Unurthed

Eight diagrams by Lewis Carroll (of Alice’s Adventures in Wonderland) from his 1897 Symbolic Logic, in which Carroll presents a symbolic method of representing propositions and visually deriving the logical outcomes of syllogisms, fallacies, and soriteses.

“First, let us suppose that the above [Biliteral] Diagram is an enclosure assigned to a certain Class of Things, which we have selected as our ‘Universe of Discourse,’ or, more briefly, as our ‘Univ’.

“Secondly, let us suppose that we have selected a certain Adjunct, which we may call x, and have divided the large Class, to which we have assigned the whole Diagram, into the two smaller Classes whose Differentiæ are x and not-x (which we may call x’), and that we have assigned the North Half of the Diagram to the one (which we may call… the x-Class), and the South Half to the other (which we may call… the x’-Class).

“Thirdly, let us suppose that we have selected another Adjunct, which we may call y, and have subdivided the x-Class into the two Classes whose Differentiæ are y and not-y, and that we have assigned the North-West Cell to the one (which we may call the xy-Class) and the North-East Cell to the other (which we may call the xy’-Class).

“Fourthly, let us suppose that we have subdivided the x’-Class in the same manner, and have assigned the South-West Cell to the x’y-Class, and the South-East Cell to the x’y’-Class” (p22-23).

For example, if x means ‘old’, so that x’ means ‘new’, and if y means ‘English’, so that y’ means ‘foreign’, we have the following diagram:

“Let us agree that a Red Counter [represented below as a dotted circle or as an ‘I’], placed within a Cell, shall mean ‘This Cell is occupied‘ (i.e. ‘There is at least one Thing in it’).

“Let us also agree that a Red Counter, placed on the partition between the two Cells, shall mean ‘The Compartment, made up of these two Cells, is occupied; but it is not known whereabouts, in it, its occupants are.’ Hence it may be understood to mean ‘At least one of these two Cells is occupied: possibly both are.

“Let us also agree that a Grey Counter [represented below as a hollow circle or as an ‘O’], placed within a Cell, shall mean ‘This Cell is empty‘ (i.e. ‘There is nothing in it’)” (p26).

By this formula we can visually represent the following propositions (p34, 35):

“The Reader should now get his genial friend to question him, severely, on [the above] two Tables” (p34).

Let us now support, firstly, “that we change [the Biliteral Diagram] into a Triliteral Diagram by drawing an Inner Square, so as to divide each of its 4 Cells into 2 portions, thus making 8 Cells altogether” (p39).

“Secondly, let us suppose that we have selected a certain Adjunct, which we may call m, and have subdivided the xy-Class into the two classes whose Differentiæ are m and m’, and that we have assigned the N.W. Inner Cell to the one (which we may call… the xym-Class)” (p40) and that we have subdivided the remaining classes in the same manner. “It is evident that we have now assigned the Inner Square to the m-Class, and the Outer Border to the m’-Class” (p40).

Thus we can visually represent propositions of the form (p49):

It is now possible to draw two propositions on the same diagram, one in terms of x and m, the other in terms of m and y, and to visually derive a third proposition in terms of x and y. Consider, for example, the following pair of propositions:

“Some, who deserve the fair, get their deserts;
None but the brave deserve the fair” (p101).

If the “Univ is ‘persons’; m = persons who deserve the fair; x = persons who get their deserts; y = brave” (p140), then the Triliteral Diagram represents that “some m are x [and] no y’ are m”:

The Biliteral Diagram to the right, relating x and y, can be derived from the Triliteral Diagram according to the following procedure: for each quarter of the Triliteral Diagram, “if it contains a ‘I’ in either Cell, it is certainly occupied, and you may mark the… [corresponding] quarter of the Biliteral Diagram with a ‘I’. If it contains two ‘O’s, one in each Cell, it is certainly empty, and you may mark the… Biliteral Diagram with a ‘O'” (p53).

Therefore the derived Biliteral Diagram above concludes that “some brave persons get their deserts” (p140).

