Sunday, February 20, 2005
The main proportional lines come from the progression of squares, every second square is half the size of the original, and the measures thus obtained are the same as described by Vitruvius.
Distinguished is also the triangle with the size of a square and apex in the navel.
It seems that the drawing, or better the original design as explained by Vitruvius, contains many layers of geometry and symbolism that concord in one single image delineating the proportions of the human body. This idea of 'reason' governing 'form' was the fundamental theme of the Renaissance and is traceable in best architecture and art in general. It would not be odd if Leonardo had a close contact with scholars that spread the source of the Renaissance thought which didn't distinguish between art, science, and magick in terms of conflicting or opposing discourses as is the case today.
Notes:
1 - This and subsequent quotation are from F. Granger's translation, Loeb Classical Library, 1970
http://www.aiwaz.net
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The main proportional lines come from the progression of squares, every second square is half the size of the original, and the measures thus obtained are the same as described by Vitruvius.
Distinguished is also the triangle with the size of a square and apex in the navel.
It seems that the drawing, or better the original design as explained by Vitruvius, contains many layers of geometry and symbolism that concord in one single image delineating the proportions of the human body. This idea of 'reason' governing 'form' was the fundamental theme of the Renaissance and is traceable in best architecture and art in general. It would not be odd if Leonardo had a close contact with scholars that spread the source of the Renaissance thought which didn't distinguish between art, science, and magick in terms of conflicting or opposing discourses as is the case today.
Notes:
1 - This and subsequent quotation are from F. Granger's translation, Loeb Classical Library, 1970
http://www.aiwaz.net
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Saturday, February 12, 2005
"The predominating module of the composition of human body is eight and many lines on the drawing coincide with the lines of the modular plain. The figure in the form of the letter Thau embraces 22 squares of the composition, whereas on each half remains 21 or 3 x 7 squares. 22 and 7 are connected through the rational approximation of p = 22/7.
Number 22 also invokes the total number of Hebrew alefbeth, and numbers 3, 7, and 12 (= 22-3-7) are the numbers of divisions of Hebrew alefbeth into three groups described in Sepher Yetzirah - The Book of Formation, a fundamental kabbalistic treatise on the nature of letters and words, suspected to originate from 13th century. The 32 Paths of Wisdom described in Sepher Yetzirah comprise 10 Sephiroth and 22 Letters. 32 Paths are written in the circumference of the modular square 8x4 = 32. The figure is positioned in the shape of T(hau), the 22nd, last letter of alefbeth. The Tetraktys and the kabbalistic Tree of Life are comparable glyphs, both comprising the ten spheres.
Vitruvius is reporting that the navel is the exact center of the human body. The circle on Leonardo's drawing has it's center in the navel, but if the figure is 'squared' the center becomes the phallos which is, concerning this drawing from the compositional point of view, more important, since it is the center of the underlying geometry that outlines the basic features of the figure.
The most fundamental composition consists of a circle, a square, and a triangle, a sigillum known to magicians and alchemist, sometimes called the Universal Seal of Light or the Seal of Hermes. The compositional triangle on this drawing is concealed, even though that it outlines important segments. It is drawn in the circle within the square and it coincides with the progression of squares as depicted on the illustration."
in
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"The two squares, the drawn and the projection square, form an octagram Pell's series are the progressions that approximate the geometry of proportions originating from the octagram The first of Pell's series is:
1 2 5 12 29 70 169 ...
Both main numbers 24 (2x12) and 29 are members of this series. Leonardo used this progression to rationalise irrational geometry of square root of 2 that rules the geometry of the octagram. As a proof, all other numbers are derived as a combination of the members of the series. The distance between the two centers, the navel and Phallos, is according to rationalized geometry 2,5 palms, and it seems that the position of palms touching the square in Thau formation of the figure equals 9,5 palms, again the measure derived from rational approximation of the geometry of the octagram by means of Pell series. Also the diagonal of the square is calculated from the series as 2x(5+12) = 34 palms. The composition founded in octagram is one of the most spread cannons of proportions in ancient and classical architecture clearly presented by enormous opus of research done by Prof. Tine Kurent of Ljubljana School of Architecture, Slovenia. Almost every important christian church has dome placed on an octagram, and gematric value of Greek spelling for Jesus, Ihsous = 888 associates the number 8 (octagram) with Jesus Christ.
Most importantly even Vitruvius mentions the value of the octagon, though in a bit obfuscating manner, while describing the winds:
4. Some have held that there are four winds: the Solanus from the equinoctial east, the Auster from the south, Favonius from the equinoctial west, and Septentrio from the north. But those who have inquired more diligently lay down that there are eight: especially indeed Andronicus of Cyrrha, who also, for an example, built at Athens an octagonal marble tower, and, on the several sides of the octagon, had representations of the winds carved opposite their several currents.
