemes which are, geometrically spoken, orthogonal to each other impene-trate each other without disturbance just like waves. The various order-schemes virtually don´t take any notice from each other so there does not happen any kind of manifestation. This is also true for ourselves as physical

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beings: If we cannot perceive a something the reason for this is found in the fact that this something is part of an order-scheme which is orthogonal to all of our other dimensions with which we are joined in one or another way and which we therefore are able to perceive. Conjunction is the prerequisite for perception, distinction and cognition. Are oscillations the prerequisite for the process of conjunction at all? Do we perceive because we are patterns of vibrations, circling, whirling beings, like everything which surrounds us? Since the geometric interpretation of the so-called imaginary numbers by Argand and Gauß (as a number-axis orthogonal on the well known number line) these numbers are used on the basis of the famous Euler formula for the mathematical handling of physical processes of oscillation. The imaginary unit „i“ represents the thus far not

explained value of the square root out of – 1: 2 1

Continuing the above considerations for the depiction of roots we obtain the following expression

12

1

What does this mean? Spoken with vivid categories here we extract the root from the reverse, the mirror image of the original – and the result is imagi-nary. The two axes of numbers span the plane of the complex numbers and therefore our field is extended by one dimension, at least calculative. Rowan Hamilton was not satisfied with two dimensions and so he con-structed out of the two dimensional area a four dimensional space of num-bers. Finally even this was extended to an eight dimensional scheme. How-ever, the calculation with complex numbers, quaternions and octonions is nothing else but the conjunction of ordering schemes which are accessible for us only mediate. We may get an about idea of this when we at first look into a mirror and then watch ourselves in a construction which in a first step is extended with one and then with two mirrors whereas each one is or-thogonal to the other ones respectively. Of course, with this experiment the meaning of -1 as basis is not explained at all. Maybe we get an answer in the second key for our gate. The extraction of roots is seen as a so-called algebraic operation just like the raising to higher powers. The other algebraic operations are the well known basic arithmetic operations. The crucial point for the algebraicity of an op-eration is to be seen in the fact that the participating operands which are

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operated on are in an immediate relationship. In case of extraction of roots it means that the result (the root) is obtained by direct application of the root exponent to the original power, the radicand respectively. As already men-tioned in former times this was attained by approximation and is accom-plished nowadays through the detour of logarithms. In such a way all the values are seen as sizes (with exemption of the expo-nents). As long as we are moving in a numeric field this calculations yield usable values – simply because of the circumstance that every formal irra-tional number in fact is reduced to a rational number. However, this kind of thinking in sizes is going to become a problem with regard to irrational numbers because: with this operation and a purely formal way of thinking the actual process on the level of order-schemes and relationships, which is the basis of the truth according to Leibniz, is completely covered. Hence, the coherence of arithmetic and analysis with the original idea of the func-tion is veiled in a decisive point of view. Finally we may state that negative exponents always deal with order and relationships which bring about order respectively and this means: with conjunctions. If there are interdimensional conjunctions, we can recognize them as root-expressions or trigonometric function-values, the resulting measures in general are irrational limits and therefore not any somehow fixable sizes.

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The Scale of Scales - From Measure to Logarithm -

We have seen the impact of dimensioning of physical values on experimen-tal physics under the overall prevailing superposition as described before. With regard to this practical and tangible oriented background and with the view on aspirations for overseas conquests together with the upcoming navigational problems the trigonometric and logarithmic tables became surpassing meanings as useful calculation utilities. We know for sure that it was already in times of ancient Greeks, most pro-bably even in ancient Egypt that their mathematicians knew the fact that the exponents of a geometric sequence themselves are yielding an arithmetic sequence. geometric sequence: 2 4 8 16 32 their equivalent exponents for basis 2: 1 2 3 4 5 Whereas the basis elements unfold through multiplication we receive their respective power-expressions by incrementing the exponent with one per step that is: a simple addition. A similar connex was available in ancient Egypt for trigonometric ratios. The later Greeks called them prostapheretic rules. The meaning for practical calculations is as follows: if we set an in-variant basis for numerical calculations all numbers can be represented by their respective exponents. As a result the elaborate multiplication- and division-tasks are reduced to simpler addition- and subtraction-tasks which can be done more easily. However, as long as the exponents are allowed to be integers only there is obviously only a minor advantage. Hence, for a comprehensive usage in everyday-life the range of allowed exponents must be extended to the whole continuum of numbers. This was exactly the vital idea of Napier and Bürgi who both independently from each other found what we nowadays call „logarithm“. So we found: starting with the famous rules for powering on one hand we allow the whole continuum of numbers as exponents and on the other hand we define an invariant basis, then the former exponents be-come logarithms which can be understood as representatives for any num-ber and we obtain the advantages for calculations as mentioned above. Because of the identical formal coherence in means of operations the proc-ess of finding the logarithm till today is said to be the second reversal of

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powering (besides the extraction of roots known as the first reverse opera-tion). However, what does it mean to find the logarithm? In the operations of powering and of extraction of roots as well the expo-nent is a given value and we conclude from the basis to a power or from a given power to its basis respectively. In opposition to these operations to find the logarithm means we are in search for the value of the exponent itself, the operator. What is expressed by this value given with the operator? It is the ratio of basis and power. Hence the exponent is a ratio-number – and this is exactly the meaning of the word „logarithm“. Why "exponent" in one case and "logarithm" in another? We already know that powering and extracting of roots are algebraic operations. The exponent then gives us the degree of the specific conjunction. The basis as well as the power are related to each other immediately – rather with integers. And: the operation is absolutely independent from any other conjunctions of the same objects or within the same scheme of order. As soon as we find logarithms there is a fundamental change. Now we view the whole context and compare relations or ratios or conjunctions respec-tively, this is: designate the ratio of ratios. This is the primary reason to set an independent basis. It is this the mechanism which allows to compare any numbers with each other, especially the irrational numbers themselves which are also allowed as logarithms. Let us remember the original idea of a function as it was shaped by Nicho-las of Cusa. By abstracting from real things it is his intention to formulate the law of relations which are varying according to this law. Thereby it doesn´t matter if these are relations among objects thought of as real things (classic experimental physics and analysis) or if the objects are relations themselves (ars combinatoria). Here with the logarithms we find the exact arithmetic equivalence to the order of orders which can be described in a (non-algebraic) formal way with the Leibniz-calculus. This is the reason why Leonard Euler justifiably assigns the logarithmic functions to the tran-scendent functions, although his reasoning was different. To reach this point one had to attain some fundamental insights with the tables of logarithms as a starting point. We already mentioned that loga-rithms in there beginning were seen as efficient tools for calculations and the values were handled as tangible measures or sizes respectively. With the squaring of the hyperbola which is to calculate the area under the graph of the function f(x) = 1/x mathematicians became aware that the logarithm as

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such is a function. That is: it depicts a lawful process of development and is therefore to be seen as a measure. However, it was not clear in that times which is the exact basis. The only clearance was that it could not be 10 which was the usual basis at that time around 1630. Only gradually it turned out that it is a value which is famous today in the whole (scientific) world as the number „e“. There is almost no natural development in which this value does not appear in one or another way – this is also true for the calculation of the area of the hyperbola (a natural function as well). Therefore Isaac Newton in his time called the appropriate logarithms hyperbolic logarithms. Leonard Euler, born in 1707, virtually a Mozart of mathematics, rather did not detect the number „e“, however he uncovered its main essence and gave this number its name. The number as such was already detected 1690 by Jakob Bernoulli when he was in search for a formula for compound inter-ests. It was also Jakob Bernoulli who passionately studied the logarithmic spiral which was already detected around 1630 by Descartes and Toricelli. Among others he found that this spiral keeps its shape independent from the scale which means independent of the distance from the centre. It is self-similar in every coil and therefore Bernoulli named it „spira mirabilis“. From an analytical point of view the derived function is identical with the original function and this is a property which this spiral shares with the exponential function (with basis e). After it became clear that this function is the reverse function of the logarithmic function with basis „e“ the loga-rithms of basis “e” nowadays are called “natural logarithms” because of the universality of the number „e“. The reasoning of Euler for the transcendence of the logarithmic function was simply that it is not an algebraic function. Neither is it a powering func-tion nor a root function and finally it does not include any of the basic arithmetic operations. Actually this is such a fundamental distinction that it is simply impossible to speak about the process of finding logarithms as a second reversal of the powering operation. One more argument against this nuisance is the rule of symmetry: every operation has exactly one reverse operation. Why should there be an exemption with the raising to powers? Once again: because of the invariant basis the logarithm is the exact equiva-lent to the numeric processing of the order of orders and this is independent of any specific problem. The logarithmic function is then to be seen as the formal equivalent. Just like we apprehend the different relationships among and between various orders in a single system with algebraic functions which is: their conjunctions, the same way we may comprehend mathemati-

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cally the whole structure, the order of orders with the transcendent loga-rithmic function. Out of this order of orders, this original synchrotopic structure of possibili-ties arises at a specific place in a specific moment a specific unrepeatable form: the origin (german: Ur-sprung) of a shape, the never-changing form which accompanies the ever-changing shape throughout its lifecycle, grants (german: ge-währ-leistet) the entity and the character of this shape because of its invariance. I Metamorphoses We may observe this process every day with ourselves as well as in our surrounding in an inexhaustible manifold of natural shapes of minerals, plants and animals as well. In the world of geometry which originally is abstracted out of these it was arguably Johannes Kepler who made the inner coherence of the so called conic sections transparent the first time by means of morphological studies of the circle.

Rene Descartes then identified this relationship from an algebraic point of view as equities of second degree with which we obtain the according graphs in the system of coordinates. Again it is the exponent, specifically the exponent 2, which shapes the unifying ribbon, the conjunction of the curves of the conic sections.

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Johann Wolfgang von Goethe, who predestined Kepler as his private saint, studied the phenomenon of the ongoing change of shape intensively later on and already depicted it aptly in his introduction for a planned complete overview of the, as he named it, “Morphology”. The central term in his teachings about this subject is “Metamorphose“ in which the phenomenon of ongoing change is condensed. We encounter the same principle in a complete different way in the world of music. The whole „Art of Fugue“ of Johann Sebastian Bach is a series of variations, in which a single motif undergoes an ongoing change and finally returns back into itself. Again the prevailing theme is the inner functional coherence of a manifold of shapes. What was it what Johannes Kepler did? He studied the silhouettes of a cir-cular plane which are produced by a wandering light cone, more precisely: he observed the ongoing transitions from one characteristic silhouette to the next one whilst the originating object which casts the shadows keeps the same. In a free manner he depicted the transitions from the circle through the ellipsis and parabola to the hyperbola. Besides that he coined the term focal point at this same occasion. With his metamorphoses of the circle Kepler laid the foundation for a ge-ometry which overcame the metaphysically overlaid perspective of the early Renaissance but only 200 years later. Synthetic geometry (opposed to the analytical geometry of Descartes) consequently uses exact fantasy, our new symbolic power. This new geometry, also famous as „projective geometry“, leads us to a flexible perception of things out of their own centre. It is not wondrous that the metrics of this geometry are of logarithmic nature whereas it is the geometric equivalent to the Leibniz-calculus: the hyper-bolic measure dedicates the ratio of succeeding steps in the movement of change as a logarithm – rather with regard on an independent, in general virtual and therefore not obvious centre of projection which becomes evi-dent only through the new symbolic power. Here we may also see a key for the meaning of the imaginary unit. II Gauge This not obvious but nevertheless evident centre of projection is the second key for the gate to our garden. Theological spoken we are talking about the central point of all religions, God. In case of the silhouettes of Kepler it is to be seen in the tip of the light cone, in case of the logarithms it is the fixed

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basis which comprehends all possible and even widespread varying appear-ances or shapes of a single form. Basically every number is a possible candidate to be the basis of a system of logarithms. In Brigg´s logarithms and in our decimal system as well it is the number ten, in computer science two numbers, two and sixteen function as the main basis equally. However, as we have already seen there is a number with a surpassing universality: the Eulerian number e, written as a decimal fraction with some decimal places it looks like this:

2, 71828182845904523536028747135 ......... Euler made the distinction between algebraic and transcendent functions but he had no distinction and hence no term for transcendent numbers. This distinction was an achievement only of the 19th century. In consideration of the particular importance of "e" it is unsurprisingly that not only exponential functions are transcendent in general but "e" as well, the basis of the natural logarithms. With its property as the centre of projection (geometrically spoken) it is the decisive value for the overall coherence of order, the stew-ard of all ordering schemes. However, the term for a decisive value is "gau-ge". As a verified and approved measure it is beyond any relativity. Hence it is the measure out of which system specific scales, which can be seen as gauges for independent order-schemes (for example the tracery of a tem-ple), ultimately obtain their legitimisation. Now we have to ask of course where from does „e“ itself obtains its author-ity. As already mentioned the value was found related to the search for compound interests, actually a really worldly issue. Not that much better is the reasoning which is founded on physical experiments which only con-firms what is presumed. In short: we are moving within an object-related thinking, shaped by metaphysical ideas, virtually sitting in the trap of the broadly discussed superposition. „e“ for us is so much self-evident that its role for the formation of the new consciousness does not appear on the monitor of our thoughts. The undeniable authority of "e" as an irrevocably principle in the setup of any order is obtained from its exceptional position within the infinite num-ber of systems of logarithms. The gradients of the (mirror-inverted) expo-nential curves correspond with the respective natural logarithm of the given basis a multiplied with the actual function-value: the derivation of ax = ax * ln (a). There are two characteristic consequences out of this in analysis: For the logarithm system with "e" as basis follows that the respective exponen-

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tial curve is identical with its own derivation and: for all conceivable expo-nential curves the gradient in x = 0 and y = 1 is ln (a). „e“ is the controller of all ordering schemes, the gauge of all logarithmic systems which themselves are decisive for "their" order-scheme respec-tively. Is it to be said that „e“ is the unrecognized and newly detected meas-ure? Due to the fact that in the realm of science there is calculated almost exclusively with natural logarithms, virtually the original, the meta-logarithm, the true meaning of "e" as the centre of projection of any order is completely disregarded. Just like in the transition-phase from the four-parted proportion to the three-parted equation One disappeared in the fun-daments of mathematics today we find „e“ that deeply burried in this same fundament that we do not notice it in its true quality. Novalis justifiably called attention to this in his writings: „What logarithms are for mathemat-ics, is mathematics for other sciences.“ III spiritus rector Why are we fascinated by a crystal? Why are regular subdivided figures so attracting – first of all a circle? What is it that makes a wheel useful? Why is a series of notes tuneful? It is their more or less obvious order. However, this order always obtains any shape from a more or less recognizable point of reference. If centre of symmetry, central point, hub or fundamental tone – there is always a kind of controller, a „spiritus rector“, who keeps an entity together in a harmonic way. In case of logarithms it is their common basis. When a master of ZEN commits a perfect circle to the paper with his brush, then he does not leave behind a puncture from a circle – he succeeds be-cause he is in his own centre himself. This is the theme of the essay „Con-cerning the Puppet Theatre“ of Heinrich von Kleist.

