Commentary on Poem "Vanishing Point":|
Matterhorn, K2, Everest he has scaled them all
Matterhorn is a mountain in the Pennine Alps on the border between Switzerland and Italy.
Its summit is 14,692 feet high, making it one of the highest peaks in the Alps. The four steep faces,
rising above the surrounding glaciers, indicate the four compass points.
K2 is the second-highest mountain on Earth after Mount Everest.
With a peak elevation of 28,251 feet, K2 is part of the Karakoram Range, and is located on the border between the
China and Pakistan. K2 is known as the Savage Mountain due to the difficulty of ascent and the 2nd highest fatality
rate among the "eight thousanders" for those who climb it. For every four people who have reached the summit,
one has died trying. K2 has never been climbed in winter.
Mount Everest is the tallest mountain on Earth. It literally means the top or the head
of the sky. Mount Everest touches the borders of China, Tibet, and Nepal and is a part of the Himalayan Range.
Its total height above sea level is 29,029 ft. The first successful ascent was by the New Zealander Edmund Hillary
and Tenzing Norgay, a Nepali sherpa climber. They reached the summit at 11:30 a.m. local time on 29 May 1953.
wikipedia.org; K2 drawing by Montgomery,
wikipedia.org; Mt. Everest, famouswonders.com)
Matterhorn (14,692 ft), East
& northside view from Zermatt
K2 (28,251 ft), Sketch of K1 & K2
by Thomas Montgomerie (1856)
Mount Everest (29,029 ft)
Tallest mountain on Earth
one vast peak he'll never reach no matter how hard he tries
The previous line tells about the mountaintops he has conquered. These are metaphors for worldly achievements.
However, in the spiritual realm, there is one vast peak that will elude all attempts at conquest.
The vanishing point is a metaphor for such spiritual goals that will keep questers busy for a lifetime
call it waters of Night or a mirage
A mirage is a naturally occurring
optical phenomenon in which light rays are bent to produce a displaced image of distant
objects or the sky. The word comes to English via the French mirage, from the Latin mirare,
meaning "to look at, to wonder at". This is the same root as for "mirror" and "to admire".
I've replaced "optical illusion" with "waters of the Night" as example of a mirage.
This image comes from the last line of James Joyce's Finnegans Wake
"Beside the rivering waters of, hitherandthithering waters of. Night!"
Dew Symbolism: All that comes down from the heavens (thunderbolt, aerolite, meteorite, rain or dew) has a sacred
character. But dew has a double significance, alluding also to spiritual illumination, since it is the true
forerunner of dawn and of the approaching day. The clear, pure water of dew is, according to some traditions,
closely connected with the idea of light. There are occasional references in the Far East to the "tree of sweet dew"
situated on mount Kuen-Lun, the equivalent of the Hindu Meru and other sacred mountains symbolizing the world-axis.
Light spreads outwards from this tree and, through the process of synaesthesia, it has come to be known as the "singing
tree" of legend and folklore (J.E. Cirlot, A Dictionary of Symbols, 1962, p. 77).
(Images: Morning Dew,
Millie Says; Dewdrop on blade of grass,
wikipedia.org; Dew on spider web,
wikipedia.org; Dew of Samaria,
Morning dew on grass
Dewdrop on blade of grass
Dew on spider web
Dew of Samaria, Israel
the more he approached it the further the goal receded from him
The deep mysteries of the soul cannot be grasped like material objects.
Even enlightened masters cannot explain it. Perhaps this is the reason
why Buddha (Flower Sermon) and Christ
(John 18.38) preferred to remain silent.
Here's an attempt to express the ineffable by the poet
Kenneth Rexroth in his
"The Silver Swan" from The Morning Star (1979):
(Images: Bridge & road to vanishing point,
Foggy Road, Crow Edge, England, by Andrew Lee, www.flickr.com)
I am dispossessed, only
An abyss without limits.
Only dark oblivion
Of sense and mind in an
Infinitely away burns
A minute red point to which
I move or which moves to me.
Time fades away. Motion is
Not motion. Space becomes Void.
