Search Results for: beyond

Symbols of Interconnectedness Everywhere

Thursday, 31 December 2020 by Bruce Rawles

As we close out a very surreal year, we wish you the peace that arises from the realization that we’re all interconnected and therefore kindness is appropriate every where and every when. Note the ring of Vesica Piscis shapes around the middle cylinder in this ceiling decoration in a hotel lobby. :-) The Vesica Piscis is the “lens” that is formed when two identical circles (symbolizing two identical seemingly separate selves) exactly touch overlapping so that one circle touches the “heart” or center of the other and vice versa. I imagine Plato (if he were around to comment) might suggest that even these helpful symbols are not the perfection – that transcends their apparent form – that the circles merely represent; the reality or essence in our minds is beyond any specific instance in space or time that the shapes, no matter how elegant or refined, could possibly convey. Like holograms, each of us contains the whole although not apparent to our senses. May 2021 be an opportunity for all of us to deepen our appreciation of the wholeness within every seeming part! :-)

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.

Social Distancing, Space-Filling Patterns, and Non-Dual Thinking

Monday, 30 March 2020 by Bruce Rawles

In light of the current (highly appropriate) global practice of social distancing to minimize the spread of a global pandemic, the ideas and issues of space, isolation, and closeness are now in sharper focus than ever before for billions of humans on this planet. One social extreme generally considered severe punishment is “solitary confinement” where prisoners are cut off from almost all communication with others. Human examples of the other extreme might be a crowded party or bus where many of us would gasp for “breathing room” or perhaps a “dogpile” or gymnastic feat of some sort involving cramming bodies together – phone booths and VW bugs come to mind so I guess I’m dating myself with those examples. :-) Interesting how just a few short weeks can shift worldwide perception about situations involving physical proximity that we perhaps welcomed before on occasion, but now avoid – both literally and figuratively – like the plague!

Geometric Metaphors: “as close as you can get”

In the realm of geometry, we have 2-dimensional tiling patterns or tesselations where space is filled without any gaps by simple geometric archetypes. In my first book, Sacred Geometry Design Sourcebook – Universal Dimensional Patterns (SGDS), pages 16 through 84 of the 256 pages are devoted to these grids of space-filling patterns: 30 pages of regular polygon tesselations, 18 pages of square, rectangular, and circular arc tilings, 10 pages of hexagon-based or dodecagon-based tilings, and 9 pages of pentagonal tesselations, just a tiny sampling of an almost endless assortment of permutations of patterns that can fill a 2-dimensional space and not leave any gaps. Here’s an example of regular polygonal tilings from page 27 of Sacred Geometry Design Sourcebook showing a few variations (indicated by thicker lines) of “unit cell” patterns that fill space in two dimensions:

The classic work of graphic artist M. C. Escher brought some unique and elegant examples of tilings and tesselations to the world a few decades ago. Here’s a video with a few examples and related software for making tesselation patterns in 2D. There are countless examples of both periodic (uniform) and aperiodic (non-uniform, such as Penrose) tilings in nature, art, and architecture.

What about 3D Space-Filling Patterns (Tesselations)?

One of the most familiar examples in three dimensions of a space-filling pattern is a cubic lattice. Here’s an (Escher) example of a 3-D grid (think steel girders on a high-rise building). Although not space-filling per se and not 100% density, sphere packing takes on various geometric patterns, including Hexagonal Close Packing, and Cubic Close Packing. Page 239 in SGDS has a chart of radius ratios and diagrams for Coordination Numbers of 3,4,6,8 and 12 of spherical packing, as typified in ionic chemical bonding on a molecular level. Here’s an excerpt from that page:

Here are some of the less familiar 3-dimensional space-filling patterns. and related honeycomb geometries. … One of the more exotic classes of 3-D space-filling forms is Rhombic Spirallohedra; here’s a related fold-up pattern. Russell Towle introduced me to these amazing space-filling shapes almost two decades ago.

So what if “close” isn’t close enough?

In our “mind’s eye” we can visualize intersecting shapes that don’t have physical counterparts in the everyday material world around us. One example might be two identical intersecting spheres where each sphere exactly touches the other at its center; we can use ray-tracing software with opacity less than 100% (partially translucent shapes) to model how these might look (see translucent spheres intersecting in Vesica Piscis cross-section rendering below)

translucent spheres intersecting in Vesica Piscis cross-section — translucent spheres intersecting: Vesica Piscis cross-section

The 2D “shadow” (or cross-sectional slice) of the imagined 3D shape would be the famous Vesica Piscis shape. This might be analogous to intersecting (colliding) spiral galaxies where their forms interpenetrate; it might be a bit chaotic in such a galactic struggle where each “PacMan” galaxy tries to absorb the other!

