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GREETINGS CITIZENS OF PLANET EARTH

I

HAVE

A

MESSAGE

I AM THE OPPOSITE OF THE OPPOSITE I AM THE OPPOSITE OF OPPOSITE IS THE AM I ALWAYS AM

A SENSE OF HUMOUR I HAVE A SENSE OF HUMOUR

DIVINE LOVE

973-EHT-NAMUH-973

 

 

 

 

The famous Perseid meteor shower has been observed for about 2000 years, ... The Perseid meteor shower peaks on the new-Moon night of Sunday–Monday, ... en.wikipedia.org/wiki/Perseids

The Perseids (pûr'sē-ĭdz, or psijdz in IPA) are a prolific meteor shower[1] associated with the comet Swift-Tuttle. The Perseids are so called because the point they appear to come from, called the radiant, lies in the constellation Perseus. Meteor showers occur when Earth moves through a meteor stream. The stream in this case is called the Perseids cloud and it stretches along the orbit of the Comet Swift-Tuttle. The cloud consists of particles ejected by the comet as it passed by the Sun. Most of the dust in the cloud today is approximately a thousand years old. However, there is also a relatively young filament of dust in the stream that boiled off the comet in 1862. The approximate rate of meteors originating from this filament is much higher than normal.

[edit] Observation

The famous Perseid meteor shower has been observed for about 2000 years, with the first known information on these meteors coming from the Far East. In early Europe, the Perseids came to be known as the "tears of St. Lawrence."

The shower is visible from mid-July each year, with the greatest activity between August 8 and 14, peaking about August 12. During the peak, the rate of meteor reaches 60 or more per hour. They can be seen all across the sky, but because of the path of Swift-Tuttle's orbit, Perseid are mostly visible on the northern hemisphere.

To experience the shower in its full, one should observe in the dark of a clear moonless night, from a point far outside any large cities, where stars are not dimmed by light pollution. The Perseids have a broad peak, so the shower is visible for several nights. On any given night, activity starts slowly in the evening but picks up by 11 p.m., when the radiant gets reasonably high in the sky. The meteor rate increases steadily through the night as the radiant rises higher, peaking just before the sky starts to get light, roughly 1½ to 2 hours before sunrise.

The Perseid meteor shower peaks on the new-Moon night of Sunday–Monday, August 12August 13 and can be seen from any place in the northern hemisphere. The Perseid meteors appear to stream away from their radiant near the border of Perseus and Cassiopeia.

The meteor rate, for an observer at a dark-sky site in the northern temperate latitudes, increases to roughly 30 per hour in the predawn hours on Saturday, 45 per hour on Sunday morning, and 80 per hour before the sky starts to get light on Monday morning.

 

 

PERSEUS PURSUES PERSEUS

IDEAS

 

 

Perseus, Perseos, or Perseas (Greek: Περσεύς, Περσέως, Περσέας), the legendary founder of Mycenae and of the Perseid dynasty there, was the first of the ...
en.wikipedia.org/wiki/Perseus

The oracle fulfilled

[edit] King of Mycenae

The two main sources regarding the legendary life of Perseus—for he was an authentic historical figure to the Greeks— are Pausanias and Apollodorus, but from them we obtain mainly folk-etymology concerning the founding of Mycenae. Pausanias[17] asserts that the Greeks believed Perseus founded Mycenae. He mentions the shrine to Perseus that stood on the left-hand side of the road from Mycenae to Argos, and also a sacred fountain at Mycenae called Persea. Located outside the walls, this was perhaps the spring that filled the citadel's underground cistern. He states also that Atreus stored his treasures in an underground chamber there, which is why Heinrich Schliemann named the largest tholos tomb the Treasury of Atreus.

Apart from these more historical references, we have only folk-etymology: Perseus dropped his cap or found a mushroom (both named myces) at Mycenae, or perhaps the place was named from the lady Mycene, daughter of Inachus, mentioned in a now-missing poem, the great Eoeae.

For whatever reasons, perhaps as outposts, Perseusfortified Mycenae according to Apollodorus[18] along with Midea, an action that implies that they both previously existed. It is unlikely, however, that Apollodorus knew who walled in Mycenae; he was only conjecturing. In any case, Perseus took up official residence in Mycenae with Andromeda.

[edit] The Perseids

Perseus by Salvador Dalí

Perseus and Andromeda had seven sons: Perses, Alcaeus, Heleus, Mestor, Sthenelus, Electryon and Cynurus, and two daughters, Gorgophone ("Gorgon Killer") and Autochthoe ("Born in the Land"). Perses was left in Aethiopia and became an ancestor of the emperors of Persia. The other descendants ruled Mycenae from Electryon down to Eurystheus, after whom Atreus got the kingdom. However, the Perseids included the great hero, Heracles, son of Amphitryon, son of Alcaeus. The Heraclides, or descendants of Heracles, successfully contested the rule of the Atreids.

A statement by the Athenian orator, Isocrates[19] helps to date Perseus roughly. He said that Heracles was four generations later than Perseus, which corresponds to the legendary succession: Perseus, Electryon, Alcmena, and Heracles, who was a contemporary of Eurystheus. Atreus was one generation later, a total of five generations.

[edit] Etymology

Because of the obscurity of the name Perseus and the legendary character of its bearer, most etymologists pass it by, on the presumption that it might be pre-Greek. However, the name of Perseus’ native city was Greek and so were the names of his wife and relatives. There is some prospect that it descended into Greek from the Proto-Indo-European language. In that regard Robert Graves has espoused the only Greek derivation available.

Perseus might be from the ancient Greek verb, perthein, “to waste, ravage, sack, destroy”, some form of which appears in Homeric epithets. According to Carl Darling Buck (Comparative Grammar of Greek and Latin), the –eus suffix is typically used to form an agent noun, in this case from the aorist stem, pers-. Pers-eus therefore is a sacker of cities; that is, a soldier by occupation, a fitting name for the first Mycenaean warrior.

The origin of perth- is more obscure. J. B. Hofmann[20] lists the possible root as *bher-, from which Latin ferio, "strike". This corresponds to Julius Pokorny’s *bher-(3), “scrape, cut.” Ordinarily *bh- descends to Greek as ph-. This difficulty can be overcome by presuming a dissimilation from the –th– in perthein; that is, the Greeks preferred not to say *pherthein.

Graves carries the meaning still further, to the perse- in Persephone, goddess of death. John Chadwick in the second edition of Documents in Mycenaean Greek speculates as follows about the goddess pe-re-*82 of Pylos tablet Tn 316, tentatively reconstructed as *Preswa:

”It is tempting to see...the classical Perse...daughter of Oceanus...; whether it may be further identified with the first element of Persephone is only speculative.”

A Greek folk etymology connected the name of the Fars people, whom they called the Persai. The native name, however has always had an -a- in Iranian. Herodotus[21]recounts this story, devising a foreign son, Perses, from whom the Persians took the name. Apparently the Persians themselves[22] knew the story, as Xerxes tried to use it to suborn the Argives during his invasion of Greece.

Cyrus Gordon, known for his daring theories, proposed[23] that Perseus is a Semitic name, from p-r-s, "to cut." Nothing in the lore or the evidence excludes the possibility of Semitic elements among the early Greeks. The Greeks thought that Perseus meant "destroyer", but p-r-s would mean that as well.

[edit] Perseus on Pegasus

The replacement of Bellerophon as the tamer and rider of Pegasus by the more familiar culture hero Perseus was not simply an error of painters and poets of the Renaissance. The transition was a development of Classical times which became the standard image during the Middle Ages and has been adopted by the European poets of the Renaissance and later: Giovanni Boccaccio's Genealogia deorum gentilium libri (10.27) identifies Pegasus as the steed of Perseus, and Pierre Corneille places Perseus upon Pegasus in Andromède.[24]

 

[edit] Modern uses of the theme

 

[edit] Notes

  1. ^ Kerenyi 1959:45; see also Danaus.
  2. ^ In post-Renaissance paintings the setting is often a locked tower.
  3. ^ Eurymedon: "far-ruling"
  4. ^ For the familiar motif of the Exposed Child in the account of Moses especially, see Brevard S. Childs, "The Birth of Moses" Journal of Biblical Literature 84.2 (June 1965), pp 109-122, and Donald B. Redford, "The Literary Motif of the Exposed Child (Cf. Ex. ii 1-10)" Numen 14.3 (November 1967), pp 209-228. Another example of this mytheme is the Indian figure of Karna.
  5. ^ Such a banquet, to which each guest brings a gift, was an eranos. The name of Polydectes, "receiver of many", characterizes his role as intended host but is also a euphemism for the Lord of the Underworld, as in the Homeric Hymn to Demeter 9, 17.
  6. ^ Kerenyi 1959:48; Pausanias (viii.25.5): "When Demeter was wandering in search of her daughter, she was followed, it is said, by Poseidon, who lusted after her. So she turned, the story runs, into a mare, and grazed with the mares of Oncius; realizing that he was outwitted, Poseidon too changed into a stallion and enjoyed Demeter."
  7. ^ The sword of Perseus is an antique weapon, a harpe with a sickle-like extension to one side of the blade, for thrust and cut. See Canova's Perseus (illustration).
  8. ^ Ordinarily the helm of invisibility belonged to Hades.
  9. ^ For the Greeks, the tamer and first rider of Pegasus was Bellerophon.
  10. ^ 12.16.1
  11. ^ 2.4.4
  12. ^ Ovid, Metamorphoses, 5.177
  13. ^ loc. cit.
  14. ^ 2.15.4, 2.16.3-6, 2.18.1
  15. ^ 2.4.4, pros-teichisas, "walling in"
  16. ^ 4.07
  17. ^ Hofmann, Etymologisches Wörterbuch des Griechischen (Munich) !950.
  18. ^ Herodotus, vii.61
  19. ^ Herodotus vii.150
  20. ^ Forgotten Scripts, Basic Books, 1982, ISBN 0-465-02484-X, Chapter 7
  21. ^ George Burke Johnston "Jonson's 'Perseus upon Pegasus'" The Review of English Studies New Series, 6.21 (Jan., 1955), pp. 65-67.

[edit] References


 

Perseus (IPA: /ˈpəː(r)siəs, -sjuːs/) is a northern constellation, named after the Greek hero who slew the monster Medusa with the help of some godly items. ... en.wikipedia.org/wiki/Perseus_(constellation)

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Perseus
List of stars in Perseus
Abbreviation: Per
Genitive: Persei
Symbology: Perseus
Right ascension: 3 h
Declination: +45°
Area: 615 sq. deg. (24th)
Main stars: 6, 22
Bayer/Flamsteed stars: 63
Stars with planets: 2
Bright stars: 5
Nearby stars: 2
Brightest star: α Per (Mirfak) (1.79m)
Nearest star: ι Per (34.4 ly)
Messier objects: 2
Meteor showers: Perseids
September Perseids
Bordering constellations: Cassiopeia
Andromeda
Triangulum
Aries
Taurus
Auriga
Camelopardalis
Visible at latitudes between +90° and −35°
Best visible at 21:00 (9 p.m.) during the month of December
For other meanings, see Perseus (disambiguation)

Perseus (IPA: /ˈpəː(r)siəs, -sjuːs/) is a northern constellation, named after the Greek hero who slew the monster Medusa with the help of some godly items. It is one of Ptolemy's 48 constellations and was also adopted by the International Astronomical Union as one of the 88 modern constellations. It contains the famous variable star Algol (β Per), and is also the location of the radiant of the annual Perseids meteor shower.

[edit] Notable features

  • α Per (Mirfak): The brightest star of this constellation is also called Algenib (a name which is used for other stars as well, e. g. γ Peg). Mirfak (Arabic for elbow) is a supergiant of spectral type F5 Ib with an apparent brightness of 1.79m lying at a distance of ca. 590 light-years. Its luminosity is 5,000 times and its diameter is 62 times that of our Sun.
  • Algol (β Per): This may not be the brightest star of this constellation, but it definitely is its most famous star. Algol (from Arabic al-Ghul, which means The Ghoul or The Demon Star) represents the eye of the gorgon Medusa. This star is the prototype of a whole group of eclipsing variable stars. Its apparent brightness ranges between 2.12m and 3.39m with a period of merely 2.867 days. It is of spectral type B8 V and lies at a distance of only 93 ly.
  • Nova Persei 1901 (GK Per), a bright nova discovered on February 23, 1901.

[edit] Deep sky objects

  • h + χ Per: These two open clusters (NGC 869 and NGC 884 respectively) belong to the most beautiful objects of the night sky for binoculars and small telescopes. They are sometimes called the Double Cluster. Both lie at distances of more than 7,000 ly and are separated by several hundred light-years.
  • M34: This open cluster with an apparent brightness of 5.5m lies at a distance of approximately 1,400 ly and consists of about 100 stars that are scattered over an area larger than that of the full moon. Its true diameter is about 14 ly. M 34 can be resolved even with good binoculars but is best viewed using a telescope at low magnifications.
  • M76: This planetary nebula is also called Little Dumbbell Nebula. It measures about 65 arc seconds and has an apparent brightness of 10.1m.
  • NGC 1499: Also called California Nebula this emission nebula, discovered in 1884-85 by the American astronomer Edward E. Barnard, is a great target for astrophotographers. Due to its low surface brightness it's a very difficult object when observed visually.
  • NGC 1333 is a reflection nebula and the location of star formation.
  • NGC 1260 contains the brightest known object in the universe, SN 2006gy.