Kenneth Rexroth (1905-1982)
The Complete Poems of Kenneth Rexroth
"The Silver Swan" XVII.55-64
Edited by Sam Hamill & Bradford Morrow
Copper Canyon Press, Port Townsend, WA, 2003, p. 738
Leonardo and Alberti tackled this problem in their art
Leonardo da Vinci (1452-1519)
was an Italian polymath: painter, sculptor, architect, musician, scientist, mathematician, engineer,
inventor, anatomist, geologist, cartographer, botanist and writer. Leonardo has often been described
as the archetype of the Renaissance Man, a man of "unquenchable curiosity" and "feverishly inventive imagination".
He is widely considered to be one of the greatest painters of all time and perhaps the most diversely
talented person ever to have lived.
Leon Battita Alberti (1404-1472) was an Italian author,
artist, architect, poet, priest, linguist, philosopher, and cryptographer, and general Renaissance humanist polymath.
Alberti regarded mathematics as the common ground of art and the sciences. "To make clear my exposition in writing
this brief commentary on painting," Alberti began his treatise, Della pittura (On Painting),
"I will take first from the mathematicians those things with which my subject is concerned."
The Last Supper
measures 15 feet x 29 feet and covers an end wall of the dining hall at the monastery of Santa Maria delle Grazie
in Milan, Italy. The angles and lighting draw attention to Jesus, whose head is located at the vanishing point
for all perspective lines.
Leonardo da Vinci, wikipedia.org;
Leon Battista Alberti, neilleach.wordpress.com;
Leonardo's Last Supper, wikipedia.org)
Dürer wrote about it in his Instruction on Measurement
Albrecht Dürer (1471-1528) was a German painter,
printmaker, mathematician, engraver, and theorist from Nuremberg. His prints established his reputation across
Europe when he was still in his twenties, and he has been conventionally regarded as the greatest artist of
the Northern Renaissance ever since. Even though he was the best artist in Germany, Dürer went to Italy
(1494-1495 & 1505-1507) to learn more on the art of perspectives. There is a receipt of his purchase of
Euclid's Geometry in Latin while he was in Venice. While there's no record of Dürer meeting
with Leonardo or Alberti, he was taught by Luca Pacioli
or Bramante on the principles of linear perspective
while he was in Bologna. Dürer's work on geometry is discussed in Underweysung der Messung
(Instruction on Measurement), an assortment of mechanisms for drawing
in perspective from models, such as the camera lucida and provides woodcut illustrations of these methods
that are often reproduced in discussions of perspective.
Man Drawing a Lute, 1523 woodcut, ouhos.org)
This vision gave birth to the Renaissance
parallel lines meeting at the horizon
at the apex called the vanishing point
Perspective (from Latin perspicere, to see through)
in drawing and graphic arts, is an approximate representation, on a flat surface (paper), of an image
as it is seen by the eye. The two most characteristic features of perspective are that objects are drawn:
(1) Smaller as their distance from the observer increases, and (2) Foreshortened: the size of an object's
dimensions along the line of sight are relatively shorter than dimensions across the line of sight.
Prior to the Renaissance, a clearly modern optical basis of perspective was given in 1021, when
Alhazen or Ibn al-Haytham, (965-1040 AD),
an Iraqi physicist and mathematician, in his Book of Optics
(Kitab al-manazir), explained that light projects conically into the eye.
By the 14th century, Alhazen's Book of Optics was translated to Italian Deli Aspecti.
It inspired Renaissance artists Lorenzo Ghiberti, Filippo Brunelleschi, Melozzo da Forli, and Donatello
to use perspectives in their artworks. Leonardo Battista Alberti, Leonardo da Vinci and Piero della Francesca
also incorporated perspectives in their paintings. Pietro Perugino's usage of perspective in his fresco
Christ Handing the Keys to St. Peter at the Sistine Chapel (1482) helped bring the Renaissance to Rome.