Check out Russell Towle’s amazing animations – each frame of these videos being a “3D slice” through a 4D polytope or 4-dimensional polyhedron… You can see how we only get a glimpse of what these 4D shapes must be like; a reminder that our senses are limited, distorted and fallible, yet can remind us to beyond them if we’re looking for the “bigger picture.”

We’re still dealing with separate identities, separate shapes, though. The great mystical traditions, along with modern physics and non-dual metaphysics suggest that – if time and space (since both are inextricably linked in the fabric of spacetime) are an illusion – or at least a woefully incomplete and inaccurate view of reality, then even identical forms inhabiting the exact same space and time in a completely congruent fashion would still be “separate” if their identities could be distinguished from one another somehow. Recent breakthroughs in quantum computing that further validate the theory of quantum entanglement – where entangled particles are synchronized (e.g. their spin axis) instantaneously, regardless of the magnitude of the space between them – give impetus to exploring this idea.

Beyond Close

A few years ago, when my wife was about to leave that morning for an extended planned work situation in another state, while she was asleep next to me in bed, I realized that I was missing her already! How could that be possible? That “Aha!” moment further propelled my renewed exploration into the mystical study and practice of non-dual metaphysics, as I realized that she – and ultimately everyone! – lives in my mind.

Let’s do what can with zoom, Skype, web, email and whatever other technologies make sense to stay connected and support each other, especially when we appear to be more physically isolated than ever while considering that – just maybe – the imagined distance between us might just be subject to reinterpretation. This mindfulness provides all the more reason for us to be kind, compassionate and generously gracious in our assessment of each other and ourselves – as ourselves. What if the mystical Oneness alluded to down through the millennia in poetry, song, and prose – that we usually are too busy to consider – holds the effective key to not only pragmatic concerns like economic and medical infrastructure – but also to sustainable peace of mind as well? A forgiving and inclusive perspective on life would then make space (or lack thereof) a less important variable. We’re all in the same boat, fighting the same difficult battle – the silly, erroneous belief in separate interests. Sacred geometry and being mindful of clues reminding us of our interconnectedness in the world can be guideposts for the mind’s journey back to the Oneness we never left.

Spirit of Science, Sacred Geometry and more – A conversation with Danushia Kaczmarek and Bruce Rawles

Friday, 2 March 2018 by Bruce Rawles

Every moment is an opportunity to see the intrinsic sameness of everyone and everything – we’re all kindred spirits. – We explore, as Danushia says, seeing beyond the veil … and having fun with it! In this video conversation, Danushia Kaczmarek inteviews Bruce Rawles about “The Spirit of Science ~ Sacred Geometry ~ The Pyramids of Egypt” in her interview series about going from head to heart. We cover a wide range of subjects including Fibonacci numbers, spirals, the golden ratio, Platonic Solids, sterograms, biofeedback, catelysts, ACIM, the double helix of DNA, modern physics ideas such as quantum entanglement, the wave/particle (double slit) phenomenon, expectations in the mind and the undoing of the Newtonian world view, flat approximations for living on a spheroid, and much more. (Quick correction; in the conversation I mentioned Mauna Kea, but it’s actually Mauna Loa, Hawai’i that is at the 19.5° north latitude.)

(This interview took place Feb. 9, 2018)

Sacred Geometry Design Sourcebook (SDGS) turns 20!

Wednesday, 29 November 2017 by Bruce Rawles

I printed and published the first copies of Sacred Geometry Design Sourcebook (SDGS) in December 1997. It took a year of intensive graphics work using Claris CAD – does anyone remember that Apple application? – to convert and extend numerous hand-drawn geometric illustrations into digital form. My wife (Nancy Bolton-Rawles) took an evening class and I started with an evening a week – while she was in class – learning how to use this early CAD program for something other than video routing switcher control panels and making these geometric archetypes with far more accuracy and resolution than I could possibly achieve by straightedge and compass (the classic geometer’s tools) or any other physical mechanical means. Those evenings quickly overflowed into seemingly every conceivable spare moment. I realized that these CAD drawings (plus a few other unique images such as a stereogram, some unusual tables, charts, spreadsheets and even a cameo illustration of a sphere by Nancy (who was taking art classes during that time) merited a book. There are over 1300 geometric CAD illustrations counting all the variations I placed in the margins of many of the larger full page (8.5″ x 11″) images.