This method may also be used to validate the correctness, or expose the fallaciousness, of a proposed syllogism. For example:

“Some epicures are ungenerous;
All my uncles are generous
[Therefore] My uncles are not epicures” (107).

If “Univ. ‘persons’; m = generous ; x = epicures ; y = my uncles” (p145):

“Hence [the] proposed Conclusion is wrong, the right one being ‘Some epicures are not uncles of mine'” (p145).

Writes Carroll, “Mental recreation is a thing that we all of us need for our mental health; and you may get much healthy enjoyment, no doubt, from Games, such as Back-gammon, Chess, and new Game ‘Halma’. But, after all, when you have made yourself a first-rate player at any one of these Games, you have nothing real to show for it, as a result! You enjoyed the Game, and the victory, no doubt, at the time: but you have no result that you can treasure up and get real good out of. And, all the while, you have been leaving unexplored a perfect mine of wealth. Once master the machinery of Symbolic Logic, and you have a mental occupation always at hand, of absorbing interest, and one that will be of real use to you in any subject you may take up. It will give you clearness of thought — the ability to see your way through a puzzle — the habit of arranging your ideas in an orderly and get-at-able form — and, more valuable than all, the power to detect fallacies, and to tear to pieces the flimsy illogical arguments, which you will so continually encounter in books, in newspapers, in speeches, and even in sermons, and which so easily delude those who have never taken the trouble to master this fascinating Art. Try it. That is all I ask of you!” (pXVII).

The reader may pursue the outcome of the following two propositions on his or her own time:

“Nothing intelligible ever puzzles me;
Logic puzzles me” (p102).

One more Qadri, this from his collection of paintings and poems, THE DOT and the dots.

Invocation -76. Click for larger version.

Writes Qadri:

“to find
some meaning in life
is to give one to it
and find,
that it is meaningless.”

Speaking again of shocks, two ink & dye works by tantric artist Sohan Qadri, cataloged in Seeker: The Art of Sohan Qadri. 

Pranayama, 2002, p101. Click for larger version.

Comments Donald Kuspit, “The ecstatic moment of full consciousness of the metaphysical truth about existence is a moment of aesthetic shock: concretizing the metaphysical truth [of the doctrine of Sunyata], Qadri’s icons give us an aesthetic shock. ‘The Pali word samvega is often used to denote the shock or wonder that may be felt when the perception of a work of art becomes a serious experience,’ Ananda Coomaraswamy writes. The perception of a work of art becomes a serious experience when it stirs ‘the will or mind’ to ‘consideration of the Eight Emotional Themes (birth, old age, sickness, death, and suffering arising in four other ways),’ and, ‘in the resulting state of distress, then gladdens it by the recollection of the Buddha, the Eternal Law… when it is in need of such gladdening’. Thus meditation on Qadri’s icons is therapeutic. The tensions in them — between contrasting colors, lines, and rhythms as well as light and dark — evoke our inner conflicts and distress even as their aesthetic resolution gladdens us, finally raising our spirits” (p14).

Purusha, 1999, p82. Click for larger version.

“Thus aesthetic shock is two-sided: it subverts ordinary consciousness by exposing the conflicts hidden by it even as it signals the extraordinary consciousness that resolves them. Qadri’s icons are as divided against themselves — fault lines run through some of them — as they are unified. They shock us into awareness of the eternal law stated in the doctrine of Sunyata. Meditation is not some mindless act of egoistic communion with oneself, but upsets one’s sense of selfhood, however, ultimately calming and enlightening by reason of its revelation of the eternal law. But the way to Buddha-like calm is through aesthetic delight, as Qadri’s icons show” (p14-15).

Speaking of shocks, a diagram by P.D. Ouspensky from his 1949 In Search of the Miraculous.

