Compiler's Introduction By Christiaan Freeling Chapter I A Spirit in the machine Dear User, Congratulations! You've got a Spirit in the machine. It's an old Spirit, but you can't outlive it. It's a deep Spirit: it sees the springs of things long before their workings become manifest. It's a wide Spirit: it sees what is hidden beyond any horizon. This is what the I says: _________________________________________________ In ancient times, when the sages made the Book of Change, in order to lend mysterious assistance to the spiritual Intelligences, they produced the rules for the use of the divining plant. Shuo Kua, Chapter I, §1. _________________________________________________ In the I there is no thought and no action. It is still and without movement; but, when acted on, it penetrates forthwith to all phenomena and events under the sky. If it were not the most spirit-like thing under the sky, how could it be found doing this? Ta Chuan, section I, chapter X, §4. _________________________________________________ It is said in the I: 'Help is given to him from Heaven. There will be good fortune; advantage in every respect'. Ta Chuan, section I, chapter XII, §1. _________________________________________________ I've long entertained a question in my mind that kept evading a satisfactory anwer. The question was: why does the I, as a rule, provide question-related answers? I must have put this very question before the I several times in the some twentyfive years that we are acquainted, and I don't doubt that the answers were to the point. But I didn't really know the book, back then, nor did I study it to any significant extent. My vision, moreover, was not as yet fit to perceive the obvious. Then a curious thing happened. But before I come to that, I will provide a different view on the history of the book. A history that shows the I's many changes on its journey towards the Connexion and your computer. Chapter II In ancient times _________________________________________________ Anciently, when Fu Hsi had come to the rule of all under heaven, looking up, he contemplated the brilliant forms exhibited in the sky, and looking down he surveyed the patterns shown on the earth. He contemplated the ornamental appearances of birds and beasts and their different suitabilities. Near at hand, in his own person, he found things for consideration; and the same at a distance, in things in general. On this he devised the eight trigrams, to show fully the attributes of the spiritual Intelligences operating secretly, and to classify the qualities of the myriads of things. Ta Chuan, section II, chapter II, §1. _________________________________________________ As was to be expected, there's no consensus about the I's ancient history. According to Legge, Fu Hsi, by the least unlikely of the chronological accounts, must be placed in the 34th century BC. _________________________________________________ Was it not in the last age of Shang Yin, when the virtue of Chou had reached its highest point, and during the troubles of king Wen and the tyrant Shin Chou, that the I began to flourish? Ta Chuan, section II, chapter XI, §1. _________________________________________________ Leaving the trigrams to gather meaning for two millennia and a few centuries, we find ourselves on firmer ground. King Wen was imprisoned in 1143 BC. by the last ruler of the Shang dynasty. Whether 'help was extended to him from Heaven' we will never know. It certainly would have had the appearance of doubtful assistance. But for some mysterious reason he did't get killed and enjoyed sufficient absence of distraction to be able to receive uninterrupted spiritual guidance from Whoever chose to put him there. Hence he wrote the Judgements. Whether he was the first to combine the 8 trigrams to 64 hexagrams is doubtful in the light of their fleeting appearance in earlier manuscripts, and no less so in the light of what the I says: _________________________________________________ Fu Hsi invented the making of nets of various kinds by knitting strings, both for hunting and fishing. The idea of this was taken, probably, from the hexagram Li (30. Clinging Brightness). On the death of Fu Hsi, there arose the clan of Shen-Neng. He fashioned wood to form the share, and bent wood to make the plough-handle. The advantages of ploughing and weeding were then taught to all under heaven. The idea of this was taken, probably, from the hexagram I (42. Increase). Ta Chuan, section II, chapter II, §§ 2-3. _________________________________________________ Fu Hsi invented the trigrams, and his supposedly deriving the idea of making nets from the hexagram Li might be considered a mistake. It may have been the trigram Li (which looks like a net's loophole). But I (42. Increase) is definitely a hexagram. According to this passage, the hexagrams date back more than 5000 years. However, there is a consensus on king Wen's being the author of the names of the hexagrams (except of course where the trigrams are doubled: these names are much older and of unknown