Showing posts with label geometry. Show all posts
Showing posts with label geometry. Show all posts

9.14.2018

eye in the level



replica of Roger Williams' compass, pocket sundial

SURVEY LINE

The pilgrim in the wilderness
like young George Washington
will draw a survey line
in order to project his progress

straight ahead, from point to point.
Primordial Providence
the paradisal focus –
your pen’s first instance.  Appoint

your 2nd Adam, then, Most High
to be the gold eye
in the level – bead the way
with your Accordion of earth & sky,

dream-song of host & guest alike.
My Christianity
is primitive, really.
This nazir chanting by the lake

was also Elohim; we sponged the vinegary
wine together, soaked
the dry bread – smoked
the peace pipe in his company.

My Providence is primitive as well.
Young Roger at the river’s
edge, his seekers, strivers –
welcomed, welcoming – a lunar shell

for pattern of a little government
upon her shoulder (Ocean
State).  Mirroring Sine
of Wave... rinsing tomorrow’s present.

9.14.18

6.28.2018

conversation for kids




LITTLE PEARL

The Hebrews found a verbal replica
for Pharaoh’s pyramids.
Conversation for kids
(& sheep, & goats).  It was Jehovah

came to intervene, to interview.
Some saw an Oedipal
triangle – shadow wall
of mud-baked bricolage (dream stew);

some saw trois anges, craning down
from Paradise – to speak
with Abraham, Sarah, Isaac
(that lightning twin would play the clown).

The pyramids are office towers.
No one will explain
how so much pain
depends on callous fingers (ours).

The just one wears a diamond pin
stuck through the heart –
QUADRANS IN IMO ET
IN SUMMA SUBTILIS (wide-eyed dolphin).

The Middle of the World, he said
& made the sign of six
ways (willow sticks,
or cottonwood).  So truth’s inbred.

Her little pearl of rectitude
is portable – rides
water as a cheek glides
tears.  That’s all (beatitude).

6.28.18

3.14.2017

then you shall have some pie



PIE SQUARED

Down by the Rio del Espiritu
Santo, the sun ignites
the pileated woodpecker’s
red-feathered crown.  The sky is blue,

the river flows, a serpentine
spark-shimmer, bending
rainbows to the engulfing
sea.  Dido’s shade will lean

forever toward the perimetric
oxhide rim of Carthage,
choking on her rage
with tears.  Dante’s epileptic

yearning for supernal Grace
paces her transcendental
number round a circle
of circles like Angela Mace

Christian, or a greyhound, hunting
down that palimpsest
of muffled tracks (geist-
hand behind the arras bunting)

to find F. Mendelssohn at last –
well-tuned, unlucky sister
polishing her Easter
song (spliced to her brother’s mast).

& as my poem’s radius inches
toward her hemisphere,
its eigenvalues (fear
& hope) rhyme where it pinches

                     *

here in Mendelssohn, where children
in the shade of worlds
their parents made, unfold
a bruised & tender leaf-pattern.

The family circle is a dented
sphere.  Your twin cousin
became a ghost – the other one
a cryptic cosine (marginal)... prevented

on path P to blossoming, somehow
(obliquity of bad faith,
lack-love).  Now each wraith
in Dante’s bowl of wrath & woe

will step into your Mirror Lake
as into Galilee,
so you might slowly see
circumference of eternity – & make

amends.  Dido weeps by cave-door.
Moses goes home free,
his daughters over Lethe
summoned, as in play (Cleo,

Ophelia, Jessie...) by paddle-wheeler
quick, now, here, gone
like a Mississippian –
irrational Thanksgiving number

Guillem d’Orange (not neon, now,
but international,
beneath his Provenรงal
shade-grove) beheld – her wavy prow.

3.14.17

9.03.2015

The Venn diagram of Ra

It is the ever-never-changing same,
An appearance of Again, the diva-dame.
- Wallace Stevens

We look around and we see pairs of things - night & day, winter & summer, man & woman, life & death.  It's as if Nature is posing a geometry problem : draw a line C from point A to point B.  Find the inter-mediator, the golden mean.  Build a bridge across that chasm.

We want to make whole what seems to be divided.  It's a psychic necessity.  Sometimes our solutions are very simplistic, and instigate more fractures than before.  Sometimes our answers are very elegant & abstruse elisions - yet despite the sophisticated technology, we end up sliding into the next ditch.