While there are numerous artworks depicting Renaissance perspectives,
I've chosen Perugino's painting
for two reasons. First, Perugino taught Raphael, who later painted
School of Athens (1511) that outshined his master. Second the image of Christ giving the Keys to Peter is echoed in
the last line of Joyce's Finnegans Wake: "The keys to. Given!" (628.15).
Joyce also uses "Given now ann linch you take enn all" (293.18-19).
What was Joyce given? Linch means "a ledge; a right-angled projection", that may
refer to Pythagorean geometry. Linch is also a collection of hamlets in
West Sussex, England featuring a 1712 St. Lukes Church with steeple and facade
in the Platonic Lambda shape. Finally, the word lapis appears before the Proclus diagram (293.11).
Lapis lazuli with an intense blue color has been associated
with the Philosopher's Stone, an alchemical substance that
can turn lead into gold. The αλπ diagram symbolizes the Soul Mysteries handed down from
to Proclus to
that he's sharing with us in Finnegans Wake.
(Image: Perugino's Christ Handing the Keys to St. Peter, wikipedia.org)
Here the road is a mountain laid flat on earth
Unlike mountains and hills rising vertically that can be climbed, the "vanishing point road"
appears as "a mountain laid flat on earth". While this "flat mountain" may not be as strenuous
to traverse as real mountains, nevertheless it poses a challenge for hikers who try to reach its end. That's
because the road's apex is an optical illusion or mirage.
(Images: Burgundian Vineyard,
photograph by Geoff Martin, www.tonmeister.ca; Highway Road, stacey-'s photstream, www.flickr.com)
some call him a fool going nowhere
THE FOOL (0):
The zeroth trump or Major Arcana card of Tarot decks, the Fool is the spirit in search of experience.
The Fool Tarot card (at left) is from the Rider-Waite Tarot Deck (1909),
illustrated by Pamela Colman Smith from instructions of mystic
The Fool represents the mystical cleverness bereft of reason within us, the childlike ability to tune into
the inner workings of the world. The sun shining behind him represents the divine nature of the Fool's
wisdom and exuberance, holy madness or 'crazy wisdom'. On his back are all the possessions he might need.
In his hand is a rose, showing his appreciation of beauty. He is seemingly unconcerned that he is
standing on a precipice, apparently about to step off. The dog next to him may be barking and
warning him of his impending fall. This raises the question "Is The Fool making a mistake, or
is The Fool making a leap of faith?" Interpretations: The number 0 is a perfect significator
for the Fool, as it can become anything when he reaches his destination as in the sense of "joker's wild".
The Jester is symbolic of common sense and of honesty,
notably in King Lear, the court jester is a character used for insight and advice on the part of
the monarch, taking advantage of his license to mock and speak freely to dispense frank observations
and highlight the folly of his King. Only as the lowliest member of the court can the jester be the King's most useful adviser.
In the Lakota tribe, Heyóka play contrarians, jesters, and sacred clowns. They act
both as a mirror and a teacher, using extreme behaviors to mirror others, thereby forcing them to
examine their own doubts, fears, hatreds, and weaknesses. They are healers through laughter and
awaken people to deeper meaning and concealed truth. The root of the word "fool" is from the Latin
follis, which means "bag of wind" or that which contains air or breath.
We had seen earlier how breath is linked to the human soul (Genesis 2.7).
Zero is nothing, a lack of hard substance, and as such it may reflect a non-issue or lack of cohesiveness for the subject at hand.
Since Sunyata (emptiness and the void) is cultivated in Buddhist practice to attain
wisdom and inner peace, perhaps there is wisdom in the Fool's Tarot card designated as zero.
(Image: The Fool,
but he still pursues his dream at the School of Athens
The School of Athens
is one of the most famous paintings by the Italian Renaissance artist
It was painted between 1510 and 1511 as a part of Raphael's commission to decorate
with frescoes the rooms now known as the Stanze di Raffaello, in the Apostolic Palace in the Vatican.
The picture has long been seen as "Raphael's masterpiece and the perfect embodiment
of the classical spirit of the High Renaissance." In the center of the fresco,
at its architecture's central vanishing point, are the two main subjects:
Plato at left, pointing his finger to the heavens while holding Timaeus,
his treatise on cosmology and the origin of the world. At right is his younger pupil
Aristotle holding a copy of his Ethics while describing the earth and the wide realm
of moral teaching with his extended hand in an elegant horizontal gesture.
