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Preliminary Proposal Y.I.Khay 4/87



  1. AIM

  2. Participants

  3. Possible (and alternative) Scenarios

  4. Display

  5. Example of Display for the PASCHALIA

  6. First application - an IPM Pass-Over Game

  7. Guidelines for Developing Meaningfull Letter Patterns



To develop a marketable Game System for the AMIGA PC (as well as other PCs with decent sound and graphics) which is inspired by the Book "Calculator Saturnalia" by Pask et. al. (Wildwood House, U.K., 1980 and Vintage Books, N.Y. 1981). The inspiration may use the original story (as in that book or in Pask's Micro-Musical "The Catastrophe Girls"), or a story similar in intent and tone. It will certainly be modelled on Pask's two-level structuring of the Book and of his instructional systems as described in Pask's many papers and books.

B) Participants:

    - Prof. Gordon Pask, Amsterdam University and the A.A.

    - Dr. Yitzhak (Isaac) Hayutman, Haisseman Bros.

    - Ofer Raz, Computer Wiz Kid, the Bossmat School.

    - possibly Dr. Itiel Asmon, Haisseman Bros.

    - possibly John Michell, author of "Dimensions of Paradise".

    - possibly Dr. Darla Dietz, Fraiche Approach Inc.

C) Possible (and alternative) Scenarios:


Based on the "Calculator Saturnalia" or the "Catastrophe Girls":

Three mathematicians, Pask and two English associates, go around the world trying to employ and sell Lullian Wheels and Babbage-type Analytical Engines in a world full of IBMs. Their mathematico-magical skills lead to proliferation of homunculi and other unexpected actualizations bred in the games.

Saturn-2 (alias "the PASChALIA"):

Three itenerant cyberneticians (in fact covert Rosicrucians pedling with Philosopher Stones), Pask and his two Israeli associates, attempt to sell Gothic Design Aids while everybody around is having the latest CAD tools. Their own old tools may include Pythagorian and Platonic Forms, Lullian Wheels, Fuller Domes and Dymaxions and Kabbalistic formulae. Their special magic skills may consist of "Under-Standing" and "Passig- Over" in order to implement their own designs and patterns within their client, or rival, organizations.

(Points on their itinerary may include:

London, Mt. St. Michel Chartres and Paris, New York, Montreal, S.F. Bay Area, Kumasi, Heidelberg, Amsterdam, Prague, Haifa Tel Aviv and Jerusalem).

Note that the name "Paschalia" (perhaps "Paskalia"?), as used for musical pieces by Bach and others, is a homage for Pask's long and pioneering seminal work in cybernetics. The name is inevitably also associated with the Christian and the Jewish Paschal rituals and mythes, which are probably the world's most important, and still influential, mythos of the Redemption of mankind. SATURNALIA


The story line of "the Architect's Guide for Building Heavenly Jerusalem" shown by me to Pask in 1975 (enclosed Appn.) with whatever modifications suggested by partners and associates.

Saturn-4 (Alias "the HEJERA Game"):

Currently being developed by me within the overall "The HEJERA PLOT" - the player goes through a system of twelve stages, each a complete and different computer game which inputs the results of the last game to fashion the biases (competitive-cooperative) of its emvironment. At each stage he meets his Shadow figure (e.g.- as Isaac meeting Ishmael) and Anima figure. Trickster and Wise Old Man archetypes are merged into a wizard figure modelled on Pask (alias logi-Loony?). The story leads from the ruines of Babel (Babylon - reminiscent of Borges' Library of Babel) through intermediate Biblical and historic episodes to the Future New Jerusalem. The scenes also follow the evolution of life forms from Autopoietic Bubbles and Cells (reminiscent of Italo Calvino's "Cosmicomics") to a coordinated multi billion loci entity - a societal Brain - that produces harmonious and intelligent consciouseness.

D) Display:

Agreeing with Pask's observation that calulators are "tetchy contrivances with generally unreadable displays", the Amiga now offers good enough clarity, choise of colors, stereo sounds (and even speech of text) and graphic features such as animation, 3D rotations etc., so as to do justice to the skills and concepts which we want to train in. Following is a short list of types of displays that are deem appropriate for the above scenarios, with the "PASCHALIA" script as our aim. They are mentioned so that the partners may consider graphics and images from the outset of their drawing their scenario:

D1) Diagrams that have much symbolic meanings:

examples include Mandalas and Yantras, The Kabbalistic "Tree of Life" and related diagrams, the above-mentioned Lullian Wheels. It may be good to have some formal style considerations for including the modern diagrams such as directed graphs, bits of Entailment Structures and related "Proto- Language" expressions and Petri Nets. The diagram that will be discussed below is "the New Jerusalem Diagram" shown by John Michell in "The View Over Atlantis" (1969 &1984) and his later books.