[edit] Graphic visualization

The stars of the constellation Perseus can be connected in an alternative way.

Perseus' body is formed by the stars β Per, κ Per, ι Per, α Per, σ Per, ν Per, and ε Per. α Per and β Per are of the second magnitude. The star ε Per is of the third magnitude.

The stars α Per, γ Per, τ Per, and ι Per form Perseus' head: gamma Persei is of the third magnitude. Stars γ Per, η Per, and τ Per form Perseus' cap.

The stars α Per, ψ Per, δ Per, 48 Per, μ Per, and λ Per form Perseus' left arm and hand: δ Per being of the third magnitude.

The stars ι Per, θ Per, and φ Per form the right arm and hand. Perseus' right hand, φ Per, is yanking at one of Andromeda's feet (51 Andromedae), intent on liberating her. (After liberating her, he marries her.)

Stars ε Per, ξ Per, ζ Per, and ο Per form Perseus' left leg and foot: ζ Per being of the third magnitude.

Finally, stars β Per, ρ Per, and π Per form Perseus' right leg and foot.

[edit] References

  • H. A. Rey, The Stars — A New Way To See Them. Enlarged World-Wide Edition. Houghton Mifflin, Boston, 1997. ISBN 0-395-24830-2.
  • Ian Ridpath and Wil Tirion (2007). Collins Stars and Planets Guide, HarperCollins, London. ISBN 978-0007251209.

 

 

ISAIAH

C 7 V 14

"Therefore the lord shall give you a sign: Behold a virgin shall concieve and bear a son and shall call him Imannuel" 

IMMANUEL

THE WORD IMMANUEL REDUCES VIA THE MAGIKALALPHABETZ SYMBOLIC INTERCHANGE

INTO 88 (first change)VIA 34 (second change)TO ITS ROOT NUMBER OF SEVEN

THE WORD

 SAINT

TRANSCRIBED INTO NUMBER, REDUCES VIA ITS NUMERICAL PLACING IN

THE

MAGICALALPHABET 

 FIRSTLY INTO NUMBER

63

AFTER ITS SECOND METAMORHIC CLARIFICATION IT BECOMES

18

EIGHTEEN

 ADD TO REDUCE REDUCE TO DEDUCE

1 + 8 OR 8 + 1

MERGING UNTO EACH OTHER IN LOVING EMBRACE

BIRTHS

 THE WHOLLY HOLY NUMBER

 9

 LADIES AND GENTLEMEN FELLOW BEINGS ALL

 9

DRAW YOUR ESTEEMED ATTENTION TO THE BLESSED VIRTUES OF THE ONE AND ONLY NUMBER

 9

THE UPSIDE DOWN OF THE DOWNSIDE UP

SIX XIS

ZION = NOIZ

HINOSXZ ZXSONIH

ON BEHALF OF ALL GODS CREATION
 
 
 

THE

MAGICALALPHABET

FORMED FROM THE ENGLISH ALPHABET OF CAPITAL LETTERS

 
ABCDEFGHIJKLMNOPQRSTUVWXYZ
123456789,123456789,12345678
 
 
ADD TO REDUCE REDUCE TO DEDUCE
 
I = 9 R = 18 and 1 + 8 = 9
 

THE

MAGICALALPHABET ROOT NUMBER

OF

I

 
 
I numerical placed at 9 added to R numerical placed at 18 transposes initially to 27 which reduces via
2 + 7 to the numerical root balance of 9

 

THE TOTAL NUMERICAL VALUE OF THE ENGLISH ALPHABET
=
351
3 + 5 + 1
9
 
A+B+C+D+E+F+G+H+I+J+K+L+M+N+O+P+Q+R+S+T+U+V+W+X+Y+Z
First Total = 351and 3+5+1 = 9
 
Second Total = 1+2+3+4+5+6+7+8+9+1+2+3+4+5+6+7+8+9+1+2+3+4+5+6+7+8
second total 126 and 1+2+6 = 9
 
THE
BLESSED
9
 

 

 

THE INITIAL TRANSPOSED NUMERICAL VALUE OF THE LETTERS

ALBERT EINSTEIN

ISISIS

153

1 + 5 + 3 = 9

THINK 153 FISHES

 

 

THE INITIAL TRANSPOSED NUMERICAL VALUE OF THE LETTERS

GENERAL THEORY OF RELATIVITY

ISISIS

351

3 + 5 + 1 = 9

 THE BLESSED WHOLLY HOLY

NUMBER

9

I

ISISIS

9

ME

ISISIS

9

I AM ME ME AM I

9 AM 9 9 AM 9

 

 

 

To simulate, Baudrillard says initially, is to pretend to have what one has not. He compares previous notions of extreme simulation with a Borges' story in ... www.hku.hk/english/courses2000/7006/introbau.htm

SUMMARY

Jean Baudrillard. "Simulacra and Simulations", in Jean Baudrillard: Selected Writings. ed. Mark Poster, Polity Blackwell, 1988.pp.166-184

To simulate, Baudrillard says initially, is to pretend to have what one has not. He compares previous notions of extreme simulation with a Borges' story in which the conceptual (a map) exactly replicates the original (real territory). Today, however, we have simulacra - 'the generation by models of a real without origin or reality: a hyperreal.' Baudrillard posits the end of metaphysics, of questions of imitation or reduplication of the 'real', and the start of "substituting signs of the real for the real itself". To simulate, in fact, implies more than just 'pretending'. It produces the same symptoms/signs/images as the 'real' and so operates on a different level from the 'false' or the 'true'. Baudrillard makes a comparison with a religion in which there are only icons or images of a non-existent God

Subsequently, Baudrillard argues that there are four phases of the image: one that reflects a basic reality; one that masks or perverts a basic reality; one that masks the absence of a basic reality; and one that bears no relation to any reality (is its own pure simulacrum). He then discusses these phases, and particularly the fourth, in relation to Disneyland and Watergate. As a development of this, one of Baudrillard's most famous and provocative claims is that "Illusion is no longer possible." He gives the example of a bank raid and argues that the apparatus at a Western bank is so geared towards reading the signs of a 'real' bank raid that it would be impossible to simulate one: the established order 'devours' attempts at simulation. This is because simulation is threatening (especially of categories like truth and falsehood, certainty and uncertainty, good and evil). "Whence the characteristic hysteria of our time: the hysteria of production and reproduction of the real."

Botticelli, then at the height of his career, plays the role of an “anti-Protogenes” whose views .... to explain why Leonardo's advice to painters, even ... etext.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv1-47

CHANCE IMAGES

Strictly speaking, an image made by chance is an absurdity. Explicit, fully articulated images, our experience tells us, must be the result of purposeful activity, which is the very opposite of chance in the sense of mere randomness. The dilemma can be resolved either by (1) attributing a hidden purpose to chance, which thus becomes an agency of the divine will personified under such names as Fate, Fortune, or Nature; or by (2) acknowledging that chance images are in fact rudimentary and ambiguous, and are made explicit only in the beholder's imagination. The former view, characteristic of prescientific cultures, is akin to all the beliefs based on the “ominous” meaning of flights of birds, heavenly constellations, the entrails of sacrificial animals, and countless other similar phenomena. It was prevalent until the Renaissance and has not entirely lost its appeal even today. The latter view, although
adumbrated in classical antiquity, found adequate expression for the first time in fifteenth-century Italy; it has been adopted and verified by modern scientific psychologists who made it the basis of projective tests such as the ink blot series named after Hermann
Rorschach. Both views, however incompatible, are strongly linked with past and present ideas concerning the nature of artistic activity, in theory as well as in practice.

I

Classical antiquity seems to have confined its attention to chance images of three kinds: those in rocks, blots, and clouds. For the first two, our earliest source is Pliny's Natural History, although his references to these phenomena are clearly derived from Greek
(probably Hellenistic) literature. He tells of an image of Silenus found inside a block of Parian marble that had been split open with wedges (XXXVI, v) and of “the agate of Pyrrhus on which could be seen Apollo with his lyre and the nine muses, each with her proper attribute, rendered not by art but by nature, through the pattern of the spots” (XXXVII, i). The context from Page 341,
Volume 1 which Pliny lifted these passages cannot be reconstructed; the images, absurdly perfect down to the last iconographic detail, are apparently cited as evidence of the miraculous generative powers of Nature, superior to any man-made artifact. Somewht more illuminating is Pliny's story about a panting dog in a picture by the famous Hellenistic painter Protogenes (XXXV, x). The artist tried in vain to represent the foam issuing from the mouth of the animal until, in a rage, he hurled a sponge at his panel and thereby achieved the desired result. This dog, Pliny states, “was wondrously made,” since the natural effect was the work of fortuna. The same story, he informs us, is told of another famous painter, Nealces, with a horse taking the place of the dog. A variant of the latter version, substituting Apelles for Nealces, occurs in the sixty-fourth oration of Dio Chrysostom, which deals with the workings of fortuna. Here again the chance image is so perfect as to surpass any human intention. The inference to be drawn from the sponge story, it would seem, is that Fortune reserves such “strokes of luck” only for the greatest of artists, as if on occasion she took pity on their ambition to achieve the impossible.It must have been these accounts of incredibly perfect chance images that provoked the following skeptical rejoinder from Cicero: Pigments flung blindly at a panel might conceivably form themselves into the lineaments of a human face, but do you think the loveliness of the Venus of Cos could emerge from paints hurled at random?... Carneades used to tell that once, in the quarries of Chios, a stone was split open and the head of a little Pan appeared; well, the bust may not have been unlike the god, but we may be sure that it was not so perfect a reproduction as to lead one to imagine that it had been wrought by Scopas, for it goes without saying that perfection has never been achieved by accident (De divinatione I, xiii).

This early hint at the rationalist explanation of chance images corresponds to the classicistic taste that dominated Roman art of the late Republic and the Augustan era (note the references to classic Greek masters). The story of the sponge-throwing painter, in contrast, reflects an admiration for spontaneity, for inspired groping by a great individual as against an impersonal ideal of perfection. If fortuna favors only artists of the stature of Protogenes, Nealces, or Apelles, is she not just another name for genius? Such an unclassical (one is tempted to call it romantic) attitude seems to have existed in Hellenistic art, although it cannot be documented from surviving examples. An echo of it may be found in another passage of Pliny's Natural History (XXXV, cxlv) that speaks of painters whose unfinished pictures were sometimes even more admirable than their completed work, because they still showed the lines of the original sketch and thus revealed the working of the artist's mind. The agate of Pyrrhus, too, although obviously myth ical, has a bearing on artistic practice. Greeks and Romans greatly admired carved gems of varicolored semiprecious stones, as attested by the large number of preserved specimens. In many of these, the design takes advantage of, and may indeed have been suggested by, the striations of the material. Thus the value of a gem stone was probably measured by its potential in this respect even more than by its rarity, and those that lent themselves particularly well to carving would have been looked upon as miraculous “images made (or at least preshaped) by Nature.” How far human skill has been “aided by Nature” in any given case is of course difficult to assess after the carving is finished, although certain gems indicate that the artist wanted to suggest that such aid had been considerable. The ancient marble sculptor's interest in chance effects, suggested by the tales of images found in cracked blocks, is even harder to verify. One wide-spread feature of later Greek and Roman decoration, the foliage mask, may have originated in this way. Ladendorf has proposed that it developed from the acanthus ornament crowning Attic grave steles, which sometimes tends to assume the appearance of a human face. This physiognomic effect is so unobtrusive that, in the beginning at least, it could hardly have been intentional. A stele (an up right stone slab or pillar) evokes the image of a standing figure, and its upper terminus thus may be viewed as its “head.” Perhaps this notion was unconsciously present in the carver's mind. In any event he must have become aware at some point of the face hidden among the foliage, and from then on the effect was exploited quite explicitly. The foliage mask, then, could be termed an “institutionalized chance image.” Figures that are seen in clouds are noted by Aristotle (Meteorology I, ii) and briefly mentioned in Pliny's Natural History (II, lxi) and other ancient authors. Because of their instability and remoteness, however, they were not given the significance of the miraculous images made by Nature or Fortune in rocks and blots, and their origin rarely excited speculation. An excep tion is Lucretius (De rerum natura IV, 129ff.), who found them a challenge to his theory that all images are material films given off by objects somewhat in the manner of snakes shedding their outer skin. Since cloud figures are unstable, there cannot be any objects from which these image films emanate; Lucretius therefore postulates the spontaneous generation of such films in the upper air—an ingenious but hardly persuasive solution. By far the most interesting analysis of the phenomenon, linking it for the first time with the / Page 342, Volume 1 process of artistic creation, occurs in a memorable dialogue in Philostratus' Apollonius of Tyana (II, 22). Apollonius and his interlocutor, Damis, agree that the painter's purpose is to make exact likenesses of everything under the sun; and that these images are make- believe, since the picture consists in fact of nothing but pigments. They further agree that the images seen in clouds are make-believe, too. But, Apollonius asks, must we then assume that God is an artist, who amuses himself by drawing these figures? And he concludes that those configurations are produced at random, without any divine significance; it is man, through his natural gift of make-believe, that gives them regular shape and existence. This gift of make-believe (i.e., imagination) is the common property of all. What distinguishes the artist from the layman is his ability to reproduce his mental images in material form. To Philostratus the difference between cloud figures and painted images would thus seem to be one of degree only: the artist projects images into the pigments on his panel the way all of us project images into the random shapes of clouds, but he articulates them more clearly because of his manual skill. Although this view clearly reflects the growing ascendency of fantasia over mimesis—of imagination over imitation—that had been asserting itself in the attitude of the ancients toward the visual arts ever since Hellenistic times, it retains the traditional conception of painting and sculpture as crafts or “mechanical arts” as against the “liberal arts.” That the artist might be distinguished from the nonartist by the quality of his imagination rather than by his manual training did not occur to Philostratus. If it had, he would have anticipated an achievement of the Renaissance by more than a thousand years. Nor did ancient painters think of the pigments on their panels as a “hunting ground” for images analogous to clouds; they seem, in fact, to have been repelled by clouds—the skies in ancient landscapes are devoid of them, and even where the subject requires them (as in The Sacrifice of Iphigenia, Naples) they appear as the merest wisps. This aversion was clearly a matter of aesthetics, not of disability. Ancient painters commanded all the illusionistic techniques for rendering clouds, and bequeathed them to Early Christian art, where clouds are conspicuous.

