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

Monday, December 12, 2022

Chasing Ancient Pentagrams Part III: The Quintessence - The Fellowship of Pentalpha

A floor mosaic - featuring a stellated dodecahedron - in St Mark's Basilica, Venice by Paolo Uccello circa 1430.


Featured in the center of the image (above) and in center of the image inset left is the geometrical figure known as the small stellated dodechahedron.

I don't know that this polyhedron has any specific esoterica attached to it - apart from it's obvious relationship with the pentagram and the regular dodecahedron - and, yet, its presence in the mosaic  and the print seem to hold a special significance for both artists... in spite of the fact that more than 400 years and several countries separated them.

Maurits Cornelis (M.C.) Escher (1898-1972), was a Dutch graphic artist especially known for the mathematical figures and motifs in his work, while Italian painter, Paolo Uccello, was not. Uccello accomplished amazing feats of perspective in his paintings, but his online oeuvre contains only one other example of a geometric solid. And, yet, it's his polyhedron which is unquestionably the "star" of the mosaic at St. Mark's basilica... surrounded by what looks like a string of... well, sliced zucchini (but don't quote me). In any case, regardless of the vegetables, his dodecahedron is a powerful icon.

In M.C. Escher's still-life, however, the same stellated polyhedron has become an illuminated life form... or a small, extraterrestrial vehicle which has landed in a patch of earthly refuse... a broken egg, bottle, pipe, discarded tin can, etc. It seems as if the two images could not be less alike.

But, there is one continuum between Uccello's mosaic and Escher's drawing.  Both images glorify the stellated dodecahedron while, at the same time, revealing its fundamental source: the pentagram.

Inset left is a great shot of Escher inking in a most amazing spiral. The full image - Sphere Surface with Fish - is below the jump.

Tuesday, November 15, 2022

Chasing Ancient Pentagrams Part II: The Quintessence - The Egyptian Duat

An Egyptian limestone panel, 400-200 BC / Metropolitan Museum, New York

"The Star which guided them is that same Blazing Star, the image whereof we find in all initiations. To the Alchemists it is the sign of the Quintessence; to the Magists, the Grand Arcanum; to the Kabalists, the Sacred Pentagram."

- A reposting of a quote (see Halloween post) via Albert Pike, a 19th century American Freemason.

While Pike doesn't specifically mention the ancient Egyptians in the quote above, and, while the Egyptian's 5-fold star wasn't technically a pentagram, the five-fold star inscribed within a circle (essentially a pentacle) was a crucial symbol in their world. It symbolized the Afterlife or Underworld; that is, the Duat, the medium in which a departed soul was judged, and a dimension in which there was no day or night. The Duat was the home of some of its most important gods: Osiris, Anubis, Thoth, Horus, Hathor, and Maat. The sun-god, Ra, also passed through its regions every night in his solar barge.

In the large image (carved in relief) above, two baboons are worshiping the Duat, which hovers above the scarab - a sun symbol often used as a talisman for protection and placed inside a mummy's shroud - which, in turn, is set above the sun, placed here beneath the Duat.

(Note: Compare this design with the Kabbalistic tree-of-life inset right. Although not an actual match, there is a certain likeness in the way the elements are placed.)

This relief has a number of Underworld motifs... the most prominent being the pair of baboons facing each other. Baboons were said to be sacred animals in the Egyptian pantheon, and when depicted singly represented the great ibis-headed god, Thoth, a lunar god, who, in a sense, was Ra's (or Re's) counterpart.

In some tales, Thoth (inset left) was self-created at the beginning of time and, as an ibis, lay the cosmic egg that holds all of creation.  In others, he was thought to have created the art of writing and the calendar. He was also the god of both mathematics and magic and served as a scribe in the Duat.  Moreover, he had the ability to control space and time!




Above is a beautiful artifact which also features a set of baboons facing each other across a large scarab. Each wears the lunar crown of Thoth, however, so, we might assume that symmetrical pairs of baboons also portray Thoth. Note the small star (Seba) symbols embellished on the bar above them; it is likely they represent the night sky.

Returning to the larger image, there are what appear to be (Greek) Omega symbols over the primates' heads, but, these are likely to be shen rings - associated with Horus and his mother, Isis - which symbolized power, protection and, (eventually) eternity. This shen ring (at the Metropolitan museum in New York) inset right was found as a talisman alongside the mummy of a prosperous Egyptian, circa 1800 BC.

Note also the two Wedjats encircled by the baboons' arms. These are the twin (lunar) Eye(s) of Horus - one of which often accompanies images of Thoth - and used singly or dually represent healing and regeneration. They were also frequently used as talismans of protection for both the living and the dead.

Oddly enough, the Wedjat (also later referred to as the solar Eye of Ra) is also the name of the ancient goddess of Lower Egypt, the cobra goddess, Wadjet (or Wedjat)...

Saturday, October 15, 2022

Chasing Ancient Pentagrams Part I: the Roman Dodecahedra

A "Roman Dodecahedron" found in the UK by Brian Campbell in 1987.

 
The Gallo-Roman Dodecahedra
_________________________________________________________
 
 
(This post was originally intended to be the first of the pentagonal phi series, and much of it was written early last year. It has been revised, however, and will contain new material. It may also run into two parts.)
 