It’s amazing to reflect on the journey of explorations that have branched off (fractals, anyone?) from this first book by countless colleagues. I am profoundly grateful to one and all for the links, shared discoveries, and inestimable support in 2 dimensions, 3 dimensions, 4 dimensions and beyond over the past two decades … and before and after that, too – since we’re all interconnected beyond time and space! It’s been wonderful fun to get emails, postal mails of unexpected geometrically-inspired gifts, and other correspondence via Facebook (GeometryCode.com and Geometry Code) plus other social media, etc. Thanks, everyone, for your generous and steady contributions and support over the past two decades! :-)

If you are new to this website (or would like to peruse some of these topics again), you might want to start with this introduction to sacred geometry and then explore many years of bulletins, posts, and articles about related geometric coloring books – of which SGDS is a prime example! – and other sacred geometry art, books, calendars, food, audios and interviews, jewelry, music, news, physics, spaces, toys and videos, the golden ratio, Fibonacci numbers, other interesting numbers and proportions, the Platonic Solids and Archimedean Solids, other polyhedra, plus even some interconnections with the ancient, timeless Hermetic Laws and their relationship to modern physics … and metaphysics … which led to my second book, The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation.

To commemorate this 20th anniversary month (December 2017) of SGDS, here is an illustration that I added later, but didn’t make it into the book: a fold-up pattern for the Rhombic Triacontahedron, also known as Kepler’s Solid, which is an example of a zonohedron.

Here are the pages and posts on this website that refer to SGDS; enjoy! :-)

Last, but not least, I’m copying the content from a personal blog post (from a decade ago) which provides details on many of the images in SGDS, including how to draw many of the 2-D patterns (which took the form of an email Q and A response):

(Question)
Dear Bruce:

I was reading your web pages about your book SACRED GEOMETRY DESIGN SOURCEBOOK and I wondered if you could tell me whether the book provides the reader with details of how to draw the 2-D patterns for themselves or whether they are just templates without such instruction.

(Answer)
The simplest answer is “yes and no”, depending on which of the 1300+ images you’re referring to.

The detailed answer is (here goes!) that I cover some of the philosophy and underlying math, concepts and archetypal ideas in the beginning of the book, and provide a generous assortment of references in the back of the book. For the remainder (majority of the 256 pages), I give the images as much room as possible so that not only can the patterns be photocopied easily (I went with spiral binding just for that reason), the image quality would be as high as possible for an 8.5″ by 11″ format.

Some of the illustrations give step-by-step procedures (in graphical form, assuming some basic familiarity with how to use a compass and straightedge), such as:

page 44 (showing how “unit cells” for the tiling patterns can be used to create an enormously expanded variety of additional patterns by recognizing how the space-filling shapes can be varied; this applies to the “unit cell” examples on pages 16-43,

page 45 (showing how each of the patterns on pages 16-43 can embellished with fractal or other inscribed detail for each of the polygons for an infinite (literally!) variety of possible variations, (which actually also applies to the majority of the remaining images in the book; page 237 gives a 3D example of this),

pages 46-84 have either explicit (most of these pages) or simple to observe implicit “unit cells” which show how these can be created in a great variety of ways,

page 84 (Pentagon Rotation Grid) gives the 73.2% proportion crucial to the exact construction of this pattern,

page 85 (Genesis of the Seed of Life) shows the step-by-step “compass only” construction of this important and universal pattern,

page 86-95 (variations on Seed of Life and Flower of Life) show how once the Seed of Life is constructed, so many other patterns can be easily derived – Flower of Life, Hexagonal Grid, 2nd Harmonic Overlay (which is used in Mika Feinberg’s beautiful LightSOURCE screensaver animation; see my Resources page, Tree of Life, Fruit of Life, Heart and Ankh matrices, recursions, Metatron’s Cube, etc.),

page 95: since the Dodecahedron is the most complicated shape to derive from Metatron’s cube, the top center illustration on this page shows which vertices are used to create the “dodecahedron 2D shadow” with small circles highlighted in the larger image,

page 96: The general instructions for creating Nested Inscribed Polygons appear on this page,