II

The Middle Ages inherited most of the classical accounts of chance images, but did not respond to all of the three types discussed above. The “lucky blot,” known from Pliny's story of Protogenes, seems to have evoked neither repetition nor comment. References to cloud figures occur as a rhetorical device in theological writings, stressing their instability and lack of substance, as when Anselm of Canterbury (Cur Deus homo, ed. F. S. Schmitt, Darmstadt [1960], p. 16) compares certain fallacious arguments to “figments painted on clouds” (perhaps indirectly echoing Philostratus); Michael Psellus, in a similar vein, says that demons Page 343, Volume 1 can change their appearance as easily as the ever changing configurations of clouds, which may resemble the shape of men, bears, dragons, etc. Albertus Magnus seems to have been the only one to attribute material substance to cloud figures, although his explanation differs from that of Lucretius: exhalations from the earth, he claims, if aided by heavenly constellations, can form in the clouds perfect though lifeless animal bodies, which may actually drop from the sky (On Meteors, III, iii, 23, citing Avicenna). Elsewhere he also records the chance images inside locks of marble, stressing their miraculous characters; he even reports that he himself once saw the head of a bearded king on the cut surfaces of such a block that had just been sawed in two (On Minerals, II, iii, 1); all who witnessed the event agreed that Nature had painted this image on the stone. Both of these accounts of “natural miracles” were given popular currency toward the end of the Middle Ages by Franciscus de Retza, who cited the animal body dropping from the ky as well as the head in the marble as arguments for the Immaculate Conception in his Defensorium in- violatae virginitatis Mariae (ca. 1400). The scenes were even illustrated in an early printed edition.By far the most widespread chance images, however, were those of the “agate-of-Pyrrhus” type. The ancients' love of gems continued undiminished throughout the Middle Ages; indeed, these stones were the only artistic relics of the pagan past to enjoy continuous and unquestioned appreciation. Thousands of them were incorporated in medieval reliquaries and other sacred objects, regardless of their pagan subject matter, and reports of chance images recur in treatises on mineralogy from the lapidary of Marbod of Rennes to Ulisse Aldrovandi and Athanasius Kircher. (The accounts of these pierres imagées have been collected and analyzed by Baltrušaitis.) Their effect on artistic practice, however, is difficult to measure. One clear-cut—and so far unique—instance was discovered by Ladendorf: the tiny faces hidden among the striations of the multicolored marble columns on the canon table pages of the Gospel Book from Saint Médard, Soissons. The artist who painted these columns in the early years of Charlemagne's reign may have seen such faces in early Christian manuscripts, or he could have “discovered” them in his own brushwork while he was at work. In either case, his intention must have been to characterize the material of these columns as miraculous and uniquely precious—and hence worthy to frame the words of the Lord. A certain propensity toward chance images seems to have existed throughout medieval art, even though the subject is far from fully explored. Thus, in the Nativity scene of an early Gothic German Psalter, there are no less than three faces on the ground in the immediate vicinity of Saint Joseph. The one farthest to the left appears to have been developed from a piece of drapery; the other two fill interstices be tween clumps of plants. Perhaps the most plausible explanation for them is that the artist “found” (i.e., / Page 344, Volume 1 projected) them in the process of copying an older miniature whose stylistic conventions he did not fully understand. His readiness to interpret unfamiliar details physiognomically suggests that he knew the “institutionalized chance image” of the foliage mask, which had been revived at least as early as the twelfth century and was well-established in the repertory of Gothic art. Since these masks sometimes carry in scriptions identifying them as images of pagan nature spirits or demons, the faces in our Nativity may have been intended to evoke the sinister forces overcome by the Savior.That Gothic art continued to be receptive to chance images even in its final, realistic phase is strikingly shown by the Hours of Catherine of Cleves, a Nether landish manuscript of ca. 1435-40 distinguished for its elaborate painted borders. One of these consists of butterflies, rendered with painstaking attention to the colorful patterns of their wings. Among them is a butterfly whose wing pattern resembles a cavernous human face, like that of a decaying corpse come back to life. There can be no question that the effect is intentional, yet it could hardly have been planned from the start; in all likelihood the artist became aware of it only in the process of ainting, and then chose to elaborate upon it so that the beholder could share his experience. What made him do so, we may assume, was not only an interest in chance images (there is evidence of this on other pages of the same manuscript) but the role of the butterfly as a symbol of vanitas, which associated it with death. Despite such links with orthodox iconography, there is a strong element of playfulness in medieval chance images. The purest instance of this is a drawing of 1493 by the young Albrecht Dürer, one side of which shows a self-portrait, a sketch of his left hand, and a pillow, / Page 345, Volume 1 / while six more pillows appear on the other side (Figure 8). Ladendorf was the first to recognize the purpose of these pillows: a search for faces hidden among the folds. Most easily recognizable is the one in the lower left-hand corner—a bearded Turk with a huge turban. Turning the sheet upside down, we also discover that the pillow in the upper left-hand corner contains the craggy face of a man wearing a pointed hat. Since these are the only image-bearing pillows we know of in the history of art, Dürer presumably discovered their physiognomic potential by accident, perhaps while sketching a pillow in preparation of a print or a painting. What enabled him to play this game, however, must have been a familiarity with chance images in other, more traditional materials such as stone. He might indeed have looked upon his pillows as “malleable rocks” from which such images could be elicited by manipulation. Yet he seems to have kept his discovery to himself, so that the pillow-faces never be-came “institutionalized.”

III

The Renaissance phase in the history of our subject begins with the opening sentences of Leone Battista Alberti's treatise De statua, written about 1430. Here the origin of sculpture is described as follows Those [who were inclined to express and represent... the bodies brought forth by nature] would at times observe in tree runks, clumps of earth, or other objects of this sort certain lineaments which through some slight changes could be made to resemble a natural shape. They thereupon took thought and tried, by adding or taking away here and there, to render the resemblance completeBefore long, Alberti adds, the primeval sculptors learned how to make images without depending on such resemblances latent in their raw material. This passage is the earliest statement of the idea that what sets the artist apart from the layman is not his manual skill but his ability to discover images in random shapes, i.e., his visual imagination, which in turn gives rise to the desire to make these images more explicit by adding or taking away. How did Alberti arrive at this astonishing insight? Classical art theory provides no etiology of sculpture, and its etiology of painting is purely mimetic: the first artist traced a shadow cast by the sun. Moreover, in contrast to the agate of Pyrrhus and the heads supposedly discovered in cracked blocks of marble, the chance images in Alberti's tree trunks and clumps of earth are rudimentary rather than miraculously complete. Perhaps the key to the puzzle is the fact that Alberti postulates wood and clay, not stone or marble, as the sculptor's aboriginal materials. If he started out by wondering what the earliest statues were made of, he could have found an answer in Pliny (XII, i), who concludes a discussion of the central importance of trees in the development of religious practices by stating that the statues of the gods, too, used to be ex arbore. In view of the anthropomorphic shape of certain trees, reflected in such myths as that of Daphne turned into a laurel, this must have seemed plausible enough. Another early work of Alberti, the dialogue Virtus et Mercurius, has Virtus complaining of persist ent abuse at the hands of Fortuna: “While I am thus despised, I would rather be any tree trunk than a goddess,” a notion suggestive both of the Plinian tree deities and of the tree trunks in De statua. This “trunkated” Virtue-in-distress was translated into visual terms by Andrea Mantegna, whose image of her might almost serve as an illustration of the Destatua text. It also resembles actual idols such as the pair of tree-trunk deities carved by a Teutonic contemporary of Pliny and recently unearthed in a bog near the German-Danish border. Like many another explorer of new territory, Alberti did not grasp the full significance of what he had / Page 346, Volume 1 / discovered. His chance-image theory is subject to two severe limitations: it applies to sculpture only, and to the remote past rather than to present artistic practice. In his treatise on painting, written a few years after De statua, he merely cites the ancient shadow-tracing theory but adds that “it is of small importance to know the earliest painters or the inventors of painting.” When he mentions the chance images in cracked blocks of marble and on the gem of Pyrrhus recorded by Pliny, he does so in order to fortify his claim that painting is a noble and “liberal” activity, since “nature herself seems to take delight in painting.” He also explicitly denies that painting is comparable to the kind of sculpture “done by addition,” even though the painter works by adding pigments to a bare surface. This puzzling gulf that existed in Alberti's mind between the two arts reflects the singular importance he attached to scientific perspective as the governing theory of painting. His treatise focuses on painting as a rational method of epresenting the visible world, rather than as a physical process, and hence leaves little room for the chance-image etiology he had proposed in De statua. We do not know who first applied it to painting and to present-day conditions. The earliest explicit statement occurs in the writings of Leonardo, but the passage strongly suggests that he learned it from older artists: If one does not like landscape, he esteems it a matter of brief and simple investigation, as when our Botticelli said that such study was vain, because by merely throwing a sponge full of diverse colors at a wall, it left a stain... where a fine landscape was seen. It is really true that various inventions are seen in such a stain.... But although those stains give you inventions they will not teach you to finish any detail. This painter of whom I have spoken makes very dull landscapes (Leonardo's Treatise on Painting, ed. and trans. Philip McMahon, Princeton [1956], I, 59) Apparently Leonardo here records an experience he had about 1480, shortly before his departure for Milan; Botticelli, then at the height of his career, plays the role of an “anti-Protogenes” whose views Leonardo turns to his own advantage. In another passage, Leonardo recommends that painters look for landscapes as well as figure compositions in the accidental patterns of stained walls, varicolored stones, clouds, mud, or similar things, which he compares to “the sound of bells, in whose pealing you can find every name and word you can imagine.” The spotted walls, clouds, etc., here obviously play the same role as the tree trunks and clumps of earth in De statua. Leonardo, moreover, states more clearly than Alberti does that chance images are not objectively present but must be projected into the material by the artist's imagination. While he presents his idea as “a new discovery,” there can be little doubt that he did in fact derive it from Alberti, whose writings are known to have influenced his thinking in a good many instances. That Leonardo should have transferred the chance-image theory from the remote past to the present and from sculpture to painting is hardly a surprise in view of his lack of interest in historical perspectives and his deprecatory attitude toward sculpture. At the same time, the reference to Botticelli (whose remark may well have been aimed at Leonardo himself) suggests that there was some awareness among early Renaissance painters of the role of chance effects in actual artistic practice before Leonardo formulated his chance-image theory of pictorial invention.That such was indeed the case may be gathered from some visual evidence which in point of time stands midway between Alberti's De statua and “Botticelli's stain.” Interestingly enough, these are images in clouds, rather than in the more palpable substances that had yielded chance images in medieval art, thus indicating a new awareness of the unstable and subjective character of chance images. The best-known instance is the tiny horseman in Mantegna's Saint Sebastian in Vienna, which has resisted all efforts to explain / Page 347, Volume 1 / it in terms of the overt subject matter of the panel. Not only is the image so unobtrusive that most viewers remain unaware of it; it is also incomplete, the hind quarters of the horse having been omitted so as not to break the soft contour of the cloud. Did Mantegna plan it from the very start, or did he discover the horseman only in the process of painting that particular cloud and then, like the primeval sculptors of De statua, added or took away a bit here and there in order to emphasize the esemblance? Be that as it may, we can only conclude that he must have been taken with the idea of cloud images, and that he expected his patron, too, to appreciate the downy horseman. This patron would seem to have been a passionate admirer of classical antiquity, for the panel is exceptionally rich in antiquarian detail; the artist even signed it in Greek. Apparently the horseman is yet another antiquarian detail, a visual pun legitimized by the discussion of cloud images in Greek and Roman litera ture. It has been kept “semi-private” so as not to offend less sophisticated beholders. If this view is correct, the horseman need have no connection at all with the chance images of Alberti, even though Mantegna must have been well acquainted with Alberti's writings We know rather less about a second cloud image, contemporary with Mantegna's horseman, that occurs in the Birth of the Virgin by the Master of the Barberini Panels. Here a cloud assumes the shape of a dolphin A possible clue to its meaning is the flight of birds next to it, which may be interpreted as a good omen for the newborn child according to Roman belief. Since the scene takes place in a setting filled with references to pagan antiquity, an “auspicious” flight of birds would be in keeping with the rest; and the cloud-dolphin would then be a further good omen (dolphins having strongly positive symbolic connotations), whether the image was planned or accidentally discovered. Flights of birds as a means of divination are mentioned so frequently in Roman literature that they must have been well-known among fifteenth century humanists.These early cloud images, however small and unobtrusive, are the ancestors of a wide variety of figures made of clouds in sixteenth-century painting. Mantegna himself institutionalized the technique in his late work (Minerva Expelling the Vices from the Grove of Virtue, 1501-02, Paris, Louvre), Raphael introduced cloud-angels in his Madonna of Foligno and Sistine Madonna, and Correggio depicted the amorous Jupiter as a cloud in his Io. Even the human soul, hitherto shown as a small figure with all the substance of living flesh, could now be given a cloudy, “ectoplasmic” shape, as in El Greco's Burial of Count Orgaz. What began as a semi-private visual pun had become a generally accepted pictorial device for representing incorporeal beings. It would be fascinating to know whether Leonardo practiced what he preached. If he did, no evidence of chance images derived from spotted walls or similar sources has survived among his known works. A Madonna and Saints by one of his Milanese followers indicates that Leonardo's advocacy of chance images was not confined to the theoretical plane. The group is posed against an architectural ruin among whose / Page 348, Volume 1crumbling stones we discern the face of a bearded man wearing a broad-brimmed hat. Evidently the artist, alerted by Leonardo's teachings, felt that no ancient wall surface was complete without a chance image. The influence of Leonardo's chance-image the-ory can be seen also in the work of the Florentine painter Piero di Cosimo, who according to Vasari was in the habit of staring at clouds and spotted walls, “imagining that he saw there equestrian combats and the most fantastic cities and the grandest landscapes.” Some of Piero's pictures show extravagantly shaped willow trees with pronounced chance-image features but based on a close study of actual trees, which he must have gone out of his way to find. Finally, Leonardo's discussion of chance images may have inspired a curious pictorial specialty that flourished, Volume 1mainly in Florence from the late sixteenth to the eighteenth century. These paintings are done on the polished surfaces of agates or other strongly patterned stones in such a way that the colored veins become part of the composition, providing “natural” back grounds of clouds, landscape, etc., for the figures. They were prized as marvels of nature no less than of art (a description cited by Baltrušaitis terms them “an interplay of ars and natura”) and tended to accumulate in the cabinets of royalty. Linked with the legendary gem of Pyrrhus, they might be defined as elaborated chance images were it not for the fact that the painter's share always remains clearly distinguishable from nature's. Apparently a real merging of the two spheres was deemed aesthetically undesirable. Despite his interest in unorthodox techniques—confirmed by recent studies which show that he often painted not only with brushes but with his fingers—Leonardo did not favor homemade chance images such as “Botticelli's stain.” Nor does he reveal how the images found in spotted walls, etc., are to be transformed into works of art. Apparently he thought of this process as taking place in the artist's mind, rather than on the surface of the painting, where the task of “finishing the detail” would be impeded by the inherent vagueness of images resulting from thrown sponges. His ideal of objective precision, inherited from the early Renaissance, gave way in sixteenth-century art theory to values more attuned to the concept of genius. Among them was sprezzatura, a recklessness mirroring inspired frenzy at the expense of rational control, which meant a disregard of accepted usage in literature and a rough, unfinished look in the visual arts. The story of the sponge-throwing Protogenes could now provide a supreme example of such recklessness, as it does for Montaigne (Essays, I, xxiv, xxxiv), who cites it to illustrate the close relationship between chance (good luck, fortuna) and inspiration