"One August day in 1987, Brian Campbell was refilling the hole left by a tree stump in his yard in Romford, East London, when his shovel struck something metal. He leaned down and pulled the object from the soil, wondering at its strange shape. The object was small—smaller than a tennis ball—and caked with heavy clay. 'My first impressions,' Campbell tells Mental Floss, 'were it was beautifully and skillfully made … probably by a blacksmith as a measuring tool of sorts.'

Campbell placed the artifact on his kitchen windowsill, where it sat for the next 10 or so years. Then, he visited the Roman fort and archaeological park in Saalburg, Germany—and there, in a glass display case, was an almost identical object. He realized that his garden surprise was a Roman dodecahedron: a 12-sided metal mystery that has baffled archaeologists for centuries. Although dozens, and perhaps hundreds, of explanations have been offered to account for the dodecahedrons, no one is certain just what they were used for."

- Via an excellent article on Mental Floss found here. Inset right (above) is a Roman Dodecahedron exhibited in the Württembergisches Landesmuseum, Stuggart, Germany, and found in this article.


"A Roman dodecahedron or Gallo-Roman Dodecahedron is a small hollow object made of copper alloy which has been cast into a dodecahedral shape: twelve flat pentagonal faces, each face having a circular hole of varying diameter in the middle, the holes connecting to the hollow center. Roman dodecahedra date from the 2nd to 4th centuries AD.

Since the first dodecahedron was found in 1739, at least 116 similar objects have been found[1] from Wales to Hungary and Spain and to the east of Italy, with most found in Germany and France. Ranging from 4 to 11 centimetres (1.6 to 4.3 in) in size. A Roman icosahedron has also come to light after having long been misclassified as a dodecahedron. This icosahedron was excavated near Arloff in Germany and is currently on display in the Rheinisches Landesmuseum in Bonn.

No mention of them has been found in contemporary accounts or pictures of the time. Speculated uses include as a candlestick holder (wax was found inside two examples); dice; survey instruments for estimating distances to (or sizes of) distant objects; devices for determining the optimal sowing date for winter grain; gauges to calibrate water pipes, army standard bases, a coin measuring device for counterfeit detection. Use as a measuring instrument of any kind seems improbable since the dodecahedra were not standardized and come in many sizes and arrangements of their openings. It has also been suggested that they may have been religious artifacts, or even fortune-telling devices. This latter speculation is based on the fact that most of the examples have been found in Gallo-Roman sites. Several dodecahedra were found in coin hoards, providing evidence that their owners considered them valuable objects. Other suggestions include a knitting frame for creating gloves, supported by the fact that many are found in the northern range of the empire.

Smaller dodecahedra with the same features (holes and knobs) and made from gold have been found in South-East Asia along the Maritime Silk Road. They have been used for decorative purposes and the earliest items appear to be from the Roman epoch."


- Via the Wiki entry for Roman or Gallo-Roman dodecahedron. Inset left is a museum photograph of 2 Roman dodecahedrons and the icosahedron mentioned in the quote. In my eyes, the icosahedron, although a polyhedron and similar in size to the dodecahedrons, does not seem to be in the same family of objects as the former.


***

Did you know there is a geometry in running water... or that small objects of equal mass - specifically small and lightweight - tend to fall into groups of three? Regarding the latter, at one point this year, I noticed this so often during my waking hours that I began to document these geometrical events, snapping photos with my cell phone whenever they occurred. Is this madness? Precisely. But it's a sort of "magical" madness involving a particular phenomenon which very likely spawned numerous oracles in the past; everything from casting knuckle bones, dice, sticks, coins, tea leaves, etc. for the purposes of divining or interpreting the resulting patterns as a narrative of the future.

In reality, small objects very often fall into rudimentary geometric patterns or figures - a little understood phenomena Jungian psychologist, Marie-Louise von Franz, 1915–1998, once described as a form of synchronicity or "meaningful chance" especially in regards to divination and the role of natural numbers.

Inset right is one example I shot with my cell-phone September 8, 2020; an interesting triangle formed by the random distribution of red pepper seeds scattered during the course of making a salad! I didn't see the figure at first; the pattern had formed on the far side of the table on which I was working. It was during clean-up that I came across it, and I swear I felt like some mystified farmer who discovers a crop circle in his field one day; it was eerie.

The X-file factor of this event was that the triangle bore a strong resemblance to the triangle I'd been working with over a year (and you've been encountering on this blog for months): the pentagonal golden triangle. Had it fallen out of my head and imprinted itself on the table? Who can say? But, I saw it as an affirmation of an artist's journey well taken. And, for an artist who faithfully follows the muse down one rabbit hole after another, affirmation is a much coveted thing... because, what is a "rabbit hole" other than some strange anomaly stumbled across during an intellectual excursion which might potentially lead one to the greatest of epiphanies or the most confounding of delusions?

But, while it may have ended that way, my journey down this particular rabbit hole did not begin with a random distribution of pepper seeds. It began with an online article regarding that unusual metal object currently staring at you from the top of this post... its empty cyclopean eye revealing just about everything we know regarding its existence...which is pretty much nada.