page 100-102: other examples of the crucial proportions needed to create these image either by hand or with a computer graphics program; numerous pages provide these instructions in the text without detracting from the space given to the images,

pages 104-105, 110-113, 123-124, 128, 130, 138-139, 144-145, 155, 163, 166, 171, 176-180, 182-187: all have instructions and details on how to create the images,

page 146: very detailed step-by-step instructions for inscribing a pentagon within a circle,

page 147: very detailed step-by-step instructions for inscribing a pentagon starting from one side of a given length,

page 156: very detailed step-by-step instructions for creating a golden rectangle (including “whirling squares and more),

page 156: very detailed step-by-step instructions for dividing a line by the golden ratio,

page 157: very detailed mathematical information about golden ratio progressions and powers, illustrated graphically,

page 188: shows how the Parthenon at the Acropolis in Athens, Greece incorporates the golden ratio

page 189: an amazing amount of data on this page about the Great Pyramid at Giza, Egypt showing phi (golden ratio) and pi proportions, and the proportions of the so-called “King’s Chamber” although the so-called “sarcophagus” (granite box) within is too large to fit through the only passage leading into that chamber, which violates the generally accepted funerary rite theory,

page 190: the classic “Measure of Man” (Vitruvian Man) by Leonardo daVinci, copied around the world, showing the golden ratio proportions in the human body,

page 191: the only known CAD drawing adaptation (to my knowledge) of Leonardo’s “Ideal Church” sketch,

page 192: detailed specifics about the Shoemaker’s Knife of Archimedes, giving several variations all showing the mathematical principle,

page 194: details of the geometry of the classic 1991 Barbury Castle, England crop circle formation,

page 195 and page 52: the details of the geometry encoded in the Sri Yantra (a classic Hindu mandala) and the cross section of the Great Pyramid at Giza, Egypt (also the “squaring the circle” conundrum), both with a 1-Phi-Square Root of Phi triangle which has a 51 degree, 51 minute slope,

page 196: numerous details common to the 5 Platonic and 13 Archimedean Solids,

pages 197-214; numerous details specific to the 5 Platonic and 13 Archimedean Solids, including how the insphere/intersphere/circumsphere/side length proportions are calculated,

pages 215-224: similar details specific to the 4 Kepler-Poinsot solids, the Star Tetrahedron (a.k.a. Stella Octangula) and related polyhedra,

pages 225-229: numerous graphics showing how the Platonic Solids relate to each other in a myriad of fascinating – awe-inspiring, really! – ways,

pages 230-235: numerous relationships between 3D polyhedra with 5-sided symmetry and the “shadow” they cast on a decagon (10-sided polygon), with construction details,

page 236: step-by-step instructions on creating an accurate drawing of the Icosahedron and Dodecahedron starting from a Golden Rectangle,

pages 237-255: generous appendices for hands-on explorers of all ages and levels of experience, including tables and charts of regular polygon angles, apothem, radius and side ratios and areas, radius ratios by coordination number for Ionic Chemical Bonding (which relates to properties of materials at the molecular and planetary levels), Fibonacci Numbers, Perfect Right Triangles (when I put the book together, I wasn’t aware of the Phi-1/Phi-Square Root of 3 Right Triangle that Mike Green of British Columbia introduced me to), Prime Numbers, extensive tables with all sorts of data on the Platonic and Archimedean Solids (useful for a variety of purposes, including model construction and computer simulation and animation, a map of planet Earth showing superimposed Platonic Solid Vertex Latitudes and (example) Longitudes, a fun stereogram with 6 Small Stellated Dodecahedra (there, I gave the clue away , a short bio of myself, 3 pages of bibliography (more on my links pages and blog), and unique graphical index to all the illustrations in the book. Whew! I’d almost forgotten how much I packed into this labor of love over a decade ago!

Many of the 1300+ images are somewhat self-explanatory graphically (especially if you have created the basic shapes like the Seed of Life, Golden Rectangle and a few others by hand with compass and straight-edge, which I highly recommend for anyone as mentor Keith Critchlow so aptly reminded me when reviewing my original manuscript)…

… and of course, if you are finding re-creating one of the patterns challenging, I’d be happy to answer other questions via email that I can share with other enthusiasts on my blog (which I’ll do with this reply; thanks for asking! :-)

I’m also working on a number of related projects that will complement the book with video “hands on” procedures, etc. Stay tuned!