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Cedar sprig symbolism: Freedom or fragmentation?

Monday, 16 January 2023 by Bruce Rawles

Button art: Yachats New Year's Day Peace Hike 2023 — Button art: Yachats New Year’s Day Peace Hike 2023 – art by Loren Dickinson

I started the new year by participating in the annual Peace Hike here in Yachats which I look forward to every year since moving to the Oregon coast 6 years ago – it’s always a great reminder to share in the willingness to look at past atrocities of non-connected thinking and use the contrast of that insanity to the peace we really want to motivate us to deepen an all-inclusive sense of community – and not make avoidable mistakes by forgetting the lessons we have been given. I feel blessed to live in a community where that egalitarian spirit is highly valued all the while realizing that this is the longing of every heart and mind around the world, however frequently ignored or seemingly deeply buried.

In addition to the hike from the Commons Building to the Amanda Statue (near the new bridge*) the yearly ritual involves giving all participants a little sprig of cedar leaves to put on the common fire to symbolically represent our renewed commitment to peace and anchor our intention. The very fractal geometry of cedar sprigs gives us an opportunity to look at our ongoing motivations for everything we think and do – we can either metaphorically follow the smallest branches back through larger and larger gatherings of self-similar shapes to find the source or root where we realize we share the same pattern, the same intrinsic design, the same essential identity. If we traverse the fractal in the opposite direction – from unity to individuality, we may lose sight of the unifying generalization by a preoccupation with individual, specific divergent paths. This is one of the countless examples of how a geometric symbol can be used to join and strengthen … or as a tool for divisive thinking. It all depends on how we look at life each moment, either from the freeing kindness of inclusion … or the cruel fragmentation of exclusion. This is explored in greater depth in The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation.

Here are a few more fractal images from prior posts on this website and other media I’ve made:

IMception: fractal flotilla? — source: https://img.einnews.com/large/196490/imception-02.png#4096×2304

fractal dodecahedron from sketchup.google.com

pentagram fractal (made with Adobe Illustrator, Bruce Rawles)

Mandelbrot Set - Deep Dive — Mandelbrot Set – Deep Dive

tetrahedral-fractals - low resolution image of page 226 from SGDS (Sacred Geometry Design Sourcebook - Universal Dimensional Patterns by Bruce Rawles) — Tetrahedral-Fractals – low-resolution image of page 226 from SGDS (Sacred Geometry Design Sourcebook – Universal Dimensional Patterns by Bruce Rawles)

toroidal fractal by Bruce Rawles (POV-Ray) — toroidal fractal by Bruce Rawles (made using POV-Ray software)

* Last year’s theme for the local Polly Plumb Productions banner project was “Paths to Yachats” to coincide with the completion of the new suspension footbridge. If you look for my (Bruce Rawles) banner art on this page, you’ll see my notes about my submission:
“Inspired by the symbolism of new higher, more sustainable footbridge connecting Yachats to Cape Perpetua, I combined the multi-ridge skyline of the cape as seen from Yachats Ocean Road with the general shape of the bridge from a photo I took shortly after the bridge was opened. Realizing that there are more than just human “paths” to our lovely community, I thought of adding an eagle or seagull or two but ended up just complementing the human traffic with the vast aquatic migration by means of a sea star and a whale fluke. I’m reminded that I must keep the bridges in my mind open to graciously receive all, regardless of form.”

Since I now have two artist depictions of a suspension bridge as visual bookends for this post, it reminds me of a geometric shape that occurs with a rope, chain, or other flexible material suspended between two fixed points, the catenary, which sounds like a cross between a cat and a canary – or perhaps the shape of the belly of a cat that ate a canary? The actual shape of suspension bridges with additional non-uniform weight is probably different, but it’s a good place to start for a first approximation.

Mirrored geometric solid cameo on new whodunit

Friday, 30 December 2022 by Bruce Rawles

Spoiler Alert: This post will reveal the Platonic Solid that stole the show (at least for me) on the latest flick by director Rian Johnson. If this isn’t an issue, read on! May I have the envelope, please…

I don’t often watch murder mysteries unless there’s a generous amount of tongue-in-cheek involved, such as my favorite classic of this genre, “Murder by Death” which I recommend if you haven’t seen it. The “22 Twain” punny address of the mansion at the beginning of that film had me hooked at the get-go.