origin). The Shang dynasty was finally overthrown, and king Wen liberated, the next year. It must have been towards the end of the twelfth century BC. when his son Tan, the duke of Chou, finished the work of his father by adding a peculiar 'judgement' to each of the 384 lines. They can be found under 'The Lines', in the text of the separate hexagrams. These judgements, to me, are the core of the mystery of the I. They seem capricious and without any clear meaning in themselves, but if viewed in the context of an actual divination, they have a knack of taking on a definite problem-related meaning. This is what the I says: _________________________________________________ The words are indirect, but to the point; the matters seem plainly set forth, but there is a secret principle in them. Ta Chuan, section II, chapter VI, §4. _________________________________________________ The I is a book which should not be let slip from the mind. Its method is marked by frequent changing. Its lines move and change without staying , flowing about into any one of the hexagram's six places. They ascend and decend, ever inconstant. They change places so that an invariable rule cannot be derived from them: they vary as their changes indicate. Ta Chuan, section II, chapter VIII, §1. _________________________________________________ Beginning with taking note of its explanations, we reason out the principles to which they point. Thus we find that it does supply a constant and standard rule. But if there be not the proper men, the course cannot be pursued. Ta Chuan, section II, chapter VIII, §4. _________________________________________________ The 'secret principle', for me, was hidden by inability to perceive the obvious. I will yet come to that. The last two paragraphs seem contradictory, but they are not. Invariable rules, be it in social sciences, physics or even mathematics, only exist in limited environments. The I, representing all of it, is no more predictable in its inner workings than reality itself. The 'constant and standard rule' refers to its answers, and those in turn depend on a proper interpretation. Thus only 'proper men' may unveil and pursue its advice. I'll come to that in Interpretation. Lao Tzu and Confucius At this point we leave the I to flourish for several centuries, till it meets with two other undying spirits (though in a more fragile housing), Lao Tzu and Confucius. The latter lived from 551-479 BC. while the former preceded him by half a century. Its unlikely that they ever met, though legend of course dictates otherwise. Lao Tzu wrote one small book, the Tao Te Ching , which is strangely unsettling for the open-minded. The common man is well-protected against its wisdom. This is what the I says: _________________________________________________ The benevolent see it and call it benevolence; the wise see it and call it wisdom. The common people, acting daily according to it, yet have no knowledge of it. Thus it is that the Tao as seen by the superior man, is seen by few. Ta Chuan, section I, chapter V, §3. _________________________________________________ Lao Tzu knew the I and may have known the early chapters of the Shuo Kua, but the ten Wings originated around and after Confucius, and not in a day either. This explains why Lao Tzu may have had more influence on the I than vice versa. The Ta Chuan has a distinct taoist flavour, and where the Tao Te Ching has captured the interest of those wrestling with quantum mechanics and the 'nature of reality', the I says: _________________________________________________ Therefore in the I there is the Grand Extreme, which produced the two elementary Forces. Those two Forces produced the four images, which in turn produced the eight trigrams. Ta Chuan, section I, chapter XI, §5. _________________________________________________ This is quite another story than Fu Hsi devising the trigrams. It shows how all diversity is produced from One. As a symbolic representation of our concept of the 'Big Bang' it seems strangely accurate. It would take a Taoist mind to work its way back to an intuitive knowledge of it. Legge, unfamiliar with the concept, of course couldn't but miss the point, as he admittedly does. Confucius' authorship Confucius is often quoted as having said that if fifty years were added to his life, he would use them to master the I, thus avoiding to fall into great errors. If anything , it shows that he held the book in high regard. Yet, like me, he felt little hesitation to change its course. Unlike me, he did it by adding substantially to its contents. Many consider him the author of the ten Wings. I don't, because it would imply his distinguishing himself from himself on numerous occasions by using the sentence 'The master said:', in both the Wen Yen (commentaries on the separate lines in the first hexagram, A4-A9) and the Ta Chuan (sec. I chap. VII, §1; sec. I chap. VIII, §§ 5-11; sec. I, chap. IX, §10; sec. I, chap. XI, §1; sec. I, chap. XII, §§ 1-2; sec. II, chap. V, §§ 1 and 5-14; sec. II, chap. VI, §1). This, if