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What is it that detains us to recognize this mysterious centre which arranges all parts in a „prestabilized harmony“ with respect to each other? The development of the first key has already shown to us that the extraction of roots usually leads to irrational numbers. They are not values by them-selves but actually they are ratios. Whereas roots determine the conjunc-tions between two countable, tangible objects within categories which are different from each other, logarithms express the relation between schemes of order. In general they are also irrational. Besides that we can find valid roots in almost all cases only with the help of logarithms. In the case of physics we discovered that the function emerges much more purely the better we succeed in keeping apart the objects from its relation-ships. Within mathematics the distinction is then expressed by an appropri-ate symbolic notation. Until now we describe the various types of numbers in categories of set theory and declare them progressively as supersets of the preceding ones regardless of the difference between counting numbers and ratios.

However, this distinction was already made by ancient Greeks when they used separate terms for logoi and arithmoi. Till today we ignore this distinc-tion and locate the complete set of numbers on one line, the continuum of numbers as it was introduced by Descartes.

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Undoubtedly the geometric interpretation of the order of numbers is an extremely helpful tool. As a symbol it should convey a coherence which is invisible as such, but which nevertheless is a real one. However, if a symbol is not consistent it conduces for more confusion than clearance of the actual facts with its suggestive appeal. According to the deliberations up to now in case of the line of numbers it is consequent to resolve the single line of numbers in lines on which numbers are put according to their functions: 1. as exclusively positive rational counting numbers and values, 2. as arational proportions and 3. as controllers of relations.

With this the manner of speaking about irrational numbers has come to an end. It was Kepler who already justly pointed out that the „alogoi” (remem-ber: those which cannot be spoken out and ...) which are translated as “irra-tional” are „verified in their existence by best reasons (rationes).“ Not these numbers are irrational but rather the occurrence is irrational where the mat-ter of fact person Rene Descartes deliberately expands the counting num-bers with the ratios to the continuum of numbers. We may concede that this happened in the course of the described process of overlay and in the elation of the overpowering of the infinite. It is of particular importance to recognize that the integer and fractioned proportions as well are not unambiguous identifiable discrete values but rather like the infinite roots they are limits in the sense of the conjunction of order schemes. Therefore it means that these numbers also represent a proc-ess, something in motion, an oscillation. For example the values 3,9999...

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and 4,0...01 embrace the limit 4 which is the arational proportion 4/1, but not the number 4! In other words: The square root out of 16 is not identical with the counting number 4. Behind every operation to generate a relationship, beginning with the dif-ference via the fraction and ongoing to the root, there is a reversal process. As we have seen in the explanation of the first key this process is always represented by the symbol “ -1 ”. It was exactly this value within the proc-ess of the squaring of the hyperbola ( f (x) = x -1 ) which led to the insight that the logarithm in fact is a function. In the already mentioned projective geometry the inversion of the circle is also a reversal process (mirroring), a fundamental transformation wherein the central point becomes the point of infinity. In such a sense we may say that every generation of relationship, each reversal means a passage through the infinite. Within the plane of complex numbers this step is a sliding transition. On this way of generating relationships, especially of relations amongst logarithmic bases in the very end we get to the essence, the number “e”. It is only when we clearly bear in mind the hierarchy of order schemes and their controls that we perceive the ultimate shaping, in-form-ing centre. However, therefore the distinction between „logoi“ and „arithmoi“ is inevi-table. Interestingly enough „information“, the process which gave its name to our actual era, is defined by a negative logarithm and the mathematician and physicist Hartmut Müller defines „e“ as the gauge for information. Finally we may remark that it was in times before Christ that in central- and north-ern Europe „ ê “ had the meaning of religion in the sense of the “everlasting order” or “everlasting law” or Greek: logos!

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Enlightened Consciousness of Arbitrariness or: From the De Facto to the Possible

Now actually we have unlocked the gate to our garden. Standing on the threshold we may cast a glance back before entering the garden itself. What we can see first and foremost in this transition to a new level of con-sciousness is a renewed differentiation of the number: logarithms describe ratios of relations among each other. The various static terms for numbers so far are enriched by the flow of information. It is the secularised time through which our existence has won a new dynamic which we comprehend mathematically with the function. The Leibnizian „ars combinatoria“ ope-ned a complete new world of possibilities – however, its unconsidered ap-plication is going to run out of control more and more.

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The slogan of modern times seems to be: do whatever is feasible. Alfred Anders justly said that we fabricate more than we are able to conceive. A tremendous knowledge is at our disposal which we often use for mischie-vously behaviour. Generally spoken we are missing the necessary wisdom. When little children are behaving mischievously almost always we can clear up the matter without consequential damages. When adult children behave mischievously with all the available possibilities of our time the conse-quences cannot be foreseen any longer. It is the fiction of absolute preci-sion, of exact calculability of all and everything which lends wings to our delusion that everything is under control and encourages us in our believe in an unchecked progress. With the separation of part and measure, according to the separation of object and relation, we tread the path for the clearance of the actual relations of order. As we have seen all the new types of numbers since Fibonacci (zero, negative, real decimal fractions) are proportions without any excep-tion. But these cannot be fixed! Although our arrogant constructing away, despite our extravagance in the manner of teenagers right now not everything is destroyed and some things are running well. One reason for this fact is a high threshold of tolerance of nature but at least of the same importance is the fact that we include in al-most all calculations the number „e“. However, this is not because we are that much conscious about the above mentioned properties of „e“ but be-cause of its approval in the field. At this point we can observe how the new consciousness effects the present. The currently prevailing, so called enlightened consciousness is a con-sciousness of arbitrariness. As such it marks the crest of the transition. Neither after the first nor after the second step in the development of con-sciousness there was any central point discernible in our scheme. Neverthe-less we never lost the certitude of its existence. In default of an obvious point we put „God“ instead.

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Today after the third step we notice with Nietzsche: „„Who gave us the sponge to erase the whole horizon? God is dead. God remains dead!“ We don´t need „him“ any longer. With the proportion we gained a visible cen-tral point. However, what we are missing is an appropriate consciousness of form. With the three-parted equation we buried the unity, but this is the essence of the proportion. Shortly after that we ceded the sovereignty of our questionable consciousness to our mind by using irrational solutions, writ-ten as decimal fractions thinking of them as the ultimate conclusion of wis-dom.

With this single point of view in the centre we are focused on progress in a perspective manner. Within our primitive-linear understanding of time we secretly still cherish the fiction of precise determination, the hope once to be able to retain the infinite. What is necessary is the appreciation of the Eigenzeit of every form (every thing in its essence has its own time). The small cannot control the bigger one. What we can do is: we may bring our own rhythm into resonance with the rhythm of somebody or something else. Oscillation is movement and needs space. Therefore the point must be expanded to an area. This will be accomplished if we expand this figure, the so-called Pythagorean Tetraktys (= fourfold) to the fivefold Pentaktys.

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The Road (der WEG) to Integrated Consciousness - Quantised Forms -

Our garden is small and plain, just like the gate. This should be the garden of a Queen? The Queen is Mathesis and she is immortal. She reigns since primeval times and will reign along once we, who we are now thinking about it, have gone for a long time. She is reigning with the intense light of wisdom and not with the superficial glamour of plenty of knowledge, a knowledge which is always knowledge about something. Sheen needs a provider like Gold for example. Today we are accustomed to wealth, the big number. The more and bigger, the better. Quantity is the only point of view to talk and think about num-bers. This garden is readily comprehensible and I led you hither that it may convey you a feeling what numbers can be beyond the aspect of quantity. Once we come into a greenhouse or on a golf course we are overwhelmed because of the pure quantum, the intensity of colours, the monotony. Here is not that much new: once we have seen a tulip we have seen all of them, once we have seen a blade of grass we know the whole course. Mathematics is the language of nature. Although it is of tremendous variety it has only one faculty. Since Leibniz we eagerly studied the grammar of this language but the vocabulary is still fairly pure. The words of mathemat-ics are the numbers. One may opine the vocabulary is huge, almost reaching the infinite. However, here the vocabulary is measured by the number of viewpoints we have upon a single number. Indeed there can be no talk of a plenty of viewpoints. The viewpoint is one and is just restricted to quantity as it is written in the form of a decimal number. With algebra we learned a lot about the grammar of this language, however without to spare a thought to its words. The signs of the „characteristica universalis“ became a reality on themselves. We know all the possibilities of connections of allegedly arbitrary elements. And because we have deeply investigated the grammar now we are able not only to read in the book of nature but we can also write ourselves into this book. However, the prob-ability to construct a series of meaningful connections, which means: to bring about a reasonable sentence decreases with the abundance of possi-bilities since the probability of a hit relates inversely proportional to the number of possibilities. This is evident to everybody from the lottery. More numbers mean more possibilities of combinations, and more combinations mean less chance of winnings. And beyond that: because the signs, which means numbers and terms as well, are not bonded to any objects any longer

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they have become shiftable. They are variables and everyone gives to a word that meaning which suits him best in this very moment. The German poet Rainer Maria Rilke put this fact into a perfect picture when he wrote: „The meaning dangles from the words.“ In the realm of language this mechanism is known as ideology. Those who are in control of the language (and the channels of communications, the media as well) control the people. In light of the dominance of arbitrariness the fear of chaos is undoubtedly justified. However, the facts of nature are in contrast to this way of thinking. In nature there is no arbitrariness. It uses all liberties and at the same time there is complete order and harmony everywhere. Leibniz talks about the best of all possible worlds with credit to a prestabilized harmony. Not eve-rything which is possible according to grammar or formal calculation is realized. Leibniz refers to the principles of extremes or infinitesimals re-spectively when discussing the striking security of choice of nature. How-ever, he cannot explain why we are facing preferred particular prearranged relations or conjunctions respectively always and everywhere. It was Gottfried Wilhelm Leibniz who developed the „ars combinatoria“, who gave autonomy to signs and who put God inward when he wrote his teachings of the monads. Leonard Euler was a mere nine years old when Leibniz passed away in the age of seventy in the year 1716. Euler was a fervent protestant and had no use for the God as a gardener as it was con-ceived by the enlightened Leibniz. That is how it came that the intellectual world of Leibniz, which was represented in Euler's time by Christian Wolff, was vehemently fought by Euler. The contradiction was also mirrored in the realm of mathematics. Euler was a magician with regard to numbers. One said that for him calculating was a process as breathing is for other people. Euler didn´t need a pocket calculator (if there were any), he was a calculator – and a scientific one! So, whereas one of them preferred to attend to the grammar of the language of nature the other was completely addicted to the vocabulary of this language. What was not accomplished, not least because of the theologic-philosophical antagonism, was the connection between arithmetic and algebra. This connex was attacked systematically only one generation later by Carl Friedrich Gauß. He was six years when Euler died in 1783 seventy seven years old. For this task he could go back to the rich analytical investigations of Euler. The theory of the section of the circle was published in 1801 in his „Disquisitiones aritmeticae“, a groundbreaking mathematical work till today. The group theory which developed out of this work later on however lost sight of the numerical aspect again. This theory introduces numbers as vir-

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tually arbitrary but nevertheless particularly convenient examples of groups because herein all connections work seamlessly. One gets the impression that algebraic structures are existing independent of numbers as an autono-mous universe of signs. What one can recognize is a tendency to escape in purely formal intellectual systems, into an empty but nevertheless keen mathematical symbolism without any relation to physical reality. However, if other objects are used instead of numbers, the process of group operations finally brings us back to the order of numbers. With this we get proof that not only arithmetic is a priori (as shown by Kurt Gödel) but numbers as well. For the Germans Albrecht Dürer or Agrippa von Nettesheim in the 16th century the number was still meaningful. If you are talking about numbers in categories of quality you may be appraisingly (dis)qualified as a numer-ologist by tendency. Actually we may state that “structure” which became explicit with the „ars combinatoria“ is rooted in the inner coherence of the natural numbers. This is the answer to the seemingly paradoxical statement of the faithful Albert Einstein: „The everlasting incomprehensibility of the world is its comprehensibility.” However, how does this coherence look like? Coherence is relationship, made out of one or more relations, proportions. Beforehand we were already concerned with various kinds of the appear-ance of proportions and we identified the difference as the simplest one. Now it is obvious that we cannot meet the standard of natural phenomena with a purely additive or subtractive relationship respectively. In terms of group theory we have to concern ourselves with multiplicative connections. This was already understood by our ancestors even without group theory. Proportions relative to the unity were outstanding proportions all along. At this point I may remind you to the basic fractions of the Egyptians but to the resolution of the four-parted proportion into a vacuous decimal fraction as well.

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I Harmonical Proportions With regard to this subject the world of music is of special interest besides the world of things. While the seemingly linear musical scale for the ear sounds in an equal-additive manner on a physical measurable level it shows a multiplicative coherence. Therewith we are in the midst of the problem where orders have to be set in relation to each other. In other words: in the world of logarithms. Whoever plays three or more octave tones on the key-board of a piano is taking logarithms. The octave marks an interval with utmost resonance. Physically this matches the simplest proportion to be thought of: the doubling or bisecting respectively of the length of a string or the air column in a wind instrument. Expressed in numbers: 1/2 – the sim-plest of basic fractions. Whereas the series of basic fractions evolves out of the series of natural numbers and therefore show a hyperbola as a functional graph, harmonical intervals which we know from music as the scale, evolve out of the respec-tive supplementary value to the unit (here shown as fractions and as pow-ers):

1 / 2 1 / 3 1 / 4 1 / 5 1 / 6 2-1 3-1 4-1 5-1 6-1 1 / 2 2 / 3 3 / 4 4 / 5 5 / 6 1x 2-1 2 x 3-1 3 x 4-1 4 x 5-1 5 x 6-1

This is what was detected by Pythagoras in due time and what is known to be the birth of science: he abstracted the coherence between the pitch and the length of a vibrating string and expressed it in means of numbers. This was virtually the way from the quality (of listening) to the quantity (of the measuring experiment). As Ernst Rasmussen says there should be also a way back from quantity to quality. But there is no way back behind the symmetry breaking of modern times, all we can do is to conquer the old wisdom with new expedients in our own manner. As it looks with the non-local quantum physics we are indeed on a good way. „The insight into the importance of the abstract idea of periodicity stood at the very beginning of mathematics and European philosophy as well. … And now in the twentieth century we find physicists to a large extend dealing with the analysis of the periodicity of atoms” wrote Alfred North Whitehead.