D2) Geometric Patterns:

Such as grids and tessalations of Islamic art (see Kritchlow's books) which may be used as base for figures to be filled (such as in children coloring books) as the player has more tokens to place upon them and/or as bases for displays of Tessalation Automata.

D3) Pictures:

Can be readily drawn in the Amiga or readily entered as digitized reproductions of any available picture, using the Amiga IFF facilities. An example: almost-postcard-quality image of the Chartres Cathedral, followed by zooming into some detail (e.g. a gorgoyle sculpture from the facade, followed by the famous rose- window used hence as a basic pattern (see sec. E below). Gordon might do his line drawings with the Amiga mouse, etc.

D4) Geometrical Solids:

Ofer Raz is interested in making a library of "C" sub-routines that will allow the exploration of 3D objects from any perspective, enter them, etc. This is a major task which is justifiable if one intends to sell such as utility program for architects, game designers etc. We ought to consider whether we are interested to have such 3D explorations of mazes, cities etc. as important part of the script (e.g. the exploration of(?)nese Labyrinths in the Saturnalia).

D5) Special Amiga Graphic Features:

There are many which are worth exploiting.

Two such are

  1. the ready creation of color cycles which make the picture or parts of it seem to move, and

  2. taking a part of the picture or a specific pattern that appeared on it as a stamp (or a D.Paint Brush) that can be readily reproduced at any other place in the display or move about it as a sprite. With this feature, many types of self-reproduction can be shown without need for too complex algorithms.

D6) Covert Mapping:

Perhaps the most interesting built-in feature of the Amiga (and other mouse-driven PCs) is the ability to prepare a screen so that toucing a point on it with the cursor, which is moved by moving the mouse, and then clicking the button acts like a magic wand which causes something to happen to the whole program. It occures to me that the points to be tauched need not be clearly visible, at times they might be hard to find and/or even invisible.

This means that many riddles, such as in orientation problems, can be programed in and the clues to their solution hidden in the screen. In the simplest form, consider multiple-answer tests that one answers by pointing to the place of her choise in the table of alternative answers and clicks the button. More advanced is a game of pointing to the cells in a tessalation (which might be a worked Entailment Mesh) which one guesses are those which are within a hidden configuration (as in the popular game of Submarines which had already been picked as an element of the CALCULATOR SATURNALIA system). The occult configurations mentioned above could thus be used as really occult powers that one who literally gets in touch with them gains great advantage in his-er Paschal Game. Using old symbols people have used to aid their Messianic quests may still have effect for reviving people's confidence and skills for the work of Redemption! (There are various other covert or subliminal cueing devices which can be pre-programed into our Game System, but since our own committment is for exteriorising and realizing overt understandings, we need not consider them here).

E) Example of Display for the PASCHALIA:

The Amiga graphics screen is a 1:2 horizontal oblong which we shall regard as two squares, for players A and B. Centered on each square will be a circle or a projected dodecahedron, surrounded by four concentric and staggered circles of 12 elements each (hence "rings"). This is a figure much like the Rosaries of Chartres Cathedral which are made of 49 elements. Near the top and bottom of the center line there are two dodecahedrons which can rotate in 10 directions, one for each player. These dodecahedrons will also serve as dice for the games - each of their 12 faces will become associated with some attribute which may be used in the 12-fold rules of a particular game, and the rotation will be enacted by a 2 digit random number where the first digit give the direction of rotation and the second digit gives the number of rotations.

Symbolically, the 12-fold geometry is seen as that of the Zodiac, as well as of the Tribes of Israel and of the gates of the New Jerusalem. The 49 elements (plus the occult black framework - or the dodecahedron) of the Rosary may represent the "fifty gates of Understanding", since Understanding (Binah) is the Kabbalistic meaning of the Heavenly Jerusalem.

Let us note some of the visual game procedures which could be shown through this display:

E1 - Altogether we have exactly 100 elements over the field, each can appear, disappear, blink, have any of 4096 colors (generally from a smaller, 16 or 32 color pallette) or carry a letter from a variety of alphabets. In the aggregate, these 100 elements can represent percentages of whatever quantity which is acquired by the players. The greater power, however, is when these elements are used to deliniate various configurations.

E2 - the "rings" may use the color cycle of the Amiga to produce as fast rotations as may be required by the game to have roulette- type motions or other motions. They can most easily serve also as Lullian wheels.

E3 - Various types of symmetries, parities and reflections between elements of the two Rosaries can be readily discerned visually. Certainly the types of symmetries employed in the first CALCULATOR SATURNALIA games could be detected by an appropriate program and shown to the players (e.g.- by blinking the two matching sections).