nothing else, goes against philosophical etiquette. It would also imply his being the author of such notorious nonsense as can be found in the third chapter of the Shuo Kua and occasionally in the Hsü Kua. Would he be pleased with the honour? I think not. It seems safe, however, to assume that the words following the sentence 'The master said:', are indeed the words of Confucius. There's no evidence against his being the author of the commentaries on the Judgements either. But for most of the rest of the Wings there seems to exist a multiple authorship. Moreover, parts of the Shuo Kua date back farther than Confucius. The I, being a book of divination, found itself in a select class of literature that escaped the great bookburnings of Chin in 213 BC. without major damage. Some of it may be lost though, and some experts argue that the Wen Yen commentaries must have once existed for all 64 hexagrams, but failed to escape the fires. On mathematics We are now in 200 BC. and ready to look at another aspect of Chinese civilization: its achievements in mathematics. By then the Chinese had been using te decimal system (base ten of course: this was considered as arbitrary as having ten fingers) for twelve centuries in increasingly sophisticated versions of the abacus, had reserved a place for zero for two centuries, and were just about to invent the use of negative numbers. They also had the binary system. This binary system, of course, is the I itself. The hexagrams literally represent the numbers 0 (2. K'un) to 63 (1. Ch'ien). My age at this moment, 47 going on 48, could thus be represented as 14. Ta Yu going on 20. Kuan. The binary system is elegant, but unpractical in anything but a computer. The Chinese may very well have realized that the hexagrams could thus be used to represent numbers, but without any practical application this knowledge would hardly have been considered more than a peculiarity. With that observation we leave the I yet again for the best part of two millennia. Chapter III More recently The discovery of the binary system is usually attributed to Gottfried Wilhelm von Leibnitz (1646-1716), a german mathematician, philosopher, inventor of calculus and genius in general. He is considered to have gotten the idea from the hexagrams of the I. He also worked out a very intricate mechanical computer. This machine was never finished because his relatives refused to pay the instrument maker after his death. So it goes. But this is what it shows: that the I stood at the cradle of the very computer you're looking at! To those who consider a computer an unfit place for the I, I would like to say that the reverse is true: even without the Connexion, fast access to cross-references provides a better interaction with the book. But the Connexion takes things one step further: generating a Connexion requires a computer, and for more reasons than speed alone. I'll come to that in Interpretation. Meanwhile back in China, the Imperial Edition of the I had been published in 1715. This is the book Legge based his translation on. James Legge's first attempt to translate the I took place in 1854 and 1855, embracing both Text and Wings. He felt dissatisfied with the result from the onset. In 1870 the manuscript was soaked in the water of the Red Sea for more than a month, before it was miraculously recovered so as to be still legible. A few years later, ironically, he felt that his translation was of little use and decided to have a better and better prepared go at it. He now used the Imperial Edition, that keeps the Text and the Wings separated. He also had reached the conclusion that his first translation was too literal, and that his task would be to translate, like a poem, the idea rather than the words. This translation was published in 1882 and is basically what you will find in this program, be it that I decided to use a different lay-out. With due apologies to Legge, those parts of the Wings that refer to specific hexagrams, once again come with these hexagrams. Chapter IV Modern times Well, in terms of people, that is. In 1980 computers were still in ancient times. We're at the University of Twente, the Netherlands, in the middle of the most flourishing period of the games-club 'Fanatic', with sessions twice or trice a week, playing anything interesting enough, and till deep in the night. Most members were students, but some came from outside the university, and among them were two inventors, Martin Medema and myself. Ed van Zon, who wrote this program, was one of the graduates back then. Martin and I had different fields of interest. Mine was very restricted: I invented abstract games of pure strategy on such themes as checkmate, elimination, territory or connexion. I managed to make something of a name in the field, and major parts of my work can be found in R. Wayne Schmittberger's "New Rules for Classic Games" (John Wiley & Sons, Inc. New York; ISBN 0-471-53621-0) and David Pritchard's "The Encyclopedia of Chess Variants" (G&P Publications, P.O. Box 20, Godalming , Surrey GU8 4YP, U.K. ; ISBN 0-9524142-0-1). Martin covered a much wider field. Occasionally he managed a good abstract game, but he invested most of his time in making highly intricate and intelligent science-fiction and dungeon-like games. Fanatic was all about intelligent fun, back then. The Night of the Labyrinth In the autumn of 1980 came the 'Night of the Labyrinth', though no one had announced it as such. Most of us were already present when Martin came in. He seemed even more pleased with himself than usual, and said that he had a new game, and that, for this one occasion, we could play it for the sake of trying to figure out the rules. His would be the role of Game-master. He then proceeded to set up a screen, put a piece of paper behind it and a big draughtsman in front, and asked who was in. Ed was in, I was in, and five more were in. Seven small coloured counters were put on top of the draughtsman, so as to represent us standing in a room. Six more draughtsmen were arranged around our room, to represent adjacent rooms that we were able to 'see' from our position. Then Martin sat back and waited. Without any clues, what could we do? Two of us picked a room and walked in. Zapp! They were gone. That is, our representatives were unable to see them from their position. But we could from ours: Martin put a new room elsewhere on the table, and there they were. And sure enough, there were adjacent rooms visible from their position also, but not that many. They also seemed safe enough (and they were: there were as yet no unpleasant monsters in the labyrinth, nor invaluable items worth pursuing). I decided to join them by entering the same room, but instead of zapping away, I only ended up in that very room, able to see my compagnions and vice versa. But sure enough a new room appeared opposite of the room I had come from. Soon we were all over the place, now walking now zapping , discovering more and more rooms. Sometimes a new room suddenly gave the mutual surprise of seeing another party in the adjacent room. The previously separate parts of the labyrinth were then united in their correct relative positions, allowing further speculation on our part. Martin was indeed the Game-master, keeping track of our actions and all consequences involved. I must confess that I felt utterly at a loss most of the time, although I clearly sensed the presence of consistency in the logic. The first ever Connexion What we had entered was in fact the first ever Connexion. Click Verify under Connexion and see what it may have looked like. Imagine entering it without a map, only finding new rooms (hopefully) adjacent to rooms newly entered. Martin had build in a teleportation system, based on the labyrinth's inner logic, that 'zapped' us to the very rooms which this logic dictated. In order to move about according to purpose, one had to discover the nature of the labyrinth and the zapp-system. It was Ed who figured it out, finally. He has a very deductive mind. It took me some time to grasp the concept with which I'm so familiar now. When I got the picture at last, I stood some time in admiration of it. 'How in the world', I finally said, 'did you manage to get 64 draughtsmen in an arrangement where each differs from all others in terms of the pattern its very neighbours make around it'? 'That', Martin replied, 'is a very beautiful puzzle'. The set There was a good deal of competition between Martin and me, back then. Ideas were quickly picked up and elaborated on. On the way back I pictured Martin with his draughtsmen, and the problem that adding one to the structure inevitably changes the nature of its neighbours. This makes strategy very complex and in demand of constant administration. Then I jumped to the idea of the final picture and, for a moment not distracted by its beauty, saw that simply marking all the positions that represent doors, would turn each draughtsman into a 'fixed room'. That was it! That really was it. I figured this would reduce the time to make a labyrinth to, what? minutes? The next day I made the first set, marking 64 hexagons with an arrow (to allow the required fixed orientation) and spots to represent doors. The set looked like this, though the arrows are omitted for clarity:  the set It is identical to what you get when you click Connect under Oracle. It allowed making a labyrinth, which the computer does in seconds, in some twenty minutes. Generalizations A hobby of mine, and I was on fertile ground. I did for squares (16 pieces), triangles (2x8 pieces) and cubes (64 pieces), what Martin had conceived for hexagons (without conceiving the idea of marking the doors beforehand). I also found another type of solution and coined the terms 'transcendental' and 'compact' to distinguish between the two. Martin later discovered yet another type of solution, which he called a 'starmap', and of which very few exist. He also coined the name 'China Labyrinth' for what is now called a Connexion. In terms of doors and walls, a Connexion has all walls on the outside and all