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The Geometry Code (Kindle edition) turns 8 today! :-)

Monday, 28 September 2020 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 these past 8 years 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.

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

Here is a recent timely and popular conversation I had – including ways of coping during 2020 with its challenges – with Gary Renard and his equally insightful wife, Cindy Lora-Renard.

Filed Under: 2D Geometries, Hermetic Laws, sacred geometry books Tagged With: Gary Renard

Stella Octangula projects Paul McCartney, Hendecagon architecture, Irrational Phi

Saturday, 29 August 2020 by Bruce Rawles

Hendecagon-based architecture, IndiaAnother super quick, fun update for sacred geometry enthusiasts!

  • Check out this fun, animated articulated model of Leonardo da Vinci‘s “Stella Octangula” (a.k.a. stellated octahedron or star tetrahedron – fold-up model here) making a cameo appearance as a holographic projector on a sci-fi Paul McCartney music video which seems inspired by Princess Leia’s classic hologram “Help me Obi-wan” plea.
  • The image above shows the uncommon 11-sided (hendecagon) geometry from a lovely slideshow gallery of images from this article: India’s New Parametric Temple to Reinterpret Vernacular Design in Koppur.
  • Starting with a clear explanation of how a flower might optimize seed spacing geometrically (with insightful animations) this Numberphile video shows why the Golden Ratio is so irrational.

Filed Under: 2D Geometries, 3D Geometries, polyhedra, sacred geometry animation, sacred geometry spaces, sacred geometry videos Tagged With: Paul McCartney

Flat Land and Beyond: Above and below the familiar three dimensions

Thursday, 30 July 2020 by Bruce Rawles

4D polytope (NumberPhile video screen snap)Here’s a super quick but loaded update for enthusiasts of dimensional exploration!

What do the numbers 1, 1, ∞, 5, 6, 3, 3, 3 (and 3 forever after that) have to do with geometry? Check out the 2nd video below!

  • To conceive how the limitations and illusions of our 3-D world might be somewhat cleared up from a higher dimensional perspective, check out the Flatland: The Film (2007) movie in entirety here!
  • For a superb and lucid explanation of 4-dimensional polytopes and beyond, check out this excellent Numberphile video with great visual explanations
  • If you want to explore further into the realm of non-dual metaphysics, here’s an article about going beyond symbols I wrote earlier today on one of my other websites.

Filed Under: 2D Geometries, 3D Geometries, 4D Geometries, sacred geometry videos

In memoriam: Keith Critchlow

Sunday, 31 May 2020 by Bruce Rawles

Keith Critchlow
Keith Critchlow

I recently learned of the passing of Keith Critchlow through this obituary in The Guardian. One of my first introductions – in the early 1970s – to what has become known as sacred geometry was through the books of Keith Critchlow, notably Order In Space and later, Islamic Patterns: An Analytical and Cosmological Approach. The former book has small illustrations of the tesselations (2-D tiling patterns) comprised of regular polygons. I thought these classic regular tilings all merited a full page (along with numerous archetypical variations) – so these make up a considerable portion of my first book, including pages 16-42, plus other tiling patterns inspired by these on pages 43-95, many unique to SGDS.

Here’s an example (page 27) of one of the small sketches from Prof. Critchlow’s book that I expanded and gave an entire page, in order to facilitate photocopying, coloring – for adults or “kids” of any age, arts, crafts or what have you…

You’ll note that on these 2D tesselation pages I’ve also added “unit cell” variations that show some of the possible groupings of polygon components that can make “step and repeat” (via horizontal and/or vertical translation) patterns that tile the plane in two dimensions.

Sacred Geometry Design Sourcebook example: 4 Triangle, 2 Square Grid (page 27) copyright (c) 1997 Bruce Rawles

I’m not sure if Order In Space was my first exposure to the 5 Platonic Solids and 13 Archimedean Solids, but this may be likely, and pages 196-214 in Sacred Geometry Design Sourcebook – Universal Dimensional Patterns were certainly inspired – in part – by Critchlow’s illustrations. You can find other useful tables in the back of SGDS that were also helped by the example of Critchlow’s generous offerings of useful patterns, ideas, and interconnections.

Elsewhere in Order In Space, he shows a matrix grid chart of the various possible permutations of nesting the 5 Platonic Solids inside each other. Again, these lovely little sketches seemed to merit full-page treatment, so they contributed to pages 224-229 in SGDS.

When I was nearing completion of SGDS in 1997, I sent a review copy to Professor Critchlow, and he sent a very thoughtful reply which included this testimonial:

“A valuable source book of geometric patterning, very useful data, a reminder of the supra human source of such mathematical forms.”

He also provided some very appropriate advice (which certainly aligned with my own experience) in advance of the initial publication, so I added this underlined sentence to page 5 of SGDS paying homage to what must be many millennia of geometers using straightedge and compass for discovery:

“I strongly encourage experimentation and particularly duplication with your own hand.”

Thanks for many years of inspiration, Keith!


Lots more to explore!!! In the process of researching archives online as well as my own prior work to find 2D tilings and tessellations, I found this excellent Wikipedia page: List of regular polytopes and compounds, which expands this topic into many fascinating connected subjects. Here’s a particularly lovely example image from the Hyperbolic star-tilings section:

Filed Under: 2D Geometries, 3D Geometries, Archimedean Solids, Platonic Solids, polyhedra, sacred geometry art, sacred geometry books, sacred geometry coloring books, sacred geometry news Tagged With: Keith Critchlow

Golden Ratio Revisited

Saturday, 25 April 2020 by Bruce Rawles

Looking for a way to measure golden ratio proportions in your garden, home, studio, or office? Here are golden ratio calipers that can help find this fascinating, ubiquitous proportion in existing mineral, plant, animal, and human examples all around you. This tool can help with both finding and propagating this quintessential proportion of interconnectedness: the golden mean.

Golden Ratio Calipers

You can also employ this tool when making 2D or 3D art, sculpture, or other creative media, confirm your intentional use of the proportion that was used by luminaries including Leonardo Da Vinci, Michelangelo, Raphael, Georges Seurat, Piet Mondrian, Salvador Dali, Le Corbusier and other notables in art, architecture, music and more.

Another related essay shares thoughts on the Most Memorable Golden Ratio Examples in Modern Art.

Here’s a well-illustrated article on How To Use The Golden Ratio In Art, Composition & Design. with some classic examples. (Thanks to brother Jim for the link.) … and another related

Filed Under: 2D Geometries, Fractal Geometry, sacred geometry art, sacred geometry videos

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