I've been working on a poem-project in which the two parts of the binary, the two points of the calipers, are spread so wide that I can often seem to lose my way - but it also allows for a lot of creative mulling & curious detours.

I knew from the beginning the poem was involved with geometry.  I usually do with this kind of thing.  I start getting unaccountably intrigued by certain numbers & their divisors, how these numbers might be fleshed out in stanzaic and other patterns.  It's a kind of numerology.

The poem is anchored in a Venn diagram - the overlap of two congruent circles, each circumference passing through the other's center.  A pun is a sort of imperfect Venn diagram - the overlap of two meanings in one sound.  The name of the poem is Ravenna Diagram (you see what I mean).

I seem to have many thematic motives (over)determining this basic layout.  One of the main motives has something to do with the traditional Orthodox doctrine of the Incarnation.   Here three Persons overlap as one God.  In the Incarnation we have, very roughly speaking, a Venn diagram of the unity of human & divine.

It occurred to me this afternoon that another facet or motive of this design has to do with Time.

A poet, or any writer, always writes from where they are.  They express their place & time - their "Now".  But a poem or any fiction can project another "Now" as well.  Proust dwells on this mystery with magisterial complexity in his great novel (In Search of Lost Time).

For the ancient Christians, I think, Time was duplex, dimensional.  There is ordinary time, the successions & cycles of clock time - & then there is God's time, Eternity.

History, for them, involved the terrific drama of the intersection of these two dimensions - played out as the destiny of Humankind on earth.  There is a subtle concept called in Greek pleroma - the "fulness of time".  This can refer, apparently, both to the "climax" of the plot of sacred history - God's actual historical presence on earth - and to a sense of time as a kind of ripening of eternity within clock-time (these two notions are obviously close kin).

With Ravenna Diagram I have these two "historical" points of the calipers, a pair of points in spacetime.  There is the "Now" of the author, the poet, me - speaking out of my own experience & character, my place in time & space.  Then there is a second "Now" : that of the historical Jesus, the person who actually lived in Galilee and Judea 2000 years ago.  & then there is a kind of aesthetic middle term - a third "Now" in spacetime : the Italian town of Ravenna, where Dante is buried, where he finished his Paradiso - & where towering, awesome mosaics, representations of Orthodox Christianity, glimmer in their cave-cathedrals (some of these glittering icons found their way into Dante's poema as well).

Jesus tells a parable somewhere - & I forget the exact details - but he concludes with a riddle about time.  Something about a man inviting all his friends to a wedding banquet, but everyone makes excuses.  So he flings open the door & invites all comers.  However, some people show up not clothed properly for a wedding - they are tossed out.  Jesus says something like, "the Kingdom of Heaven is like this too.  So when the Eternal comes upon you, make sure you are prepared."

I've probably botched & oversimplified this parable.  But what interests me is this phrase about "when the Eternal comes".  It seems to goad the listener toward attempting to grasp a certain sense of the layers of time.

We live in a doctrinaire & factional era.  Our "side" is always ready to pin a simplistic label on the other "side".  They are deluded idiots.  Fundamentalists are convinced that old books are roadmaps through life's foggy ambiguities.  Secularists are convinced that religious believers are basically mystified by myth.

I think there might be a kind of philosophical, reasonable aspect to this religious concept of a duplex Time - spiritual and material, temporal and eternal.  The stereotype of puritanical Christianity, clinging to the spiritual at the expense of physical pleasure, is a very old cliche - with some basis in history (think of the desert monks renouncing the world).

But it's possible to think of the religious emphasis on the spiritual as a pragmatic counterweight to life swallowed up by the chaos & futility of the purely material.  A balancing, not a rejection : a synthesis.

This is how I conceive of Jesus' admonition about "when the Eternal comes".  The Eternal is always there : it's only as we get older that we begin to sense the limits to clock-time - our limits.  An awareness of mortality is a spur to long thoughts.  Then we start to sense the presence of the Eternal.

I noticed this with my father - not only while he was dying, but actually long before.  There was a kind of intellectual detachment.  Not that he didn't enjoy life, or care about others - but there was this sense of limits, the fleetingness.

Such a sense can result in a reshaping of priorities.  "What am I doing with my life?"  People are always ready with quick answers to this one, too - usually addressed to others.  But to grapple with it for oneself is the issue.