IV

The chance images discussed so far all have one feature in common—the artist finds them, or pretends to find them, among the random shapes of the outside world. He does not create them but merely discovers them and “makes the resemblance omplete” while leaving the identity of the matrix (stone, foliage, pillows, clouds, etc.) untouched. This limitation may help to explain why Leonardo's advice to painters, even though enshrined in the text of his Treatise on Painting, had little practical effect until the dawn of the modern era. At that time it was suddenly revived, with appropriate modifications, by the British landscape painter and drawing teacher Alexander Cozens, who in 1785-86 published an illustrated treatise entitled A New Method of Assisting the Invention in Drawing Original Compositions of Landscape. It describes “a mechanical method... to draw forth the ideas” of artists, which consists of making casual and largely accidental ink blots on paper with a brush, to serve as a store of compositional suggestions.Cozens recommends that these blots be made quickly and in quantity, and that the paper be first crumpled up in the hand and then stretched out again. The next step is to select a particularly suggestive sheet of blots, place a piece of transparent paper over it and make a selective tracing; the author cautions us to “preserve the spirit of the blot” by not adding anything that is not suggested by it. The drawing is then finished by adding ink washes.Cozens cites Leonardo's words about the images to be seen on dirty walls, etc., but adds proudly that he thinks his procedure an improvement, since it permits the artist to produce his chance images at will, without having to seek them out in the world of nature. Oddly enough, he fails to quote the Leonardo passage dealing / Page 350, Volume 1 / with “Botticelli's stain,” which anticipates his own procedure so closely that one wonders if he was really ignorant of it. The ink blots of Cozens' Method, how ever, are not meant to be entirely ccidental; he defines them as “a production of chance, with a small degree of design,” since the artist is expected to think of a landscape subject in general terms while producing them. His own sample of such a “blotscape” is clearly a work of art, displaying a highly individual graphic rhythm. Its purpose, he makes clear, is to free the artist from involuntary servitude to conventional schemes of landscape composition by making him relinquish deliberate control of his movements as much as possible in the beginning; the selective tracing of the blots is intended to redress the balance.To his contemporaries, on the other hand, Cozens' blots seemed sheer chaos, and an occasion for endless ridicule. Neo-classic taste was so opposed to the ideas implicit in the Method that it rejected even the hallowed story of Protogenes. In a critique of the pictures shown at the Paris Salon of 1783 (Le Triumvirat des arts, ou dialogue entre un peintre, un musicien et un poète, published anonymously as a pamphlet) the poet ridicules one painting by pronouncing it a masterpiece à la manière de Protogène. Henry Fuseli notes that “many beauties in art come by accident that are preserved by choice,” but is quick to add that these have nothing in common with the sponge of Protogenes or “the modern experiments of extracting compositions from an ink-splashed wall,” an obvious reference to Cozens (Aphorism 153). Yet Cozens' very notoriety kept his Method from being forgotten. Its liberating effect on Constable and Turner, the great Romantic landscape painters of the early nineteenth century, must have been profound.That Cozens anticipated a general trend toward free, spontaneous brushwork transcribing the artist's creative impulse more directly than before, is amusingly attested by a French cartoon of 1844 which shows the Romantic painters, with Delacroix in the foreground, as simian virtuosos who do not even bother to look at their canvases while they paint. The Method also seems to be the ancestor of the Rorschach ink-blot test. A parlor game based on it enjoyed a certain vogue in England and may have helped to popularize it on the Continent, especially among amateurs. Elaborated blots are to be found in the drawings of Victor Hugo, and in the 1850's the German physician and poet Justinus Kerner produced Klecksographien, ink blots on folded paper which he modified slightly to emphasize the chance images he had found in them (Figure 19). He wrote little descriptive poems based on these images and collected this material in his Hadesbuch, which remained unpublished until 1890. The belated / Page 351, Volume 1 / rediscovery of Kerner's Klecksographien makes it likely that they were known to Hermann Rorschach, who used the same folded-paper technique for his tests but substituted oral for graphic interpretation of images Meanwhile, Alberti's hypothesis about the origin of sculpture was also being put to the test. In the 1840's Boucher de Perthes, one of the pioneer students of Paleolithic artifacts, collected large numbers of oddly shaped flint nodules which he claimed had been treasured by the men of the Old Stone Age because of their accidental resemblance to animal forms. As evidence he adduced what he regarded as efforts by these primeval sculptors to modify the shape of these “figure stones” so as to make the likeness more palpable. His discovery caught the imagination of other students of “antediluvian antiquity,” and figure stones soon turned up in England as well, while the skeptics denounced Boucher de Perthes and his followers as self-deluded or fraudulent. The skeptics eventually won out, but the issue may never be fully resolved; after all, the men of the Old Stone Age might have prized
these nodules for their image-bearing quality even if there is no proof that they modified their shapes.Nor was the controversy useless, for it probably alerted students of the Paleolithic to the existence of modified chance images in the cave art of Spain and the Dordogne, which was discovered a few decades later. The aesthetic attitude of the Romantics not only favored impulsiveness at the expense of rational control; it also undermined the classic view that “painting is mute poetry” by enthroning music as the highest of the arts. To those who espoused this belief, the subject of a picture was little more than a peg on which to hang attractive combinations of form and color. Their most articulate spokesman, James Whistler, began in the early 1860's to call his works “symphonies,” “harmonies,” “nocturnes,” or “arrangements,” in order to stress his convinction that descriptive values in painting are as secondary as they are in music; the subject proper was mentioned only as a subtitle, for the benefit of the ignorant ublic.Whistler's attitude toward chance effects, far more radical than Cozens', became a matter of public record during his famous libel suit against John Ruskin, who had charged him with “flinging a pot of paint in the public's face.” In painting a Nocturne, Whistler stated, “I have... meant to indicate an artistic interest alone ..., divesting the picture from any outside sort of interest which might have been otherwise attached to it. It is an arrangement of line, form and colour first, and I make use of any incident of it which shall bring about a symmetrical result.” By “incident,” he clearly meant accidental, unforeseen effects, and “symmetrical” to him was a synonym for “harmonious.” Some of Whistler's works are indeed so divested of “outside interest” that without the aid of the subtitle we would be hard put to recognize the subject. How much accident went into the painting of them is impossible to say, for we are approaching the point where chance and intention become inseparable.Unlike Cozens, who still wanted his blots to yield recognizable images, Whistler solicits chance effects /Page 352, Volume 1 / for the sake of “symmetry”; representation, taken for granted as the aim of art from the beginning of time, is about to give way to a new primary reality, that of the brush stroke itself, and when this happens we lose the frame of reference that enables us to differentiate between accident and purpose. The nonfigurative art of the twentieth century is strikingly forecast in Whistler's thinking (and to a lesser extent his practice) The retreat from likeness that began with Impressionism would seem to leave no room for the concept of images made by chance. Not surprisingly, the subject is disregarded—as extra-aesthetic, we may assume—in theories keyed to Cubism and abstract art. Still, an awareness of it persisted, as evidenced by the following story, which Picasso told to Françoise Gillot. During the most austere phase of “Analytical Cubism,” when he and Braque were working in closely related styles, Picasso one day went to look at his friend's latest work. Suddenly, he became aware that there was a squirrel in the picture, and pointed it out to Braque, who was rather abashed at this discovery. The next day Braque howed him the picture again, after reworking it to get rid of the squirrel, but Picasso insisted he still saw it, and it took yet another reworking to banish the animal for good. Whatever its literal truth, this anecdote suggests that the artist's imagination remains ba sically iconic, and hence ready to find images where none were intended, even under the discipline of an abstract style. Picasso's own later work, from the 1930's on, abounds in chance images of every sort. The most striking cases occur among his sculpture, such as a bull's head composed of the seat and handlebars of a bicycle, or a monkey's face made of a toy automobile Making the resemblance explicit here involves, in the first instance, no more than putting the bicycle parts together in a novel way; in the second, the artist forces us to share his interpretation of the toy automobile by constructing the rest of the animal around it. Perhaps it was visual adventures of this kind that made him recall the story of Braque's squirrel some thirty years after the event. During the interval, the artistic climate of the West ern world had been thoroughly transformed by Dada and Surrealism, which acclaimed chance as the basis of aesthetic experience. As early as 1916-17, Hans Arp was producing compositions of torn bits of paper which he claimed were “arranged according to the laws of chance”; later, he wrote eloquently in praise of “the
Muse of Chance.” Marcel Duchamp, the most influen tial member of the movement, was an equally persuasive advocate and practitioner of chance effects. What the Dadaists sought to elicit was not chance images so much as “chance eetings”—unexpected juxtaposi tions of objects which by their very incongruity would have a liberating effect on the imagination. The creative act to them was a spontaneous gesture devoid of all conscious discipline. Surrealism supported this out look with an elaborate theoretical framework invoking the authority of Sigmund Freud for its view of the unconscious. It also invented a number of new pictorial techniques, or variations of older ones such as ink blots, for soliciting chance images, its orientation being una bashedly iconic. Nor was this reversal of the retreat from likeness confined to the Surrealists; the same trend can be found among artists independent of or only loosely linked with the movement. The result has been a renewed awareness of the link between chance and inspiration. The sponge-throwing Protogenes, were his story better known today, would be the ideal hero of many mid-twentieth-century artists.

