Cinco de Mayo - the New Mexican Skies (revised & completed May 9)

Albuquerque clouds in May - cellphone photo - 2025, DS.

(Text added May 7)

This past Monday was Cinco de Mayo - the 5th day of the fifth month in the 25th year of the 3rd millennium. You might say, due to all the 5's, it was a golden day, and, coincidentally enough, one tradition of the holiday is kind of an unintended nod to the pentagonal golden spiral.

The China poblana, the colorful costume featuring a voluminous castor (circle skirt) worn by festival dancers - like the one inset left above (found here) - are really something to see in action. The circle skirts generate spiral shapes continuously as the dancer swirls through her routine. For a regular Phi festival view the short video below the jump break.

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Albuquerque clouds in May (#2) - cellphone photo - 2025, DS.

(Text added May 9)

I guess, in keeping with the times, it isn't too weird that this post has been almost completely revised before it was even finished. But, don't worry, I have no desire to address the "times" nor the shit-storms that (too) many of us are dealing with these days. My goal is to regain a vestige of mental equilibrium again and experience tells me there's only one place to go: back to the natural world. Some of my most serene moments in New Mexico were spent photographing the Sandia mountains, and, in ways, I'm doing the same again; but my view of the mountain range has changed... and, this time I'm obsessed with the clouds.

(Continued below the jump...)

The Mirror of Venus: 5 Keys

The Mirror of Venus: The 5 Keys - 2023, DS.

"Moving now from the decad to its half - we meet one of the most brilliant personalities of the 'society of numbers;' the pentad and the characteristics of the number five. In arithmology or number mysticism the number five partially pertains to the essence and importance of the decad as being its half and its condensed image, but it is also the gamos, Aphrodite's number as goddess of the fruitful union, the generatrix of love, and the abstract archetype of reproduction."

- From the 1931 investigation of phi and the pentagram: The Golden Number: Pythagorean Rites and Rhythms in the Development of Western Civilization, written by Matila Ghyka, a book I've just read recently. The above quote is the first of five similar brief references to Aphrodite and the pentagram found throughout the book; three of which combine Aphrodite with the Egyptian goddess Hathor.*

But, while Ghyka acknowledges an ancient connection between Venus/Aphrodite and the pentagram, it seems to rest upon the idea of marriage, a "fruitful" union... conjugal bliss. He calls this incarnation of Aphrodite "Gamelia," that is, "of the wedding." But, Gamelia was a name given to many, if not all the Olympian gods; specifically Hera, wife of Zeus; it wasn't amongst Aphrodite's major titles, and, regarding the pentagram, is too literal a translation of the "love goddess" and is, ultimately, a red herring.

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Inset left, above: the contemplative Venus of Arles... (seemingly) holding an apple up to her broken-off, handheld mirror. Inset right,  is an actual bronze mirror (Greek, circa 460 BC) supported by the figure of Aphrodite who is holding a dove, while 2 winged erotes stretch their hands towards a point centered above her head. If you connect the point at the top of the goddess's head with the two doves perched above on the mirror, you'll have an inverted golden triangle. Below, inset left, is another similar bronze mirror from the same period, currently in the Met Museum. This one features dogs chasing hares; the hare is another Aphrodite symbol. Hint: we've seen the dogs and the hares before.**

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So, mythologically speaking, marriage was never known to be Aphrodite's strong point... although love, both carnal and celestial, was. The Venus of the pentagram, however, is significantly more complex, and we have to approach her from a higher ground, so to speak. From Theoi we have:

"According to the cosmogonic views of the nature of Aphrodite, she was the personification of the generative powers of nature, and the mother of all living beings. A trace of this notion seems to be contained in the tradition that in the contest of Typhon with the gods, Aphrodite metamorphosed herself into a fish, which animal was considered to possess the greatest generative powers." 

And, there is so much more. One might say, Ghyka was trivializing the Venus/Aphrodite connection. While he inserts the word gamos in his brief comment, he neglects the word heiros (sacred). Nor does he infer in any way that the "wedding" is, in essence, chymical. So, my strongest impression of the book is that the deliberate omissions Ghyka (amusingly) accused other writers of making - including Vitruvius - might've been tip-offs to those of his own. That being said, he probably connects more esoteric "dots" in the pentagram's long journey within the pages of this book than you'll find anywhere else. But, keep in mind, the author may be sticking to traditional "fraternal" codes of secrecy all the while... something also mentioned quite often in his book.