doors internal. That is in fact the source of its transcendency. But using the new set, it was now also possible to allow both 'door to door' and 'wall to wall' contact. This was called 'compact'. There's no trancendency in a compact solution: remove its markings and all information is lost. To make a compact solution, a specific form of 64 hexagons must be chosen, the puzzle being to fill it up with the set so that all doors (and as many walls as will prove necessary) are internal. For transcendental solutions no such specific forms can be given, because the form of a trascendental solution, by its very transcendency, already is the solution. I also expanded to 'second order sets', featuring doors not only in the middle of the walls, but also in the corners. The most important set in this category is the 'Octopuszle', which consists of 256 squares, with eight positions for doors, allowing the king's move in Chess to get from one room into another. The Octopuszle, like all other sets that emerged, allows both transcendental and compact solutions. I don't believe anyone ever tried his hands on a compact solution other than the obvious 16x16 square. Ed made one such solution, and eight years later I made one. Then a curious thing happened. But for the moment I had made the system open to investigation, and many games and puzzles emerged from it that would make interesting reading elsewhere. The mathematical properties of transcendental solutions (such as the number of groups being equal to the number of loops in a Connexion) proved very interesting too. Many solutions featuring different types of symmetry emerged, both transcendental and compact. And last but not least, I had come to realize the one-to-one relation between the hexagons of the first set, and the hexagrams of the I Ching. The Octopuszle Most of the interest went into the original set and the Octopuszle. The latter was made in the same way I made the first set: 256 squares were marked with an arrow for orientation, and with every possible combination of spots on the edges and corners. Ed made his one compact 16x16 solution in 1981. Of course he copied it for all who were interested, so I had a copy in my archives. In 1989 I wanted to make a compact 16x16, specifically to turn it into a work of art. I decided to make a new set, using lines radiating from the center, instead of spots, for marking the edges and corners. The horizontal and vertical lines (towards the edges) were black, the diagonal lines (towards the corners) red. This turned out to be a great improvement in display. You can judge for yourself:  the Octopuszle set The solution took me some ten days. This is due to the nature of the puzzle: the first 250 pieces usually take an evening or so; the last 6 may take anything between a few days and a a few weeks. Endless sequences of interchanging pieces must be performed to finally add one more piece to the solution, and most of those sequences will be found to end in a dead end. If you don't believe it, try it. I was very pleased with the solution I finally got:  my solution Throughout the process I had maintained the symmetry of the corner-squares. I also had taken care to keep the 'blank' inside the solution rather than on the edge. This is considered good form. Now I appeared to be rewarded with a very attractive looking octagon on one of the diagonals of the solution. A nice focus-point for the work of art I had in mind! Then a curious thing happened In fact the most curious thing that ever happened to me. I was so pleased with the graphics of the new display, that I decided to take pictures for the archive. I also decided to copy the two other solutions I kept there, that were still in the old 'dots-display'. One of these was Ed's solution. Copying them with the new set was easy. Then, just when I was about to take the pictures, I made a stunning discovery. There was a striking similarity between Ed's solution and mine!  Ed's Solution There was the octagon again, in exactly the same position! Admittedly a small section of its contour is missing , but its very appearance was, I thought, remarkable. When I also discovered the 'blank' in exactly the same position, my feeling of surprise became even greater. Little did I know the the infinitely bigger surprise the pictures held in store for me, although it was right before my eyes! That very evening I took the pictures to two friends, Gerard Dijkman (who later provided the astrological data for the I Ching Clock featured in this program) and Theo Steine. Gerard considered the coincidence remarkable and left it at that. We went into a conversation about one thing or another, while Theo took a closer look at the pictures. We were used to Theo being silent most of the time, but after a quarter of an hour we realized that he was still looking at the pictures, so I went up to him and asked if anything was the matter. I'll never forget his reply. He said: "Well, it seems to be in the red, mainly" (meaning the diagonals). I said: "What do you mean"? He said: "Well, I haven't been able to discover a difference yet". I said: "WHAT"!!? I'm a mathematician. I know about chances. I knew this couldn't be. I felt myself being taken upward on a tidal wave of astonishment. My eyes were literally eating the pictures. This couldn't be!!! But it was: Both solutions feature the same diagonal complex. Here they are again:  my solution  Ed's Solution A thorough investigation followed the discovery. As it turned out, apart from having the identical diagonal complex, the puzzles featured 114 pieces in identical positions (coloured green above). The chances of this happening are 1 : 114 factorial. That's not even taking the identical diagonals in the remaining 142 squares into account. 