Ouspensky quotes G., “‘The results of the influences whose source lies outside life [i.e., esoteric influences] collect together within him, he remembers them together, feels them together. They begin to form within him a certain whole. He does not give a clear account to himself as to what, how, and why, or if he does give an account to himself, then he explains it wrongly. But the point is not in this, but in the fact that the results of these influences collect together within him and after a certain time they form within him a kind of magnetic center, which begins to attract to itself kindred influences and in this manner it grows. If the magnetic center receives sufficient nourishment, and if there is no strong resistance on the part of the other sides of a man’s personality which are the result of influences created in life [i.e., nation, climate, family, education, wealth, customs, etc.], the magnetic center begins to influence a man’s orientation, obliging him to turn round and even to move in a certain direction. When the magnetic center attains sufficient force and development, a man already understands the idea of the way and he begins to look for the way. The search for the way may take many years and lead to nothing. This depends upon conditions, upon circumstances, upon the power of the magnetic center, upon the power and the direction of inner tendencies which are not concerned with this search and which may divert a man at the very moment when the possibility of finding the way appears'” (p200).

“‘If the magnetic center works rightly and if a man really searches, or even if he does not search actively yet feels rightly, he may meet another man who knows the way and who is connected directly or through other people with a center existing outside the law of accident, from which proceed the ideas which created the magnetic center'” (p200-201).

Ouspensky’s embodiment and, below, its legend (p204).

A drawing by Edward Ardizzone from his 1953 Tim in Danger.

“It was a lovely day when Tim, Charlotte and Ginger were playing on the beach. The sky was blue, the sea was blue, and the white yachts were sailing in the bay.

“But something was wrong with Ginger. He would mope.

“Charlotte thought that he was remembering the time when he was a ship’s boy and was pining for a life at sea once more. She was right, for early the next morning, when Tim woke up, he found Ginger’s bed empty and a note from Ginger on it to say that he had run away” (p1-2).

Fed up / have run away to see (p3).

A sandpainting by Miguelito from Navajo Medicine Man Sandpaintings (originally published in 1939).

The Shock Painting, plate XXI. Click for larger version.

“Occassionally when a very complete [Fire Dance] ceremony has been agreed upon, the rite of the Shock-caused-by-bear is given. Since Holy Man [who represents man’s contacts between the earth and sky powers] was learning everything, it was performed for him on the fifth day [of a nine-day ceremony]. The painting was made in sand and the patient sat on it. Then one person dressed as a bear and one impersonating Holy Man rushed in [to the hogan] and frightened the patient into a fainting fit. The chanter and all concerned then proceeded to restore the afflicted, after which he would no longer fear anything natural or supernatural.

“The four white tracks leading to the painting signify the tracks of white cornmeal made by Changing Woman [god-mother of man] when Holy Man returned from the Sun’s House [god-father of man]. The base of the painting is a rainbow [a protective measure of Water Sprinkler]. The tracks on the black background are bear tracks. The Big Black Snake… has the markings described for Big Snakes: rectangular figure for snake’s house, chevron for deerhoof or game, curved lines for moon phases… The blue on the neck of the snake represents earthy things and people; the red bands, the breath or life. The spruce twigs around the snake stand for the Dark-circle-of-branches of the Fire Dance” (p66).

A sketch by Charles Altamont Doyle (father of Arthur Conan Doyle) from a diary he kept while interned at the Montrose Royal Lunatic Asylum (1889).

The man to whom life is full of seriousness — he is a cleaner at Sunnyside who does his Work earnestly (p20).

A diagram by Umberto Eco illustrating Harold Conklin‘s study of the Hanunóo color system (“Hanunóo Color Categories”, Southwestern Journal of Anthropology, 1955, v2, p339-344).

Eco’s depiction of the Hanunóo color system, appearing in Marshall Blonsky’s On Signs, p170.

“Color distinctions in Hanunóo are made at two levels of contrast. The first, higher, more general level consists of an all-inclusive, coordinate, four-way classification which lies at the core of the color system. The four categories are mutually exclusive in contrastive contexts, but may overlap slightly in absolute (i.e., spectrally, or in other measurable) terms.