The central vanishing point is at Plato's left hand, close to the eye height
of the standing figures in front of the steps, and just where it should be if
the viewer was standing with them on the lower floor. Commentators have suggested
that nearly every great Greek philosopher can be found within the painting.
Dante's four levels
may be applied to interpret this Raphael's painting.
(Image: School of Athens, www.ski.org)
learning about the swan's whiteness
Swan's whiteness is a metaphor for the soul's purity.
In Sanskrit hamsa means swan & soul the sounds of breathing.
The in-breath sounds like Soooooooh
and the out-breath sounds like Haaaaaaam. Breathing in and out has a sound like Soham.
Breathing out and in has a sound like Hamsa. Soham translates as "I am that".
Hamsa in Sanskrit translates as "Swan of the Soul"
hamsa and soham mantras).
A second story relates to one night in the year 407 B.C. Socrates had a dream. He saw a graceful
white swan flying toward him with a melodious song trilling from its throat
and landed on his bosom. The next morning Plato came to become his student
Anthony Damiani first told
me this story in Ithaca (1968) which I found later in
Olympiodorus's "Life of Plato" in
Volume 1 of Thomas Taylor's 55 Dialogues of Plato (1804).
Thirdly, Socrates teaches about the soul and compares it to the swan's evening song when dying
"A philosopher's soul will take the view which I have described... this soul secures
immunity from its desires by following reason and abiding always in her company,
and by contemplating the true and divine and unconjecturable, and drawing
inspiration from it, because such a soul believes that this is the right way
to live while life endures, and that after death it reaches a place which is
kindred and similar to its own nature, and there is rid forever of human ills...
There was silence for some time after Socrates had said this. He himself, to judge
from his appearance, was still occupied with the argument which he had just been
stating, and so were most of us, but Simmias and Cebes went on talking in a low voice...
Evidently you think that I have less insight into the future than a swan; because
when these birds feel that the time has come for them to die, they sing more loudly
and sweetly than they have sung in all their lives before, for joy that they are
going away into the presence of the god whose servants they are."
Plato (428-348 BC),
Phaedo 84a, 84c, 84e (360 BC),
(trans. Hugh Tredennick), Edited by Edith Hamilton & Huntington Cairns,
Plato: The Collected Dialogues, Bollingen Series LXXI,
Princeton University Press, 1961, p. 67
(Image: Mute Swan, 1959 Russian postage stamp, Scott #2219, 1 ruble, colnect.com)
mysteries from the master himself
There were two Eleusinian Mysteries, the Greater and the Lesser. According to Thomas Taylor,
"the dramatic shows of the Lesser Mysteries occultly signified the miseries of the soul
while in subjection to the body, so those of the Greater obscurely intimated, by mystic
and splendid visions, the felicity of the soul both here and hereafter, when purified from
the defilements of a material nature and constantly elevated to the realities of intellectual
[spiritual] vision." And that according to Plato, "the ultimate design of the Mysteries...
was to lead us back to the principles from which we descended... a perfect enjoyment of spiritual good."
"The master himself" may refer to Raphael
the painter who teaches about the art of perspectives. But it is really
the philosopher who teaches about the soul (Seventh Letter).
(Images: Eleusian Mysteries, wikipedia.org;
Plato (427 BC-347 BC)
He sees the Platonic Lambda now here everywhere
The Fool going "nowhere" stands still "now here" and experiences everywhere.