Book I. c. VI: 4
Further on he describes that even the town-planning has to be done according to the octagonal scheme of the winds. It seems that Leonardo incorporated, in multiple layers, the whole cannon suggested by Vitruvius. It is a strange coincidence that the area of a square with a side of 24 palms is 576 square palms, which is gematric equivalent of Greek word for the wind meaning also Spirit, Pneuma = 576.
The calculated area of the circle is 660 square palms, and the difference between the circle and the square is 660-576=84, which is invoking the gematric value of the master himself:
LEONARDO = 12+5+15+14+1+18+4+15 = 84.
The 'fundamental' measure of 24 palms comes directly from Vitruvius' definition of human height being 4 cubits or 24 palms. Number 4 is of great importance in the composition of the drawing, emphasized with a square. Number 24 is important because it is 1x2x3x4 = 24, comprising the multiplied members of the Tetraktys. Vitruvius postulates the smallest module the division of 10 which also resembles the Tetraktys along with the previously mentioned diagonal of the square, 34 palms long: (1x2x3x4)+(1+2+3+4) = 34 - the Tetraktys numbers multiplied and added up. Half way between 24 and 34 is the diameter of the circle, 29 palms: (24+34)/2 = 29."
in
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Saturday, February 05, 2005
"The subject of Ginevra de' Benci has nothing of the Mona Lisa's inward amusement, and also nothing of Cecilia's gentle submissiveness. The young woman looks past us with a wonderful luminous sulkiness. Her mouth is set in an unforgiving line of sensitive disgruntlement, her proud and perfect head is taut above the unyielding column of her neck, and her eyes seem to narrow as she endures the painter and his art. Her ringlets, infinitely subtle, cascade down from the breadth of her gleaming forehead (the forehead, incidentally, of one of the most gifted intellectuals of her time). These delicate ripples are repeated in the spikes of the juniper bush.
The desolate waters, the mists, the dark treess, the reflected gleams of still waves, all these surround and illuminate the sitter. She is totally fleshly and totally impermeable to the artist. He observes, rapt by her perfection of form, and shows us the thin veil of her upper bodice and the delicate flushing of her throat. What she is truly like she conceals; what Leonardo reveals to us is precisely this concealment, a self-absorption that spares no outward glance."
in
http://www.ibiblio.org
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Thursday, February 03, 2005
"The below passage, from Vitruvius' De Architectura, is a source of inspiration for Leonardo's drawing in his sketchbook, the famous Vitruvian Man. This passage is also providing the Key of the composition of the ancient architecture, firmly revived in the Renaissance. The emphasize is on rationalisation of geometry, by means of small whole numbers to build the composition - in this manner Vitruvius delineates the proportion of a male human body that Leonardo so faithfully reproduced. Rationalisation as the basic rule of composition and the simplicity of an ingenious design (proportioned by means of small whole numbers) are often ignored.
Both Leonardo and Vitruvius make no mention of the Phallos as the center of the square, but it plays an important role. The side of the square is 4 cubits or 24 palms as can also be measured on the ruler beneath the square, and deduced from the Vitruvius' text. The diagonal of such a square comes close to 34 palms (33.94... exactly). If we rotate the square around Phallos for 45 degrees we get the upper point of the circle, and from this we can calculate the diameter of the circle as 29 palms (the difference between the square and the circle is 5 palms)."
in
aiwaz.net institute
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Vitruvius, De Architectura: THE PLANNING OF TEMPLES
"1. The planning of temples depends upon symmetry: and the method of this architects must diligently apprehend. It arises from proportion (which in Greek is called analogia). Proportion consists in taking a fixed module, in each case, both for the parts of a building and for the whole, by which the method of symmetry is put to practice. For without symmetry and proportion no temple can have a regular plan; that is, it must have an exact proportion worked out after the fashion of the members of a finely-shaped human body.
2. For Nature has so planned the human body that the face from the chin to the top of the forehead and the roots of the hair is a tenth part; also the palm of the hand from the wrist to the top of the middle finger is as much; the head from the chin to the crown, an eighth part; from the top of the breast with the bottom of the neck to the roots of the hair, a sixth part; from the middle of the breast to the crown, a fourth part; a third part of the height of the face is from the bottom of the chin to the bottom of the nostrils; the nose from the bottom of the nostrils to the line between the brows, as much; from that line to the roots of the hair, the forehead is given as the third part. The foot is a sixth of the height of the body; the cubit a quarter, the breast also a quarter. The other limbs also have their own proportionate measurements. And by using these, ancient painters and famous sculptors have attained great and unbounded distinction.