Based on Johnson’s prior whodunit, we thought we’d give his new one a go, and enjoyed it, also. So… for silly fun, we recently watched (streamed at home) “Glass Onion: A Knives Out Mystery” which featured – in addition to the expected absurd assemblage of characters with a preposterous plot, and a fun puzzle box invitation featuring a “whirling squares” (Fibonacci) spiral, other familiar geometries plus assorted over-the-top glass sculptures in a billionaire island mansion with an infinity pool – a few witty pop-culture-for-nerds cameos like a Boston Dynamics “dog robot” porter and momentary dialogue about Google alerts – which I find helpful every week for feeding me news about sacred geometry and other metaphysical topics.

Regular readers will recall that this isn’t the first time I’ve featured the lovely geometric artwork of artist Anthony James … The (virtual envelope) contents of that award-winning geometric art (from my perspective) is … cue the drum roll … James’ Mirrored Icosahedron with the illuminated interior edges presenting the viewer with an exotic labyrinthine landscape of triangular tunnels. That’s it! At the focal point heart of the bulbish-shaped centerpiece glass onion sphere-like feature of the larger mansion sits a mirrored icosahedron which sure looks a lot like James’ handiwork! (If anyone knows any different, please let me know.)

The screen snap of a frame from the trailer doesn’t do it justice… Here’s a frame close-up from a video giving the “star” more exposure:

Speaking of mirrored and/or virtual polyhedra, see also: Sara Frucht’s Kaliedoscapes!

Alternate ending: If you were hoping for a dodecahedron, you might want to read this post on my other niche blog; the original model that appeared in the Lawrence Livermore Lab bulletin my Dad brought home early in the development of laser fusion showed a translucent plexiglass dodecahedron with 12 plexiglass cones centered on each pentagonal face all converging at a hydrogen pellet target.

Happy New Year all!

Spirals, Ferns, and Universal Unfolding Motifs

Thursday, 1 December 2022 by Bruce Rawles

While I try not to obsess about geometric forms, I do observe when certain motifs appear more frequently in various locales. When we visited San Miguel de Allende, Mexico earlier this year, I noticed an abundance of small stellated dodecahedra (and similar shapes) particularly evident in metal lamps, yet also in other art forms as well; each pentagonal pyramidal stellation arm encodes the golden ratio. …

Having just returned from a second visit to New Zealand, it seemed that one of the most ubiquitous geometric shapes we saw on this trip was the spiral, which appears in Maori jewelry, carving, tattoos, art, and culture, connecting the natural world with the art of the indigenous people of Aotearoa. Below I made a mirrored tiling pattern from an image of an unfurling silver fern frond which exhibits an excellent example of fractal geometry.

Wikipedia says “The koru is a spiral shape based on the appearance of a new unfurling silver fern frond. It is an integral symbol in Māori art, carving, and tattooing, where it symbolizes new life, growth, strength, and peace.”

Reflecting intuitively on our spiral “journey” through life like the homeward trajectory Dorothy embarks upon in the Wizard of Oz when she follows the yellow brick road, we find context in the cyclical, yet ever-evolving, ever-unfolding awareness with each revolution of the spiral. In three dimensions, we have the double helix of the DNA molecule in everything we typically call life in this world, embodying the golden ratio in each pentagonal molecule appendaged to the helix and also in the (Fibonacci proportion) 34/21 Angstrom ratio of each complete turn of the helix. Every year, each season has familiar patterns and signs, yet there is a much larger progression we discover when we “zoom out” a bit from our myopic, provincial perspectives. The Chambered Nautilus shell has a pleasing uniformity as one spins the shell around, since each accretion uses the same angular template as the preceding one, and builds upon the strength of sameness throughout.

Here are a few more spirals from our most recent NZ trip; enjoy!

New Zealand: Napier museum; Maori wood carvings with numerous spiral forms

Auckland Airport ceiling lamp fixture — Auckland NZ Airport ceiling lamp fixture

Auckland NZ Airport ceilng art: spiral fish school

New Plymouth, NZ art gallery staircase; spiral flourishes

Napier NZ boardwalk art with overlapping complementary spirals

In memoriam: William Goldstein

Friday, 14 October 2022 by Bruce Rawles

I recently learned of the passing of William Goldstein (a.k.a. Will Gold), who left us on August 11, 2022. William was a fellow geometer, researcher, historian, mystic, and much more. It was only fairly recently (September 2021) that I discovered his work, our many common interests, and favorite books while exploring his extensive fascinating writings which are a great complement to my more mathematical leanings. I began a brief stint as his webmaster and I was hoping to be able to share many recorded conversations between William and myself with my GeometryCode readership, but that was not to be.