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The idea of oscillation as the basic pulse of creation goes far back in the ideas of mankind. The investigations of Pythagoras not only yielded the Tetraktys but also a scheme he called Chi and which is constructed out of two multiplication tables: the Gamma with natural numbers and the Lamb-doma with rational proportions.

In the course of education in the ancient world „Harmonics“ was one of four ways in the so called Quadrivium. Ancient mathematicians shew an

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admirable deep understanding with regard to proportions, which is exactly what we are seemingly missing today. They already distinguished the three mean values which are well-known to us as the arithmetic, the geometric and the harmonic mean. Therefore they were also familiar with the fact that every basic fraction is the harmonic mean between its two neighbours. By means of the appropriate equation of proportions even the Babylonians were able to obtain fairly good approximations for square roots. (The most simple and at the same time the most perfect equations of proportions with regard to harmonics are encrypted in the already mentioned Pythagorean Tetrak-tys.) Although faced with the problem of scaling because of the series of musical intervals and although Pythagoras knew the law of tones he did not break through to the phenomenon of the logarithm. One reason for this might be that the pitch depends directly from the length of the string or the height of the air column, which means: from a linear, one-dimensional medium which covers the logarithmic effect. On the other hand there is a quantum effect which causes that only rational divisions are audible as pitches at all but not at all at any arbitrary chosen point on a string or air column which we may think of as a continuously length. In 1619 Johannes Kepler renewed the knowledge about harmonic propor-tions in a vigorous way with his book about the „Harmonics of the world“ (Harmonices mundi). It was his view of the world which led him directly to the laws of planets which are named after him. It was then exactly 72 years later, which is one day in the platonic year, when the secret of the catenary curve was disclosed with the methods of analysis. In modern notation the formula shows a kind of mean value of two exponential functions with the basis of „e“. It was then only close to the end of the 20th century when Horst von Hasselbach pushed the Pythagorean Theorem to a new level by means of the catenary formula. He invented a new mean value called „relative biharmonics“ which shows the direct coherence between the pythagorean triangle and the chainline. In the thirties of the 20th century Hans Kayser developed his partial coordi-nates starting with the Pythagorean Chi. His researches confirmed Har-monic as the universal principle of design in an impressive manner and shows it in accordance with leading edge scientific research. Kayser took zero as the reference point as shown above and calculated the respective logarithmic values. For Arnold Keyserling this table of partial coordinates

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was then the template to develop the “Wheel” as the numerological key of analogous thinking to world-wisdom. The usage of the word „harmonic“ doesn’t seem to be very fortunate in mathematics because of its use in common speech as an expansible term. Hans Kayser would say it fits with the casualness of the equal temperament. Referring to Kayser in the mathematical-exact context further on I shall use the term “harmonical” and reserve „harmonic“ for the informal-emotional use. With no doubt music is also part of this area as an elementary sensual phenomenon. Very often music is set into one with harmony likewise spaces are associated with architecture. Because of the archetypal character of numbers we state that harmonic is a musical phenomenon not at all but the reverse is valid: music is a harmonical phenomenon. Let us consider sensual impressions for one more moment: whereas num-bers of oscillations or frequencies are multiplying and wavelengths are divided in parts accordingly our ear hears an evenly rising series of tones. It is not only our ear, but all our senses are organized in a logarithmic way. This means our brain, our senses to be more exactly, calculate the physical impressions of our recipient organs which are the gulfs of our senses in ratios automatically. But from a mathematical point of view these are noth-ing else then logarithms. The line of logarithms is the facilitator between the ordering, ratio-building instance and all the quantitative phenomena which can be measured physically. It is of fewer and fewer interest as it was at the beginning of experimental physics to measure a whole in its relationship to its environment. But today science is dealing more and more with relationships inside of a whole, espe-cially a living wholeness. What we perceive as a shape is always owed to an information-process which, once initiated, all the time generates the form, the unchanging soul of an outwardly ongoing changing shape. The informa-tion-process grants the relationship with the ruler. This succeeds only when the whole at the point of its coming into existence is situated on the physical line which is to be gauged or calibrated. Mathematically spoken the zero-point of the line of logarithms is set to the unit, the One on the line of values (e0 = 1). The zero-point of the line of logarithms for me as a human as well as for every other shape is the point of identity which is the central point out of which the shape has to prove itself. The corresponding point on the line of numbers, the line of values of physical measures, the One is the shape in its unity as it is perceived by other people. It is this distinction of Identity and Unity in which we can grasp the actual meaning of zero which came to Europe in the beginning of the13th century: at first it makes the ruling

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background transparent, the background on which things only can exist; and the more we become familiar with this wisdom with the help of zero this background of reality becomes more an more tangible for everyone. In the centre of every scheme of order there is „e“. „e“ is the ruler of highest authority. But - what does this number „e“, this decimal monstrosity 2,718281828459...... has to do with the inner coherence of natural numbers, a number without an end, which shows no periodicity and above all is tran-scendent? Like the circle number „π“ „e“ to almost all people and espe-cially the scientists seems to be without any inner regularity. Chaotic irra-tionality even seems to be an inevitable attribute of transcendence. We have seen earlier that the entities of numbers which are mainly ex-pressed by their structure of divisibility experience a deformation and are totally veiled by the decimal presentation because of its binding to a specific basis. This is also evident for the number „e“. Here again we meet Leonard Euler, the great mathematician which gave the name to this fundamental number. It was already in the 16th century during the development of the decimal calculus when few mathematicians in parallel used to write numbers in a different way, the so called chain fraction. Leonard Euler with its feeling for numbers and structures then developed the rules for this form of representa-tion in a systematic way. Even more: he presented some of the famous irra-tional numbers as chain fractions right away. However, in the course of practical use chain fractions almost did not play any role until the 20th cen-tury.

For the depiction of numbers as chain fractions the following attributes should be kept in mind:

• all values on the continuous line of numbers can be presented as chain fractions

• all elements of a chain fraction are natural numbers without any exception

• all natural numbers can be built out of prime numbers

• the presentation of a number as a chain fraction is not bound to any “basis”. This is contrary to the presentation by decimals

• rational numbers yield finite chain fractions – arational numbers yield infinite chain fractions

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• the developement of chain fractions of quadratic arational num-bers is periodic

• if all part denominators of a regular chain fraction are identical, it is called a just periodic chain fraction

• the internal structure of a chain fraction is fractal

• chain fractions are the shortest presentations of numbers with best approximation at the same time

The inspired Euler has shown various chain fractions for „e“. One of these chain fractions unfolds the whole sublimity of this ruler of all rulers and at the same time it shows crystal clear the rank of harmonic in the creation of the world. So at the very beginning we meet the most spectacular flower in our garden, the number „e“ presented as a chain fraction.

Can you identify the stepwise series of harmonical intervals which couples itself at the 2 like a cascade?

II Rhythmic Ratios The presentation of „e“ as a chain fraction proves nicely the statement of Rudolf Stössel, who wrote „that not only the little whole numbers and their proportions are part in the harmonical consonance of our world as it was said by [Pythagoras and] Kepler but the irrational and transcendent numbers as well.“ Because of the separation of the line of ratios from the line of values we now know that they actually should be called arational numbers. Here we are exactly at the point where natural logarithms gave us a more

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deeply insight in the structure of ordering schemes which is beyond the venerable knowledge of ancient times. Our universe is an application of this principles and this knowledge applied in a wise manner allows us to write in the book of nature ourselves, makes us as human beings actually creative beings. As we read few lines above every shape is hold in form by its own in-form-ation-process. We may describe them as complex patterns of oscillations, vortices which permeate and interact (with) each other in an ongoing proc-ess. The central method to calculate these circular or hyperbolic effected conjunctions respectively is trigonometry, the teachings of the measuring of triangles. We may present such rotations in an analytical way as waves as they are shown in sine and cosine-functions. If this is known ever since (mathesis = what is known ever since) for me the question arises if the fa-mous epochal invention of the wheel actually was that much magnificent and if it really upraises us as descendants above the wheel-less cultures or if the actual or supposed primitiveness of our ancestors was grounded in the holiness of the wheel as a symbol of the vortex of life which was then pro-faned with this invention. Has man conceivably made available the inner energy of life with the physical wheel likewise we caught the time from the sky 700 years ago with the mechanical clockwork? – and thereby lost the rhythm of life? There is a chance that the wheel is brought back to its appropriate place with modern mathematics, more precisely: with the invention of the plane of complex numbers. Before the geometric interpretation around 1800 Leo-nard Euler stated that the imaginary unit relates the circle and the hyperbola. A multiplication with the imaginary unit, which represents a complex con-junction, means a circular dilation in geometrical terms. In physics „i“ func-tions as the time coordinate at least since the theory of relativity of Einstein and in electrical engineering it is used to represent periodic oscillations. In the field theory of Burkhard Heim „i“ represents the dimensions “above” the three-dimensional world of our „normal“ perception with regard to ele-mentary structures of matter. In regular school lessons imaginary solutions of square roots in general are discarded as irrelevant. Nevertheless in the long run we may find „i“ as the key which represents the back-coupling of our existence to the totality of the universe, the energetic-informational mirror of reality. The linear time of early nominalists comes into motion more and more. An indication for that is the Kozyrev-mirror which allows us to observe coming manifestations in the present. Another scientifically based evidence is given by the chemist Klaus Volkamer, who probably first

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time gave a proof of “negative masses”. This means we have another in-strument at our disposal to show conjunctions with dimensions which can-not be perceived with our consciousness as it is till today. The imaginary unit „i“ thus interferes the vital and identity-establishing information proc-ess, mathematically made comprehensible with the orthogonal oriented (hyperbolic) sine- and cosine-functions. On this occasion I want remind you to the „Hyper-Pythagorism” of Horst von Hasselbach. Information grants the form, the entity of a given shape. This form can be read from the ratio of the inner relations, the meshing of various threads. However, as seen before the ratio of ratios is expressed by logarithms and “logarithm” means the coverage of a ratio by numbers. We already mentioned that the entity of a number is expressed by its struc-ture of divisibility. Actually this is nothing else than its specific relationship to the unit, the One. We may also observe this structure as its specific fre-quency-pattern, its unmistakeable fingerprint. What is to be understood by such a specific relationship? In the case of the arational numbers which can be roots and logarithms as well this relationship is expressed in its chain fraction. The chain fraction reveals a more or less distinct rhythm which can be recognized by

• the count of various numbers, • the particular sequence and • the length of a period in such a series.

The smaller the occurring numbers, the less the value of different numbers and the shorter a periodic series the higher the stability and therefore the force of attraction of the represented relationship. The „deeper“ we „descend“ in a chain fraction the more refined the fibre of such a mesh. It was such a picture or similar which G.W.Leibniz may have had in mind when he said correspondingly that if one unravels the unlimited universe in more and more smaller elements, the wholeness of energy in always smaller quanta, the worldwide history in always thinner threads of individual activities one may obtain more and more minimal worlds which will be more and more similar to the macrocosm. And at the very end where the infinite small and the infinite big touch themselves we shall witness the borderline case, the passage through the essence of life.

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In the case of the natural numbers the distinct relationship to the unit is given with the decomposition in their prime factors. Hartmut Müller says that the fractal of prime factors which is build above the line of numbers and which shows itself as a standing wave once it is logarithmical shortened is the basic fractal of arithmetic and therefore of mathematics as such. Whether chain fraction or prime factorization: according to the above men-tioned criteria the lawful structure is literally decisive for the rank of a number in granting of conjunctions of ratios. The individual order of rela-tions as a pattern is like a memory and presents itself to us mathematically as a quantised fractal build out of whole numbers. Today we encounter the so called logos of the times of Heraklit, the inner order of the cosmos, as logarithm – or probably better: as logarhythm. If we take the criteria mentioned above as the basis for attractiveness of a ratio it is not wondrous any longer, that the simplest polygons as we obtain them by the regular division of the circle were of high importance ever since and of course will be forever. On the following page we present the chain fractions of the ratios of side-lengths by the radiuses of the perimeters

• in the equal sided triangle (√ 3)

• in the square (√ 2)

• in the pentagon ( at first φ , the golden mean)

• the ratio of radius to the side length is a variation of the golden mean ( √(φ²+1); a first approximation) )

• in the (half)circle ( π ).

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III Decisive Ratios

The one who knows the thread stretched, To which the entities are adhered, Yeah, the one who knows the thread of threads, He knows the big Brahman force.

These lines can be found in the Atharvaveda. Did the wise men of India know about „e“? „e“ is the polestar above the ever moving sea of propor-tions. All activities without „e“ are disoriented. As I already said at the beginning the primarily concern is to spin the thread itself completely new. However, as long as we only have knowledge instead of wisdom our situa-tion remains precarious.

It is this life shivering for its balance Like water at the edge of the Lotos leaf. The wise man however can show us instantly The bridge over this sea of change.

How can a boy at the age of ten write such words? Where from does he get his insights? They are part of a longer poem which was written by Shankara around 700 A.C. He may have known the thread of threads. Each entity is the creation of imperturbable mathematics of heaven and the whole cosmos is measure and number. When there is written in the bible in the Book of wisdom „However everything you ordered by measure, number and weight.“ then we should take for serious this distinction between measure and number likewise we discriminated between values and ratios on the line of numbers. In all teachings of wisdom and in every religion the main con-cern is about sapient order. This arises out of the persistent orientation on the particular determining One. We have already heard how the detachment from things in the West-ern world in times of Renaissance at the same time brought the loss of measure. As a very last consequence this is tantamount to spiritual sterility. „to take measure“ is used in the bible similar to “recognize” with the mean-ing of procreate. Hugo Kükelhaus tells the truth when saying: „Only when man clearly bears the Units in his visual mind which give the measure for life he is enabled to judge and act in an appropriate way. Without them he is unable to bring about order.“

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First of all we state that the „detachment from things“ does not mean neces-sarily the „detachment from order“. Relations which have come into focus with the thinking in categories of function obey themselves to an order as it is given in the sequence of natural numbers. Numbers are quanta, to count is to quantise. Any cardinal number includes in itself the whole development until its own position, it is virtually its own memory. Its individuality is legible in its prime factors. If it is a prime number itself then, spoken in musical terms, a new spectrum of overtones is established. This is because of its immediate connection with the Unit. A new branch sprouts out of the tree of numbers, a new family is founded, one more autonomous scheme of order will develop. But it is also in this new scheme however that the deci-sive proportions are the key for order. Decisive proportions are resonances. Designated number-ratios are causal for all of what we like, with which we as a per-son come into re-son-ance or vice versa: for all the things and beings we dislike, to which we feel aver-sion. To come into resonance means to oscillate together. „per-sonare“ originally meant in theater to „speak through the mask“. It also has the meaning however to cause something to sound or that a human being is in unison with the cosmos. The maximum of resonance is given mathematically with rational numbers which are built of smallest possible numbers. For systems which are com-plex in a high degree, deeply structured and rich conduplicated there is an inevitable force for precise tuning among the parts and with respect to the whole as well. It is the degree of refinement of the structure and complexity which determines the precision of the rhythm which grants in turn the co-herence of the whole. The patterns of frequency of various order schemes which are intended to co-act in an encompassing whole must be well-attuned to each other in every moment. More than 100.000 flawless attuned reactions within a single cell per second and at the same time with a maxi-mum of energetic efficiency is impossible without such a maximum of fine-tuning or coherence. Anything in nature which intends to endure – and who or what does not – can venture in the long run to ignore the decisive ratios or even act against them. The breaking of symmetry means refinement of structuring, enhancement of the levels of order and energy. However, it also means increased fragility which only can be compensated by a more pre-cisely and ingenious organization according to the exponential multiplied number of conjunctions.