Now, the general opinion among experts (and one must always use this term loosely) is that a lot is known - and verified - about the past. Even the long past. But, don't be fooled. The past is as elusive (and illusive) as the future. New discoveries keep popping up each day with the potential to completely overturn all previous determinations. There are, after all, numerous newsworthy items. And, no, I 'm not referring to those well-documented abominations of the world's daily affairs. I'm talking about those little, weird tangible things - the products of human ingenuity - which emerged in the days before "artificial intelligence" was even a bad dream in somebody's head. This is not so say that the days of which I speak - and, no, none of us witnessed those days in any memorable way - were benign or utopian, but, intriguingly enough, ancient humans were admirably capable of flummoxing the oh-so-sophisticated humans of the future (us),  producing artifacts that we - with all of our modern expertise... and some highly sophisticated calculators - are unable to identify.

Which brings us back to that cyclopean object resting above - the subject of this section - the Roman dodecahedron inset left. No one seems to have a precise explanation for its presence on the earth - although the general drift is towards some practical, utilitarian instrument (such as a candle holder or knitting device) or complicated measuring device (such as a military range-finder) - and, yet, at least a few ancient folk across a number of countries - and all living in the earlier centuries AD - created these objects for reasons of which we can only speculate. Over a hundred of them have been dug up in parts of Europe and one imagines more may be found. I find this oddly exhilarating; there are still things the experts, admittedly, can't explain. In any case, I'm sure that all intuitive readers have realized by now that this mysterious little artifact is quintessential rabbit-hole material... and, yes, it most surely was!

In any case, "Cyclops" is actually believed to have been created around 200 AD... somewhere within the vast Roman Empire. Which is how it got its name: The Roman dodecahedron. The thing is,  despite archaeologists finding more than a hundred of them, no written reference to them has ever been discovered. And this might be a our most important clue: perhaps the objects had no practical use whatsoever and were never intended for the general public.

What's more, the object is an early example of a polyhedron - and the dodecahedron is the most complex of the Platonic solids - artifacts which we rarely see in the ancient world (despite the contributions of Pythagoras and Plato). As it so happens, this blogger loves polyhedra - even documenting a set of my very own (inset right, above: the dodecahedron, the icosahedron, and the pentakis dodecahedron). Not very long ago, I posted about some unusual Scottish sundials (example below the jump)...

Monday, February 14, 2022

The Power of Love

Diagramming a Force: the Rose Pentagram - 2022, DS


“The transformative power of love is not fully embraced in our society because we often wrongly believe that torment and anguish are our ‘natural’ condition.”

“When angels speak of love they tell us it is only by loving that we enter an earthly paradise. They tell us paradise is our home and love our true destiny.” 

 “Knowing how to be solitary is central to the art of loving. When we can be alone, we can be with others without using them as a means of escape.”

 “If I were really asked to define myself, I wouldn’t start with race; I wouldn’t start with blackness; I wouldn’t start with gender; I wouldn’t start with feminism. I would start with stripping down to what fundamentally informs my life, which is that I’m a seeker on the path. I think of feminism, and I think of anti-racist struggles as part of it. But where I stand spiritually is, steadfastly, on a path about love.”

- Four quotes by the great feminist writer, bell hooks, who passed away recently but whose insight and lucidity regarding the world and its people has, in my opinion, not been matched by anyone in the past 50 years. For more of bell's wisdom see this Trans-D post, or this Goodreads page.

Vale, bell hooks. You are not alone on your path. We wish you well.

 ***

I'm having an almost impossible time writing these days. Pictures and music - specifically those involving Phi and the pentagram (snails & stars) - are the best I could do.

Meaning: my original plan for a golden ratio series has stalled. And, whatever appears on this blog from this point on is... well, is whatever appears on this blog from this point on.

Call it: metaphysical, existential overload.

Meanwhile, I hope you've had a Love-ly day.💕

And, failing that - and you are allowed to fail, you know - there is always the power of love... and the power of love - which costs nothing - takes (only) one heart and not necessarily (or physically) two (or more).

 

For your listening pleasure: a Phi-based tune... brought to you by Michael Blake:




Friday, December 31, 2021

2022 - A Tentative New Year


 

Alas, it's that dreadful day again... that is, my birthday. A day in which everyone basically celebrates the next day... which can never come soon enough. A day in which everybody gets inebriated, gets maudlin about the past and unrealistic about the future... while doing and saying regrettable things they will, in time, forget. This was the world I entered many moons ago, and mostly, it suited me just fine... except the weather; I still hate the cold.

I would love to toast the future. After 2 very creepy years I would be most happy to experience a New Day... a New Year. Wouldn't you? But it remains to be seen. There seems to a conflict of interest across the globe today. The Fear-Mongers*, Dope-Peddlers**, and Bad News Boys*** of this world seemed as pleased as punch when a 14th Covid variant reared its ugly little microscopic head. After all - and it doesn't take a Conspiracy Theorist to follow the money trail - the Pandemic has been very lucrative for them. Not so for you, me, and everybody else in the world... specifically those who have lost jobs, homes, businesses (and loved ones)... not to mention autonomy, mobility, sanity and a joy of life.

So, Bad News Boys, you can keep your New (abnormal) Normal. I need a New Year which is nothing like the previous 2. I want to see people's faces again when I talk to them; I want to see mine. I want to see different parts of the world before I die. I want to align myself with a creative culture, not a Disease Culture. In short, I want my life back. And that (dear readers) is my only Birthday wish (and New Years resolution). Oh, and this: I wish the same for you.

HAPPY NEW YEAR!

__________________________

 * The Covid PR group.