V

The history of our subject in Western civilization has a close parallel in the Far East, although the evidence is even more fragmentary and its frame of reference difficult to interpret. As early as the eighth century, toward the end of the T'ang dynasty, there were Chinese painters using procedures astonishingly similar to Cozens' Method. Their style, called i-p'in (“untrammeled”), is known only from literary accounts such as that concerning one of them, Wang Mo: Whenever he wanted to paint a picture, he would first drink wine, and when he was sufficiently drunk, would spatter the ink onto the painting surface. Then, laughing and singing all the while, he would stamp on it with his feet and smear it with his hands, besides swashing and sweeping it with the brush. The ink would be thin in some places, rich in others; he would follow the shapes which brush and ink had produced, making these into mountains, rocks, clouds, and water. Responding to the movements of his hand and / Page 353, Volume 1/ following his inclinations, he would bring forth clouds and mists, wash in wind and rain, with the suddenness of Crea tion. It was exactly like the cunning of a god; when one examined the painting after it was finished he could see no traces of the puddles of ink (S. Shimada, 1961). Such a display of sprezzatura was surely an extreme manifestation of the i-p'in style. Yet Wang Mo and the other “untrammeled” painters had a catalytic effect upon the development of Sung painting analogous to that of Cozens on the Romantics. Their works may not have survived for long, but descriptions of their methods did, providing future artists in both China and Japan with a model of the creative process stressing individual expression and an exploratory attitude toward the potentialities of ink technique. There are later accounts, ranging from the eleventh to the nineteenth century, of painters soliciting chance images in ways comparable to those of the i-p'in pioneers. None of the surviving examples, however, ap proach the freedom of Cozens' “blotscapes.” It is hard to say, therefore, how accurately the literary sources reflect actual practice. One recurrent element in these accounts is the claim that the work—almost invariably a landscape—looks as if “made by Heaven” or “brought forth with the suddenness of Creation,” rather than like something made by man. Such terms of praise imply that the picture in question seems completely effortless and unplanned; a work of nature, not a work of art. This aesthetic ideal musthave led the Chinese to the discovery that certain kinds of veined marble could be sliced in such a way that the surface suggested the mountain ranges and mist-shrouded valleys characteristic of Sung landscapes. The marble slabs would be framed like paintings and supplied with an evoca tive inscription. Since they were small, durable, and produced in large quantities, it seems likely that some of them reached the West with the expansion of the China trade in the eighteenth century. If so, these Far Eastern chance images may have helped to stimulate the train of thought that produced Cozens' Method

BIBLIOGRAPHY

Jurgis Baltrušaitis, “Pierres imagées,” Aberrations, quatre essais sur la légende des formes (Paris, 1957). Ernst Gom-
brich, Art and Illusion (New York, 1960). H. W. Janson,“After Betsy, What?”, Bulletin of the Atomic Scientists, 15 (1959), 68ff.; idem, “The `Image Made by Chance' in Ren aissance Thought,” De Artibus Opuscula XL, Essays in Honor of Erwin Panofsky (New York, 1961), pp. 254-66. Ernst Kris and Otto Kurz, Die Legende vom Künstler (Vienna, 1934). Heinz Ladendorf, “Zur Frage der künstler- ischen Phantasie,” Mouseion, Studien... für Otto Förster
(Cologne, 1960), pp. 21-35. John Plummer, The Hours of Catherine of Cleves (New York and London, 1966). Patrik Reuterswärd, “Sinn und Nebensinn bei Dürer,” Gestalt und Wirklichkeit, Festgabe für Ferdinand Weinhandl (Berlin, 1967), pp. 411-36. Karl Schefold, “Zur Frage der künstler- ischen Phantasie,” Antike Kunst, 4, No. 2 (1961), 79. S. Shimada, “Concerning the I-p'in Style of Painting—I,” Oriental Art, n.s. 7, No. 2 (1961), 3-11. Osvald Siren, Chinese Painting, 3 vols. (New York, 1956), I, 216.H. W. JANSON [See also Chance v1-46  ; China v1-48  ; Fortune, Fate, and Chance v2-27  ; Genius v2-35  v2-36  ; Iconography v2-57  ; Mimesis v3-27  ; Virtù;. v4-64  ]"

 

 

PLATO'S PROGRESS

Gilbert Ryle

1966 Edition

Page 23

Chapter 2

The Publication of the Dialogues

"The literary simulacrum has to be posterior to the real thing and to lack the life of the real thing.

It smells pro -/ Page 24 / leptically of the reader's lamp. There is no such smell in Plato's earlier dialogues.

(b) Aristotle frequently contrasts 'exoteric' discourses with other discourses designed for academic recipients"

 

 

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5
-
5
1
T
20
2
2
-
-
1
E
5
5
5
-
5
1
R
18
9
9
-
-
1
D
4
4
4
-
-
1
E
5
5
5
-
5
1
P
16
7
7
-
-
1
E
5
5
5
-
5
1
N
14
5
5
-
5
1
D
4
4
4
-
-
1
E
5
5
5
-
5
1
N
14
5
5
-
5
1
C
3
3
3
-
-
1
E
5
5
5
-
5
15
INTERDEPENDENCE
141
78
78
-
40
1+5
-
1+4+1
7+8
7+8
-
4+0
6
INTERDEPENDENCE
6
15
15
-
4
-
-
-
1+5
1+5
-
-
6
INTERDEPENDENCE
6
6
6
-
4

 

 

-
INTERDEPENDENT
-
-
-
-
-
1
I
9
9
9
-
-
1
N
14
5
5
-
5
1
T
20
2
2
-
-
1
E
5
5
5
-
5
1
R
18
9
9
-
-
1
D
4
4
4
-
-
1
E
5
5
5
-
5
1
P
16
7
7
-
-
1
E
5
5
5
-
5
1
N
14
5
5
-
5
1
D
4
4
4
-
-
1
E
5
5
5
-
5
1
N
14
5
5
-
5
1
T
20
2
2
-
-
14
INTERDEPENDENT
153
72
72
-
35
1+4
-
1+5+3
7+2
7+2
-
3+5
5
INTERDEPENDENT
9
9
9
-
8

 

 

-
-
-
-
-
INTERDEPENDENT
-
-
-
I
=
9
-
5
INTER
66
30
3
D
=
4
-
9
DEPENDENT
87
42
6
-
-
13
-
14
INTERDEPENDENT
153
72
9
-
-
1+3
-
1+4
-
1+5+3
7+2
-
-
-
4
-
5
INTERDEPENDENT
9
9
9

 

 

7
CONNECT
74
29
2
8
CONNECTS
93
30
3
9
CONNECTED
83
38
2
13
CONNECTEDNESS
140
50
5
5
INTER
66
30
3
12
INTERCONNECT
140
59
5
13
INTERCONNECTS
159
60
6
14
INTERCONNECTED
149
68
5
15
INTERCONNECTING
170
89
8
18
INTERCONNECTEDNESS
206
80
8

 

 

-
INTERCONNECTEDNESS
-
-
-
-
-
1
I
9
9
9
-
-
1
N
14
5
5
-
5
1
T
20
2
2
-
-
1
E
5
5
5
-
5
1
R
18
9
9
-
-
2
CO
18
9
9
-
-
1
N
14
5
5
-
5
1
N
14
5
5
-
5
1
E
5
5
5
-
5
2
CT
23
5
5
-
5
1
E
5
5
5
-
5
1
D
4
4
4
-
-
1
N
14
5
5
-
5
1
E
5
5
5
-
5
2
SS
38
20
2
-
-
18
INTERCONNECTEDNESS
206
98
80
-
45
1+8
-
2+0+6
9+8
8+0
-
4+5
9
INTERCONNECTEDNESS
8
17
8
-
9
-
-
-
1+7
3+5
-
-
9
INTERCONNECTEDNESS
8
8
8
-
9

 

 

-
RENEW
-
-
-
-
-
-
-
-
1
R
18
9
9
-
-
-
-
9
1
E
5
5
5
-
-
-
5
-
1
N
14
5
5
-
-
-
5
-
1
E
5
5
5
-
-
-
5
-
1
W
23
5
5
-
-
-
5
-
8
HARMONIC
81
45
9
-
-
-
-
9
-
INTERCONNECTEDNESS
-
-
-
-
-
-
-
-
1
I
9
9
9
-
-
-
-
9
1
N
14
5
5
-
-
-
5
-
1
T
20
2
2
-
2
-
-
-
1
E
5
5
5
-
-
-
5
-
1
R
18
9
9
-
-
-
-
9
2
CO
18
9
9
-
-
-
-
9
1
N
14
5
5
-
-
-
5
-
1
N
14
5
5
-
-
-
5
-
1
E
5
5
5
-
-
-
5
-
2
CT
23
5
5
-
-
-
5
-
1
E
5
5
5
-
-
-
5
-
1
D
4
4
4
-
-
4
-
-
1
N
14
5
5
-
-
-
5
-
1
E
5
5
5
-
-
-
5
-
2
SS
38
20
2
-
2
-
-
-
31
FIRST TOTAL
352
172
118
-
4
4
65
45
3+1
ADD TO REDUCE
3+5+2
1+7+2
1+1+8
-
-
-
6+5
4+5
4
SECOND TOTAL
10
10
10
-
4
4
11
9
-
REDUCE TO DEDUCE
1+0
1+0
1+0
-
-
-
1+1
-
4
ESSENCE OF NUMBER
1
1
1
-
4
4
2
9

 

 

LOOKING FOR THE ALIENS

A PSYCHOLOGICAL, SCIENTIFIC AND IMAGINATIVE INVESTIGATION

Peter Hough & Jenny Randles 1991

Page 77 (photograph omitted)

9

Life on Mars

 

"The remarkable 'face' on the surface of Mars taken from Viking 1. Is this really an alien construction or an accident of light and shade? Compare it with the rock simulcra on the Sedona photograph on page 81. (NASA)"

Page 81 (photograph omitted)

"This New Age community has been set up in the red rock country around Sedona, Arizona.. Here psychics channellers and other esoteric believers live together. Note the human face on the rock to the left. This is simulcra, an accident of erosion and lighting, or as some believe - an alien artefact like the face on Mars. (Jenny Randles) "

 

 

LOOKING FOR THE ALIENS

A PSYCHOLOGICAL, SCIENTIFIC AND IMAGINATIVE INVESTIGATION

Peter Hough & Jenny Randles 1991

12

Page 98

Somewhere over the Interstellar Rainbow

"In 1985, Glasgow University astronomer Professor Archie Roy was in buoyant mood. He told a journalist from the London Observer that, with new efforts to search the universe for intelligent signals, 'we can expect to make contact very quickly, probably within a decade.' He added that he thought civilizations were 'ten a penny' in the cosmos.

A year later, in an interview with Paul Whitehead in Flying Saucer Reuiew (volume 31, number 3,1986) Professor Roy confirmed this view by saying, 'if we are the product of natural evolution, it is highly improbable that we are alone in the universe.' Presumably this leaves the door open just in case we are not solely the product of natura1 processes (as scientists understandably assume), but are also the creation of a mystic force, otherwise known as God.

Roy actively pursues his broad1y based interest in this search. He subsequently became associated with Flying Saucer Review, and he has also become an active researcher and spokesperson in the heated debate over the potential 'alien' messages said by some to lie behind those crop circles recently found dotting the rural landscapes of our world.
However, the astronomer's seemingly reasonable hopes are, as yet, a long way from being fulfilled. Contact is proving unexpectedly elusive, which has led to some quite contradictory statements.

For instance, in 1981 Michael Papagiannis, of the astronomy department at Boston University, said that:

The euphoric optimism of the 'sixties and early 'seventies that communication with extraterrestrial civilizations seemed quite possible is being slowly replaced in the last couple of years by a pessimistic acceptance that we might be the only technological civilization in the entire galaxy.
(Royal Astronomical Society journal, volume 19, pp.277-281)

One can hardly find more polarized opinions than these, and they represent a crucial debate that increasingly dominates the field. While there seems to be a gut reaction based on deductive logic shared by most scientists, implying that life should be 'out there' in great abundance, there is mounting concern at our continued failure to find it.

Long before we understood the universe in any detail, we dreamt about this quest for alien life, and, as we have seen, still speculate on /Page 99 / what forms such beings might take. When science fiction became popular during the last century, we even began to wonder how we might establish contact.

Early ideas were ingenious, but impractical: such as building a giant mirror and using sunlight to send Morse-code signals to the (then still plausible) inhabitants of the moon or Mars. Of course, the limitations of physics meant that this could never work, even if there were Martians to see the signals. Only the brightest light that we can produce (a nuclear explosion) is potentially visible from another world and this lasts such a brief time that it is hardly likely to produce incontrovertible proof of life on earth. Alien scientists would dismiss any sightings just as freely as ours now reject claims about UFO appearances.

Another problem concerned the code to be used. How could the Martians have recognized the message, even if they had been able to see it? To thcm it would have been a meaningless series of flashes. How would they have unravelled any meaning bchind it?

This problem exists even if it is assumed (as it nearly always was back then) that Martians, although probably looking like bug-eyed monsters, would still think like human beings. The truth is surely that aliens would be alien in every way and their thought processes would not work in the same manner as ours. That said, the chances of any message from us to them being remotely comprehensible appear to be feeble.