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It is in this sense that specific numbers as distinguished ratios play a special role. I call this numbers proto numbers. Thus proto numbers are stable who-lenesses in themselves with a high quality of resonance. We perceive them in terms of natural numbers immediate as countable units, as prime factors or as parts of chain fractions. To regain the measure according to the con-temporary, to our time, means to learn how to distinguish numbers with regard to their quality of resonance. From this point of view Leibniz’ saying about prestabilized harmony wins its content. Quality of resonance here does not mean the ability to come into resonance with as many other ratios as possible. Very often this is markedly undesired. What is rather meant here is that a specific ratio is stable in itself at a high degree and therefore because of its attraction effect is capable to integrate and hold together an entire wholeness. With this we also got a clue that form and therefore ratios are decisive for the energetic potential of a distinct shape. If we pick out the extremes of the distinguished ratios with regard to their attitude in respect of resonance at one end we find the octave relation 1/2 and at the other end the golden mean, the number which is shown with the symbol „φ“. The octave ratio represents the most rational of all ratios whereas „φ“ represents the most arational relation. Resonance also always includes interference – this can be positive as it was intended or in a harm-ful way which is most probably undesired. Thus we find the ratio of the golden mean anywhere where an order intends to develop itself undisturbed and without interference of other order schemes as far as possible. This is true for planetary orbits in the macrocosm as well as in the microcosm of organisms. Dan Winter dedicates himself intensively to this relation which is obviously fundamental for live. In all the various fields of research he was led to remarkable results like in biology with the frequency patterns of the heartbeat, gravitation or the emergence of colours. The actual value of the golden mean can be approximated not only by means of a chain fraction but also with a series of simple ratios, the so called Fibonacci series. It was Fibonacci who once dispersed the One in the basement however, it was also him who saved it in another way indirectly in the chain fraction of „φ“. At the very beginning of this series their elements are identical with the simplest musical intervals (compare this with the chain fraction of e!), among others there is the value of 2/3. This is the suc-cessive interval behind the octave and is well known in music as the fifth.

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It was already under the headline „alogoi“ where I mentioned the idiosyn-crasy of ancient Egyptians to note all measures as sums of basic fractions – with the exception of the value 2/3. One reason for the exceptional position which was most probably known by them is that 2/3 on one hand yields a high degree of consonance and on the other hand obtains a very close ap-proximation to the ideal of a maximum of arationality with very small val-ues. The interval of the octave 1/2 with its double property as a basic frac-tion and at the same time as the first harmonic interval shows an absolute static character. Opposed to this the fifth means imbalance – and this is the precondition for movement and therewith for development and vitality. Kurt Schneider shows that this exceptional position of the fifth, a high de-gree of consonance and at the same time a maximum of arationality, also find its expression in the relationships of the spatial angles of the two five-counting platonic solids which are known as icosa- and dodecahedron. This becomes discernible however only when the sine-values are represented as fractions and the roots out of this fractions instead as decimal numbers. The resonance of relationships which is shown in the exponent of the square root is elegantly veiled in this case because the radicand which is 4/9 is com-posed of the two smallest of the square numbers and therefore easily can be resolved into 2/3. With logarithms and the representation method of chain fractions quality, shape and wholeness got a renewed mathematical basis. After the almost forgotten „sacred geometry“ and the simple ratios symmetry, harmony and rhythm now again take their ancestral places and they do so more vigorous than ever. Before starting the investigation of the tracks of this development we shall consider the new order of numbers with regard to the (newly in-vented) proto numbers at the end of our short stroll.

Wholeness of numbers

Proto numbers

Decimal number Chain fraction

discrete N natural P prime consonant

↓ R rational (Q) H harmonic ↑

continuous A arational (R) E eminent dissonant

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The two outer columns of the table show tendencies which are tied to the respective representation as shown in the top row. Here we presuppose the legacy line of numbers to be split in values and relations according to the key as it is given above. On the line of values there are exclusively positive values. They are either whole natural numbers (N) or true fractions which means pure rational numbers (R) or (if between natural numbers) ficticious ones, combined out of N + R respectively. As can be seen this is a matter of the well known line of countable discrete numbers with 1, the Unit as its centre. These numbers occupy the line in a dense way as discrete points. The proto numbers on this line are the building bricks of arithmetic: on one hand the prime numbers and their basic fractions (P) and on the other hand the harmonic ratios with their reciprocals (H) as they are well known from the theory of harmony. The line of relations is a matter of a continuous line on which we find oscil-lating limits exclusively. These arational numbers (A) represent the patterns of frequencies of an unlimited number of information processes. The proto numbers on this line which are to be seen as a subset of the whole set likewise as on the line of values I call the eminent numbers (E). The two transcendent numbers „e“ and „π“ belong to them as well as the golden mean and the square roots of the elementary numbers 2 and 3. It will be interesting to see if any other numbers which till now only carve out an inconsiderable existence as a decimal fraction will show up in the series of the eminent numbers in the future. Because arational numbers throughout are ratios of ratios we may distin-guish them as direct (+) and inverse (-) relations, hereby referring to a pro-posal of Gauß. The centre of the line of relations is marked by the identity, the 0-relation.

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Translucency of the Crystal - Tracks of exemption -

The momentum which initialised the transition to a new level of conscious-ness is aimed for the enlightening of matter, for the form which becomes conscious of itself. The theme was realised paradigmatically in the erection of the gothic cathedrals at the beginning of the 13th century. It was already 200 years before when Alhazen in Baghdad documented the laws of optics, described lenses made of glass and built parabolic mirrors. However, at its beginning this is nothing else than the rediscovery of knowledge which was already at the disposition of ancient Egyptians as is shown by Robert Temple. What made the men of Renaissance with this knowledge? In this field again we can observe effects of superposition. Whereas vision in the late Middle Ages was undergone as a spiritual-emotional experience and one assumed that the eye as the light of soul is sending a beam of sight, in times of Ren-aissance when self-consciousness became stronger the conviction asserted progressively vision is a mechanic-optical process where the eye is just a passive receptor. It is indeed the eye which chooses by focusing but never-theless it can be described as a technical instrument. As a result men devel-oped the concept of the „camera obscura“ and eventually the camera of our days. After men learnt to produce and grind transparent glass at the beginning of the 17th century Galilei invented the binoculars and Johannes Kepler con-structed the first astronomical telescope. The gateway was opened to the width of outer space in which only since a short time the earth is just one sphere among others. With its own Transcendental philosophy the German philosopher Immanuel Kant attacked the obsolete metaphysics and total freedom for all human beings came within reachable vicinity. The idea of an absolute and linear unwinding time brought a kind of think-ing in means of an always ongoing progress. The endeavour of the whole process is to leave the cabinet which was built in men’s mind, to transcend the boundaries and leave the earth to which men is tied by gravitational forces. However, until now any spatial and timely struggle only resulted in a situation which can be described such that the corset in which we jammed ourselves with our mind and which we intended to get rid of simply has grown with our efforts and at the same time has become threatening for every single being more and more. With the help of our comprehension we

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neatly split the world in most diverse faculties and therefore any thought for coherence recedes into the distance more and more. The distance between arts and science is wider than the one between Pluto and our Sun. The hope for liberation changed more and more into the nightmare of a hardly com-prehensible and chaotic apparatus which not only mentally but more and more physically takes our breath. With the beginning of the Age of Aquarius a turning point is set. Slowly but speeding up we get to the insight that we as human race can develop only when we bethink ourselves to our skeleton. The structure of the chain frac-tion may be a good symbol for this development. Man owes his upright posture and his faculty of speech not least to the circumstance that he can adopt himself, unlike the ironclad insects which live in a capsule, relatively easily to most diverse alterations because of his skeleton structure. Trans-ferred to the mental realm such a change in mind means a focusing to the own centre instead to any outward chimera. In the scientific field we have seen in Leibniz work the turnaround from God as a watchmaker to God as a gardener. Later on Goethe could write the following poem:

What a God who only pushes from outside, Circling the universe just with his finger! To him it befits to move the world inside, Nature in itself, himself to nourish inside nature, So that all beings living and weaving in him, Never will miss his force nor his spirit.

His contemporary Georg Christoph Lichtenberg adverts, that „not only tangible things can be made transcendent but things of the spiritual world can be made retroscendent back to the world of tangibles.“ The project of the enlightening of matter which also includes ourselves can succeed only when we turn to our centre. It is one thing to designate our own centre and another concern to perceive things from their own centre point. Here we may remember the ZEN-master and the “Puppet Theatre” of Kleist. With all the means as they are available today we have become creative beings. However, we shall never reach a felicitous creation as long as there is no draft underlying in which the point of translucency, the point of crystallization is determined in an absolute clear way. Where the enhanced freedom of the sign-bound logic (as it is given with the symbolic power of Leibniz Languages) opens up a new di-

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mension which is the freedom of an ample design there we need as a coun-terweight a profound term about the decisive ratios as an anchorage. We observe a change of metaphors with regard to the construction of the cosmos: from the hierarchy in the Middle Ages via the clockwork in times of classical mechanics through to the control loop of cybernetics. The cen-tral theme which runs through all these concepts is an idea of control from outside from a subjective all overlooking point of view. Why not conceive world as a hologram? From different viewing angles we perceive the same thing in different ways. Absolute time as is depicted in the coordinates as ongoing clocked particles has not that much in common with the reality of life. The life of any being however is going to proceed in the non-linear rhythm of its Eigenzeit. The American seer Edgar Cayce wrote in the thir-ties of the 20th century: „Every model includes by nature its own plan to grow and to develop itself, and this corresponds to the sound of a specific note.“ and the architect Louis Kahn developed his plans on the basis of the insight: “The essence of a thing is its desire to come to itself.” It is all about the centre, the salient point of maximum resonance, the iden-tity as it is marked with zero on the logarithmic line of proportions. It is this point to which the ongoing change of any shape is backcoupled by means of the respective information process. And it is this process which allows a unit to understand itself as a Unit and to have a continuous consciousness about itself ever. I The Gothic Project This is the fundamental idea of the gothic project. Put in the shape of the cathedral it is the counterdraft to the pyramids of the Egyptian Pharaos. Light makes stony matter levitating, statics start moving. Reinhold Schnei-der wrote: „It is the window, the actual change agent, from which every-thing depends in the gothic building. Pillars, walls and the vaulting are there because of the windows.“ The beam of light brings space and time in stream, the rhythms of time and development attain into our horizon of perception and we gain the intellectual space to yield real new creations. The electric light of the Enlightenment led to the contrary. However, it is not only the light transparent glass which is part of the win-dow but it is the frame as well. In case of the cathedral windows the frame has the absolute same significance with respect to the mental change as it is given by the coloured glasses. The wall resolves itself, becomes the form

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which as such becomes the condition for the possibilities of the play of colours. Thereby the dissolution does not happen somehow but follows the strict rule of a tracery. This gives us the impression of the rhythmic over-coming of gravity besides the resolution of space by the light. With these concepts in the construction of churches in the 13th century essential ele-ments are anticipated which are decisive for the mathematical foundation of the modern development: the invention of logarithms around 1600 and the self-similarity of fractal structures in the geometry of the 20th century. With the gothic cathedral totally new worlds of visual perception were opened. The rediscovery of the perspective in the 14th century is to be seen in close coherence with this phenomenon. However, here we also have another kind of superposition by the legacy which is: the Euclidian view of the world. The spatial impression is flattened to a tableau and the spectator of a picture which is constructed according to the rules of the central per-spective is tied to a single standpoint which is the view of the painter. It lasted about five hundred years until geometry got rid of the subjective view of space which is thought of to be absolute. The process led through some stopovers like Kepler, Pascal and Desargues in the 17th century and culminated in the freely moving metamorphosis of the so called synthetic or projective geometry. However, the term “geometry” still suggests bonds to outside space, the measurement of the earth (although it was Plato who denoted already such an assignment as ridiculous). I call this stringent art radiography. It allows us to visualize complex conjunctions literally bound-less analogue to sheer symbolic algebra. Whereas in Euclidian geometry only points and circles are ultimately radiography is an art of beams (beam = radius) and therefore can be performed (at least theoretically) with the straightedge exclusively. Literally we are dealing with a radiating design of the world. For practical purposes with the bondage to the restricted three dimensional space however the compass is still helpful. This is especially true for the construction of mirror images at the circle. This construction is in so far of extraordinary importance because it is giving us an idea of the arch circle and its points in the realm of the infinite as the counterpart of the central point. It is the arch circle out of which any being obtains its existence. It was Kepler already who clearly realized when investigating optics that world and therefore any shape always is made out of two radiating central points. Energetically spoken it is the germinating nucleus on one hand and

