Bruno’s Mathesis
June 21st, 2009
Three diagrams representing the Hermetic trinity, as devised by Giordano Bruno in his 1588 Articuli centum et sexaginta adversus huius tempestatis mathematicos atque philosophos, and as appearing in Frances A. Yates’s 1964 Giordano Bruno and the Hermetic Tradition.
“These three figures are said to be most ‘fecund’, not only for geometry but for all sciences and for contemplating and operating” (p314).

Figura Mentis, p307. C.f. Cusanus’s paradigmatic diagram and the mouth of Ra.
“There is… a ‘supernal triad’, consisting of the Father, or mind, or plenitude; of the Son, or the primal intellect; of Light which is the spirit of all things, or the anima mundi… ‘Ancient theologians,’ Bruno continues, understand by the Father, mind or mens, who generates intellect, or the Son, between them being fulgor, or light or love. Hence one may contemplate in the Father, the essence of essences; in the Son the beauty and love of generating; in fulgor, or light, the spirit pervading and vivifying all. Thus a triad may be imagined; ‘pater, mens; filium verbum; et per verbum, universa sunt producta’. From mens proceeds intellectus; from intellectus proceeds affectus or love. Mens sits above all; intellectus sees and distributes all; love makes and disposes all. This last is light or fulgor which fills all things and is diffused through all. Whence it is called the anima mundi and spiritus universorum, and is that of which Virgil spoke when he said ‘spiritus intus alit’” (p309-310).

Figura Intellectus, p307.
“A remarkable feature of [Bruno's] De monade is the use which [he] makes in it of Cecco d’Ascoli’s necromantic commentary on the Sphere of Sacrobosco… The longest quotation from Cecco comes when Bruno is discussing ten, the number sacred to the ten Sephiroth. He mentions these, but later describes orders of demons or spirits whose hierarchies can be contemplated in the intersection of circles. ‘These (the orders of demons) are contemplated in the intersection of circles, as Astophon says in libro Mineralium constellatorum. O how great, he says, is the power in the intersection of circles.’ This is a quotation of Cecco’s quotation from the Astophon who is to be heard of nowhere else and was probably invented by Cecco. It throws light on why intersecting circles are such a prominent feature in the diagrams by which Bruno represents his Hermetic trinity…” (p322-323).

Figura Amoris, p307.
“Light, says Bruno, is the vehicle in the inner world through which the divine images and intimations are imprinted, and this light is not that through which normal sense impressions reach the eyes, but an inner light joined to a most profound contemplation, of which Moses speaks, calling it ‘primogenita’, and of which Mercurius also speaks in Pimander. Here the Genesis-Pimander equation, so characteristic of the Hermetic-Cabalist tradition, is applied by Bruno to creation of the inner world” (p336).
The Art of Place and Journey
May 29th, 2009
Two paintings by Aboriginal artists, collected in Wally Caruana’s Aboriginal Art.

Paddy Jupurrurla Nelson, Paddy Japaljarri Sims, and Larry Jungarrayi Spencer, Yanjilypiri Jukurrpa (Star Dreaming), 1985 (f109).
“The Australian deserts appears empty and inhospitable to those who do not know them, but to the Aboriginal groups who inhabit these areas, the lands created by their ancestors and infused with their powers are places rich in spiritual meaning and physical sustenance.
“Geographically, the desert includes mountain ranges and spectacular rock-formations, grassy plains, strands and eucalypt and mulga trees, lakes, salt pans, sandhills, and stretches of stony country occasionally broken by seasonal watercourses and rivers and punctuated by rare permanent rockholes, springs, waterholes and soakages… Across this landscape spreads a web of ancestral paths travelled by the supernatural beings on their epic journeys of creation in the Jukurrpa or Dreaming, linking the topography firmly to the social order of the people” (p97).
“The basic elements of the pictorial art are limited in number but broad in meaning… Characteristic of the range of conventional designs and icons are those denoting place or site, and those indicating paths or movement. Concentric circles may denote a site, a camp, a waterhole or a fire. In ceremony, the concentric circle provides the means for the ancestral power which lies within the earth to surface and go back into the ground. Meandering and straight lines may indicate lightening or water courses, or they may describe the paths of ancestors and supernatural beings. Tracks of animals and humans are also part of the lexicon of desert imagery. U-shapes usually represent settled people or breasts, while arcs may be boomerangs or wind-breaks, and short straight lines or bars are often spears and digging sticks. Fields of dots can indicate sparks, fire, burnt ground, smoke, clouds, rain, and other phenomena.
“The interpretations of these designs are multiple and simultaneous, and depend on the viewer’s ritual knowledge of a site and the associated Dreaming. The meanings are elaborated and enhanced by the various combinations or juxtapositions of designs in the paintings, and also by the social and cultural contexts within which they operate — whether for ceremony or public domain, for instance. The combinations of designs allow for endless depth of meaning, and artists in decribing their work distinguish between those meanings that are indented for public revelations and those which are not, and provide the appropriate level of interpretation” (p98-99).