"The mirror also, in turn, symbolizes revelation and truth: the mirror often shows the face, and the eyes, as shown in the painting Venus At Her Mirror or Rokeby Venus or Venus-Aphrodite by Diego Rodriguez de Silva y Velazquez, in which the goddess gazes into the mirror with only her face revealed. The eyes, in turn, are the paths to truth: they are the “window to the soul”, or, ever-more interestingly, the “mirror of the soul.” Aphrodite, in gazing into the mirror, is therefore not merely enjoying the sight of her own beauty, but is acknowledging the truth of all that resides within her – for, as Aphrodite Ourania, she is that which keeps together the entire cosmos and continues the survival of all."

- A quote found here, introducing us to to the most important facet of Aphrodite: Aphrodite Ourania or Urania, the celestial Aphrodite, and the Venus/Aphrodite who will concern us most in upcoming posts. She shares some of the attributes of Urania, the Greek muse of astronomy and the stars, in some cases mistakenly,  but, in others, possibly an indication of the evolution of Pentagonal Venus and the golden meme.

***

The diagram above, a sort of gateway into the Venus subset of the golden meme, is already somewhat obsolete regarding the pentagonal journey I unintentionally began taking around Thursday, April 4, 2019, after my vision of the rose pentacle. I wrote at the time that I anticipated something "larger." But, really, I had no idea of the many roads left to travel. Needless to say, Venus/Aphrodite had her foot in the door from Day 1.

I have since learned that the Venus pentagram, in its entirety, is not merely one arrangement of five symbols but, possibly, an arrangement of 10. Moreover, each of first five symbols composing the "mirror" represent metaphorical hallways with numerous doors. In other words, the Venus pentagram remains true to the pentagram's nature - it's a fractal - very possibly as colorfully layered as (what appears to be) a phi-based Julia set, inset right. Additionally, Venus/Aphrodite is not merely 2 goddesses in one... she's worn many hats over the course of her very long career and has several hybrid forms as well, so, it's a very tangled web, indeed. 

In spite of all of the above, the first five symbols I'd originally chosen for the diagram still stand, but, while I had hoped to address each of them briefly here, I've come to realize it isn't presently feasible. There is no "brief" in this discussion. 

As for now, I will include in this post some bits which have already been written regarding several symbols in the diagram.

(Note: I was originally going to conclude this post with one more bit of information via Prince Ghyka which might interest us, and it concerns Albrecht Dürer. This "bit of information" was eventually accompanied by other bits of information to necessitate adding a dedicated Part III to Albrecht Dürer and the Divine Ratio Parts 1 & II. As I said, there is no "brief" in this discussion. Stay tuned.)

(Continued after the jump...)

An Auspicious Day

The Three Golden Eggs of Happiness, G-DS-2024
Alternative title: 3 Sleeping Doves

We seem to be experiencing a grand trine of celebratory days today: the first day of spring, the neo-pagan and Wiccan holiday of Ostara, and the first day of the Persian new year! So, put aside your woe and despair and knock yourself out with the pleasure of impractical things - we've hit the jackpot!

I found three (pretty-much) perfect golden eggs (sourced here)... and, now, you have!

Smile. You'll feel better. It's a known fact. :-)

The Paisley Pattern & the Golden Meme

Phi shells served up on a modern paisley fabric (sourced here).
Geometry: 2024, DS.

"meme - n. a unit of practice or belief through which a society or culture evolves and that passes from one generation (or even one person) to the next. In this sense, the term — coined in 1976 by British  biologist Richard Dawkins (1941–  ) and derived from the Greek word for “imitation”— is a kind of metaphorical parallel to the term gene."

-  An interesting definition of "meme" found in the online American Psychological Association's Dictionary. As a "metaphorical" gene, in lieu of its lack of actual physicality, we can expect a meme to operate in a manner similar to the gene: subconsciously and/or subliminally. Unlike the gene, it is transferred from one mind to the other... often in the form of a symbol, although not necessarily a visual symbol.