When you try to write a poem or fiction with two such compass-points, you are immediately handed a wealth of difficult artistic/philosophical problems.  How do I represent my "Now" - and that other "Now"?  But hopefully I put my trust in the creative process.  The whole impulse of poetry is toward integration & wholeness - to enter the rapture of the mesmerizing song.  My pleroma & that other Eternal might in some sense be one & the same, or at least connected.  After all, some such conundrum was the challenge Beatrice threw down before Dante, too...

Mosaics in Mausoleum of Galla Placidia, Ravenna

3.10.2004

John Latta at the Hotel on Abstract Expressionists, Zukofsky's object-at-rest. I just finished reading N. Cusanus's Compendium, so offer his simple four-foldity :

point / line / plane / solid object
letter / syllable / word / sentence

(& more obscurely : Capability / Equality / Unity / Similarity - which I suppose could be figured as:

Power = point/letter
Equality = line/syllable
Unity = surface/word
Representation = object/sentence

Cusanus writes : any shape - a line, a circle, a sphere - is an image formed of equality.

3.04.2004

Wallace Stevens' poetry is sometimes orotund, coinciding with the general repleteness & rotundity of WS, as in similar modus William Shakespeare offers a mighty graceful Globe;

and as WS oftentimes mentions the poetry to be found in philosophers,

so, I recommend Nicolaus Cusanus, or Nicholas of Cusa, whose interest in roundness surpasseth all others;

quotes to follow -

Therefore the edge of the world is not composed of points, but its edge
is roundness [rotunditas], which consists in one point.


Roundness cannot be composed out of points for, since a point is indivisible
and does not have quantity or parts or a front and back or other differences,
it cannot be joined to another point.


Only length and width can be seen. But in roundness nothing is long or wide
or straight. Roundness is a kind of circumference, a certain convexity led
around from point to point whose top is everywhere. And its top is the atom,
invisible because of its tininess.


The round world is not that roundness itself than which no roundness can be
greater, but that roundness than which nothing can actually be greater.
Absolute roundness is not of the nature of the roundness of the world, but is its
cause and exemplar; the absolute roundness of which the roundness of the world is
the image. I see the image of eternity in a circle where there is neither a beginning
nor an end since there is no point in which it would be the beginning rather than
the end. [italics mine]


Listen to this subtlety :

Moreover unity is more perfect and simple to the degree that it is more uniting.
Hence the Trinity, which is one in such a way that it is also in three persons, each of
which is one, is more perfect. And unity would not be most perfect in any other way.


similarly :

Consequently you must open up the gaze of your mind, and you will see that God
is in all multitude because he is in the number one, and in every magnitude because he
is in the point. From this it is established that divine simplicity is more subtle than the
number one and the point which gives the unfolding power of multitude and magnitude.
Hence God is a greater enfolding power than that enfolding power of the number one
or of a point.


Edward J. Butterworth (rotund moniker) has a perfectly succinct essay in the book Nicholas of Cusa in Search of God and Wisdom (Brill, 1991), clarifying these concepts & relating them to the earlier Alan of Lille, who wrote : Deus est spaera intelligibilis, cuius centrum ubique, circumferentia nusquam. Moreover, Lille :

The creature is called the center because, as time, compared to eternity, is thought
a fleeting motion, so the creature, compared to God, is a central point. Therefore, the
immensity of God is said to be the circumference, because it disposes all things in
such a way that it encompasses them and enfolds all things within its immensity.


It's possible to find only word games & rhetorical sleight of hand here. But not if you take into account Cusanus' commitment to the (negative-theological) absolute otherness of God. Mathematical terms are applied to simplicity, while concrete (physical) terms are applied to multiplicity (as in Alan of Lille). Yet otherness and the physical universe are joined, related to one another, by shared geometrical terms & analogies (in a relation of material actuality, on the one hand, and ineffable, invisible & infinite (yet intelligible) perfection, on the other). Alan of Lille's "Intelligible Sphere".

Leading (Butterworth illuminates, partly via Einstein) (& around again) to Cusanus' limpid, rotund contradiction :
Therefore the edge of the world is not composed of points,
but its edge is roundness, which consists in one point.
(All Cusanus quotes from
De Ludo Globi (The Game of Spheres))

what's that Dickinson line? "My circuit is circumference" [?]