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the sun as the radiation centre on the other hand. In radiography these two points correspond with the focal points of the conical sections. It is only the mutual relatedness of two points which leads to the free formation of the immanent form in the process of metamorphosis. The radiances as tangents build the envelope curve of the emergent shape. Here we have the exact counterpart to the terms transcendence and retroscendence of Lichtenberg. Arthur Zajonc verbalises like this: „Two lights are there which brighten our world. Sun and eyesight. It is only because of their sisterhood that we can see: if one is missing we are blind.“ Like in any other being we also find in the human being what I call the receptive point of crystallisation. To find its own centre is to find this point and to appoint oneself into it and this is the way to the brilliant man, the human diamond. As long as we do not overcome the copying of the outside world with our cameras which is to overcome the central perspective we are prisoners of the Euclidian space. The only one-sided radiating eyesight of perspective leads into exorbitance likewise the plane orthogonal system of coordinates leads into torpidity. The visible light was one if not t h e one driving force behind the devel-opment of physics of the 20th century. Einstein said: „For the rest of my life I shall give consideration to the question ‘What is light!’” It is desirable that we are successful to change our point of view in such a way that the inner light comes into our vision as well. Obviously it is not enough always to declare the right thing. Rather we are relying on the ability of true percep-tion if we do not want to get lost out of sheer right and therefore than even-tually come out in total bewilderment. II Perception (wahr-nehmen) Euclidian geometry and logical thinking in terms (geman: Begriffe von: be-greifen) led to a preference and eventually the exclusive esteem of material. What is intangible does not exist. The distinction between form and shape is dropped likewise the distinction between reason and mind. This is espe-cially true for the English and French languages. However it is the language which determines our way of thinking and subsequently our way of acting. Space has always been understood, and is often still understood, as an inner space and form as the case which prevents us to leave this room. “Form“ is understood as restriction, this is also true for social forms. Thus our descen-dants are anxious again and again to dissolve the prevailing forms, they

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intend to shatter them so there can arise something new at the same place. However, as a result we most often have to realize that there are new and bigger spaces with even more insurmountable restrictions. Form however is not the outside restrictive shape. Form is the force of con-junction itself, the already available integrative force with the ability to connect the various elements to a closed inner entity. Only when we be-come conscious of this force again we shall not any longer make any efforts like Sisyphus to shatter concrete materialized shapes. We shall watch the things out of their own centre, out of their hub of force, out of their con-stituent relations and then be able to change them facile because of our varied manner of reception. Form is force and at once condition for an infinite number of possibilities. Integral perception means perception of the forms. Once we located the formative centre of force, the form of a shape then we are enabled to grasp the whole complex of a structure at once – whether in its spatial expansion or likewise in its timely development. Richard Buckminster Fuller saw his duty in making the invisible visible. What is in his mind are the forms, the unswervingly and at the same time invisible proportions which determine a shape in all of its appearances. It is not important to see what is done al-ready but above all to see through the becoming. To behold a shape at once in all of its metamorphoses by perceiving its essential form means integral perception. Lynkeus, the lynx-eyed watchman expresses this in the watchman’s ballad in „Faust“ of Goethe: „Born for watching, appointed for looking”. Ralph Waldo Emerson also recognized that things become transparent to us only when the axis of looking falls into one with the axis of the things themselves. The development of a flexible playful perception is equivalent to the forma-tion of a new organ. It is for sure one of the most urging tasks to develop and train our feeling for the subtle and hidden forces. This is the exact meaning of the word “aesthetics”: aesthesia = sensibility. Friedrich Schiller recognized this central problem of mankind in our phase of transition and attended to this matter in his letters „About the aesthetic education of men”. At that time however he assumed an ideal of beauty which was lacking of any mathematical foundation. Thus every talking about aesthetics is in limbo as are similar talks about ethics. Like I said: Nature has only one faculty and is likewise spirit and physics.

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It was six years after Schiller published his letters about aesthetics in Jena when the 24 years old Carl Friedrich Gauß in Göttingen published his work with the theory about sectioning the circle. Number and figure became again a unit in the rhythmically divided circle. The number which mean-while volatilised in the formulas to a calculating scheme without any entity regained its quality and therefore its dignity by Gauß as a rhythmic-cyclic shape of number. In this quality the force of eminent proportions is founded. It is herein where we find the reason for Einstein’s incomprehensible com-prehensibility of the world. Aesthetic feeling which means recognition of shape is inconceivable without resonance of proto-numbers. There are the prime numbers, the harmonics and the eminent numbers which intercede between idea and shape. This is absolute obvious in the shape of melodies – I guess we have some practice in musical perception. However the world of hearing is in an obvi-ous contradiction to the world of vision as it is taught to us by Euclidian geometry. Thereby the discrepancy is given not at all by any anatomic rea-son like a linear organization of the eye and a logarithmic of the ear. As mentioned earlier all of our senses are laid out for logarithmic perception. As creative man who are enabled nowadays technically for almost all and everything it is inevitable to acquire an appropriate view to the world which corresponds with reality instead with superficial illusions. It is absolute essential to develop a visual perception which is equivalent to the auditive perception. Auditive perception is fed by the theory of harmony and its mathematical foundation is identical with the basis of radiography. With the help of radiography we should succeed in changing this spatial designed world into a beaming world before it decays completely as a radioactive contaminated world. III Cognition (erkennen) The new symbolic power of modern mathematics altered the creature man into a creative being. We did not hesitate even one second to deploy this ability in actions, which suits perfectly to Faust: „This globe still imparts space for big deeds.“ Goethe however, the poet of “Faust”, makes us con-sidering else-where, more precisely in „Wilhelm Meister’s Apprenticeship“: „There are only few who have the sense and are capable for the deed co-evally.” Anywhere man meets only himself in form of his activities. We distinguish the acting from the recognizing, the handler and practitioner from the theo-

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retician. Only rarely we meet the one who is acting on the basis of true cognition. It lacks original power of design. In consideration of the vast amount of questionable results in the 20th century from several sides there was a demand for a theory of design. All the demands were backed by a vision of human technique. It was not readily obvious that design is an autonomous form of cognition besides theory and practice. However, with this insight a theory of design is a contradiction in itself and it is not only a small part which is played by theory, understood as abstract logic, which obstructs a successful design. Again we encounter the phenomenon of superposition at the point of inter-section of two levels of consciousness. On one hand the traditional Euclid-ian, spatial oriented perception and on the other hand the new symbolic power as a tool of cognition. Mathematical formulas are the utmost high developed symbolic forms derived from the rationality of the visible and invisible nature as well. Simplicity and clarity are owed to it. Applied in a purely formal way it may happen easily that the accomplished calculations are virtually hovering above reality. Thinking becomes embogged in the cleverness of the algebraic calculus of possibilities, but avoids the way into resurrection. Werner Heisenberg, the nuclear physicist, described the situa-tion as follows: „The pure mathematical speculation becomes infertile be-cause it cannot find its way back out of a game with the plenty of possible shapes to the very few forms which actually determine all shapes in nature.“ For me one of the reasons why we did not emancipate till today from the superposition seems to lie in the fact that the overwhelming majority of the thinkers as well as of the doers till today is not aware of the nature of sym-bolic forms. The symbol, understood as an element of a former level of consciousness, is not recognized as a form among others. In general we are missing the insight that every symbolic form is a legitimate instrument of cognition. Within each of these forms manifests itself another layer of coin-cidence or resonance between what is in existence and our ability for cogni-tion. At the beginning of the 20th century Charles Sanders Peirce as well as Ernst Cassirer published profound studies about this issue. Man not only is a creative being, he is also a spiritual being gathering mate-rial experiences. What does "spiritual" really mean? Spirituality of man derives from his ability for distinction and therefore the cognition of order and patterns of order respectively. Mathesis is the direct result of this cogni-tive ability. Max Bense rightly says: „The number is the true signature of

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the Spirituality." and „It is only through mathematics that man comes to know what spirituality is." Only with the linkage to the number we shall come into the power of the original and equally creative design. This is valid especially for the natural logarithms based on „e“. Indeed, this number is seen to be a more or less arbitrary fact not only by few people and which is used careless as needed. Primacy of algebra is undaunted and above all in the age of cybernetics it experiences sustainable support. What we need is not a theory of design but a perceptiveness according to our ability of fabrication. Out of both there may develop a consciousness which is adequate to the new symbolic power understood as a potential for cognition. It is only when perception and cognition are balanced, when thinking and feeling interleave on one level, the potential of the newly ob-tained power can unfold towards the blessing for life. IV design (gestalten) The new symbolic power has deluded us to exorbitance. Symbols have become secular shells which seemingly are to be used in arbitrary ways. Creation is degenerated to arbitrary design. Indeed we become aware more and more that we miss any form in the limitless mass. We realize that our doing is not genuine, that we hamper ourselves to see the truth because of huge numbers. Titus Burckhardt: „What truth is on the cognitive level is form on the sensuous. No spiritual watch without adequate shaping: if con-scious fails form fails as well and the ever lasting valid keeps invisible." „Design“ has to do with designation and order. „design“ means to delimit or bring out of the sea of possibilities which are given mathematically by the „ars combinatoria“. It is in artistic design where the repeatedly upcoming conflict, the trial to free oneself out of the superposition of old patterns of perception and feeling, is brought to stage with clearest consciousness. A series of expressions emerged and are still emerging, the audience is watching it without understanding or else with theoretical expertise. Very often a connection with reality is simply not given or else the problem in focus is mastered not at all or only in a deficient manner. We observe an absolute exception in the works of Maurits Cornelius Escher. He created his "impossible worlds" with mathematical precision and like no one else he

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managed with his work to make our seemingly natural view of the world questionable. A complete different category of so-called art is the getaway in creative arbitrariness or fantastic simulations. Thereby most modern electronic me-dia are used to render homage in high-tec manner to the oldstyle perception of the existing as well as to a simply functional concept of time in an end-less rapture of motion. It is clear that the measurable time of decay and the measured space of the existing cannot be a criterion for design which is adequate to today's reality. For this we need the orientation to the rhythmic-creative concept of time of the becoming to open up new realms of real creative design. One of the most influential schools of modern design is the „Bauhaus“ in the first half of 20th century and after 1950 the „Ulmer Hochschule für Gestaltung“. One of its directors, Max Bill, said about concrete art of which he was a co-founder: „the aim of concrete art is to develop artefacts for spiritual use similar like man creates artefacts for material use. in its last consequence concrete art is pure expression of harmonic measure and law.“ Another Swiss, the historian for architecture Siegfried Giedion, emphasises the splendid sketches of architects who recovered the "cosmic contact with elements of nature and past" (for short: with life.) Beyond others he namely mentioned the architect of the Sydney Opera House, Jørn Utzon. Using the example of this building Giedion shows how in this building as in all felici-tous sketches the all integrating pivot as the formal central point which gathers the whole construction in a focus, that this focal point is invisible and can be constructed only in an backward manner which is literally a re-construction. 1967 Richard Buckminster Fuller was in charge for the US-Pavillon on the EXPO in Montreal, a huge sphere, a so-called Fuller-Dome. Fuller is also the titular Saint for the already mentioned Fullerenes or Buckyballs, the temporarily stars of molecular chemists in late 20th century. They designed a third configuration of carbons which is not found on earth as a natural deposit. Another clear sign of new consciousness in design is set by the architect Frei Otto with his tented roof-constructions. The most important, at least impressive one till now seems to be the roof of the Olympic stadium in Munich from 1972. At the turnaround into the 3rd Millennium the Spanish

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architect Santiago Calatrava leaves his marks all over the world. His bridge-constructions are legendary and some of them seem to be copied right out of a teaching book of radiography. Significantly all of the mentioned projects originated after 1962, the en-trance into Aquarius. The early smaller tent-constructions of Frei Otto were realized between 1955 and 1963. His „Institut für leichte Flächentragwerke“ was an decisive stimulus for all following „natural“ constructions, in which archaic principles of construction, high-tech-material and the most modern ways of production interleave in a most appreciative manner. We have to await how far one may have overshot with regard to the last two points mentioned. Indeed, with science which does justice to the spirit of loga-rithms and thereby to a new geometry (radiography) it should be possible to transform these fields out of the state of unrestrained and reckless experi-mental happiness at the boundaries of mathematical feasibility into the steady state of organic-harmonic calculation. Actually, till now and world wide we are in a phase in which the words of Giedion from 1964 are still valid: „Nothing seems to be harder today than to enforce respect for the simple needs of life." V Physics of creation Originally in Greece language „physis“ meant (natural) growth. Each growth is going on according to the individual information by immanent measures. Today's physics is a theory of measurement. "Measure" therefore is an element of the operation of measuring and not at all an immanent de-termination of the phenomenon, which is to be measured. We can confi-dently agree with Georg Picht who asserts: „The measuring overgrows the insight of measures." It is at least since the times of Max Planck we observe a fundamental change in physics. Einstein was talking about classical physics as a theory of objects whereas quantum physics is going to be a theory of relationships. This change shows how a process which already took place earlier in ma-thematics in the transition from Descartes to Leibniz recurs in science. As algebra once was at the beginning of mathematics of possibilities and prob-abilities we may designate quantum physics as physics of probabilities. It is remarkable that the mathematical foundation of new physics emerged from the interpenetration of radiography with means of higher algebra. The Heisenberg matrix mechanics is a pure algebraic construction and one of the famous calculi in the beginning of quantum physics. Alfred North White-

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head summarizes the situation of that time: „Modern physics abandoned the standpoint of definite localization. Physical things rather must be conceived as modifications of a field which is spanning the wholeness of space and time. The thing refuses stubbornly all trials to be thought of as a pure con-temporary fact. It rather represents a momentary temporarily state of excita-tion, consisting of a distinct coordination of space and time sections. Therewith we reverted to one of the fundamentals positions of Plato.“ Quantum physics as pure theoretical physics operating in the tow rope of algebra is at risk, likewise mathematics itself, to lose itself in really ingen-ious mathematical symbolism. Its models which by some scientist from time to time may be misunderstood as reality itself may be confirmed again and again in form of a gigantic tautology. Within this kind of physics far and wide one cannot recognize that there is even the shred of an inkling that one knows what "measure" really means. Thereby it is old wisdom that something which does not stick with its specific intrinsic measures will not be of long standing. (And here of course we are talking about the measure as it is given for each form individually.) For Richard Feynman, one of the leading quantum-physicists in the middle of 20th century, geometry is a book of seven seals and he coquets with his lack of understanding for the attributes of conic sections. In one of his lectures he is talking about an elementary geometrical proof of Kepler and then says: „’Elementary’ means you need only little prior knowledge but an indefinite high level of intelli-gence for comprehension. One does not need knowledge but intelligence to understand an elementary proof.“ This is a highlight on the situation in modern science around 1960. Besides the ideas of Burkhard Heim the theory of „Global Scaling“, which was developed by Hartmut Müller, marks an eminent step in physics. Both took place in the beginning of the eighties of the 20th century (in parallel to Mandelbrot's fractal geometry) and seem to be the beginning of the third phase in the tristep from the primitive via the complicated to the simple. With „Global Scaling“ physics reached the point which was already ob-tained in mathematics in the middle of the 19th century: radiography. Although the logarithm was inevitable in physics since its beginning – at first it emerged as a tool for the simplification of complicated calculations and then it shew up in a widespread field of formulas likewise hyperbolic relations – however, it never was recognized as an expression of the funda-mental truth that all relevant relations are happening in the realm of loga-rithms and are actually projected into the space of matter by the logarithmic functionality itself. This is: every formula which is operating with a loga-

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rithmic expression connects these two spaces, the space of logarithms with the space of matter. Similar interferences are happening once we operate with imaginary units and interlock disparate dimensions or structures of order respectively with each other. In „Global Scaling“ logarithms are part of the basic model. The model pos-tulates a global standing wave of the vacuum on the logarithmic scale. The dispersion of matter which is constitutive for classic physics on the line of numbers in a linear world in the third dimension is then to be seen as a pro-jection according to the rhythms which arise by the resonance of the small-est ratios on the logarithmic scale. In this process the proton acts as a gauge and physics turns out to be nothing else than calibrated mathematics. From time immemorial rhythm plays a key role in all cultures. My rhythm is the measure of my existence. Tagore from the Indian subcontinent knew: „Rhythm provides reality to things which are without stability and own meaning.“ and the African Leopold Senghor from Senegal wrote: "Rhythm is the architecture of the Being, the inner dynamic which gives form to it, is the wave-system which the Being sends to another Being, is the one expres-sion of vigour." Besides rhythm the octave interval, the doubling on the logarithmic scale, is present as resonance phenomenon in elementary ordering patterns. You can not only find it in music but in the periodic table of chemical elements, in the double helix of DNA as well as in the colour spectrum of the rainbow. Translated into Euclidian space we conceive this pattern abstracted as the square e.g. on the chessboard as a plan for the royal game of life or else in the figure of the octagon as a double-square. From this point of view new physics actually is not new. This is also con-firmed by measurements at the Gizah Pyramids. However, it is new with regard to classic physics which deals with real things and insofar as the logarithm provides a reliable tool for precise calculations. However, as shown before even the logarithm is nothing without its basis and here „e“, the ruler of rulers. This inevitable number as an approved measure is owed equally to analytics as well as to algebra and the functional thinking respec-tively and pure relational sign-bound logic. After this ramble we can expand our tetraktys of levels of consciousness to the pentaktys. Within this figure the central fixed point is now expanded to an area. Together with the according periphery this field reflects the cyclic move from perception via cognition to design. The corners are given by: the aspect of functions for the perception of metamorphic shifts, the proportion as the sensor of cognition and the tensor as a calculus for optimized design.