** The Covid R&D Group.

*** The Media.

 ___________________________

 

Note on the image which proceeds the text (also inset left): this diagram was the result of laying a pentagonal Golden Triangle over the nested lunes of a Lune Spiral. Each horizontal line in the triangle represent points where the triangle and the lunes met. It looks like a harp and that is it's name: A Golden Harp, or, just "harp."

Of interest: as you can see from the diagram, no matter where you slice off the base of a Golden Triangle, a Golden Triangle remains. The rectangles you see, however, are not Golden. The ratio of the side to the base of these pentagonal rectangles is this: 1.54545454545454... which is in keeping with the plethora of other embedded 9s in the pentagon's (and pentagram's) numerical structure. (For instance, the pentagram's angles: 36, 72 and 108 degrees; each adds up to 9.)

Inset right is a lune, also referred to as a crescent, although, in this species, the grand circle and the inner (lesser) circle are touching but not overlapping.

Theoretically, there are almost as many lunes within a circle as there are circles, and therefore, an almost infinite variety of lunes, lune spirals and harps. I will eventually document a few of them later in the "Golden" series.

But, getting back to the harp, I've been thinking "musical instrument" from the day I first devised it. In  reality, an actual harp, is a musical instrument built on a very strong angle.  Although I don't think any are built upon the very acute golden angle, I wonder if it's possible and what it might sound like.

(Later note:  There's a possibility a Renaissance harp used the golden angle!

For your listening pleasure: virtuoso harpist, Hanna Rabe beautifully performs Eric Satie's eerie, melodic tone poems, Gnossienes 1, 2 &3.

 

 

 

 







Saturday, December 25, 2021

Botticelli & the Spiral


Cestello Annunciation, 1489–90, Sandro Botticelli, Geometry: 2021, DS.

 

Above is a Christmas greeting card of sorts, composed of Sandro Botticelli's enigmatic Annunciation* and my own minor embellishment (meant to dazzle you, of course). And, while I'm not saying Botticelli actually used the pentagonal Golden Spiral to design his masterpiece, it does somewhat explain Mary's unusual posture.  She seems to be holding the geometrical apparatus up with both hands!

It doesn't explain the most important relationship in the image, however... that is, the odd relationship between Gabriel's and Mary's hands... but, perhaps an additional spiral might tell us something.

 


Put the two together and we have this:

 


Note the diagonal the two triangles have in common; when extended, it pierces Mary's hand. It's as if Gabriel was throwing her a curve-ball and she caught it!

Hmmm... but is that the end of the analysis....?

Alas, no...

Sunday, October 17, 2021

Fractal Unit 5


Fractal Unit Five - 2020, DS.


It's fundamental.

  ***

 (Note: The bulk of the content which originally appeared in this post (under the title "Forever Young") has been deleted after YouTube deleted one of the two featured videos. Sorry, but I wasn't up to repairing the post. If fact, I'm certain that there are many links, videos, etc, which  need my attention - especially on the sidebar -but time is in short supply these days.

I have a holiday post which will hopefully go up in a couple of days but, if, for some unforeseen reason it doesn't, I'll leave you with the video below. It's by a (relatively) new band - yes, darlings, I've finally discovered a band created in the 21st century I actually like: Sea Power. Their 2021 video (Two Fingers) below can also be found on their website and YouTube channel.  Dia, 10/26/21)







Friday, September 24, 2021

Reflections on Water

 

 

 “'I’m touched by your impatience over the Images. What happened was this: the first piece, ‘Reflets dans l’eau,’ doesn’t satisfy me at all so I decided to write another based on different ideas and in accordance with the most recent discoveries of harmonic chemistry…My apologies for this slight delay—which in any case won’t last beyond the end of the week. I’m starting to see things clearly again in my imagination and my thinking machine is gradually getting back into gear.'

Nothing in the composition of the piece has been written without consideration for phi and Debussy is unconcerned whether or not anyone, aside from himself and Durand, listens for the ratio unpacking, building itself, and then deconstructing itself over 94 measures and 375 beats. The new Reflets dans l’eau is an andantino molto that is almost as quiet as a droplet of water falling into a silvery lake. The piece divides asymmetrically into a beginning that stretches to the climax at the fifty-eighth measure and a smaller stretch that ends the piece. The climax, marked double fortissimo, is at the exact point of phi in the song, the mathematical equivalent of the golden ratio."

- Excerpt of an article found here regarding Debussy's use of the Golden Ratio (Phi) in Reflets dans l'eau,

The video is a re-mix of Reflets dans L'eau, (Reflections on Water) from Images I by the French composer, Claude DeBussy. It was created for electronic media by CJ Images and designed by CJ (Christopher John) for the game Flowscape. I chose this video (from numerous others) because some of its electrical sounds actually bring to (my) mind the golden spiral. To your right is the pentagonal golden spiral constructed by its 2 golden triangles.

"Among the mysteries of the irrationals, one number holds a special place: the so-called golden ratio. The golden ratio’s value is about 1.618 (but not exactly 1.618, since then it would be the ratio 1,618/1,000, and therefore not irrational) and it’s also referred to by the Greek letter φ, which is pronounced “fee” if you’re a mathematician and “fie” if you are in a fraternity. If you want an exact description, the golden ratio can be expressed as (1/2)(1+√5.)

People have been making a fuss over this number for centuries. In Euclid, the proportion goes by the more mundane name of “division into the extreme and mean.” He needed it to construct a regular pentagon, since the golden ratio is the proportion between the diagonal of such a pentagon and its side. A golden rectangle is one whose length is φ times its width; it has the agreeable quality that if you cut it crosswise so that one of the two pieces is a square, the other one is a smaller golden rectangle."