The images posted above, and inset right, and inset left and right below are the result of a new 2-dimensional toy I developed last year and introduced in The Universe in a Phi Shell: phi shells. I can't remember what inspired me to make phi spirals into phi shells, but it was probably pretty elementary. However, once I saw the effect the shells produced on some images, I was astounded. In so many cases the phi shell was like an envelope - die-cut to fit a golden spiral - or a custom-made template... with maybe a little wiggle room.

Sometimes, working with a phi shell leads to repositioning the original spiral. Inset right is a prime example: Boy Blowing Soap Bubbles by 17th century Dutch painter (and Bentvueghel), Karel Dujardin. (See the post for the former spirals.) As concise as this spiral appears, it could be larger and better... but, As we see time and time again, some portion of the necessary image area is missing. What sold me on the orientation of this spiral, however, is the way the boy's right arm - holding the bubble pipe - falls so neatly into the small triangle. It's as if the boy is drawing the spiral in the air.

"Proponents theorize that memes are a viral phenomenon that may evolve by natural selection in a manner analogous to that of biological evolution. Memes do this through the processes of variation, mutation, competition, and inheritance, each of which influences a meme's reproductive success. Memes spread through the behavior that they generate in their hosts. Memes that propagate less prolifically may become extinct, while others may survive, spread, and (for better or for worse) mutate. Memes that replicate most effectively enjoy more success, and some may replicate effectively even when they prove to be detrimental to the welfare of their hosts."

- A cautionary quote from the Wiki entry for "meme," and one that might make a certain amount of sense to those acquainted with what I've come to refer to as the "Golden Meme." I could even go so far as to says this might be reflected in my own experience... including the "detrimental to their hosts" bit, but, I try not to entertain fantastical innuendos that accelerate my level of paranoia.

"When Pacioli (the Renaissance mathematician) wrote in his Divina Proportione: '.. just like God cannot be properly defined, nor can be understood through words, likewise this proportion of ours cannot ever be designated through intelligible numbers, nor can it be expressed through any rational quantity, but always remains occult and secret, and is called irrational by the mathematicians'... he seemed to be equating the golden ratio with a variety of magical formula. That is, through his recognition and understanding of "this proportion of ours" he was attempting a marriage between several disciplines: science, art and mysticism. And, this wasn't unusual for the early Western scientists, many who dabbled in astrology, numerology and alchemy side by side with astronomy, mathematics, botany... and the arts. The scientific field was wide open - the hard lines were still blurred...

The "new scientists" were seeking enlightenment, autonomy, discovery, truth. And, it was into this slowly reawakening world that the pentagonal spiral made its appearance... and not necessarily for the first time. Similar to the sign of the pentagram - by which the followers of Pythagoras "knew each other" - perhaps, the "sign" of the pentagonal spiral enabled the Baroque artists to identify like-minded artists... kindred spirits in a world in which freedom did not, yet, ring."

"Keep in mind that the spiral was also present in Baroque ornamentation... and possibly somewhere in Baroque music, too.  So, were the artists, artisans, and musicians completely aware of its proportions and using it as a measure of perfection and beauty? Or, was the proliferation of golden spirals (at that time) an almost paranormal thing... or a variety of subliminal meme... an unconsciously recognized icon which was possibly a symbolic presentiment on the part of an artistic community who were, without noticing it, heralding an evolutionary phase of a whole society?"

A Baroque flourish (w/ phi shells). G-DS-2024.

- Two quotes via my blogpost: The Gentilischi Spirals and a Series Afterword. One painting appearing in that post is the image reposted (inset right) above the flourish: Orazio Gentileschi's Young Woman with a Violin. It's phi shell is looser than the original spiral I gave it, which, resting on her lap like a humongous sea shell, gives the image a somewhat comical appeal... but the spiral and triangle intercepts the young woman's bow perfectly, so, we have to admire its cleverness.

The flower painting, inset left, above her, however, was the work of Dutch Baroque artist, Willem Van Aelst and can be found in Part III of the Bentvueghel series, where we become acquainted with the curious appearance of the garden snail in flower paintings. And, really, if the Dutch flower painters used the snail as a clue indicating that a larger spiral was deliberately embedded in their paintings, well, all I can say is, what a brilliant idea!

Directly above is a portion of a Baroque ornament recently found (now decorated with phi shells). Not all Baroque flourishes were as golden as this one, but, considering the quantity of spirals appearing on furniture, architecture and textiles, the golden meme was alive and well.