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Yanlorum and Gizdelspil - Freedom and Form -

After men knew about their roots in the spiritual world over thousands of years and always understood themselves as grateful guests on earth this consciousness was lost step by step. Today we are on the way to get this consciousness back on a refined level. A new symbolic power is at our disposal, we have become creative. What we are missing however, is an appropriate consciousness. What is it that hampers us till now to realize our potential truly according to the new possibilities? How can we succeed in moving the emphasis of our existence from the fight for survival to our true work? Is that what we want our own will for sure? Isn't it actually the will of someone else who persuades us to want this or that? Are we really free in our will? At the beginning we have seen how the idea of the Self developed in times of Renaissance. An original healthy self-consciousness changed in the course of technization progressively to pure complacency, into selfishness which is oriented towards outwardness only. The sense of basic trust into our own centre which could provide true freedom was sacrificed to exterior mobility. The effect of superpositioning by legacy consciousness is over-powering. Bound to material prosperity we are always only busy organizing the unstoppable decline of the existing on a high level. We call it economy. We won the Self but we lost the measure. „In our culture we observe a radi-calisation of the ideal of the self." wrote Erich Neumann. Our mind rather banned and bound the gods and demons but we missed to transform them. We refuse to give recognition to the early symbolic forms, the deeper levels of our soul, we don't want to see them as what they are and with our barren terms we are incapable to come beyond abstract analysis. Therefore it is that the gods of consciousness return unchanged and powerful in times of twi-light of the gods. Who is able to detract himself from their forces without preparation and committed to mind only? We grew apart from the secret of the becoming, of life. We have the crea-tive potential and at the same time we are afraid of the real new. We en-trench ourselves behind the allegedly security of matter, identify ourselves with the dead, existing but not with life. We are afraid of freedom and flee in defensive institutions because of our anxiety to lose this identity. This institutions are the defensive positions of the prevailing consciousness. In these castles the allegedly freedoms of the Enlightenment are transformed

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with somnambulatory certainty into their contrary. We still prefer man-made outer adjustments no matter in which facing as a substitute for the still unknown inner order, prefer the corset before the skeleton. It is true we handle new means masterfully – but only from the position of the secured old consciousness. We don't have a real relationship with the essence of technique simply because we mainly do not know what the es-sence of technique is at all. With every fail the perpetrators appeal them-selves to their lack of knowledge ("We couldn't have anticipate this!") and the patient victims call on ethical behaviour. Everyone knows that the sub-sequently given promises are nothing more than lip services. So we con-tinue to try the new and observe the effects from the allegedly secure dis-tance along the lines: "Let me have my cake and eat it, too." Mind is in search for secure standing, it is not ready to entrust to the river of life or even to subordinate itself to reason. Despite all the dynamics of modern times we still didn't get the sense for motion. At best we are in a dizziness of motion. Neither we perceive things nor ourselves in their proper motion or our own respectively. What we find manifested in today's martial technique is our fear of the end of the old and likewise the unfolding of a new consciousness. Even when mind always and everywhere takes pride of place with regard to the tangible things, the earthly existing we are captivated in rational covered age-old symbolic-material thinking. In relation to our mental images of the world we model a fictional continuum based on a thinking in logic or functional terms and in relation to our zeal to creativity we simulate fanciful worlds without the shadow of a consciousness of form. However, religions with their hierarchi-cal world of gods as well as stupid calculating devoid of any intelligence insults reason likewise. Actual social organization with all its institutions is one single withdrawal action – we try to evade the allegedly irrational. Actually, the age of reason or enlightenment is based on the thus far so-called irrational numbers. The only irrational of those numbers is our belief to fix every random value with decimal figures exactly. Indeed the firmness of almost all of the numbers represented in a decimal manner leaves much to be desired. We deceive ourselves and become unfree by this. The state at a time of scientific models is given for sure. Even if it is only statistical safety every aberration from average is raised to question - but this is: life as such becomes questionable! Therefore the uncertainty of life leads to the absurd situation that man has to justify himself all the time against institutions which means self-appointed

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wisenheimer, experts, censors and other judges ("Do you have any proof?"), really, one has to apologise for being alive at all. The only one who is hampering us to deal with the new acquired knowledge of modern times in a decent manner and to organize the civil society as a human community is me myself with my ordinary, shallow egotism without trust in the laws of the universe. There is an intelligent smart youth without an inkling of spirit, confused, abused, besotted. Feelings, also in a means of sensitive perception, often are disqualified as irrational and at the same time they are exploited with all available psychological tricks. However, about feelings we may state the same as about freedom: where it takes place we take them for granted. Where they are suppressed the basic impulse is de-tracted from life. What can be done in this situation? How can we get out of our defensive positions, how do we come back into the flow of life? In view of this misery (literally rootlesness) after First World War Hermann Hesse wrote „... we must start at the very beginning, with the formation of personality, ...". In the Gospel of Thomas which was detected in middle of the 20th century we may read: "The pharisees and scribes got the key of cognition and hid it. They did not go inside themselves, but they also prevented those who wanted to go inside from doing so. Woe to the pharisees! Since they are similar to a dog who is sleeping on the crib with the cattle. Neither he is eating nor does he allow cattle to eat." With arational numbers and their rhythms I think we found the key again. Now it is essential that we really use this key and chase the dog or dogs respectively from the crib! It is up to every one of us to unlock the door and walk out. Indeed, we should not be afraid of the light of the truth and finally command the courage for true responsibility which is the responsibility for our own life. To find our centre, to apply our gift to our unique task, this is the answer to our self. Out of this centre our life obtains its sense and meaning. These elements rule our life, not beneficing and comfort. Within them we find what makes us free people. With them we become really creative and we detect our true will with creative activities, it comes out of ourselves and makes activity to be a joy. As long as we do not comprehend ourselves and all the things around us out of our own or their centre respectively then things will comprehend us in our centre. Fully up with knowledge and devoid of any natural intelligence and therefore apart of life nothing is given for granted any longer. Man in

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technical civilization is leading a second hand life. Almost nothing happens immediate, everything is mediated, we need experts for everything and life seems to be a complicated affair. A central issue in the Perceval-poetry from 13th century is revolving around the necessity to ask for the (now virtually not longer) natural, for our value (val) as a part (= perce), the big picture. As a part we represent a shaped unit (1), however we obtain our identity (0), our being-in-ourselves, our very centre from our relative posi-tion in the complex ordering scheme of relationships in the big whole (e). The laws of form are inscribed into the soul of man, actually they are the paragon of what we call "soul" or our "self". Soul controls in-form-ation, determines out of which elements or frequencies form is made of. Reso-nance is the criterion to filter the right elements for itself. However, in re-verse the little Ego, the Unit is unable to control the bigger Self. We have no choice, the breaking of symmetry is irreversible. The meta-physical prerequisites of our existence are sunken down to subconscious-ness. The God of metaphysics, ghosts and gods, all of them are surrogates for uncontrollable energies and thus for the irrational, they are all dead and what we have left over is the mathematical substrate. What we have at our disposal is a new symbolic power and the preservation of man depends on our ability and readiness to accept the ever lasting order of nature which is unavailable for us as the irrevocably power. The particular symbolic power designates the horizon of possibilities in handling of energy. The various symbolic forms, and among them of course the symbols in the narrow sense, are the visible and audible expression of this power on the various levels of consciousness. The optimal implementa-tion of possibilities adequate to the given potential requires a corresponding consciousness, a consciousness of form. Georg Picht: „The power of spirit manifests itself in structures and not in contents." For us this implies: the one which has to be mastered, namely the complex of forms or the scheme of orders, has been here all along, is age-old; what we find to be new are the available possibilities in handling of these energies which eventually are always energies of form. Now it is essential to develop senses and sensitiv-ity for form. This however is the project of aesthetic education. What constitutes man as a spiritual being is his attentiveness for order, for the forms of life. The Greek word for the inner order of the cosmos is logos ("word" in today's sense not at all). Just then when the individual faces the universal sphere of the logos he wakes up to perception. „At the point where constructive mind pairs with receipting reason thinking becomes creative.“

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says Georg Kühlewind. Indians of whole America call this the white way: „Bring your mind home.“ (Tony Gwilliam) The condor of South American Andes should reconcile with the eagle of North American Rocky Moun-tains. „To bring mind back to reason“ also has to do with beauty, with feel-ing which is aesthetics. At the latest now we got a mathematical argument for beauty: proportions of numbers are causative for all the things which please us, to which we are in resonance. Resonance is what we feel and a lot will depend to redevelop this feeling consciously. Part of it is intuition, the re-ception (german: ver-nehmen and the noun: Ver-nunft), listen to the "memory of the future" as it was called by Sri Aurobindo. At the latest since the works of the Russian scientist Kozyrev this wording has a scientific basis. The above mentioned mathematical substrate for the comprehension of the logos at first was the measure as we have seen before. It is because of this that Heraklit declared at the beginning of the Greek age: „This cosmos is created neither by one of the gods nor by man but it always has been, is and will be: for ever living fire, inflaming in measures and going out in meas-ures." After the recent breaking of symmetry of modern times it is the loga-rithm. Rather we should write: Logarhythm, because it is the Rhythm which becomes obvious in the presentation as chain fraction and which determines the degree of order as well as the specific outreach. The complexity of a structure, the mathematical equivalent of a comprehensive scheme of order, is measured on his part by the variety of immanent proportions of equilib-riums, the richness of immanent measures. Whether chain fraction or prime factors, we are always led to the order of natural numbers which are seen by C.G.Jung as the "Archetype of order which has come to its own consciousness". Archetypes are described in depth psychology as consistent and therefore unchangingly dispositions of structure of consciousness. Interestingly natural numbers come into the limelight of physics with power at the beginning of the 20th century and give their name to the prevailing direction for the whole century: quantum physics. Masses of energy which can be seen as complex interleaved balls of oscillations emerge in principle as whole-numbered multitudes of Planck's constant. This circumstance is fundamental for the structure of atoms and thus for the whole matter. As well as for the teacher of a series of quantum physicist, Arnold Sommerfeld, as well as for one of his out-standing students, Wolfgang Pauli, natural numbers are the ultimate ele-ments of structure of the being.

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The new consciousness is something like a new aggregate phase. We al-ready sketched it under the headline "Knights jump". There will be no new time and no new thinking. Rather we have to bring our thinking, or even better our thoughts, back to flow. The physicist David Bohm proposed the term „Rheo-Mode“ for this context. Only thinking in flow, in motion, in oscillation can come into resonance with other thoughts and then reach a conscious state of what is practiced by nature anyhow and since thousands of years: hyper-communication. This complete different way of communi-cation allows what we may call group-consciousness. However, all these are phenomena which are taking place on the logarithmic scale. Many of the impulses which paved the way to the new consciousness came out of the middle of Europe. Hence it is not astonishing that the big con-flicts of the last five hundred years in the form of open or covered wars likewise took place above all in this region of the world. The old conscious-ness which is still passed on through an extremely efficient system of up-bringing, education and media fends with all means against the end of its supremacy. The bearers of this tradition which meanwhile is to be referred to as a literal awful tradition have thousands of years of experience within their horizon which is the horizon of logical thinking, a thinking in terms. This tradition and with it this consciousness is sustained and defended not only by its official bearers but by their antagonists as well. Any trial to abolish the conventional systems with their own means is futile. Any attack if with arguments or in a forceful manner not only is wasted energy but on the contrary it enforces the established structure. The apparatus is anxiously thoughtful to purposefully concentrate this kind of energy in clubs and whichever organized groups. The moribund consciousness is enforced all the more when we submit our responsibility to institutions in such a way that we rely on them or even explicitly demand for them. Thus it is better to ask: "who am I really?", "what are the really important things for me?" and concentrate our energy to the answering of these ques-tions. By taking responsibility for our self in such a way the "old" con-sciousness and with it the legacy institutions will deflate by themselves and run dry. To put it crudely, the point is simply to pull the plug of the appara-tus (have in mind: we all are the apparatus) and cut off the current. This is not a great outward act. It can only occur in our heads but even more in the heart of every single individual.

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It is only then when we do not conceive "form" any longer as restriction

- but instead as the condition for possibilities and when we do not reduce "freedom" to negative freedom only which is to boundless freedom for mobility and expression

- but realise it as something positive which means the realisation of our unique task by utilising the whole variety of forms

then we will be able to enjoy the sweet luck of luck.