- Via the Slate article: The Most Irrational Number. Inset left is a beautiful photograph (found online) of the chambered nautilus, featuring a spiral similar to the golden spiral.

 ***

Well, it took me long enough to write this post (!), but, then, I was somewhat intimidated by it. In terms of this blog, it's an important one; revealing just exactly where I've been at (creatively) for the past 2 years. Never mind that the past 2 years have been for myself and, I imagine, most people, a regular mind-f*ck. (After all, who amongst us did not in some fashion get sick?) However, the show must go on. And, for an artist, to create is to live... and to live is to create. Nothing changes this equation.

My creative journey began during 2019 and was referred to in this April interlude, upon the creation of the Rose Pentacle graphic. Later that year I began sculpting a 3-dimensional version of that image in clay for a ceramic casting (which is still in progress). I also began to envision a series of paintings which might bring the Night Garden to life while, at the same time developing a mythology relative to both the garden, the Rose Pentacle and the inherent mysteries I sensed were involved.  It's a big project.

But, as the Pandemic fell into place, I lost my place in the journey. The dream went on hold, and I turned, instead, to the one component of the Rose Pentacle that could be investigated in two dimensions on a computer monitor: the pentagram, its history, but, most importantly, its geometry... from which a series of diagrams eventually emerged (a few of which appear in this post.)*

(More after the jump...)

Tuesday, April 30, 2019

A Journey to the Bottom of a Rabbit Hole (Interlude #3)

Rosslyn Chapel - window on north side. Photo credit ©: Rob Farrow.
(All images in this post can be clicked-on for original size.)

"The building of cathedrals was part of a colossal and cleverly devised plan which permitted the existence of entirely free philosophical and psychological schools in the rude, absurd, cruel, superstitious, bigoted and scholastic Middle Ages. These schools have left us an immense heritage, almost all of which we have already wasted without understanding its meaning and value."

- A quote attributed to P.D. Ouspensky. sourced from Tim Wallace Murphy's Enigma of the Freemasons: Their History and Mystical Connections (2006). Inset right is a column from the Cathedral of St. John the Divine in New York, featuring the Kabbalistic Tree of Life symbol.

"The Gothic cathedral, that sanctuary of tradition, science and Art, should not be regarded as a work dedicated solely to the glory of Christianity, but rather as a vast concretion of ideas, of tendencies, of popular beliefs, a perfect whole to which we can refer without fear, whenever we would penetrate the religious, secular, philosophic or social thoughts of our ancestors."

- Another quote sourced from Murphy's book which originated from Le Mystère des Cathédrales (1926) by a mysterious French alchemist known only as "Fulcanelli." Inset left is another - more enigmatic - column from the Cathedral of St. John the Divine.


From Chartres Cathedral in France: a mechanized astrological clock added in 1528.

***
What's this? A third Interlude?

Alas, yes. As you may have guessed, I've been tottering on the brink of one rabbit hole or another for months now, so, I suppose it was inevitable I'd lose my footing eventually. Originally, I intended to add 2 quotes I found recently (now posted above) to the Chinese Sewing Basket addendum - in which I mention Notre Dame de Paris - and, for all sensible reasons, that's where the operation should've ended.

But, no. Instead, I decided to Google the French alchemist Fulcanelli (who wrote the second quote above)... a man I was unfamiliar with. After all, a writer should know her subject matter, right?

Famous Last Words. For, at that very moment, although unbeknownst to myself, a massive black rabbit hole was silently opening directly beneath my feet like the mouth of a terrestrial Moby Dick.

Maybe it's the topic itself: alchemy - specifically hermeticism - the black hole of the esoteric world. The further you go, the less you know. And, as for Fulcanelli... ah, yes, Fulcanelli, now there's a name to conjure with. And, certainly many have. For some he's the man-who-never-was with an ongoing archive of potential identities (see the Fr. Wiki entry).

But, ultimately, this post isn't about Fulcanelli any more than it's about cathedrals. As it so happened, while ferreting out info about Fulcanelli I discovered his friend, Julien Champagne, also a French alchemist and an artist. It was he who created the frontispiece emblem (inset left) for Fulcanelli's Mystère des Cathédrales.

(Continued below the jump...)

Friday, December 11, 2015

Wild Orchids; The Tribal Green Woman (& Two Triangulations)

Wild Orchids - Digital - © 2016 (revised), 2015, Dia Sobin
(Newest version uploaded 2017)
(Click to enlarge)


"The genus name Cypripedium is derived from the Greek words "Cypris" an early reference in Greek myth to Aphrodite, and “pedilon” for sandal. This is because the fused petals that form the orchid’s pouch or modified lip (labellum) resemble a slipper or shoe. The staminode (sterile stamen) is often showy and seems to welcome the insect into the pouch where it makes its way to a back-door exit and in so doing transfers pollen to the stigma.

...The Cypripedium orchids of North America are hardy terrestrial plants that can grow in cold climates and flower in early to mid-spring when there is plentiful moisture and cool temperatures. Species such as Cypripedium guttatum and C. passerinum that grow in Alaska are so well adapted to cold their shoots sprout up under the snow in the spring.