***

For the past few years, I've spent a lot of quality time pondering the meaning of the appearance of the pentagonal golden ratio in works of art, artifacts and in architecture. I can't say for sure why this is so anymore, but, once upon a time, there seemed to be a point. I had a plan. Nowadays, I have to ask myself, why in the world would anyone actually sit down and spend a great deal of quality time blogging about obscure topics to an evaporating audience while everything in the surrounding area (the world, that is) seems to be either rapidly going down the tubes, or up in flames?

And, this isn't the first time I've asked myself this question!

On the other hand, blogging about obscure topics to an evaporating audience - in view of the tubes and flames - presently encourages my survival. Perhaps, blogging is kind of a therapy after all. Or, perhaps, in an absurd world, doing nonsensical things in response to Armageddon is appropriate.

And, it is in this state of mind I will reveal my latest pentagonal phi epiphany... which just happens to regard a description I've used previously: subliminal meme. The kind of meme that just might slip into an image while the artist was totally unaware of it, as it did in 2012, when I created Metamorphosis Interrupted, reposted (inset left), with a phi shell that fits the unfortunate worm like a chrysalis! (See: A Virtual Can of Worms.) 

Generally speaking, the unconsciously produced spirals in the images referred to in the Worms post were not all that strong. However, the worm's proportions in Metamorphosis is very close to perfect. But, while I was aware that I was being very finicky about the shape of the worm's body while creating it, in reality, at the time of its creation, I had never even heard of the pentagonal golden spiral!

 

So, is this an indication of phi "on the brain"? Are our brains somehow wired to its aesthetic or does it go deeper than that? Is this why the ratio was referred to as "divine" - in that it is embedded so deeply in our consciousness we assume it is an outer force? Or, when we find it in organic life, is it merely the imprinted diagram of actual physical forces science is already aware of?

Or, taking into consideration the nature of a meme, can you actually "catch it" like the common cold?*

Speaking of brains, I was delighted to find an image of one that seamlessly fits into a phi shell (inset right). Of course, humans tend to have rounded skulls, so it should come as no total surprise. But, then again, the image is an illustration and not an MRI, so, this is an artistic interpretation (and a very nice one) by Hank Grebe.

I didn't notice this till I was adding my geometry "stamp" to the image, but what lies at (a very important) 3-cornered junction of the spiral nearest to the coil - technically, the apex of the smallest golden triangle (and its spiral) - is that notorious pine-cone-shaped brain element, the mysterious pineal gland or "third eye." Oddly enough, it is depicted here as another tiny golden triangle (click for enlargement.)

(Continued below the jump...)

The Universe in a Phi Shell

M74, or the Phantom galaxy... embellished with a phi shell. (G-DS-2024).

'The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new dark age."

- H. P. Lovecraft, The Call of Cthulhu, 1926.

"Messier 74, also called NGC 628, is a stunning example of a "grand-design" spiral galaxy that is viewed by Earth observers nearly face-on. Its perfectly symmetrical spiral arms emanate from the central nucleus and are dotted with clusters of young blue stars and glowing pink regions of ionized hydrogen (hydrogen atoms that have lost their electrons). These regions of star formation show an excess of light at ultraviolet wavelengths. Tracing along the spiral arms are winding dust lanes that also begin very near the galaxy's nucleus and follow along the length of the spiral arms.

M74 is located roughly 32 million light-years away in the direction of the constellation Pisces, the Fish... In its entirety, it is estimated that M74 is home to about 100 billion stars, making it slightly smaller than our Milky Way."

- Via this Hubble page, we are introduced to the M74 galaxy discovered by the French astronomer Pierre Méchain in 1780. It is a kind of go-to spiral galaxy for those seeking spiral perfection. Of course, for the golden (pentagonal) spiral hunter, gazing at it's sinuous, twisting, mollusk-like proportions is sheer bliss... as, if there were a God and It had a face, this would be it. (God the mollusk! The Mollusk god. So, burn me at the stake. See if I care.)