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“All divine messengers must be mathematicians.” („Alle göttlichen Gesandten müssen Mathematiker seyn.“)

- Novalis - There always were and will be people who report as messengers from the realm of spirit and we get the idea that they know more or something differ-ent than the ordinary mortal. These princes of soul know the law and in-formed us about it again and again – even in mathematical notes. But we lost the ability to listen to their words, to re-ceive them. We lost the true rai-son. Today we are law-makers on our own behalf and imagine that we are able to freely rebuild the world and the solar system according to our own ideas with our restricted mind and a poor gone per-ception. I cannot affirm that I see us on a promising track. Those with their faith in progress who now confront me to be pessimistic I answer with a quote of Hans Pestalozzi: „I am not a pessimist, but you are naive!“ In the following pages I hand over to a series of these messengers. Amongst them you will find scientists and mathematicians aside of poets and natural philosophers. This more poetic style may help us to interpret texts of these people (e.g. old traditions) against the newly gained mathematical back-ground in a quite reasonable way. With this background a lot of as yet sur-real, puzzling, fairytale-like or simply silly appearing statements may show up in a new or at least in a different light. Sri Aurobindo : The life you are leading hides the light you are! Behind every thing in life is an absolute which every thing is in search for in its own way. Every finite attempts to express an infinite from which it feels to be its own essential truth. The logic driven mind is able only to master what is fixed and finite.

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Gottfried Wilhelm Leibniz : „Once there will be a time where the high value of a more sacred philosophy will be re-cognized by the people who returned to themselves, mathematical studies then will be given an orientation o partly towards sharpening of a judgement which is practiced in a more serious way, o partly toward the aspiring cognition of the essence of harmony and the archetype as it were of beauty; · natural science anew

o become subserving in glorification of the creator of the nature who shows us in the visible world the image of the ideal (world),

but eventually all studies are focused again towards the acquirement of blissfulness“ Heraklit : Nature in its essence is constituted like that, that the crowd of people must evade its horrifying sight and in face of the truth of the logos has to find an evation in the befuddling of its arrogated own cognition. But they will pay for that with their doom. Although logos is a common one, the many live like having personal in-sight. Conducive is the cognition of the own measure; since the one who does not fulfil his measure or exceeds must fall. Ignorance to the being besieges the planet. Invisible harmony is stronger than the visible one. Erich Neumann: Man as "homo creator" is the crucial matter of our time, whose recovery and development depends thereof, if the individual is able to experience himself again as creative which is to be related with his essence and the essence of the world.

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Proklos: So this is mathematics, the remembrance to the invisible forms of the soul; and its accomplishment, as it is given in its name, is as follows:

it vitalizes its own insights, it wakes up spirit and cleans mind, it brings ideas to light which are intrinsic in ourselves, it eliminates oblivion and ignorance which we got by birth, it looses the chains of the irrational pursuant to the god

who is the true custodian of this science, who let shine the gifts of spirit, who fulfils everything with divine forms and moves the souls to spirit and arouses them like from a deep sleep of death, who brings them back by scientific work to themselves and accomplishes them by midwifery,

and by letting find them the clear reason leads to the true blissful life.

For the contemplation of nature mathematics contributes the highest value by unveiling the well-ordered structure of thoughts upon which the universe is built ... and exhibits the simple arch-elements in their whole harmonic and even composition which is at the basis of the whole sky by adopting in all of its specific parts the particular forms. Novalis: The life of gods is mathematics.

All divine messengers must be mathematicians.

Everything man intends to work on he must concentrate his undivided attention or his self.

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Ralph Waldo Emerson: Once reason is prompted to even more serious looking, shapes and surfaces become transparent and cannot be seen any longer; causes and spirits are viewed through them. These awakenings of the higher power are the highest moments in life. Andreas Speiser: To invoke geometry and the numbers simultaneously not only is possible but rather therein lies the whole purpose of our life. Geometric symmetries are the true virtual shaping forces. Besud Erdini: Pure mathematics is the essence of nature. Aesthetics becomes objectively mathematical. Nikolaus von Kues: So I conclude, the first instance of things in the soul of the creator must be the number. This is obvious by the delectation and beauty which is inherent of all things and which is given by the proportion which in turn is given by the number; hence the number is the most splendid pathway leading up to wisdom. Ernst Buchholz: For Albrecht Dürer mathematics is the science which explores the forms of spirit, is in search for their coherence and ferrets out the "laws of spirit" as harmonical symmetries. Gaston Bachelard: Rarely are those among us to whom life gave the full measure of its cosmic relationship.

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Hermann Weyl: It is on this on which in the first place relies the feeling for the mystery or magic of numbers: that with the help of the series of numbers spirit creates out of itself an infinite variety of well characterised specific beings; empa-thisable also for us e.g. in the obscure law of the distribution of prime num-bers. One can only hardly overvalue the depth of geometric fantasy and ingenuity which becomes visible in these patterns. Their construction is far of being mathematically trivial. The art of ornaments includes implicitly the oldest piece of higher mathematics we know. Hugo Kükelhaus: The self cannot free itself by any other measure than through the fact which is concluded in the word measure itself. Tracery and being in awe for life, life in crystal, plant, animal, metal and stone is one. Agrippa von Nettesheim: Everything created from the very beginning of things is shaped according to numerical proportions which lay as archetypes in the spirit of the creator. Therefore great and sublime forces are living within numbers. Everything which is and is becoming exists through specific numbers and obtains its force out of them. However, above all we must notice that the simple numbers indicate the divine things. Carl Gustav Carus: All we call natural shaped is: a structure of the ever becoming according to the everlasting laws of form and number, a structure which differs from law as such only everywhere in that it never realises itself without any muted sprinkling of something irrational.

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Albertus Magnus: The forming forces which ceaseless flood into matter from out of the worlds of light of the origin and intelligences exist more perfectly in the origin and in the light successions of the intelligences than in matter. And they do not flood shaping into the realm of matter to have a material existence but whereas matter of course yearns for them as something divine, a good thing. So, we cannot say that those forming forces, which are said to be cosmically, flood down to show their plethora of wealth of sources because it is not the style of gorgeous plethora to deplete its substance in inferiority. Hence it must be like this: that they flood down to create some divine being and accomplish a divine mission. The divine being and the divine missions can act out only to the full apart from matter and we know that this separation can be performed by the human soul only. And therefore it is necessary for the world that they are led back to the divine being by the intelligence which is releasing from matter. Such a leading back to the origin does not happen by the cosmic intelligence. Because that intelligence comprehending all forms resides purely supernatural in divine being and virtue. Hence it must happen necessarily by the intelligence of man, who owns the forces and organs for this, that he receives back while staying in matter the revelation of the divine forms.

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Dante Alighieri (The divine comedy): In wrong delusion you cocoon yourself, you make your life difficult yourself and cannot see what you could see if your sight is free: you are not on earth any longer as you believe. All things are well arranged in order to each other: it is the form by which the universe is similar to its creator. In it the higher creatures recognize the trace of the eternal force, of the high destination to which the mentioned standard and order is set. Preposterous entanglement in earthly sorrow, how poor your arts of thinking, so you scarcely raise your wings from the ground! Man should not act like being that sure in their judgement and not estimate the oates on the field as long as they are unseasoned. The mysterious things which here are giving themselves as phenomena are kept hidden in a way to the eyes down there that your existence there is based on belief entirely. But because in your schools people are taught that English nature has mind, memory and will I speak even more clear so you can watch the truth pure and plain, which is muddled there in an ambiguous scholarship. Now a doubt comes to your mind and makes you quiet; but I shall release the difficult knot into which you are entangled by your sophisticating thinking. But because eyesight was amplified in myself by watching, the single phenomenon for me changed because I changed myself.

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Werner Heisenberg: The variety of phenomena can be understood because it is based on standard principles of form which are accessible for mathematical representation: this is the complete program of science. The root of all phenomena is the mathematical law which defines funda-mental operations of symmetry and therewith designates the frame within which all events occur. Hans Kayser: The harmonic order of the universe is an order of the numbers. Regine Kather: The cognition of beauty as a perception of shape also includes the percep-tion of the shaping force. Beauty sensitises for the veiled sides of reality, trains the sight for the forces providing structure. Light, symbol of timeless presence and perfect consciousness, becomes the medium between matter and spirit. Plotin: So the idea joins in, that what should become a unit by composition out of many parts is ordered by it, the idea put it to a consistent structure and makes it one with itself and coinciding. V. Geilen: The infinite needs a symbolic normalisation which is founded by such a concept of number which describes the crucial step from any outwardly, rigidly, deadly concept of number to a more deeply, freely, lively under-standing of the essence of number as a rhythmic pulsation, to a concept of number which finds its natural and at the same time perfect vividly expres-sion in the symbol of the pulsing wave.

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Diogenes: On the hunt for amusement at all cost life becomes more cheerless and more tedious and whereas they believe to provide for themselves they perish piteously out of sheer sorrow and prudence. Goethe:

Even in the moment it grabs raw; Grasps what comes across, makes it his own, Throws it away, without pondering, without considering How one may shape it for higher utility. So they stride with giddiness of children And with raw fumbling taking the day as it comes. Would they more pay heed to the past, Take the present more by shaping It would be good for everyone, this is what I wish.

What else is harmony than rules and melody its practice. Whole nature is a melody in which is concealed a deep harmony. Max Horkheimer : To oppose enlightenment and progress by regression back to a more primi-tive level does not mitigate the permanent crisis – on the contrary this kind of ways out lead from historically reasonable to extremely barbarian forms of social regimen. Ernst Jünger: We are in the act to cross the line: we already half-way crossed it with our head. Rolling Thunder : One of the most important principles is that it is not allowed to harm others. Neither check nor manipulate, neither try to take control of foreign matters. Every living creature has the right to organise its own life according to its own perceptions.

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B e y o n d T i m e - On the tip of Consciousness -

There is no outward measure for luck, for a felicitous life. The measure is inside of myself and there is no task which is more important and along with it more auspicious than to find this measure and than to adjust ones life to it. He who is able to stand steadily on the tip of his consciousness and therewith keep his balance is happy. This will be accomplished once we are in our centre and nothing can throw us. - This does not mean that somebody cannot lead a pretty wild life at all – if it is his pattern and he therefore is in his centre – why not? One of the best indicators to recognize that somebody is not in his centre is given in the sentence: "I have no time." An Egyptian proverb says: "Every-body is afraid of time – its only time which is afraid of the Pyramid!" Actu-ally in today's hustle and bustle of the world time seems to be the most important thing to have. Our life appears to us as a limited span of time towards a final point, the death to which (almost) all of us are afraid of more or less. Do we lead a happy life when we experience as much as possible in this time-span, when there happen a lot of things? As a result all people are always under way, rushed and but finally unhappy. Permanently we compare ourselves to others. This is actually one of the best methods to be unhappy. It starts in school and seamlessly continues in the advertising messages which flow around us intentionally or inadver-tently. Hence we are perpetually at risk to be expelled from our own centre. Things determine us as long as we ourselves are not in our centre and do not perceive the things out of their specific perspective. Then our doing is he-teronomous and oriented to a purpose. We do not act from an inner pulse but because of something different to reach an objective, a purpose. Op-posed to this manner creative acting is autonomous. This requires that we are aware of ourselves in our centre and are able to say: I am and I am iden-tical with my Self. So, is unhappiness really related to lack of time? Where from comes the anxiety to have no time. Why do we struggle against those who decide over our time or even only try to do so? Basically it is not a lack of time but it is the "being beside of oneself", the "not being in ones own centre" which conveys us the sense of time at all.

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Our subconsciousness has a good feeling once we move out of our centre or somebody or something tries to expel us from our centre. The feeling of time which is running out arises out of this situation. Hence, actually it is not lack of time we are afraid of but the fact that we are not in our centre and even still further depart or else do nothing to come into our centre. Life proceeds on a spiral curve and if someone believes he is walking along a straight line the fallacy is based on the fact that he is to far from his centre. This very point, the central point of our life, correlate mathematically the 1 (unit) and the 0 (identity) on our line of numbers. The tip of the pyramid, the perfect crystal, is a symbol of our identity. However, various concepts are related to the pyramid. On one hand the pyramid is the symbol of the actual form of organisation of our societies. A rigid enclosure based on institutions which have the effect above all that we do not come to ourselves, into our centre and therefore hamper us to be happy. The only subconscious aware centre is projected into the tip of the pyramid. On the other hand there is the tangible pyramid. It is the one which time is afraid of. The planetary symbol of time is Saturn, the slowest planet revolv-ing around the sun and its day of the week is (consequently) Satur-day. Time as we know it stops existing namely when black charcoal is trans-formed into the crystal clear transparent diamond which is that we come into our centre. Diamonds crystallise preferably as octahedrons and rhombic dodecahedrons. The tips of this crystal shapes correspond exactly the outer shapes of the two smaller pyramids on the Giza plateau in Egypt. Hence, what should concern us primarily is to realise this pyramid in ourselves. A third kind of pyramid we are faced with is the pyramid of needs as it is modelled by Abraham Maslow, one of the founders of humanistic psychol-ogy in 1962. Like all pyramids this one as well ends up in an apex and ex-periences a kind of seclusion. However, because the tip of human needs is self-fulfilment and therefore luck, I would like to modify the image of this pyramid of needs in such a way that it opens up again to the plethora of infinite possibilities after passing the apex which is the finding of our iden-tity. Eventually it consolidates in the big picture with the basic needs at the basis of the pyramid.

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At this point I would like to remind you of the letters about aesthetics of Friedrich Schiller: In his analysis about formal drive, game and beauty he concludes that man coming from the realm of necessity can reach the realm of freedom only by game in which time is abrogated within timely exis-tence. Whereas in the realm of necessity or existence the sensual drive is prevailing, it is in the realm of freedom where the formal drive is dominant. Even the Greek Sokrates considered that man should not be serious to re-cover in games later on but rather he should gamble because of that what is the most serious: for the sake of gods and attainments.