Rather than have this important body of work disappear, I offered his family the opportunity to keep the site going so that others might benefit from his insights, and helpful resources including an extensive library of unique and interesting books, most of which are still available. The newly relocated website (formerly Chartres-sacred-geometry.com) is now live at Chartres.GeometryCode.com. It is my hope that my readers will avail themselves of his thoughtful and insightful writing and excellent book (and other media) recommendations of particular value for geometry enthusiasts, particularly the in-depth cultural and historical underpinnings behind so many important discoveries and real human progress.

Here is the prior article I wrote about William’s site which I would recommend reading as well.

Thank you, William, and to your family as well!

The Geometry Code (Kindle edition) turns 10 today!

Wednesday, 28 September 2022 by Bruce Rawles

On this day in 2012 – a few months after introducing the print version, I made the Kindle version of my second book available: The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation. I’ve appreciated all the support and encouragement during the past decade for this work, intended to be a bridge between two primary interests: the principle of interconnectedness reflected in geometric archetypes … and pure non-dual metaphysics.

The cover art and the opening graphics for the last 7 chapters in the book are symbolic interpretations of the 7 Hermetic Laws – covered in detail on this website.

However, I just realized that I never gave very many details on the first geometric image used in the book, so here are a few. The image below depicts a geometer’s compass spanning an infinity symbol – to represent ideas that are “all-encompassing” – and the Great Pyramid of Giza, Egypt (the last remaining of the seven wonders of the ancient world) with the Great Sphinx in the foreground. There is abundant fascinating geometry in both the exterior and interior of the Great Pyramid including the phi and pi proportions, squaring the circle, many terrestrial proportions, etc. which are covered in various talks and essays on this website spanning several decades.

The Pyramid’s foundation idealizes the square, connecting the compass (vertical axis) and square (horizontal plane of materiality.) The four sides of the pyramid and the overall shape of the compass are triangular, signifying the reconciliation of polarities, meeting in the capstone atop the pyramid and the apex of the compass where both vision and inspired guidance are possible through the exalted perspective that sees all as equal.

Here is the foreward to the book by Gary Renard:

I met Bruce Rawles in Medford, Oregon in 2008 and again in 2009 and 2010 in Ashland, Oregon when he and Ed Karlovich hosted and promoted seminars I did there. During one of the car rides to the airport, he mentioned a book that he was working on that sounded unique and original. I was curious as to how he would incorporate the diverse disciplines of sacred geometry (which he has studied extensively), Hermetic philosophy with its unchanging laws of nature, and the non-dual metaphysics that is the essence of my life work, best known to many by the spiritual masterpiece, A Course In Miracles (ACIM).

He was quick to point out that it’s easy to get distracted or diverted by external indicators like geometric symbols and get bogged down in specifics or interpretations that lead away from wholeness and toward the problematic belief in the concept we call separation or ego. At best, symbols can be mirrors or reflections within a dualistic world that attest to principles guiding our minds back to an awareness that has no opposite, an experience of love that transcends anything that can be conveyed by words or symbols of any kind. These symbols, seen from that view that embraces oneness, reflect a healed mind, but are never the cause of it.

He also recognized that the very ‘universal’ laws that can seem to keep us stuck in the dream (to our detriment) can also be reinterpreted for everyone’s benefit by the inner teacher of kindness that ACIM refers to as Holy Spirit and my teachers abbreviate metaphorically as ‘J’. We can learn to trust this inner teacher and use every bit of feedback as cues or reminders to practice, practice, practice the spiritual art of quantum forgiveness, which sees our ‘problems’ as causeless, and therefore completely benign and forgivable.

Having acknowledged these two caveats, he has done a remarkable job of sharing how – by developing trust in the inner Inclusive Guide we all have in common – we can include the symbolic contents of our unconscious mind in very familiar forms, such as geometric ones, as feedback devices or memory jog aids to deepen our trust in our inner teacher. For example, Bruce points out how egos use circles dualistically to exclude and banish ‘others’ to the outer regions (and the equally unhelpful ‘special love’ for those ‘within the circle’), but can just as easily be reinterpreted to be infinitely large, including All as One.

Similarly, with his explanations of seven laws of nature, it becomes obvious that these unchanging rules (starting with the fact that the universe exists only in mind) can be directed by either the 100% sane thought system or the 100% insane thought system that we all share. The choice is up to us, moment by moment. Without the specific people and events of our lives – including the exemplified laws and forms we encounter – our unconscious guilt would never be revealed, released, and healed.

Countless other examples demonstrate the importance of forgiving the dreamer of separation; this work is a fun and useful addition to the list of ACIM studies books. Bruce and I share the kinship of all (not just those one would call students) learning to practice forgiveness, gently awakening our dreaming minds to Love that is beyond any words or symbols. Enjoy, and awaken.

– Gary R. Renard, the best selling author of The Disappearance of the Universe