"Messier 74 (also known as NGC 628 and Phantom Galaxy) is a large spiral galaxy in the equatorial constellation Pisces. It is about 32 million light-years away from Earth. The galaxy contains two clearly defined spiral arms and is therefore used as an archetypal example of a grand design spiral galaxy. The galaxy's low surface brightness makes it the most difficult Messier object for amateur astronomers to observe. Its relatively large angular (that is, apparent) size and the galaxy's face-on orientation make it an ideal object for professional astronomers who want to study spiral arm structure and spiral density waves. It is estimated that M74 hosts about 100 billion stars."

- This quote was sourced from the Wiki entry for M 74, along with the galaxy image used in this post (inset left). That the Phantom is considered an "archetypal example" of a "grand design spiral galaxy" is kind of interesting... in light of the fact that it is composed of 2 near-perfect pentagonal golden spirals. (And, when discussing massive deep-space objects, "close" is about as good as it gets.)

"This Hubble Space Telescope photo of Messier 74 reminds us that spiral galaxies are some of the most beautiful and photogenic residents of the universe. Nearly 70 percent of the galaxies closest to the Milky Way are spirals. New research finds that spiral arms are self-perpetuating, persistent, and surprisingly long lived."

"How the spiral arms form continues to puzzle scientists. One theory suggests the galaxy arms could be the result of density waves traveling through the outer disk. Encounters between galaxies could cause such waves as the mass of the smaller galaxy could affect the structure of the larger galaxy as the two combine."

- Two quotes from this Space.com article... reminding us of how little is known - and how much there is to know - about our cosmos.

***

I'm a busy woman these days, and I hate it. All it amounts to is more stress. But, tell that to an artist's muse. Time perplexes muses. They simply don't get it.

So, I currently have five posts sitting on the back burner, an unfinished digital image - my first formal digital image since my 2022 car accident - a ceramic project that MUST go into production this month, and a number of tedious life issues to deal with... and deal with, and deal with. But, then, last night I came across this photograph (inset right) of M74, the Phantom galaxy and, within minutes, I found myself absorbed in playing with my latest graphic toy, a phi shell (rhymes with seashell)... trying to decide which color to use from my ever-growing palette. In the end, only the white shell did the Phantom any justice, and even this had to be almost transparent... to endow it with that certain marine life appeal which, for whatever reason, seemed appropriate.

Anyway, I decided to post 2 images to the blog for the (freakish) enjoyment of those who, like myself, delight in this sort of thing. (Yes, in case you haven't noticed it, we constitute a minority.)

Oh, and incidentally, the "phi shell" - my attempt to give the common mathematical diagram a little extra-dimensional pizazz - will be appearing quite often in the coming days. I confess; I'm hooked on phi shells now, and there's no help for it!

Adieu, till next time... :-)

Via the ESA: a multi-observatory view of the Phantom.

The Heart Nebula & the Flaming Heart of Venus

The Heart Nebula (detail) - Photo credit: 2022, Ernie-Jacobs. Geometry: 2024, DS.

 "What's that inside the Heart Nebula? First, the large emission nebula dubbed IC 1805 looks, in whole, like a human heart. It's shape perhaps fitting of the Valentine's Day, this heart glows brightly in red light emitted by its most prominent element: hydrogen. The red glow and the larger shape are all created by a small group of stars near the nebula's center. In the heart of the Heart Nebula are young stars from the open star cluster Melotte 15 that are eroding away several picturesque dust pillars with their energetic light and winds. The open cluster of stars contains a few bright stars nearly 50 times the mass of our Sun, many dim stars only a fraction of the mass of our Sun, and an absent microquasar that was expelled millions of years ago. The Heart Nebula is located about 7,500 light years away toward the constellation of the mythological Queen of Aethiopia (Cassiopeia)."

- Via this NASA archive page: In the heart of the heart nebula. Basically, the Heart Nebula - in the constellation Cassiopeia, composed of 5 major stars - seems to be an artifact created by gases from the birth processes of new stars, but, well, nothing I've read simplifies it to that degree, so it's merely my guess. In any case,  it's very impressive looking... like looking into the innards of an exploded star (nova) or a bubbling cosmic cauldron. Also, see its companion: the Soul Nebula... and an interesting star, φ Cassiopeiae.

Inset right is a cardioid animation, created by Atomic Shoelace, and sourced from the Wiki entry for Heart Symbol. I've never seen this before, but, looking at it now, it appears that the cardioid and the pentagonal golden spiral have something in common.

(continued after the jump-break...)