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The Mesh - Centre and Periphery -

The idea of the "Realm of necessity", the "Valley of tears" in which every-body has to "work for his bread in the sweat of his brow" is an entrenched concept of the mental age and closely related with the defiance of universal laws. It is the basis of the prevalent centralistic concepts of politics and structures of power. With the loss of true royal knowledge, the knowledge about structures the knowledge about free forms of energy was lost as well. Hence, shortage of goods, devious money systems and the persecution of free minds till today are the central means for clever but not at all wise people to perpetuate a hierarchy in which all energies are led to the apex of the pyramid. By changing the social pyramid which is now a hierarchical solidified com-pulsory construction into the inner diamond in every single individual which bestows the necessary force of integration on him we observe on the structural level, metaphorically speaking in the workshop of the weavers, an epochal rebuilding towards an elastic network of autonomous fellowships. In such a global whole every single person as well as every community is a mesh in the network and at once a complex meshed whole in it self. Every-body can allege justifiably: The centre is where I am. This is true for every point on the surface of a sphere. The centre of the sphere therewith remains unaffected. At the same time every point is absolute peripheral – with re-spect to the centre of the sphere. The essential thought with all upcoming alterations is the idea of decentrali-zation. This idea is interpenetrated by the idea of tri-segmenting of society. The concept behind which is to see society analogous to the human body goes far back in time. According to this man as well as society is segmented into three autonomous units which cooperate synergetically. Within the society we distinguish the domain of economy, the sphere of justice which includes political organization as well as the monetary system (money is a legal entitlement) and the realm of culture or spirit respectively wherein we locate education and arts as well. Like in the field of mathematics here we observe serious superpositions. The slogan at the times of French Enlightenment „liberté – egalité – frater-nité“, adopted in the German slogan as „Einigkeit und Recht und Freiheit“ (attend to the reverse order of the words!) shows an immediate relationship to the thought of tri-segmentation. The meaningful assignment of brother-

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hood to economics, of egality to justice and freedom to spiritual life was and still is permuted by the apex of the pyramid which is supervised by the illuminates. As a result in all enlightened and democratic nations the reality is: Freedom for the capital in economics, egality of thinking in realm of spirit and brotherhood when it comes to the deployment of appointments in political hierarchies which means in the realm of justice. What is to be expected from these ideas after a clearing up? I Responsibility - free energy - Man is laid out towards fellowship. Likewise he pursues to realise his self as genuine as possible. If we assume that he once recognized his gifts and therewith his assignment he will strive to fulfil it at best and by this express his self. This is not opposed to cooperate with others with similar talents and that they learn from each other. What today is a privilege of relatively few namely to be able to do what one want to do according to an impulse from within and which one is fond of to do will become the normal case. Activity becomes creative, people will get into resonance with life and with themselves. The person who is in his cen-tre comes in flow and this opens the gates of intuition, energies will flow in abundance. We are not any longer dealing with the organization of the de-cay of the existing, to drive a so-called economy with big efforts and to queue up at so-called employers for basically alien jobs. Rather with an appropriate consciousness we shall succeed to lead the all over available energies into the building of own and true creations which are beneficial for everyone. „Energy is the measurable expression of the revolt of spirit against its cap-tivity in matter." (Anthony West) How may we master this revolt against spirit as long as we do not have any knowledge about spirit? Therefore again we need a consciousness of forms. Because energy creates its form itself (Viktor Schauberger) and energy is in form (Leibniz). According to this energy not least is a problem of form, it has to do with In-form-ation and thus with proportions. Without a knowledge of laws of the hierarchy of relationships and thus of numbers through which we got access to this hier-archy an effective coupling to the stream of energies is impossible. The main concern is not to cage energy but to control its eternal flow in a wise manner. Therefore reason (german: Ver-nunft) is required which

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means we have to commit ourselves to the stream and listen to it which is (german:) ver-nehmen. It is only then that we can respond accordingly and therewith take respon-sibility. Nobody will be able to bring the flow of free energy into its own service without the adequate consciousness and with pure mind only. II A u t o n o m y - regional networking - In a regional world we cannot exclude conflicts despite all community spirit. These were reconciled in foretime by wise kings and judges. It was their task to maintain justice by caring for that nobody was expelled out of his (and himself almost always unknown) centre in a complex of claims. In the balancing of practical claims in a network it is not helpful any longer to deal with appeals to moral, ethical standards and mysterious last resorts but it is all about the knowledge of structures. Structural knowledge is royal knowledge. Religio in its original sense means to be tied back to the laws of being. In such a sense religion and myth is one among other symbolic forms. In all symbolic forms so far knowledge about structures was an im-plicit, conduplicated knowledge. This was not less efficient than ours be-cause of that but it could not be communicated readily. This is the reason for the long apprenticeship of designated shamans, priests and scientists. At least in principle this royal knowledge is available to everybody today. Structure has become explicitly and is accessible by the rhythm of numbers. Obviously it is impossible to control a highly complex network with means of legacy thinking in terms of hierarchy. The term control alone is suspici-ous. This is also valid for the so-called self-controlling systems. It still reso-nates with the idea of objects and the secret desire of the part to give the direction for the whole. But this will not succeed or even lead into catastro-phes respectively as long as we do not enter the flow of change ourselves. Money makes the world go round. To govern means to control. Is money hence a means for self-control? Scarcely as it is organized today. Money as a mirror image of streams of entropy is able to increase itself by the mecha-nism of interest. Here we have an obvious contradiction with the laws of existence. If money should work even in the future as a symbol of balancing this fundamental mistake in construction has to be eliminated. How this correction can be achieved is already shown in several regions of the world in the form of regional money and with barter systems.

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III R e a s o n ( V e r n u n f t ) - aesthetic education - Man not only is a „homo oeconomicus“ and a „zoon politicon“ as well but also and above all an „animal symbolicum“. As we pointed out at the be-ginning man has the possibility to transform his principal weakness which is a lack of specialisation into a dominant power because of his abilities for cognitive perception and combinatorial arrangement. So he became a „ho-mo faber“ initially who created and used tools in a methodical manner but then he also became the author of meaningful symbols. Art and technique once were undivided. Techné is the knowledge of design, of production. So, when there is a reason for art to get an independent real-ity it is because signs took a life of their own. The described processes of superpositioning also encroached upon art: like „ars combinatoria“ opens a perspective of "everything goes" artists easily got caught up into the pull of arbitrariness. This is expressed in the formula of pure art, "art pour l'art". Actually this is a coarse misunderstanding like the bonded judgement of uselessness. Art on one hand comprehended as a refinement of symbolic power and on the other as creative self-actualisation of the artist is the kind of activity which ulti-mately determines the continuity of a culture. All kinds of arts are methods of cleaning. The main concern is always to fulfil ones own task even better. Like the bell has its pure sound only when it is rid of all dirt the task of every individual is to become clearer, brighter and more transparent. The last resort as a measure for my luck is the pureness of my oscillation which is to be in accord with my Self, one and zero become identical. Within an autonomous creative acting all what counts is here and now, I am outside of time like the child in his game. In this context I may quote the famous wording of Friedrich Schiller in his letters "On the aesthetic educa-tion of man": „Man only plays where he is man in the full meaning of the word and he is only a perfect man where he plays." In the sense of conjunc-tion of the three parts of the social organism everybody always is also an artist. Everybody should always and everywhere carry out his task as good as possible. If a gardener, a tradesman, a healer, a craftsman, a nurse or a dowser – every action bears witness of an inner attitude to the laws of being and is an exercise for the refinement and fostering of knowledge and skills. The principle immaturity of man at the time of birth and as a symptom of his species on one hand makes him receptive for news and the plethora of

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possibilities. On the other hand herein lies the risk of excessive manipula-tion by education. Because man is faced with decisions throughout his life it is one of the main responsibilities of nurturers and teachers to enable man to make right decisions for himself on his own behalf. One of the most important decisions – the one for his teacher – is always and already drawn off by an institutionalised school system. The incapacita-tion and school like regimentation produces what is necessary for the legacy system: abulic zombies. Therefore Ivan Illich wrote: "School is an advertis-ing agency which brings us to belief society as it is is a necessity.“ Actually it is the task of a seminar to enable students to live a spiritual life beyond the pure intellectual knowledge. Without a valid and reliable gauge – and this is to be found only in ourselves – perhaps all calculating is correct but rarely true. Indeed a pupil can judge the proper teacher for himself. It is the one who supports him in finding his way to himself, to his own centre. Where does he know it from? – if he was not manipulated before already this is simply a question of resonance and thereof children up to the seventh year of life have a better understanding than most adults do.

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String of Strings - invisible centre -

The curiosity of man is chance and risk at once. If it capsizes in pure sensa-tion mongering which is the satisfaction of senses perhaps till stupefaction there can be no talk of a conscious being and then it is Nothing to nudge him completely out of his area of his centre. By reference to the concept of three-parting in the context with the principle of decentralization we envi-sioned possibilities rudimentarily how to scotch this institutionalised spirit-lessness of mankind. The one or two may now be somehow sceptic about the chances for success of such rebuilding efforts considering the undeni-able disappointments. Indeed such scepticism is eligible. As I already mentioned at the very beginning the spinning shops are below the weaving shops. For structural changes on the level of weaving rooms we gave a clue. However, what these new structures not only makes looking that much powerless but makes them powerless indeed is the fact that the new fabrics are still woven with the old thread of metaphysics. Always and everywhere the talks are still about ethics and logic and law and and and .... The lack of vocabulary for the new makes it difficult to emerge from this embarrassment. Even so this is no excuse not to try it at least. On the passed pages we pointed out in detail the core of modern times na-mely mathematics and identified it as a new symbolic power which is not recognized predominantly in its true essence till today. The string of strings which is newly spun is a qualitative comprehension for numbers and its distinction into values and proportions. It is only when this thread is running through men that we shall be able to weave useful fabrics. And it is only then that tailors can design newly appealing suitable clothes. In the middle of the new symbolic power are the laws of form. They yield the frame of conditions for the inexhaustible abundance of possibilities. The invisible god of metaphysics is dead, structure has become explicitly. Be-hind all pluralism and outer differentiation we not only recognize an order-ing scheme – this was well known at all times – but today we can compre-hend it mathematically and describe it with numbers and formulas. The new symbolic power marks a new level of consciousness, the integral con-sciousness. Man himself has become a creator. For all cultures the ministration of the particular symbolic form was sacred, even if it may appear to us that much primitive. This form grants the exis-

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tence of the culture. Out of this the rituals obtain their meanings. The same holds true for the taboo and sanctions for the break of taboos. If we believe that we can waive the refinement and fostering of our newly acquainted knowledge because we do not recognize it in our blindness and therefore do not learn to esteem then that what was culture once will decay to plain civi-lisation and be forgotten within a short time. Because of this there is no more important task then to transform the intellectual deadly half-knowledge into lively wisdom. The knowledge about the relations in and among orders, the string of strings, is the basis of all things in nature. Only when we consider this kno-wledge in all of our activities and creations there will be realized what was announced by Arnold Keyserling: „The fruit of the tree of life will join in that of the tree of knowledge." Actually this was not the end of the sentence. Keyserling pointed out that this unification of head and heart, mind and reason only can be successful for those "who have the courage for the inner change." Indeed we do not need more but better mathematics. It is not about the abundance and variety of methods and formulas. We have more than enough from them like in all other subjects. There is method in confusion and it is applicative to expel us out of our centre. What is necessary is a complete new quality and approach. With respect to the contents the new is not especially difficult. The main obstacle lies in the problem to get rid of the whole rubbish and cinder with which man is covered right from the cradle. This sticks on them for their whole life and moreover prevents them to adopt and incorporate different Other. I already pointed to the importance of rituals and taboos and claim that for this symbolic power as well. The formal mathematical knowledge up to now will become wisdom of numbers only then when we refine and foster it. Like the gardener scarifies the earth to allow rain to penetrate to the roots of the plants and enable their growth with relation to mathematical knowl-edge we need patient exercises. This is necessary so much the more as more than a few people turned away from mathematics after school for good reasons. However, as a last consequence this means that they decoupled themselves from the basis of modern life. This is fatal insofar as there is no way back behind the breaking of symmetry, God is dead! Herein lies the risk which we were dunned of by Erich Neuman when he said that arche-

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types which are not brought to consciousness lead to regression and a disso-lution of consciousness. Structural knowledge is royal knowledge and must be available. It is not part of the category of knowledge of which the half-life period is below five years. This kind of knowledge remains valid beyond the life of mankind. According to this fact it cannot be imparted like one may complete a class for a machine or for a new computer program. For the conveyance and care-giving of this knowledge, for short the cultivation of this wisdom there is no great substantial effort necessary although we should thoroughly consider and subtly feel the energetic general conditions. It is desirable that there are more places like the Mathematische For-schungsinstitut Oberwolfach in Germany at least along its idea. Regrettably this inspiring place shares the fate with so many other institutions which are committed to the spiritual: it is an ivory tower. This difficulty starts with the awakening of spirit at all. „As long as spirit remains silent in the motionless world of its hopes, everything mirrors and arranges to the unity as is desired by its homesickness. However, with the first motion this world becomes brittle, it tumbles down and we have to deal with a myriad of iridescent fragments.“ This statement of Albert Camus is valid as long as the knowl-edge about the invisible order is based on belief and esoteric enlightenment. This leads to the disastrous separation of heaven and earth, the dualism of content and form etc. The so-called spiritual has to aquiesce the accusation to be out of touch with reality because of an esoteric attitude. What is said before is also valid for the order school of the players of the glass bed game in Waldzell which is considered to be elite. In his novel "The glass bed game" Hermann Hesse says a lot of true things about the function of this kind of care homes for the spirit. But he also emphasises how easy it may happen that they slide into sterility, infertility and deca-dence because of apartness and isolation. Ultimately they may fail in their actual function as a source for cultural renewal. Spirit is always struggling and at the same time opens the doors for the manipulation of those who refuse obedience to its laws. „Man is the only creature which refuses to be what it is." This witching statement of Camus again is valid only if we misjudge the real essence of man. Man is a spiritual being which is he is able to perceive order and his sensor for this are num-bers.

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This cognition is not principally new. However, „with the death of Pythago-ras the great key to the wisdom of numbers has gone lost.“ told us Manley Hall. Ever since Platon number is nothing divine, an order-principle imma-nent to things any longer. With Platon on one hand it evaporates to a tran-scendent idea of an abstract principle of order, in the minds of disciples of Aristotle on the other hand it degenerates to a pure value for calculations. The metaphysics of transcendence as it is conceptualized by Platon has nothing in common any more with the immanent order as it was understood by Egyptians, Orphics or Pythagoreans. The disregard of numbers as a qual-ity was at the centre of our thoughts about the luck of luck. Today the key is at our hands again and again we reached the incorruptibil-ity of number. The millenniums-old discrepancy between the spiritual and sensual should be overcome with the renewed wisdom of numbers. Integral consciousness will lead again to the unity of culture and everyday-life. Our activities shall become spiritual and our spirit will be immanent to our ac-tivities. We cannot expect this situation to eventuate overnight. Therefore seminar-ies and initiatives are required which try out and drill this new old form. That this is not utopian is shown by the impressive and admirable Sekem-Initiative of the Egyptian Ibrahim Abouleish. The luck of luck is open to all of us. Even though the manifest is not obvi-ous offhand it is not mysterious in any way any longer and it is up to us to simply comprehend it. With the courage for inner transformation it will be just nothing. In this sense

I wish you all the best on your way to Sad al suud,

into the luck of luck!

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