E4 - the rosaries can also serve as spiral strings of 49 beads. If these spirals draw out anticlockwise and contain letters, they produce strings of text parts of which may prove to contain legal and meaningfull words. (Letters may also be drawn out of the dodecahedrons, esp. if not only each face but also the the inside is associated with a letter, giving a total of 26 letters. Another geometrical manner to generate the letters is by the 26 directios of the 26 cubes which surround an inner cube).

E5 - Of special note are "Pass-Over Operations" whereby, while each player is identified with one Rosary the interrelated elements of which are his-er pieces, a player passes (probably briefly) to the territory of the other and operates upon pieces there.

Assuming that one's pieces are held together by some coherence (i.e.- that the Rosary models the player's mental organization), the chances are that the other player's entries would cause some local perturbations. In many cases these perturbations will be dampened and cancelled out. In other cases they may be so tuned (i.e.- they belong to the set of self-reproducing configurations possible in that domain) that they bring more or less permanenet changes in the other's organization. Alternatively, some such entries might prove destructive, while the stable configurations probably bring advantage to both sides. I guess I need not explain the cognitive and interpersonal interpretations of such games.

F) First application - an IPM Pass-Over Game:

Of the original CALCULATOR SATURNALIA games, the most important and interesting (to my mind) ones were "Robinson's Workshops", "Yourself as Another's Other" and "The Third as Other". These are actually applications of Laing, Philipson and Lee's IPM method, and a good application too. Unfortunately, they are most unwieldy as calculator games, demanding far too much calculation work for a normal game player. Obviousely a computerised version can take care of all the chores and make the games more enticing. A graphic version on the Amiga, along the lines of section E above, can show the match of the mental perspectives elicited by those games.

In Robinson's version, a personality profile is made out of twelve given attributes which are ranked by the players according to several perspectives. In "the Third as Other" each player, A&B, makes three such rankings:

  1. his own evaluation of C (the other),

  2. his guess at Player B's evaluation of C, and

  3. his expectation of B's guess of his own evaluation of C.

    A similar elicitation is made of player B who gives:

  4. her evaluation of the same person C;

  5. her guess at player A's evaluation of C, and

  6. her expectation of A's guess of her own evaluation of C.

Such personality profiles with twelve attributes fit admirably with the Rosary pattern discussed above. The three outer twelve- element rings of the two rosaries will represent the perspectives elicited: A's Rosary will include perspectives 1, 5 (!) and 3, whereas B's rosary will carry perspectives 4, 2 and 6. In other words, B's guess of A's opinion "passed over" into A's domain, where it can be readily compared in a glance to A's perceptions.

The same goes for B's domain, which must include in its midst A's perception of B. Degrees of match and mismatch of perspectives will show as similarilties of adjacent rings.

In order to make the visual evaluation clear, we would not move the place of the attributes when their rank changes, leaving them in their place (like the "houses" of astrology). The ranking will be displayed by different colors - a six color "rainbow" grading, or even a twelve-color scale (this will be decided by experiments to suit people's ease). The degree of understanding will become apparent by the color match between rings while misunderstandings will show as different, even dissonant colors. In addition, the computer will calculate the relevant matchings and display the results in appropriate lists and captions.

There are two elaborations of this scheme in the SATURNALIA games:

  1. One is the elicitation of different categories than the fixed twelve. This can make the game almost identical to the original IPM. If we are interseted in such version, we might include some category-elicitation tools, such as Kelly Grids (already developed for computers by Mildred Shaw of Brunel U.).

  2. The other elaboration is in the game "Yourself as Another's Other" where two players evaluate each other by such perspectives, each player filling (really feeling!) six forms of rankings of this sort. There are ten types of matchings that aught to be done and the data are too numerous to show simultaneousely on the display pattern discussed above. A possible solution is to keep the pattern, but to shift the perspectives across it to those that are required according to the comparison made at each case.

G) Guidelines for Developing Meaningfull Letter Patterns:

    G1. Since Letters of any recognizable ALPHABET may appear and dis- appear, replace each other by either wheel (willfull?) fashion or by neighbourhood functions (as in Pask's automata simulations and Ben Eli's EVE-2 model), letter operations can be prime processes of the SATURNALIA/PASCHALIA Display.

    G2. In the PASCHALIA, "Passing-Over" operations can be made by Re- cognizable Groups of Letters - namely WORDS. Such Letter-Groups may have a geometrical structure (e.g.- a linear string) and/or gematrical (numerical) values, and their transformation into other meaningfull groups which preserve the same geometrical and/or gematrical values may be considered as valid reproductions. The validity of words can, in principle, be checked mechanically by a computer with a dictionary program (most current Word Processors have such).