In science-fiction stories and films, such a problem is largely ignored, but that is merely an expediency to help the plot along. We suspend scientific logic to accommodate the story line. However, in any real search for life in the universe, we cannot afford to ignore such scientific reasoning. This complicates matters so much that one or two researchers even think it is a forlorn task. We will never communicate with an alien intelligence, even if we do come across one by chance. The rcsult will be like a farmer staring at a cow and attempting to convey, by spoken language or gesture, why it has to go peacefully to the slaughterhouse.
These problems receive too little attention, even today. Our ability to humanize the aliens is an extreme failure on our part, which academics refer to as 'anthropomorphism'

Page 99

"The rcsult will be like a farmer staring at a cow and attempting to convey, by spoken language or gesture, why it has to go peacefully to the slaughterhouse".

Page 219 ( see below)

"There is a fantasy story about a university professor mysteriously translated into the body of a bull. After great efforts to communicate he finally gets the opportunity to write a message in the bloody sand of the slaughterhouse.

 

 

MAN AND THE STARS

CONTACT AND COMMUNICATION WITH OTHER INTELLIGENCE

a liderating adventure for mankind? or a disaster...?

Duncan Lunan 1974

THE MYSTERIOUS SIGNALS FROM OUTER SPACE

FIRST CONTACT AFTER LANDING

Page 219

"Planetary contact 3(c)-intelligence unrecognizable by physical form. In discussing the recognition problem, we have been assuming that manipulative appen­dages, etc., are essential for intelligence, that we have enough in common with "them" for there to be an appropriate, physical response to us. But suppose, after all, such features are not necessary for intelligence. There is a fantasy story about a university professor mysteriously translated into the body of a bull. After great efforts to communicate he finally gets the opportunity to write a message in the bloody sand of the slaughterhouse. Unfortunately, the man with the gun is illiterate-"another of those steers that do a crazy kind of dance." To get at case 3(c), we have to magnify that problem into an alien mind in a non­human body; could there be intelligences like Arthur C. Clarke's Atheleni,12 unable to develop technology until they meet a race gifted with hands?"

 

SUCH

LAUGHTER AMONGST ALL THAT SLAUGHTER

 

 

"Whom the Gods would destroy they first make mad." ..... have been conditioned to seek and welcome their destruction, to regard those who would save them as ... www.racialcompact.com/whomgodsdestroy.html

 

"When falls on man the anger of the gods, first from his mind they banish understanding." Lycurgus

 "When divine power plans evil for a man, it first injures his mind." Sophocles

"Those whom God wishes to destroy, he first deprives of their senses." Euripides

"Whom God wishes to destroy he first makes mad." Seneca

"For those whom God to ruin has design'd, He fits for fate, and first destroys their mind." John Dryden

"Whom the Gods would destroy they first make mad." Henry Wadsworth Longfellow

 

 

T
=
2
-
5
THOSE
67
22
4
W
=
5
-
4
WHOM
59
23
5
T
=
2
-
3
THE
33
15
6
G
=
7
-
4
GODS
45
18
9
S
=
1
-
4
SEEK
40
13
4
T
=
2
-
2
TO
35
8
8
D
=
4
-
7
DESTROY
106
34
7
T
=
2
-
4
THEY
58
22
4
F
=
6
-
5
FIRST
72
27
9
M
=
4
-
4
MAKE
30
12
3
M
=
4
-
3
MAD
18
9
9
-
-
39
-
45
First Total
563
203
68
-
-
3+9
-
4+5
Add to Reduce
5+6+3
2+0+3
6+8
Q
-
12
-
9
Second Total
14
5
14
-
-
1+2
-
-
Reduce to Deduce
1+4
-
1+4
-
-
3
-
9
Essence of Number
5
5
5

 

 

Shakespeare Quote: Cryhavoc!”and let loose the dogs of war, That this foul deed shall smell ... William Shakespeare's Julius Caesar is first performed ... www.enotes.com/famous-quotes/cry-havoc-and-let-loose-the-dogs-of-war-that-this

 

"Cry “havoc!” and let loose the dogs of war,
That this foul deed shall smell above the earth
With carrion men, groaning for burial."

 

 

C
=
3
-
3
CRY
46
19
1
H
=
8
-
5
HAVOC
49
22
4
A
=
1
-
3
AND
19
10
1
L
=
3
-
3
LET
37
10
1
L
=
3
-
5
LOOSE
66
21
3
T
=
2
-
3
THE
33
15
6
D
=
4
-
4
DOGS
45
18
9
O
=
6
-
2
OF
21
12
3
W
=
5
-
3
WAR
42
15
6
-
-
38
-
31
First Total
358
142
34
-
-
3+8
-
3+1
Add to Reduce
3+5+8
1+4+2
3+4
-
-
11
-
4
Second Total
16
7
7
-
-
1+1
-
-
Reduce to Deduce
1+6
-
-
-
-
2
-
4
Essence of Number
7
7
7

 

 

C
=
3
-
3
CRY
46
19
1
H
=
8
-
5
HAVOC
49
22
4
A
=
1
-
3
AND
19
10
1
L
=
3
-
3
LET
37
10
1
L
=
3
-
5
LOOSE
66
21
3
T
=
2
-
3
THE
33
15
6
D
=
4
-
4
GODS
45
18
9
O
=
6
-
2
OF
21
12
3
W
=
5
-
3
WAR
42
15
6
-
-
38
-
31
First Total
358
142
34
-
-
3+8
-
3+1
Add to Reduce
3+5+8
1+4+2
3+4
-
-
11
-
4
Second Total
16
7
7
-
-
1+1
-
-
Reduce to Deduce
1+6
-
-
-
-
2
-
4
Essence of Number
7
7
7

 

 

I ME YOU I YOU ME I

ALL AND EVERYTHING EVERYTHING AND ALL

MAYA RULES OK RULES MAYA

 

 

I
=
9
-
1
I
9
9
9
A
=
1
-
2
AM
14
5
5
T
=
2
Q
3
THE
33
15
6
G
=
7
-
8
GAMBLING
65
38
2
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
C
=
3
-
5
CHEAT
37
19
1
-
-
30
-
24
Add to Reduce
212
113
32
-
-
3+0
-
2+4
Reduce to Deduce
2+1+2
1+1+3
3+2
Q
-
3
Q
6
Essence of Number
5
5
5

 

 

I
=
9
-
1
I
9
9
9
A
=
1
-
2
AM
14
5
5
T
=
2
Q
3
THE
33
15
6
G
=
7
-
8
GAMBLING
65
38
2
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
C
=
3
-
5
CHEAT
37
19
1
-
-
30
-
24
First Total
212
113
32
-
-
3+0
-
2+4
Add to Reduce
2+1+2
1+1+3
2+3
Q
-
3
Q
6
Second Total
5
5
5
-
-
-
-
-
Reduce to Deduce
1+4
1+4
-
-
-
3
-
6
Essence of Number
5
5
5

 

 

I

SAY

GOLD FOOLS GOLD

BIRTH UNTO DEATH DEATH UNTO BIRTH

 

 

SOUND THE QUESTION THE QUESTION SOUND

WHITHER GOEST THOU GOEST WHITHER

GODS GODDESSES ALWAYS LOVE BALANCING LOVE ALWAYS GODS GODDESSES

 

 

DAILY MAIL

Tuesday, December 2,008

Rocking the cradle

Fay Schlesinger

"...It seems the sound of the bedtime lullaby is changing fast.

Traditional songs such as Rock A Bye Baby and Twinkle Twinkle Little Star are no longer soothing babies to sleep."

 

 

20
ELECTROMAGNETIC LIGHT
206
98
8
21
ELECTROMAGNETIC LIGHTS
-
-
-
-
E+L+E+C+T
45
18
9
-
R
18
9
9
-
O+M+A+G
36
18
9
-
N+E+T
39
12
3
-
I
9
9
9
-
C
3
3
3
-
L
12
3
3
-
I
9
9
9
-
G+H+T+S
54
18
9
21
ELECTROMAGNETIC LIGHTS
225
99
63
2+0
-
2+2+5
9+9
6+3
21
ELECTROMAGNETIC LIGHTS
9
18
9
1+0
-
-
1+8
-
21
ELECTROMAGNETIC LIGHTS
9
9
9

 

 

-
21
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
L
I
G
H
T
S
-
-
-
-
-
--
-
-
-
-
38
-
-
-
-
-
-
-
6
-
-
-
5
-
-
9
-
-
-
9
-
8
-
1
+
=
38
3+8
=
11
1+1
2
-
2
74
`-
-
-
-
-
-
-
15
-
-
-
14
-
-
9
-
-
-
9
-
8
-
19
+
=
74
7+4
=
11
1+1
2
-
2
-
21
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
L
I
G
H
T
S
-
-
-
-
-
--
-
-
-
-
52
-
5
3
5
3
2
9
-
4
1
7
-
5
2
-
3
-
3
-
7
-
2
-
+
=
52
5+2
=
7
-
7
-
7
106
`-
5
12
5
3
20
18
-
13
1
7
-
5
20
-
3
-
12
-
7
-
20
-
+
=
106
1+0+6
=
7
-
7
-
7
-
21
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
L
I
G
H
T
S
-
-
-
-
-
--
-
-
-
-
225
`-
5
12
5
3
20
18
15
13
1
7
14
5
20
9
3
-
12
9
7
8
20
19
+
=
225
2+2+5
=
9
-
9
-
9
99
-
5
3
5
3
2
9
6
4
1
7
5
5
2
9
3
-
3
9
7
8
2
1
+
=
99
9+9
=
18
1+8
9
-
9
-
21
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
L
I
G
H
T
S
-
-
-
-
-
--
-
-
-
-
1
-
-
1
1
-
-
-
1
-
1-
1
-
-
-
-
-
-
1
-
-
-
-
1-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
2
-
-
-
-
-
4
-
2
-
-
-
-
4
-
-
2
-
-
-
2
occurs
x
3
=
6
=
6
3
-
-
3
-
3
-
-
-
-
-
-
-
-
-
-
3
-
3
-
-
-
-
-
-
-
3
occurs
x
4
=
12
=
3
4
-
-
-
-
-
-
-
-
4
-
-
4
-
-
-
-
-
-
4
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
5
-
5
5
-
-
-
-
5
-
5
5
5
-
5
-
-
-
-
5
-
5
-
-
5
occurs
x
4
=
20
=
2
6
-
-
-
-
-
-
-
6
-
-
-
-
3
-
2
-
-
-
-
3
-
2
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
7
-
3
-
-
-
-
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
=
5
8
-
-
-
-
-
-
-
-
-
-
-
-
3
-
2
-
-
-
-
3
8
2
-
-
-
8
occurs
x
1
=
8
=
8
9
-
9
-
-
-
9
9
-
9
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
-
9
occurs
x
3
=
27
=
9
45
21
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
L
I
G
H
T
S
-
-
45
-
-
21
-
99
-
45
4+5
2+1
5
-
5
5
-
-
-
-
-
3
5
5
-
2
-
-
-
-
3
-
2
-
-
-
4+5
-
-
2+1
-
9+9
-
4+5
9
3
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
L
I
G
H
T
S
-
-
9
-
-
3
-
18
-
9
-
-
5
3
5
3
2
9
6
4
1
7
5
5
2
9
3
-
3
9
7
8
2
1
-
-
-
-
-
-
-
1+8
-
-
9
3
E
L
E
C
T
R
O
M
A
G
N
E
T
I
C
-
L
I
G
H
T
S
-
-
9
-
-
3
-
9
-
9

 

 

HURRAH FOR RAH FOR RAH HURRAH

 

 

-
RAINBOW
-
-
-
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
7
RAINBOW
171
81
54
-
-
1+7+1
8+1
5+4
7
RAINBOW
9
9
9
-
-
1+7+1
8+1
5+4
7
RAINBOW
9
9
9

 

 

-
BRAIN+BODY
-
-
-
-
B
2
2
2
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N
14
5
5
-
BODY
46
19
1
9
BRAIN+BODY
90
45
27
-
-
1+7+1
4+5
2+7
9
BRAIN+BODY
9
9
9

 

 

-
BRAIN+BODY
-
-
-
-
B
2
2
2
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N
14
5
5
-
BODY
46
19
1
9
BRAIN+BODY
90
45
27
-
-
1+7+1
4+5
2+7
9
BRAIN+BODY
9
9
9

 

 

-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
--
-
-
-
-
-
8
-
-
-
-
9
5
-
6
-
-
-
9
-
8
-
+
+
45
4+5
=
9
=
9
=
9
-
-
-
8
-
-
-
-
9
14
-
15
-
-
-
9
-
8
-
+
+
63
6+3
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
--
-
-
-
-
2
-
5
-
9
1
-
-
2
-
5
-
3
-
7
-
14
+
+
36
3+6
=
9
=
9
=
9
-
-
20
-
5
-
18
1
-
-
2
-
23
-
12
-
7
-
20
+
+
108
1+0+8
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
--
-
-
-
-
20
8
5
-
18
1
9
14
2
15
23
-
12
9
7
8
20
+
+
171
1+7+1
=
9
=
9
=
9
-
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
+
+
81
8+1
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
--
-
-
2
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
--
--
--
--
-
-
4
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
--
--
--
--
--
--
--
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
4
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
41
-
-
15
-
81
-
45
-
-
-
-
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
4+1
-
-
1+5
-
8+1
-
4+5
4
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9
-
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
-
-
-
-
-
--
-
-
-
-
4
5
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9

 

 