“The four Level I terms are:

1. mabiru: relative darkness (of shade of color); blackness (black)
2. malagti: relative lightness (or tint of color); whiteness (white)
3. marara: relative presence of red; redness (red)
4. malatuy: relative presence of light greenness; greenness (green)

“The three-dimensional color solid is divided by this Level I categorization into four unequal parts; the largest is mabiru, the smallest malatuy. While boundaries separating these categories cannot be set in absolute terms, the focal points (differing slightly in size, themselves) within the four sections, can be limited more or less to black, white, orange-red, and leaf-green respectively. In general terms, mabiru includes the range usually covered in English by black, violet, indigo, blue, dark green, dark gray, and deep shades of other colors and mixtures; malagti, white and very light tints of other colors and mixtures; marara, maroon, red, orange, yellow, and mixtures in which these qualities are seen to predominate; malatuy, light green, and mixtures of green, yellow, and light brown. All color terms can be reduced to one of these four but none of the four is reducible. This does not mean that other color terms are synonyms, but that they designate color categories of greater specification within four recognized color realms.

“The basis of this Level I classification appears to have certain correlates beyond what is usually considered the range of chromatic differentiation, and which are associated with nonlingustic phenomena in the external environment. First, there is the opposition between light and dark, obvious in the contrasted ranges of meaning of lagti and biru. Second, there is an opposition between dryness or desiccation and wetness or freshness (succulence) in visible components of the natural environment which are reflected in the term rara and latuy respectively. This distinction is of particular significance in terms of plant life. Almost all living plant types possess some fresh, succulent, and often ‘greenish’ parts. To eat any kind of raw, uncooked food, particularly fresh fruits or vegetables, is known as pag–laty–un (< latuy). A shiny, wet, brown-colored section of newly-cut bamboo is malatuy (not marara). Dried-out or matured plant material such as certain kinds of yellowed bamboo or hardened kernels of mature or parched corn are marara. To become desiccated, to lose all moisture, is known as mamara (< para, ‘desiccation’)… A third opposition, dividing the two already suggested, is that of deep, unfading, indelible, and hence often more desired material as against pale, weak, faded, bleached, or ‘colorless’ substance, a distinction contrasting mabiru and maarara with malagti and malatuy.

“In short, we have seen that the apparent complexity of the Hanunóo color system can be reduced at the most generalized level to four basic terms which are associated with lightness, darkness, wetness, and dryness. This intracultural analysis demonstrates that what appears to be color ‘confusion’ at first may result from an inadequate knowledge of the internal structure of a color system and from a failure to distinguish sharply between sensory reception on the one hand and perceptual categorization on the other” (Conklin, p341-343).

A diagram of the Laws of Magic, appearing in Isaac Bonewits’s Real Magic (1971).

“A qualitative diagram showing [the Laws] primary interrelationships”. Click for larger version.

Another scroll reproduced in Ethiopian Magic Scrolls.

“This image is recognizably a development of the eight-pointed star [c.f. previous post]. Here the image tends towards formal perfection. A double movement animates it: expansion following the four vertical and horizontal arms and the angel’s heads, and penetration following the four diagonal points. We have noted… that the former are the directions of the Cross (i.e., of a body with outstretched arms), and the latter direction of the penetrating gaze. The black lobate curve articulates this double movement here, so that it appears to begin from a circular form. The eyes of the central face are placed on the transversal axis. If we consider the genesis of this picture through related motifs, we will note that what have become here the radiating points of the central face were originally part of the angel’s clothing. They have been separated from the collar and shifted toward the center, for purely formal reasons.

“The Virgin’s Prayer at Bartos says: ‘Come, you four angels who hold up the four corners of the world and who are called Fertiyal, Ferfay, Fumael and Fananyal’. The winged faces are the angels of the four directions. Who are they guarding? The hidden face of the divine? The owner of the scroll? Satan in prison? All of these explanations are current among dabtaras who make such pictures” (p118).