    G3. On a higher level of letter organization, there may appear meaningfull groups of groups, namely valid line-sentences made of valid words. (Note: Grammatically valid sentences are, in fact, processes of "Passing Over" of an Action from Subject to Object).

    There are various AI programs of valid sentence construction e.g. Winograd's work on Syntax). Ofer Raz has developed at Basmat an operational program which does that. However, practically it may be better to pass the onus of identifying meaningfull strings to the players themselves.

    G4. Yet more meaningfull - and demanding - is to satisfy semantic rules for meaningfull sentences. Ofer Raz's program mentioned above achieves this in an evolving manner by a growing list of constraints and permissible relations. We shall consider these demands as other aspect of sentence-construction. In the context of the PASCHAL Games and Display, a string of maximum 49 letters may contain a section which is a meaningfull sentence, and such a section would be stored as accomplished achievement of the player.

    G5. A still higher level of letter organization is of letter- groups of the third power, namely meaningfull collection of simple sentences. I would like to think of an attempt to make an "Auto- Poetic" Game where the players try to produce verses of poems.

    There are examples known of simple computer "poetry" (E.g. in Pask's "MicroMan" and in Watt's guide for LOGO). The challenge, I think, is to satisfy aesthetic criteria, such as phonetic and harmonic (e.g. meter, rhyme,..) for simple poetic constructions such as Limmericks and Dogerels.

    G6. In the HEJERA Games, the emphasis is on developing meaningfull communications among the players. Thus the notion of Letter Games comes around to an altogether higher level - composing and sending to each other as acts of co-respondance. The idea can already be utilized on these lower levels of meanings discussed above - if A (he) produces words which belong to the cherished repertoire of B (hers), then the chances of her responding to him becomes greater.

    The goal in some of the HEJERA Games would be to compose Letter made of several poetic verses addressed to the Other or refering to the Self. This would constitute genuine "Auto-Poesis" that shows self-and-other reference and even understanding.

    G7. An interim summary: I have shown several levels of meaningfull letter patterns which might be produced in these games. One way to show the relation among these more complex levels is by levels of payoff that players get for producing such patterns. Let us assume that players have limited stocks of letters, which are hard to get, and they compose various groups out of them:

    valid WORDS   payoff in UNITS

    line SENTENCES   "   "   TENS of Units

    one-Verse POEMS   "   "   HUNDREDS

    Poetic LETTERS   "   "   THOUSANDS

    G8. An alternative, or additional, to the above scoring method, as a way to relate these different levels, is in terms of stability in the face of an entropic tendency. We may regard the display of letters as made of shifting patterns (such as in the Conway's LIFE Game) and letter patterns, including valid words, may come about in strange and hard to control ways and may be hard to preserve and reproduce. We may, however, introduce specific routines for preserving words and word-groups, even by simply pointing at them with the mouse and clicking. We may mimic real processes of memory and cognition, where meaning helps reproduction and recall of letter-strings. For example: If valid words have been assembled into a meaningfull sentence, their letters would no longer tend to disintegrate (or do so slower, or may be more easily reproduced) since the meaning of the sentence secures its words. Likewise, if sentences are assembled into a poetic verse (with rhymes etc.), then their words become stabilized, since the poetic form makes it easier to reproduce its constituent words. Finally, if such poetic verses are assembled into a meaningfull letter - from the Self to an Other - their sentences become stabilized.

    G9. It is unrealistic, and unnecessary, to strive to build-in the criteria for all these levels of meaning as mechanical, AI, routines. The optimum is, as often as possible to let the machine take care of drudgeries and backstage procedures and to let the human players have fun in recognizing patterns and picking them.

    One should be able to delineate a pattern with the mouse, pick it for a different treatment by the computer which would then show it in a different color, keep it more stable, enter it into memory and use it as a template that can be reproduced elsewhere.

    G10. We can have a "fallback" goal in doing developments such as the above. The practical, businesslike goal would be to produce a Letter-Writing Aid. Seen as an auxiliary to major Word Processing Programs or as a stand-alone program, this aid program will prompt the writer to compose an effective letter which answers implicit expectations of the receiver. The program would include thus first a set of tests to determine actual or assumed preferences of the receiver (such as cherished words, pressing concerns, general aims and favourite style). Based on these, the program would then structure the letter-writing process. A likely procedure would be to pose a sequence of questions for which the writer types the answers (might be good to limit their length). Only these answers are then included as the paragraphs of the letter. There are some rudimentary programs like that in the market, but no interactive program with any insight, and most people are poor letter writers.

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