3. In like fashion the members of temples ought to have dimensions of their several parts answering suitably to the general sum of their whole magnitude. Now the navel is naturally the exact centre of the body. For if a man lies on his back with hands and feet outspread, and the centre of a circle is placed on his navel, his figure and toes will be touched by the circumference. Also a square will be found described within the figure, in the same way as a round figure is produced. For if we measure from the sole of the foot to the top of the head, and apply the measure to the outstretched hands, the breadth will be found equal to the height, just like sites which are squared by rule.
4. Therefore if Nature has planned the human body so that the members correspond in their proportions to its complete configuration, the ancients seem to have had reason in determining that in the execution of their works they should observe an exact adjustment of the several members to the general pattern of the plan. Therefore, since in all their works they handed down orders, they did so especially in building temples, the excellences and the faults of which usually endure for ages."
in
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Tuesday, February 01, 2005
"The concept that the ventricles of the brain are responsible for its major functions derives from Greek antiquity. The soul resides in the head, but since the soul is incorporeal its locus is in the cavities (i.e. fluid-filled ventricles) rather than in the surrounding brain tissue. Some Greek scientists, most notably Aristotle, argued that the heart and not the head is the seat of sensation and cognitive functions; one loses consciousness upon excessive bleeding, and many emotions are experienced viscerally (e.g. one has a "gut feeling" or an emotional "heart-ache"). However the majority of philosophers and scientists assigned mental functions to the brain. By Leonardo's time, the ventricular theories had become entrenched in philosophy. The brain was thought to contain an anterior ventricle (typically thought to contain the senso comune, and also phantasy and imagination); a second ventricle that mediated cognition; and a posterior ventricle that serves memory.
The Common Sense [senso comune], is that which judges of things offered up to it by the other senses. The ancient speculators have concluded that that part of man which constitutes his judgment is caused by a central organ to which the other five senses refer everything by means of impressibility [impressiva]; and to this centre they have given the name Common Sense. And they say that this Sense is situated in the centre of the head between Sensation and Memory. And this name of Common Sense is given to it solely because it is the common judge of all the other five senses i.e. Seeing, Hearing, Touch, Taste and Smell. This Common Sense is acted upon by means of Sensation which is placed as a medium between it and the senses. Sensation is acted upon by means of the images of things presented to it by the external instruments, that is to say the senses which are the medium between external things and Sensation. In the same way the senses are acted upon by objects. Surrounding things transmit their images to the senses and the senses transfer them to the Sensation. Sensation sends them to the Common Sense, and by it they are stamped upon the memory and are there more or less retained according to the importance or force of the impression. That sense is most rapid in its function which is nearest to the sensitive medium and the eye, being the highest is chief of the others. Of this then only we will speak, and the others we will leave in order not to make our matter too long. Experience tells us that the eye apprehends ten different natures of things, that is: Light and Darkness, one being the cause of the perception of the nine others, and the other its absence:--Colour and substance, form and place, distance and nearness, motion and stillness.
Leonardo da Vinci, quoted in Richter no. 838 (W. An. II. 202a [B]):
How the five senses are the ministers of the soul
The soul seems to reside in the judgment, and the judgment would seem to be seated in that part where all the senses meet; and this is called the Common Sense and it is not all-pervading throughout the body, as many have thought. Rather is it entirely in one part. Because, if it were all-pervading and the same in every part, there would have been no need to make the instruments of the senses meet in one centre and in one single spot; on the contrary it would have sufficed that the eye should fulfil the function of its sensation on its surface only, and not transmit the image of the things seen, to the sense, by means of the optic nerves, so that the soul-for the reason given above-may perceive it in the surface of the eye. In the same way as to the sense of hearing, it would have sufficed if the voice had merely sounded in the porous cavity of the indurated portion of the temporal bone which lies within the ear, without making any farther transit from this bone to the common sense, where the voice confers with and discourses to the common judgment. The sense of smell, again, is compelled by necessity to refer itself to that same judgment. Feeling passes through the perforated cords and is conveyed to this common sense. These cords diverge with infinite ramifications into the skin which encloses the members of the body and the viscera. The perforated cords convey volition and sensation to the subordinate limbs. These cords and the nerves direct the motions of the muscles and sinews, between which they are placed; these obey, and this obedience takes effect by reducing their thickness; for in swelling, their length is reduced, and the nerves shrink which are interwoven among the particles of the limbs; being extended to the tips of the fingers, they transmit to the sense the object which they touch. The nerves with their muscles obey the tendons as soldiers obey the officers, and the tendons obey the Common Sense as the officers obey the general. Thus the joint of the bones obeys the nerve, and the nerve the muscle, and the muscle the tendon and the tendon the Common Sense. And the Common Sense is the seat of the soul, and memory is its ammunition, and the impressibility [imprensiva] is its referendary since the sense waits on the soul and not the soul on the sense. And where the sense that ministers to the soul is not at the service of the soul, all the functions of that sense are also wanting in that man's life, as is seen in those born mute and blind.
in
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