114 factorial is the number 114x113x112x ...... x3x2x1, or 2543559733472187557120132004189335234812341496026552301496526393412538629248600474981599398141467853800514886431180030568224218435400019580180261753940817530060800000000000000000000000000 To provide a context, the upper limit for the number of atoms in the universe is considered to be 10 to the 87th power, or 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 Square this number and you'll get 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 Thus, the upper limit of the chance of this happening is less than one to the square of the number of atoms in the Universe! A fraud? In other words, did I construct it? Obviously I can't keep anyone from believing what he chooses to believe. I may have had my reasons. But anyone willing to try will find that there's so little room to manoeuver in the puzzle's notorious endphase - the long and tedious sequences of interchanges, many of them unsuccessful, that go before the successful placement of any one of the final pieces - that trying to fulfill, at the same time, the condition of keeping the diagonal complex invariable, is a humanly impossible task. A computer could do it though, and in his introduction into this program Ed van Zon does point out a rather straightforward way to structure such a program. But it would have required a high-speed computer, such as I didn't have (and still don't: a Performa 450 hardly meets the requirements) and a programmer like Ed. And Ed didn't do it. Doubt me and you may doubt that too. So it goes. A change of mind I did experience 'help from Heaven' in a rather penetrative way, once, when I was delivered from an impending schizofrenic exhaustion by having it taken from me in a split-second, along with my sense of 'self' and the trouble associated with inner conflict. Like it is said in the I: _________________________________________________ Showing its subject disregarding the dispersal of his own person. There will be no occasion for repentance. 59. Huan, six in the third place. _________________________________________________ As it happens, my natal hexagram is Disintegration, so this may well have been prearranged too. Who knows. But it didn't, at the time, give a feeling of Someone up there caring one way or the other. This changed in an instant, the moment the 'coincidence' became evident: not a cell in me could accept it as a coincidence! I didn't even jump to the conclusion, I was engulfed in it: Someone up there has a sense of humor! As a result I'm a Bokononist now. I believe humanity is organized in teams that do the will of Whoever's in charge up there, without ever discovering what they are doing. A program Meanwhile Ed had, in 1988, in fact written the program that made this very program possible. He had bought a MacPlus, and to familiarize himself with the machine, he decided to write a program to generate what was then called 'transcendental solutions of the China Labyrinth'. He also knew of the 'I Ching mapping' that I had worked out (already implying the idea that it might provide a framework for a deeper interpretation), but this was not at all the focus-point. Thus it came to happen that he displayed the hexagons 'point up' instead of 'side up', which, in terms of a Connexion, means a 90 degrees rotation. This was a bit of a handicap in terms of using the program for the I Ching. It wasn't a very fast affair either, and neither was the MacPlus. But it gave the first computer-generated Connexions. Chapter V Very modern times In the summer of 1994 Ed finally found the time to restructure the program. He managed to speed it up considerably by means of a smarter selection procedure (as well as a Macintosh IIsi), so I was only too glad to provide graphics & text. My Bokononist view had thrown a new light on the I. So finally Why does the I give question-related answers? This is what the I says: The I was made on a principle of accordance with Heaven and earth, and reveals therefore, without rent or confusion, the Tao of Heaven and earth. Ta Chuan, section I, chapter IV, §1. This is what I say: Because Whoever's up there, the spiritual Intelligences, use it that way to play their games with human fate.   Christiaan Freeling Enschede, december 1994. freeling@euronet.nl _________________________________________________