T
=
2
-
3
THE
33
15
6
P
=
7
-
6
PEOPLE
69
33
6
T
=
2
-
4
THAT
49
13
4
W
=
5
-
6
WALKED
56
20
2
I
=
9
-
2
IN
23
14
5
D
=
4
-
8
DARKNESS
91
28
1
H
=
8
-
4
HAVE
36
18
9
S
=
1
-
4
SEEN
43
16
7
A
=
1
-
1
A
1
1
1
G
=
7
-
5
GREAT
51
24
6
L
=
3
-
5
LIGHT
56
29
2
-
-
49
4
48
First Total
508
211
49
-
-
4+9
-
4+8
Add to Reduce
5+0+8
2+1+1
4+9
Q
-
13
-
12
Second Total
13
4
13
-
-
1+3
-
1+2
Reduce to Deduce
1+3
-
1+3
-
-
4
4
3
Essence of Number
4
4
4

 

 

T
=
2
-
4
THEY
58
22
4
T
=
2
-
4
THAT
49
13
4
D
=
4
-
5
DWELL
56
20
23
T
=
2
-
2
IN
23
14
5
T
=
2
-
3
THE
33
15
6
L
=
3
-
4
LAND
31
13
4
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
S
=
1
-
6
SHADOW
70
25
7
O
=
6
-
2
OF
21
12
3
D
=
4
-
5
DEATH
38
20
2
U
=
3
3
4
UPON
66
21
3
T
=
2
4
4
THEM
46
19
1
H
=
8
4
4
HATH
37
19
1
T
=
2
3
3
THE
33
15
6
L
=
3
4
5
LIGHT
56
29
2
S
=
1
4
6
SHINED
59
32
5
-
-
60
4
66
First Total
730
316
64
-
-
6+0
-
6+6
Add to Reduce
7+3+0
3+1+6
6+4
Q
-
6
-
12
Second Total
10
10
10
-
-
-
-
1+2
Reduce to Deduce
1+0
1+0
1+0
-
-
6
4
3
Essence of Number
1
1
1

 

 

T
=
2
-
3
THE
33
15
6
P
=
7
-
6
PEOPLE
69
33
6
T
=
2
-
4
THAT
49
13
4
W
=
5
-
6
WALKED
56
20
2
I
=
9
-
2
IN
23
14
5
D
=
4
-
8
DARKNESS
91
28
1
H
=
8
-
4
HAVE
36
18
9
S
=
1
-
4
SEEN
43
16
7
A
=
1
-
1
A
1
1
1
G
=
7
-
5
GREAT
51
24
6
L
=
3
-
5
LIGHT
56
29
2
T
=
2
-
4
THEY
58
22
4
T
=
2
-
4
THAT
49
13
4
D
=
4
-
5
DWELL
56
20
23
T
=
2
-
2
IN
23
14
5
T
=
2
-
3
THE
33
15
6
L
=
3
-
4
LAND
31
13
4
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
S
=
1
-
6
SHADOW
70
25
7
O
=
6
-
2
OF
21
12
3
D
=
4
-
5
DEATH
38
20
2
U
=
3
3
4
UPON
66
21
3
T
=
2
4
4
THEM
46
19
1
H
=
8
4
4
HATH
37
19
1
T
=
2
3
3
THE
33
15
6
L
=
3
4
5
LIGHT
56
29
2
S
=
1
4
6
SHINED
59
32
5
-
-
109
4
114
First Total
1238
527
113
-
-
1+0+9
-
1+1+4
Add to Reduce
1+2+3+8
5+2+7
1+1+3
Q
-
10
-
6
Second Total
14
14
5
-
-
1+0
-
-
Reduce to Deduce
1+4
1+4
-
-
-
1
4
6
Essence of Number
5
5
5

 

 

1
I
9
9
9
3
CAN
18
9
9
4
PLAY
54
18
9
3
THE
33
15
6
4
PART
55
19
1
2
SO
34
7
7
4
WELL
52
16
7
21
First Total
255
93
48
2+1
Add to Reduce
2+5+5
9+3
4+8
3
Second Total
12
12
12
-
Reduce to Deduce
1+2
1+2
1+2
3
Essence of Number
3
3
3

 

 

J
=
1
6
JOSEPH
73
28
1
J
=
1
5
JESUS
74
11
2
M
=
4
4
MARY
57
21
3
-
-
6
15
-
204
60
6
-
-
-
1+5
-
2+0+4
6+0
-
-
-
-
6
-
6
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
JOSEPH
1
6+1
7
-
-
-
5
JESUS
2
5+2
7
-
-
-
4
MARY
3
4+3
7

 

 

5
PEACE
30
21
3
2
BE
7
7
7
4
UNTO
70
16
7
3
YOU
61
16
7
14
First Total
168
60
24
1+4
Add to Reduce
1+6+8
6+0
2+4
5
Second Total
15
6
6
-
Reduce to Deduce
1+5
-
-
5
Essence of Number
6
6
6

 

 

 

DOES GOD PLAY DICE

THE NEW MATHEMATICS OF CHAOS

Ian Stewart 1989

Page 1

PROLOGUE

CLOCKWORK OR CHAOS?

"YOU BELIEVE IN A GOD WHO PLAYS DICE, AND I IN COMPLETE LAW AND ORDER."

Albert Einstein, Letter to Max Born

 

 

 

 

-
6
D
I
V
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
9
5
-
+
=
23
2+3
=
5
-
5
-
5
-
-
-
9
-
9
14
-
+
=
32
3+2
=
5
-
5
-
5
-
6
D
I
V
I
N
E
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
-
-
5
+
=
13
1+3
=
4
-
4
-
4
-
-
4
-
22
-
-
5
+
=
31
3+1
=
4
-
4
-
4
-
6
D
I
V
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
4
9
22
9
14
5
+
=
63
6+3
=
9
-
9
-
9
-
-
4
9
4
9
5
5
+
=
36
4+5
=
9
-
9
-
9
-
6
D
I
V
I
N
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
4
occurs
x
2
=
8
-
8
-
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
6
SIX
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
SEVEN
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
EIGHT
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
27
9
D
I
V
I
N
E
-
-
18
-
-
9
-
36
-
18
2+7
-
-
9
-
9
-
-
-
-
1+8
-
-
-
-
3+6
-
1+8
9
9
D
I
V
I
N
E
-
-
9
-
-
9
-
9
-
9
-
-
4
9
4
9
5
5
-
-
-
-
-
-
-
-
-
-
9
9
D
I
V
I
N
E
-
-
9
-
-
9
-
9
-
9

 

 

6
D
I
V
I
N
E
-
-
-
-
-
--
-
-
-
-
-
-
9
-
9
5
-
+
=
23
2+3
=
5
=
5
=
5
-
-
9
-
9
14
-
+
=
32
3+2
=
5
=
5
=
5
6
D
I
V
I
N
E
-
-
-
-
-
-
-
-
-
-
-
4
-
4
-
-
5
+
=
13
1+3
=
4
=
4
=
4
-
4
-
22
-
-
5
+
=
31
3+1
=
4
=
4
=
4
6
D
I
V
I
N
E
-
-
-
-
-
--
-
-
-
-
-
4
9
22
9
14
5
+
=
63
6+3
=
9
=
9
=
9
-
4
9
4
9
5
5
+
=
36
4+5
=
9
=
9
=
9
6
D
I
V
I
N
E
-
-
-
-
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
5
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
9
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
9
D
I
V
I
N
E
-
-
18
-
-
9
-
36
-
18
-
-
9
-
9
-
-
-
-
1+8
-
-
-
-
3+6
-
1+8
9
D
I
V
I
N
E
-
-
9
-
-
9
-
9
-
9
-
4
9
4
9
5
5
-
-
-
-
-
-
-
-
-
-
9
D
I
V
I
N
E
-
-
9
-
-
9
-
9
-
9

 

 

-
7
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
-
8
6
-
-
8
-
+
=
22
2+2
=
4
=
4
=
4
-
-
-
8
15
-
-
8
-
+
=
31
3+1
=
4
=
4
=
4
-
7
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
2
-
-
3
7
-
2
+
=
14
1+4
=
5
=
5
=
5
-
-
20
-
-
21
7
-
20
+
=
68
6+8
=
14
1+4
5
=
5
-
7
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
20
8
15
21
7
8
20
+
=
99
9+9
=
18
1+8
9
=
9
-
-
2
8
6
3
7
8
2
+
=
36
3+6
=
9
=
9
=
9
-
7
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
2
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
FIVE
3
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
9
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
19
7
T
H
O
U
G
H
T
-
-
26
-
-
7
-
36
-
27
1+9
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
3+6
-
2+7
10
7
T
H
O
U
G
H
T
-
-
8
-
-
7
-
9
-
9
1+0
-
2
8
6
3
7
8
2
-
-
-
-
-
-
-
-
-
-
1
7
T
H
O
U
G
H
T
-
-
8
-
-
7
-
9
-
9

 

 

7
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
8
6
-
-
8
-
+
=
22
2+2
=
4
=
4
=
4
-
-
8
15
-
-
8
-
+
=
31
3+1
=
4
=
4
=
4
7
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
2
-
-
3
7
-
2
+
=
14
1+4
=
5
=
5
=
5
-
20
-
-
21
7
-
20
+
=
68
6+8
=
14
1+4
5
=
5
7
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
20
8
15
21
7
8
20
+
=
99
9+9
=
18
1+8
9
=
9
-
2
8
6
3
7
8
2
+
=
36
3+6
=
9
=
9
=
9
7
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
7
T
H
O
U
G
H
T
-
-
26
-
-
7
-
36
-
27
-
-
-
-
-
-
-
-
-
-
2+6
-
-
-
-
3+6
-
2+7
7
T
H
O
U
G
H
T
-
-
8
-
-
7
-
9
-
9
-
2
8
6
3
7
8
2
-
-
-
-
-
-
-
-
-
-
7
T
H
O
U
G
H
T
-
-
8
-
-
7
-
9
-
9

 

 

-
16
D
I
V
I
N
E
--
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
9
5
-
-
-
8
6
-
-
8
-
+
=
27
2+7
=
9
-
9
=
9
-
-
-
9
-
9
14
-
-
-
8
15
-
-
8
-
+
=
99
9+9
=
18
1+8
9
=
9
-
16
D
I
V
I
N
E
-
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
4
-
4
-
-
5
-
2
-
-
3
7
-
2
+
=
32
3+2
=
9
=
9
=
9
-
-
4
-
22
-
-
5
-
20
-
-
21
7
-
20
+
=
45
4+5
=
9
=
9
=
9
-
16
D
I
V
I
N
E
-
T
H
O
U
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
4
9
22
9
14
5
-
20
8
15
21
7
8
20
+
=
162
1+6+2
=
9
=
9
=
9
-
-
4
9
4
9
5
5
-
2
8
6
3
7
8
2
+
=
72
7+2
=
9
=
9
=
9
-
16
D
I
V
I
N
E
-
T
H
O
U
G
H
T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
3+0
10
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
-
-
-
8
occurs
x
2
=
16
=
7
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
2+7
9
1
13
D
I
V
I
N
E
-
T
H
O
U
G
H
T
-
-
44
-
-
13
-
72
-
54
-
1+3
-
9
-
9
-
-
-
-
-
-
-
-
-
-
-
-
4+4
-
-
1+3
-
7+2
-
5+4
1
4
D
I
V
I
N
E
-
T
H
O
U
G
H
T
-
-
8
-
-
4
-
9
-
9
-
-
4
9
4
9
5
5
-
2
8
6
3
7
8
2
+
=
72
7+2
=
9
=
9
=
9
1
4
D
I
V
I
N
E
-
T
H
O
U
G
H
T
-
-
8
-
-
4
-
9
-
9

 

 

-
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
9
1
-
-
9
-
9
5
-
-
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
-
-
-
-
-
-
9
19
-
-
9
-
9
14
-
-
-
-
-
+
=
60
6+0
=
6
=
6
=
6
-
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
4
1
1
2
-
-
-
-
4
-
4
-
-
5
-
3
1
5
+
=
30
3+0
=
3
=
3
=
3
-
-
13
1
1
20
-
-
-
-
4
-
22
-
-
5
-
12
1
23
+
=
102
1+0+2
=
3
=
3
=
3
-
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
13
1
1
20
-
9
19
-
4
9
22
9
14
5
-
12
1
23
+
=
162
1+6+2
=
9
=
9
=
9
-
-
4
1
1
2
-
9
1
-
4
9
4
9
5
5
-
3
1
5
+
=
63
6+3
=
9
=
9
=
9
-
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
21
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
24
-
-
15
-
63
-
27
2+1
2+1
-
-
-
-
-
9
-
-
-
9
-
9
-
-
-
-
-
-
-
-
2+4
-
-
1+5
-
6+3
-
2+7
3
6
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
6
-
-
6
-
9
-
9
-
-
4
1
1
2
-
9
1
-
4
9
4
9
5
5
-
3
1
5
-
-
-
-
-
-
-
-
-
-
3
6
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
6
-
-
6
-
9
-
9

 

 