For centuries Cypripedium species have been sought after and collected not only for their unique beauty but also for the medicinal trade. Widespread collection, attempts at transplantation, and loss of habitat have drastically reduced their numbers. Wild lady’s slippers have special requirements that make them difficult to cultivate, and rarely survive transplanting from the wild. Because of that, on federal lands it is illegal to dig or pick the orchids."


- From the U.S. Department of Agriculture cypripedium page: Meet the Ladies, the Slipper Orchids 


***

Way back when - roughly about twenty years ago - there used to be a small, hidden patch of pink wild orchids in the woods behind (what was then) my parent's house. Mysteriously, one day, the lovely flowers vanished, and were never to be seen again. Perhaps, someone picked the blossoms; along with transplanting them, it's a sure way to kill the plant.

Popularly known as the Lady Slipper, or Moccasin flower, this orchid is one of the more strangely secretive denizens of the forest... blatantly wild, deceptively fragile, quietly erotic, it's always a pleasant, somewhat magical experience to happen upon them. Although I've always considered the plant a primarily North American flower, it's actually found in Europe and Asia as well; the ones illustrated in the image above, however, are a North American variety.

About the illustration: well, I did previously mention designing my own versions of a Green Woman and Three-Hare symbol (at the end of this post), predominately for carved reliefs. As it happens - and it always does regarding ones creative plans - while I was designing the Green Woman, I suddenly had the overwhelming epiphany that my Green Woman called for - no, demanded - tattoos. Perhaps, this was because I had recently considered getting a tattoo myself. As to why I'm suddenly drawn to illuminating my torso at this time in my life - well, that's another story. But, regarding the Green Woman, suffice to say, the tattoo idea changed the playing field, and, for good or ill, a full color digital image was required.

Moreover, as the tattooed person began to emerge, I had another inspiration. For whatever reason, Art Nouveau posters* by the Czech illustrator Alphonse Mucha (24 July 1860 – 14 July 1939) resurfaced in my middle eye. And, whatever your artistic taste dictates, poster art in the days of Mucha were phenomenal expressions of the marriage between art and commerce, and Mucha's images, in particular (see examples below), were awesomely designed and elegantly executed.

Wednesday, June 17, 2015

Triangulation & The 3 Hares (In Memory of a Beautiful Mind)


Four Degrees of Triangulation - 2015, DS


"Each planet has energy through it via a visible light spectrum and produces it’s own output albeit in a longer thermal wave and the production of atmospheres, and the concurrence of fluids ruled over by the Trident of Neptune. .. One could call our solar system an example of the conservation of energy...or perhaps not. Perhaps this is a strange astrology..cyclic and yet prone to flux. The visible conjoined to the invisible. And beyond this?

Is there a triadic ordering to the anomalous between existents and non existents? Is there a dipole to this that creates a dynamo that produces a music strange to our senses..attenuated to this exchange resulting not in physicality nor non physicality, but rather a reconciling force?

Your guess is as good as mine. I suppose the interdependence of what Bateson saw as two drum beats creates not a seeming harmonious rhythm but rather discordance as translated by our own triangulations."

- Bruce Deunsing, from his post The Physicality of Metaphysics



Four Degrees of Triangulation (2) - 2015, DS

"Nicola Tesla (1856-1943) in his whole life, did not own a home, he lived in hotels, never got married and besides him being a genius, his interesting personality was always the center of attention. Since he arrived to New York in 1884 he stayed in many hotels (especially the New Yorker which was the one he stayed the longest in) he would order his meal by phone, he would sit all alone in his suit at the table, since he had an obsession of numbers that could be divided by three he would order his napkins according to this and after a thorough hygiene control he would eat his meal."

-  Via this Tesla Society page.

"One of his proudest achievements was his TMT, (Tesla Magnifying Transmitter), or Tesla transponder. The few that have looked into this at a mathematical and experimental level seem to reach the conclusion that it is a system of resonant transformers harmonically balanced to the electric condition of the Earth...If the phase angle of the earth pulsation frequency lags the phase angle of the pulsating frequency, energy is abstracted from the earth's supply of energy and delivered as "free energy" to the transponders. Three distinct standing waves, each coupled to the other through two points of refraction are involved in its operation. This is GROSSLY simplified to arrive at a possible solution to our 3-6-9 problem."

- Via "Steve" from this Physics forums page: Why was Tesla Obsessed with the Number 3?


***


I thought I'd let the triangulations speak for themselves for a while before I put in my left-brained "two cents". As it stands, I'm having a difficult time writing these days, and I regret stalling on posting to this blog, but it can't be helped. I am currently immersed in 2 relief-sculptural projects - yes, I'm carving plaster again(!) - and the "brains" are battling each other for time.

Then again, I've just been informed that the planet Saturn has gone retrograde. Never a good thing, my fellow earthlings. The bottom line: beware of Karma... yours and everyone else's.

This post is sort of a companion piece to the one posted here - a memorial to fellow blogger, Bruce Duensing, who just happened to be a misunderstood genius - but it's inadvertently dedicated to another "beautiful mind" and another misunderstood genius, Nicola Tesla, with whom Bruce may have had a few things in common...

Monday, March 2, 2015

The Mysterious Caves of Fontainebleau


From the caves of Fontainebleau... (click to enlarge)

The Forest of Fontainebleau

"This forest which is now a popular recreation area, was an isolated region for thousands of years. It was a haunt of robbers, fringe dwellers and fugitives who sheltered in its caves and carved the walls with inscriptions, designs, and abstract signs. More than 2,300 square yards of rock are decorated in this way.