The Platonic Lambda, the Soul of the Universe,
is the sum of the two series (Timaeus 35b):
Sum of the double interval series (powers of 2) =
20 + 21 + 22 + 23 = 1 + 2 + 4 + 8 = 15
Sum of the triple interval series (powers of 3) =
30 + 31 + 32 + 33 = 1 + 3 + 9 + 27 = 40
Sum of the double & triple interval series (Timaeus) = 15 + 40 = 55
Now God did not make the soul after the body, although we are speaking of them in this order;
for having brought them together he would never have allowed that the elder should be ruled by
the younger... First of all, he took away one part of the whole , and then he separated a
second part which was double the first , and then he took away a third part which was half
as much again as the second and three times as much as the first , and then he took a fourth
part which was twice as much as the second , and a fifth part which was three times the third ,
and a sixth part which was eight times the first , and a seventh part which was twenty-seven
times the first . After this he filled up the double intervals [i.e. between 1, 2, 4, 8] and
the triple [i.e. between 1, 3, 9, 27] cutting off yet other portions from the mixture and placing
them in the intervals.
(Benjamin Jowett's translation Timaeus, 35b,
F.M. Cornford, Plato's Cosmology, 1937, pp. 66-67).
See also Speculations on the Soul;
Dante's 55 & Platonic Lambda;
Dante & Marilyn.
(Image: Number 55,
the soul in the center of our face
and in every step we take
Leonardo da Vinci
Proportions of the Face
While our body is visible and tangible, our soul is invisible and intangible.
The Platonic Lambda which Plato calls "Soul of the Universe" (Timaeus 35b)
appeared abstract to me until I noticed the man's legs walking by Giacometti's Walking Man
at Sotheby's Auction. It suddenly struck me that the soul's shape (upside "V" or Greek letter
Λ) is right before our eyes manifesting itself whenever we are walking or alive!
That the soul's form (Λ) supports
our torso (body) when we walk we see it in every step we take
("Giacometti's Walking Man").
Likewise, if God
created man by breathing into his nostrils a living soul (Genesis 2.7),
the nose is the prime conduit of air in keeping us alive. So the Soul
is not hidden but right in the center of our face. Leonardo's
Vitruvian Man (1487)
shows a man inscribed in a circle and square. The drawing and text are called
the Canon of Proportions, showing the correlations of ideal human proportions
with geometry described by the ancient Roman architect Vitruvius.
("Platonic Lambda Sonnet").
(Images: Proportion of the Face, www.squidoo.com;
Sotheby's 1-12-2010 photo,
Giacometti's Walking Man
Sotheby's Auction 2010
in flight of geese, the Pyramids, and in Finnegans Wake
Flight of geese: It is well known that Canadian Geese fly in V formation during migration.
Scientists found that flying in the V-formation conserves energy for the geese. Each bird can
achieve a reduction of induced drag by 65% and increase their range by 71%. On August 20, 2010,
while walking around Stanford's Lake Lagunita, a flock of geese made a landing there
It occurred to me that the geese's actual
flying pattern shows the Λ shape rather than the V-formation. The geese
leading the pack resembles the number "1" at the apex of the Platonic Lambda from
which the double & triple interval series follow ('Spring Geese Are Flying North").
Pyramids: Great Pyramid of Giza is the oldest and largest of the
three pyramids in the Giza Necropolis, Egypt. The Great Pyramid was the tallest
man-made structure (480.6 ft) in the world for over 3,800 years (since 2560 BC). Pyramid Power
refers to alleged supernatural or paranormal properties of the Egyptian pyramids and objects of similar shape.
With this power, model pyramids are said to preserve foods, sharpen or maintain the sharpness of razor blades, improve
health, function "as a thought-form incubator," and cause other dramatic effects. None has made connection
of the pyramid's shape to the Platonic Lambda, Soul of the Universe, which may explain its real power.
Finnegans Wake: James Joyce's Finnegans Wake (1939)
is a work of comic fiction, significant for its experimental style, and considered one of the most difficult
works of fiction in the English language. Chapter 8 of Part I begins with twelve words "O / tell me all about /
Anna Livia! I want to hear all" arranged in the shape of a pyramid or "Platonic Lambda".
The chapter was described by Joyce in 1924 as "a chattering dialogue across the river by two
washerwomen who as night falls become a tree and a stone." Since there are over 350 rivers
from all over the world embedded in this chapter, it is a symbol of stream of consciousness
writing which Joyce began with Ulysses (1922). The chapter ends with "Beside the
rivering waters of, hitherandthithering waters of. Night!" (p. 216).