15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
9
1
-
-
9
-
9
5
-
-
-
-
-
+
=
33
3+3
=
6
=
6
=
6
-
-
-
-
-
-
9
19
-
-
9
-
9
14
-
-
-
-
-
+
=
60
6+0
=
6
=
6
=
6
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
4
1
1
2
-
-
-
-
4
-
4
-
-
5
-
3
1
5
+
=
30
3+0
=
3
=
3
=
3
-
13
1
1
20
-
-
-
-
4
-
22
-
-
5
-
12
1
23
+
=
102
1+0+2
=
3
=
3
=
3
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
13
1
1
20
-
9
19
-
4
9
22
9
14
5
-
12
1
23
+
=
162
1+6+2
=
9
=
9
=
9
-
4
1
1
2
-
9
1
-
4
9
4
9
5
5
-
3
1
5
+
=
63
6+3
=
9
=
9
=
9
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
-
4
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
9
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
15
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
24
-
-
15
-
63
-
27
2+1
-
-
-
-
-
9
-
-
-
9
-
9
-
-
-
-
-
-
-
-
2+4
-
-
1+5
-
6+3
-
2+7
6
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
6
-
-
6
-
9
-
9
-
4
1
1
2
-
9
1
-
4
9
4
9
5
5
-
3
1
5
-
-
-
-
-
-
-
-
-
-
6
M
A
A
T
-
I
S
-
D
I
V
I
N
E
-
L
A
W
-
-
6
-
-
6
-
9
-
9

 

 

-
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
9
5
-
-
-
6
5
1
-
9
-
5
-
-
+
=
49
4+9
=
13
1+3
4
=
4
-
-
-
9
-
9
14
-
-
-
15
14
19
-
9
-
14
-
-
+
=
103
1+0+3
=
4
=
4
=
4
-
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
--
-
-
-
-
-
-
4
-
4
-
-
5
-
3
-
-
-
3
-
5
-
3
5
+
=
32
3+2
=
5
=
5
=
5
-
-
4
-
22
-
-
5
-
3
-
-
-
3
-
5
-
3
5
+
=
50
5+0
=
5
=
5
=
5
-
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
--
-
-
-
-
-
-
4
9
22
9
14
5
-
3
15
14
19
3
9
5
14
3
5
+
=
153
1+5+3
=
9
=
9
=
9
-
-
4
9
4
9
5
5
-
3
6
5
1
3
9
5
5
3
5
+
=
81
8+1
=
9
=
9
=
9
-
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
-
-
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
5
-
-
-
5
-
-
-
5
5
-
5
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
17
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
28
-
-
16
-
81
-
36
1+7
1+6
-
-
-
-
5
5
-
-
-
5
-
-
-
5
5
-
5
-
-
2+8
-
-
1+6
-
8+1
-
3+6
8
7
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
10
-
-
7
-
9
-
9
-
-
4
9
4
9
5
5
-
3
6
5
1
3
9
5
5
3
5
-
-
1+0
-
-
-
-
-
-
-
8
7
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
1
-
-
7
-
9
-
9

 

 

16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
--
-
-
-
-
-
-
9
-
9
5
-
-
-
6
5
1
-
9
-
5
-
-
+
=
49
4+9
=
13
1+3
4
=
4
-
-
9
-
9
14
-
-
-
15
14
19
-
9
-
14
-
-
+
=
103
1+0+3
=
4
=
4
=
4
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
--
-
-
-
-
-
4
-
4
-
-
5
-
3
-
-
-
3
-
5
-
3
5
+
=
32
3+2
=
5
=
5
=
5
-
4
-
22
-
-
5
-
3
-
-
-
3
-
5
-
3
5
+
=
50
5+0
=
5
=
5
=
5
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
--
-
-
-
-
-
4
9
22
9
14
5
-
3
15
14
19
3
9
5
14
3
5
+
=
153
1+5+3
=
9
=
9
=
9
-
4
9
4
9
5
5
-
3
6
5
1
3
9
5
5
3
5
+
=
81
8+1
=
9
=
9
=
9
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
3
-
-
-
3
-
-
-
3
-
-
-
3
occurs
x
3
=
9
=
9
-
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
5
5
-
-
-
5
-
-
-
5
5
-
5
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
16
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
28
-
-
16
-
81
-
36
1+6
-
-
-
-
5
5
-
-
-
5
-
-
-
5
5
-
5
-
-
2+8
-
-
1+6
-
8+1
-
3+6
7
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
10
-
-
7
-
9
-
9
-
4
9
4
9
5
5
-
3
6
5
1
3
9
5
5
3
5
-
-
1+0
-
-
-
-
-
-
-
7
D
I
V
I
N
E
-
C
O
N
S
C
I
E
N
C
E
-
-
1
-
-
7
-
9
-
9

 

 

-
9
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
9
5
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
-
9
-
9
14
-
-
-
-
-
+
=
32
3+2
=
5
=
5
=
5
-
9
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
-
-
-
-
-
-
-
4
-
4
-
-
5
-
3
1
5
+
=
22
2+2
=
4
=
4
=
4
-
-
4
-
22
-
-
5
-
12
1
23
+
=
67
6+7
=
13
1+3
4
=
4
-
9
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
4
9
22
9
14
5
-
12
1
23
+
=
99
9+9
=
18
1+8
9
=
9
-
-
4
9
4
9
5
5
-
3
1
5
+
=
45
4+5
=
9
=
9
=
9
-
9
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
5
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
23
9
D
I
V
I
N
E
-
L
A
W
-
-
4
-
-
9
-
45
-
27
2+3
-
-
9
-
9
-
-
-
-
-
-
-
-
2+2
-
-
-
-
4+5
-
2+7
5
9
D
I
V
I
N
E
-
L
A
W
-
-
4
-
-
9
-
9
-
9
-
-
4
9
4
9
5
5
-
3
1
5
-
-
-
-
-
-
-
-
-
-
5
9
D
I
V
I
N
E
-
L
A
W
-
-
4
-
-
9
-
9
-
9

 

 

9
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
-
9
-
9
5
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
9
-
9
14
-
-
-
-
-
+
=
32
3+2
=
5
=
5
=
5
9
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
-
-
-
-
-
-
4
-
4
-
-
5
-
3
1
5
+
=
22
2+2
=
4
=
4
=
4
-
4
-
22
-
-
5
-
12
1
23
+
=
67
6+7
=
13
1+3
4
=
4
9
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
--
-
-
-
-
-
4
9
22
9
14
5
-
12
1
23
+
=
99
9+9
=
18
1+8
9
=
9
-
4
9
4
9
5
5
-
3
1
5
+
=
45
4+5
=
9
=
9
=
9
9
D
I
V
I
N
E
-
L
A
W
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
3
-
-
-
-
3
occurs
x
1
=
3
=
3
-
4
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
5
5
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
9
-
9
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
9
D
I
V
I
N
E
-
L
A
W
-
-
4
-
-
9
-
45
-
27
-
-
9
-
9
-
-
-
-
-
-
-
-
2+2
-
-
-
-
4+5
-
2+7
9
D
I
V
I
N
E
-
L
A
W
-
-
4
-
-
9
-
9
-
9
-
4
9
4
9
5
5
-
3
1
5
-
-
-
-
-
-
-
-
-
-
9
D
I
V
I
N
E
-
L
A
W
-
-
4
-
-
9
-
9
-
9

 

 

-
12
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
-
-
-
--
-
-
-
-
-
-
-
9
-
9
5
-
-
-
-
-
1
6
5
+
=
35
3+5
=
8
=
8
=
8
-
-
-
9
-
9
14
-
-
-
-
-
19
15
14
+
=
80
8+0
=
8
=
8
=
8
-
12
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
-
-
-
--
-
-
-
-
-
-
4
-
4
-
-
5
-
9
5
1
-
-
-
+
=
28
2+8
=
10
1+0
1
=
1
-
-
4
-
22
-
-
5
-
18
5
1
-
-
-
+
=
55
5+5
=
10
1+0
1
=
1
-
12
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
-
-
-
--
-
-
-
-
-
-
4
9
22
9
14
5
-
18
5
1
19
15
14
+
=
135
1+3+5
=
9
=
9
=
9
-
-
4
9
4
9
5
5
-
9
5
1
1
6
5
+
=
63
6+3
=
9
=
9
=
9
-
12
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
-
-
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
5
5
-
-
5
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
FOUR
4
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
9
-
9
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
20
12
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
25
-
-
12
-
63
-
27
2+0
1+2
-
-
-
-
5
5
-
-
5
-
-
-
5
-
-
2+5
-
-
1+2
-
6+3
-
2+7
2
3
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
7
-
-
3
-
9
-
9
-
-
4
9
4
9
5
5
-
9
5
1
1
6
5
-
-
-
-
-
-
-
-
-
-
2
3
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
7
-
-
3
-
9
-
9

 

 

12
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
-
-
-
--
-
-
-
-
-
-
9
-
9
5
-
-
-
-
-
1
6
5
+
=
35
3+5
=
8
=
8
=
8
-
-
9
-
9
14
-
-
-
-
-
19
15
14
+
=
80
8+0
=
8
=
8
=
8
12
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
-
-
-
--
-
-
-
-
-
4
-
4
-
-
5
-
9
5
1
-
-
-
+
=
28
2+8
=
10
1+0
1
=
1
-
4
-
22
-
-
5
-
18
5
1
-
-
-
+
=
55
5+5
=
10
1+0
1
=
1
12
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
-
-
-
--
-
-
-
-
-
4
9
22
9
14
5
-
18
5
1
19
15
14
+
=
135
1+3+5
=
9
=
9
=
9
-
4
9
4
9
5
5
-
9
5
1
1
6
5
+
=
63
6+3
=
9
=
9
=
9
12
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
4
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
5
5
-
-
5
-
-
-
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
-
-
9
-
9
-
-
-
9
-
-
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
12
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
25
-
-
12
-
63
-
27
1+2
-
-
-
-
5
5
-
-
5
-
-
-
5
-
-
2+5
-
-
1+2
-
6+3
-
2+7
3
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
7
-
-
3
-
9
-
9
-
4
9
4
9
5
5
-
9
5
1
1
6
5
-
-
-
-
-
-
-
-
-
-
3
D
I
V
I
N
E
-
R
E
A
S
O
N
-
-
7
-
-
3
-
9
-
9

 

 

-
14
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
-
-
-
--
-
-
-
-
-````
-
-
6
-
1
-
-
9
-
9
5
-
-
-
6
-
-
+
=
36
3+6
=
9
=
9
=
9
-
-
-
15
-
19
-
-
9
-
9
14
-
-
-
15
-
-
+
=
81
8+1
=
9
=
9
=
9
-
14
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
-
-
-
--
-
-
-
-
-
-
7
-
4
-
-
4
-
4
-
-
5
-
3
-
4
5
+
=
36
3+6
=
9
=
9
=
9
-
-
7
-
4
-
-
4
-
22
-
-
5
-
12
-
22
5
+
=
81
8+1
=
9
=
9
=
9
-
14
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
-
-
-
--
-
-
-
-
-
-
7
15
4
19
-
4
9
22
9
14
5
-
12
15
22
5
+
=
162
1+6+2
=
9
=
9
=
9
-
-
7
6
4
1
-
4
9
4
9
5
5
-
3
6
4
5
+
=
72
7+2
=
9
=
9
=
9
-
14
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
4
-
-
4
-
4
-
-
-
-
-
-
4
-
-
-
4
occurs
x
4
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
-
5
5
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
--
-
6
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
10
14
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
35
-
-
14
-
72
-
36
1+0
1+4
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
3+5
-
-
1+4
-
7+2
-
3+6
1
5
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
8
-
-
5
-
9
-
9
-
-
7
6
4
1
-
4
9
4
9
5
5
-
3
6
4
5
-
-
-
-
-
--
-
-
-
-
1
5
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
8
-
-
5
-
9
-
9

 

 

14
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
-
-
-
--
-
-
-
-
-
-
6
-
1
-
-
9
-
9
5
-
-
-
6
-
-
+
=
36
3+6
=
9
=
9
=
9
-
-
15
-
19
-
-
9
-
9
14
-
-
-
15
-
-
+
=
81
8+1
=
9
=
9
=
9
14
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
-
-
-
--
-
-
-
-
-
7
-
4
-
-
4
-
4
-
-
5
-
3
-
4
5
+
=
36
3+6
=
9
=
9
=
9
-
7
-
4
-
-
4
-
22
-
-
5
-
12
-
22
5
+
=
81
8+1
=
9
=
9
=
9
14
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
-
-
-
--
-
-
-
-
-
7
15
4
19
-
4
9
22
9
14
5
-
12
15
22
5
+
=
162
1+6+2
=
9
=
9
=
9
-
7
6
4
1
-
4
9
4
9
5
5
-
3
6
4
5
+
=
72
7+2
=
9
=
9
=
9
14
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
4
-
-
4
-
4
-
-
-
-
-
-
4
-
-
-
4
occurs
x
4
=
16
1+6
7
-
-
-
-
-
-
-
-
-
-
5
5
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
--
-
6
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
14
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
35
-
-
14
-
72
-
36
1+4
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
3+5
-
-
1+4
-
7+2
-
3+6
5
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
8
-
-
5
-
9
-
9
-
7
6
4
1
-
4
9
4
9
5
5
-
3
6
4
5
-
-
-
-
-
--
-
-
-
-
5
G
O
D
S
-
D
I
V
I
N
E
-
L
O
V
E
-
-
8
-
-
5
-
9
-
9

 

 
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