Among the carvings are human figures with rectangular bodies, neck-less heads with sunken eyes and U-shaped noses. Their arms are outstretched, with the fingers spread like a fan, and often the legs are missing. A second group, in bas-relief, have their arms close to their bodies, In a third, the figures are dressed in skirts and have only three fingers on each hand.

The crosses, circles and hopscotch-like designs are almost impossible to date. They may be from prehistoric time, or they could have been drawn yesterday. All have been indexed and some are similar to designs which specialists located elsewhere. However, there are some designs which are found only at Fontainebleau. These are the irregular latticed designs which have been deeply incised into the rock. They have been found in the most inaccessible places, in cavities where only an arm can reach. Why were these engravings made under such obviously difficult conditions? They were certainly not made recently, but how old are they? What message did their engravers wish to leave, and who were they?"

- Text and photo (above) found in some older files; source currently unidentified.


***

Chances are, whenever the topic of prehistoric art crops up, the first examples that spring to mind are the stylized beasts (in shades of black, brown and red ochre) found on cave walls in France, notably those of Lascaux and Chauvet. Or, maybe, those enigmatic Paleolithic handprints which created a minor sensation in 2013; the handprints which, upon closer inspection, were tentatively judged to be the work of primarily female artists. On the other hand, the more informed Fortean mind is likely to turn to the stone carvings found at Göbekli Tepe (also, here), or the Nazca Lines.

But, my fellow fans of weird archaeology, here's another place to add to your files: the mysterious abstract carvings found in the caves of Fontainebleau Forest, located 30 miles south of Paris. While some of the designs were wrought in the late Middle Ages, others have been dated back 15,000 years to the Upper Paleolithic or Magdalenian period; and, still others may have arisen as early as the Neolithic period. So strange and sophisticated are some of the carvings - along with the nearby presence of unusual rock formations, and what appears to be a bestiary of boulders - that it's been proposed the forest of Fontainebleau may contain the artifacts of an unknown civilization...

Saturday, August 9, 2014

Matrices of Light & Shadow; Alex and Allyson Grey



Spiritual Energy System (left); Universal Mind Lattice (right) - acrylic on canvas - 1981, Alex Grey



"Looking at Grey’s paintings and other works on display, Hoffberger said, “Given the way technology is moving, do we want to become like machines? With each new high-tech invention, how do you download a ‘you’ into an ‘it’?” Grey’s powers-of-the-universe paintings, with their images of trees as fecund bodies, along with choruses of prehistoric animals, suns, eyeballs and planets, evoke an eternal, all-unifying, omnipresent spirit. Grey’s art seems more all-embracing than the ecumenical posturing of those praying, chanting, bead-rattling leaders of so-called organized religions who sometimes pause to look beyond their own belief systems and pay a little lip service to the dream of world peace."



"Love, consciousness, and creativity are the highest refinements of the cosmic evolutionary force."

"The Inevitable consequence of Love is the building of Temples."

- Two quotes by Alex Grey, found on his website.


***



"Secret Writing Magic Square with Mandala Border" - oil on wood - 1990, Allyson Grey



"Language is like a portal through which the inner world of order may pass into the outer world of chaos."

- Allyson Grey, from her website: Chaos, Order & Secret Writing.


***

In terms of the the Matrices (described here) and their relationship to the human body,  I don't think I've seem a better visual description than those presented by Visionary artist, Alex Grey in his amazing Chapel of Sacred Mirrors series. It's almost as if they were made to order for the musings of a Space Pagan, most especially his "Universal Mind Lattice," which he describes here:

 "No longer identified with or limited by our physical bodies, our essence is an individual fountain and drain of Light, interlocked with an infinite omni-directional network of similar energy cells, the interpenetrating consciousness of all beings and things."

The odd thing for me, at least, is - at the exact same time, and the exact same place (New York) - while Alex Grey was painting the huge canvases that would become the Chapel of Sacred Mirrors (see video), a far less flamboyant artist (me), was envisioning something along vaguely similar lines...

Thursday, August 7, 2014

Matrices of Paper; the Creations of Eric Standley


"Either/Or Circle" - layered paper - 2001, Eric Standley
(click to enlarge)


Inspired by Gothic and Islamic architecture, much like Cristóbal Vila, another "matrix" artist featured on Trans-D, Eric Standley takes the fine art of paper cutting to a new level. That is, approximately 100 of them! 

What appears as one cohesive - and elegant - mandala is actually composed of layer upon layer of intricately laser-cut "windows."

To see the artist in action, David Pescovitz has posted a video found here.

The artist's new website can be found here.

(Thanks, DP!)



Saturday, June 14, 2014

To Decode The Living Matrix... Featuring the Work of Cristóbal Vila


From the video: Isfahan - 3D digital still - 2005, Cristóbal Vila


matrix |ˈmātriks|
noun ( pl. -trices |ˈmātrisēz| or -trixes )
1 an environment or material in which something develops; a surrounding medium or structure : free choices become the matrix of human life.
• a mass of fine-grained rock in which gems, crystals, or fossils are embedded.
• Biology the substance between cells or in which structures are embedded.
• fine material : the matrix of gravel paths is raked regularly.
2 a mold in which something, such as printing type or a phonograph record, is cast or shaped.
3 Mathematics a rectangular array of quantities or expressions in rows and columns that is treated as a single entity and manipulated according to particular rules.
• an organizational structure in which two or more lines of command, responsibility, or communication may run through the same individual.