It's interesting that Joyce ends his most important chapter in Finnegans Wake at page 216, since 216 is the product
of the last numbers in the Platonic Lambda 8 and 27. Joyce writes of "Plutonic loveliaks twinnt Platonic yearlings"
(292.30-31), and borrows a
Vesica Piscis diagram
from Commentary on Euclid's Elements by the Neoplatonist Proclus (412-485 AD).
The intersection of two circles forms an almond-shaped mandorla
often associated with Christ and Pisces (Sign of the Fish).
The lower triangle (ALP) stands for the mother's initials Anna Livia Plurabelle, signifying the
Lower World (Plutonic or Hades), while the upper triangle (αλπ) stands
for the Higher World (Platonic Lambda or "World Soul"
with the transcendental number π on top).
I didn't know what Joyce meant by "waters of Night" until it dawned upon me it's dew! Joyce hints at this in
213.19-20: "Wring out the clothes! Wring in the dew!"
More Dew Symbolism: The light of dawn; spiritual refreshment; benediction; blessing. Sweet dew is peace and prosperity.
Celtic: The most sacred form of water among the Druids. Chinese: Immortality. The Tree of Sweet Dew grows
on the sacred mountain Kwan-lung, the axis mundi (Tree of Life). Hebrew: In Kabbalah, it is resurrection.
Mexican: The dew of the peyotl, sacred cactus, found at the intersection of the two perpendicular diameters traced
in a circle, is the dew of immortality. Neo-Platonic: Dew is the natural envelope of souls; generation. Roman:
The seminal fluid of Jupiter (J.C. Cooper, An Illustrated Encyclopedia of Traditional Symbols, 1978, page 50).
From the triangular Platonic Lambda's typography (196)
and αλπ diagram (293) as well as his call of "Wring in the dew"
(213.20), Joyce is telling his readers
about a spiritual awakening of the soul.
(Images: Flight of Geese, gettyimages.com;
Pyramids of Giza, www.globetourguide.com;
Finnegans Wake, I.8, www.trentu.ca;
Finnegans Wake, II.293; vunex.blogsport.com)
Flight of Geese
Pyramids of Giza
James Joyce's Finnegans Wake, I.8
Finnegans Wake, II.293
on his lasting quest looking for grace at end of the rainbow
James Joyce cites the RAINBOW in an acrostic in Finnegans Wake
226.30-32 and even backwards
"Winnie, Olive and Beatrice, Nelly and Ida, Amy and Rue" (227.14).
"At the end of a rainbow, you'll find a pot of gold" is the first line of the Sid Jacobson & Jimmy Krondes
song At the End of a Rainbow
that was sung by Earl Grant in 1958.
Rainbow is an optical and meteorological phenomenon
that causes a spectrum of light to appear in the sky when the Sun shines on to droplets of moisture
in the Earth's atmosphere. It takes the form of a multicoloured arc. Rainbows caused by sunlight
always appear in the section of sky directly opposite the sun. In Greek mythology, the rainbow was
considered to be a path made by a messenger (Iris) between Earth and Heaven.
In Norse Mythology, a rainbow called the
Bifröst Bridge connects the realms of Ásgard and Midgard,
homes of the gods and humans, respectively. The Irish leprechaun's secret hiding place for his pot of gold
is usually said to be at the end of the rainbow. This place is impossible to reach, because the rainbow is
an optical effect which depends on the location of the viewer. When walking towards the end of a rainbow,
it will appear to "move" further away (two people who simultaneously observe a rainbow at different locations will disagree about where a rainbow is).
I've changed "gold" to "grace" for the "lasting quest" for in the end it is not
our will but "Thy will be done". Paul Brunton advised advanced students of yoga
to give up their perennial search to better themselves, and let
Grace take over.
"Nothing is to be held within the consciousness but rather consciousness is to let itself be held by the enveloping Grace."
(Notebooks, Ch. 7, #241)
(Image: Double Rainbow,
Peter Y. Chou
Mountain View, 3-2-2011