Mick Namarari Tjapaltjarri, Bandicoot Dreaming, 1991 (f98).
“It is by the acquisition of knowledge, not material possessions, that one attains status in Aboriginal culture. Art is an expression of knowledge, and hence a statement of authority. Through the use of ancestrally inherited designs, artists assert their identity, and their rights and responsibilities. They also define the relationships between individuals and groups, and affirm their connections to the land and the Dreaming” (p14-15).
“As a statement of authority, the aesthetic in art is often articulated in terms of ritual knowledge. Through art, individuals express their authority and knowledge of a subject, the land and the Dreaming, and artists will use their authority to introduce change and innovation” (p16).
“In ritual, paintings… are not intended to be static images requiring studied contemplation. Rather, since designs embody the power of supernatural beings, they are intended to be sensed more than viewed” (p59-60).
The Symbol as Expression of a Will
May 20th, 2009
An illustration of a Pharaonic tableau by Lucie Lamy from R. A. Schwaller de Lubicz’s Symbol and the Symbolic (also see previous posts).

Seth, Master of the South, and Horus, Master of the North, the perpetual antagonists. Both of their heads emerge from a single body that stands on two horizontal bows evoking the energy potential that can make manifest the two inverse forces through the stimulation of the passage of Re (fig3).
Writes Schwaller de Lubicz, “Every circle, as a circular movement, has a center. This center controls this continuous and regular curve, which is closed; it is attractive, just as the circumference is repellent (centrifugal). This center is an abstract power which rules the phenomenon of circular movement. Two centers make an elliptical (or assimilated) movement if the curve is closed. If the curve is not closed but is superimposed, the center beomes a line or figure, horizontal for a spiral, vertical for a helicoidal curve, etc.
“The center controls; it is the will of the figure. Three axes of equal length, intersecting at 90°, are the will of the cube. The form of movement and the form of the Euclidian volume are in the center and in its radiation.
“I say that the will of a rotating sphere is the magnetic axis, and its equator is the centrifugal electrical effect. On the other hand, every magnetic effect is contradicting will, which produces the dilating, equatorial electrical effect. Inversely, every circlular electrical current provokes the magnetic axial effect. Will is esoteric; effect is exoteric.
“But where, then, is the will of the ‘container,’ the non-Euclidean volume?
“Its will is the seed, that is, the specification of the ‘contents,’ hence a genesis — that is, Time, for Time is none other than genesis. Genesis appears to us as Time.
“Now, all will of movement and of form is a specification of Energy. Will is thus identified with the seed, as the specifier, and, as genesis, appears as Time or duration.
“The seed ordains the volume, that is, Space; the genesis of this Space ordains Time. Will is what Lao-Tzu calls ‘the empty hub of the wheel.’
“The Absolute Will of the Origin includes all specifications.
“Everything that is naturally specified is a symbol and the expression of a will, hence of a specifying seed of non-objectifiable Energy: the Container, the non-polarized Sprit-substance. The specifying Will, the ‘Fire’ of the seed, was called the ‘odor’ by ancient Egyptians — the ‘odor’ of the Neter, (that is, in an esoteric sense, that which is emanated by the Neter like an ejaculated seed).
“The contained will must always be sought in the symbol, when the symbol is selected for an esoteric teaching. The character of this Will is that which will always compel Spirit — non-polarized Energy — to define itself in Time and Space, hence in the form of the symbol. This is the ‘magical’ meaning of the symbol. With regard to Spirit, this ‘magic’ operates like the Platonic Idea, just as rhythm acts on our will of movement; we obey despite and at odds with everything, even when we do not give in” (p69-70).
The Five Aspects of Perceptual Contemplation
April 30th, 2009
A 1530 painting by a follower of Massys, appearing in John Armstrong’s Move Closer: An Intimate Philosophy of Art.
Armstrong describes: contemplation is the “scrutiny of what is there to be seen. It is, literally, spending time with [an] object — not just time around it or standing before it, but time devoted to looking at it. ‘Contemplation’ has an august history used in Western thought to describe the mind’s approach to God and in Eastern philosophy to characterize the highest state of existence, but it remains — even in more modest uses — an obscure term. What goes on when we contemplate something, what are we actually doing?
“The process of perceptual contemplation of an object has, classically, five aspects:
1. Animadversion: noticing details.
2. Concursus: seeing relations between parts.
3. Hololepsis: seizing the whole as the whole.
4. The lingering caress.
5. Catalepsis: mutual absorption” (p81).
“Contemplation — in its initial aspect of animadversion — is time spent noticing details; that is, the process of becoming visually aware of parts of the picture which our habitual rapid scanning tends to gloss over. This is a process which sometimes requires conscious effort, we feel we are literally turning our attention on to different parts of the canvas and saying to ourselves: Well now, what is actually there?” (p83).