ORIGIN late Middle English (in the sense [womb] ): from Latin, ‘breeding female,’ later ‘womb,’ from mater, matr - ‘mother.’


North American Wood Thrush

“As we listen we lose the sense of time—it links us with eternity…Its tones…seem like the vocal expression of the mystery of the universe, clothed in a melody so pure and ethereal that the soul still bound to its earthly tenement can neither imitate nor describe it.”
- Anonymous Twentieth Century naturalist describing the Wood Thrush


"It was dawn and as I lay there listening to the birds w/ my eyes shut I began to see a weird pattern emerging from the darkness... an almost graphic pattern similar to computer graphics... It looked like chopped meat being criss-crossed (sic) by a rapidly moving concentric ring pattern... similar to my cyclocentric* patterns but more intricate. From this emerged what seemed like another darker dimension - again filled with cyclocentric patterns but these were made of various colors of light... and some were large and whirlpooling (sic) while smaller brighter patterns emerged... all of them moving and vibrant and living and all of them revolving and forming harmonics by which even tinier glowing patterns emerged. It was as if I was delving into a series of many dimensions... but I could only glance at certain aspects (of the patterns) for milliseconds at a time (as they were) far too complex and enmeshed for human resolution...

Wednesday, March 5, 2014

The Merkabah and a Sixth Sense - A Practical View (Annotated)





"The idea or reality of the esoteric chakra system may or may not be relevant to the phenomena I am referring to - from what I gather, the chakra centers are considered symbolic and psycho-spiritual and have no apparent physiological manifestation - but, as I am not aware of any other "maps" at my disposal, contemporary "subtle energy" diagrams provide one place to begin the inquiry.

In the tradition of the Eastern mystics - and Western alternative healers - the chakras (Sanskrit for "wheels") are basically 7 main energy vortices or focal points that lie along the spinal column and skull. The uppermost point, and the one that concerns us here, is generally known as Sahasrara, the seventh, or "crown chakra". In some systems, the seventh chakra lies directly at the top of the head, but in others it lies above. In some systems there are a number of energy centers above the head - the uppermost, and the one that corresponds to my sensory zone is sometimes referred to as the "transpersonal point". In all chakra literature, the crown chakra's primary function seems to serve as a conduit for consciousness, generally of the "cosmic" or collective variety."

- From a web article "Non-Local" Causes and Effects on the Human Body (Tactile Sensations from a distance), Dia Sobin, uploaded 2007 (see: .pdf).


(Added June 9th 2020):

"I can't explain the science behind it, but I just tried it for myself - raised my hand to above the top of my head, and I could feel a sensation like the hairs standing on end - only in a small spot, nothing dramatic, but a definite tingling. I don't think I was imagining it because I can still feel the tingling now."

- A comment left on Posthuman Blues post in 2007 by "Bumble," a female reader of Mac's. His post links to the original web article mentioned above, although the link is now broken. I just found this comment recently and it made me smile. From her description, It seems the woman did, indeed, find the epicranial occult locus.




***


No, it's true, I wasn't lying. I am "exiting the blogosphere." Unfortunately, I spent so much time laying Post-Mac Blues to rest, I haven't had time to deal with Trans-D at all. Meanwhile March has arrived. It still looks like January where I am, mind you, and, yet, it could always be worse... it could look like war. But, as is apparent (and not out-of-character), I was a bit premature when designating "Imbolc" as the "last post". There will be this post and one more to come. I'm aiming for exactly 90 posts. It's a matter of symmetry and symbolism.  Esoterically, the number 9 is the perfect place to tie up loose ends and let loose the finished "product" - ones little spaceship careening towards the galaxy's edge.




How poetic.

But then, my muses - and/or my unconscious self - have/has an agenda... and, generally one I can't figure out till the last phase of a project. The agenda of this post started innocently enough. My urge was to post another scan. On a whim I had scanned into this machine a small crystal Merkabah - a recent birthday gift from my friend, Moo. As we know, I love minerals, and scanning them sometimes provides startling results. So, allow me to explain the scans above and to your left.

First off, Merkabah is an esoteric name given to a certain polyhedron - essentially a triakis octahedron and/or a stella octangula... It has a kind of weird shape that combines both the cubic and the hexagonal - in other words, viewed from one angle it looks square, from the other it resembles a 6-pointed star (hence the "stella"); this is a result of the fact that it is comprised of two interlocking tetrahedrons. Kind of like physical reality. My aim was to capture both angles via my flatbed scanner. To this end I taped my Merkabah - with packing tape - to the inside of a shallow box. Posted above are the results. Posted below (and below the jump) are the same scans with the tape digitally removed.

But, it's the light artifacts in the tape which interest me. While its true that cellophane material will create some cool image scans, I was a little startled by the weird effects produced in conjunction with the crystal polyhedron. Let's just say that, optically, light had a field day. One might also be inclined to consider certain myths concerning the Merkabah in a more sympathetic light.

Originally, the word "Merkabah" arose from early Judaic mysticism and referred to the "chariot of God", specifically that envisioned by the prophet Ezekial.  Of course, nothing is so sacred that it can't fall under the auspices of New Age jargon (or, for that matter, Ancient Alien lore). But, kernals of truth are found in the strangest of places.