Follower of Massys, St Luke Painting the Virgin and Child, circa 1530 (p85).
“Concursus… involves seeing together many individual elements of the picture. Its pay-off comes in an enrichment of visual significance, of meaning. Scrutiny of a work of art frequently involves a rhythm of attention to individual parts and to the relations between those parts. This rhythm is required by art and it is also native to the perceiving mind. In fact we can see here how works of art respect and play up to the natural character of exploratory and synthetic attention; it is a native resource of the mind which we can bring into active, and developed, service in the engagement with works of art and which artists usually presuppose we will bring into service” (p91).
“The ambition of concursive attention — the ambition of drawing things together and seeing them in relation to each other — naturally expands to incorporate more and more elements of the work; its logical maximum reveals a further aspect of contemplation” (p91): hololepsis. “Hololepsis yields an archetype of completeness and coherent explanation — thus responding to two of the great aims of mental activity. The contemplation of art of this kind and in this way can satisfy yearnings which the world generally frustrates. The world frequently springs the unexpected and sprawls in seemingly meaningless disorder. The prestige of systems of total explanation — religious, scientific, historical, philosophic — indicates a general need to grasp the world as a coherent whole in the face of its apparent confusion. A work of hololeptic art has the advantage over some of these systems in that its coherence does not rest upon falsehood; it has the advantage over others that what it offers is visible and palpable rather than abstract. Yes, of course, the price a work of art pays for this is that its completeness is bounded by its own small physical extent. It answers a yearning, but only in a restricted area. Hololeptic contemplation, thus, links the experience of art to the wider demands of reflective life and suggests how, to a certain kind of person, the experience of art could be of prime private importance” (p95).
“When we keep our [hololeptic] attention fixed upon an object which attracts us [a lingering caress], two things tend to happen: we get absorbed in the object and the object gets absorbed into us [catalepsis]… The quality and virtue of contemplation may depend… upon what it is we are giving ourselves over to. We can visually contemplate anything which we can see; but do some objects reward this kind of attention more than others? The belief that it makes a difference what you contemplate relies upon the assumption that what you contemplate gets inside you; contemplation is the spiritual analogue of eating” (p99-100).
Diterlizzi’s Modron Memories
April 19th, 2009
Speaking of modrons, a duodrone drawing by Tony Diterlizzi, reprinted in Dragon magazine (April 2007, #354).

Reminisces Diterlizzi: “If you’ve had a chance to see the Planescape books (especially the early ones from ‘94), you’ll see something amazing that happened in RPGs: a new philosophy on how gaming booklets could be presented. It wasn’t just my art — it was the awesome concepts and story hooks, and the (then) state-of-the-art graphic design and production that made these gaming supplements stand out. It was about a great group of people who were really excited about creating something new and imaginative for gamers who were tired of the usual hack-n-slash dungeon crawl. And I was honored to be a part of it.
“I did so much art back in those days. I don’t own much of it anymore, I sold most of it off to my loyal fans over the years at various cons. But there are a few gems that I still treasure and have to this day, and among those are my drawings of the modrons.
“I remember designer Zeb Cook phoning me up while I was working on the campaign setting to tell me that they were toying with the idea of re-introducing the modrons via Planescape. My response was, ‘Those weird little circle and square guys from Monster Manual II?’
“He replied, ‘Those would be the ones,’ and encouraged me to revisit the concept behind them. I did, and knew right away that they HAD to be in Planescape” (p41).
“Anyways, I moved on from gaming to pursue my dream of creating fantastic tales for children, and did my last fully illustrated Planescape book, The Planewalker’s Handbook, in my New York City studio in 1996. Of course, there was a modron in it.
“The rethinking of how a hackneyed or contrived character looks was a very big lesson for me. That type of thinking is what ultimately fueled the designs of the faeries, trolls, and goblins that inhabit all of The Spiderwick Chronicles books that I did later on with author Holly Black…” (p42).
Tim All Alone
March 9th, 2009
Another drawing by Ardizzone, this from his 1957 Tim All Alone.
Having found his mother at last, “Tim told her all about his adventures” (p43).

The flames were tremendous (p43).
Carroll’s Symbolic Logic
March 2nd, 2009
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).
Qadri on Meaning
February 10th, 2009
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.”
A Moment of Aesthetic Shock
January 24th, 2009
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).
The Search for the Way
January 21st, 2009
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).
| V | life |
|---|---|
| H | an individual man |
| A | influences created in life, that is, in life itself — the first kind of influences |
| B | influences created outside life but thrown into the general vortex of life — the second kind of influences |
| H1 | a man, connected by means of succession with the esoteric center or pretending to it |
| E | esoteric center, standing outside the general laws of life |
| M | magnetic center in man |
| C | influence of man h1 on man h; in the event of his actually being connected with the esoteric center, directly or by succession, this is the third kind of influences. This influence is conscious, and under its action at the point m, that is, in the magnetic center, a man becomes free from the law of accident |
| H2 | a man, deceiving himself or deceiving others and having no connection, either directly or by succession, with the esoteric center |

