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! :-)
Search Results for: interconnect
Circle as symbol: Inclusion or exclusion?
The Introduction to this website (Sacred Geometry Introductory Tutorial) begins with a geometric symbol that is perhaps the simplest and yet most profound – the circle. Circular patterns and archetypes appear in countless variations in nature, art, architecture, engineering, and just about every area of life we can imagine. Here are a few familiar examples; I’m sure you can think of countless others, both microscopic, macroscopic (telescopic) and in between, in all dimensions of space, time, metaphor, and thought. We touched on the sphere (Music of the Spheres – The Planets) in a recent post; the 2-dimensional counterpart to the sphere is the ubiquitous circle and provides the foundation for it’s rotation into spheres of any number of dimensions – the quintessential template for polytopes beyond our imagination. Rather than getting boggled or bogged down with those mind-warping ideas, let’s return to the simplicity of the circle.
All of these visual examples are reflections of a form reflecting an ideal; here is what appears in the Introduction to this website (slightly edited from the original):
The Sphere
(charcoal sketch of a sphere by Nancy Bolton-Rawles)
Starting with what may be the simplest and most perfect of forms, the sphere is an ultimate expression of unity, completeness, and integrity. No point of view is given greater or lesser importance; all points on the surface are equally accessible and regarded by the center from which all originate. All atoms, cells, seeds, planets, and globular star systems echo the spherical paradigm of total inclusion, acceptance, simultaneous potential and fruition, the macrocosm and microcosm.
The Circle
The circle is a two-dimensional shadow of the sphere, regarded throughout cultural history as an icon of the ineffable oneness; the indivisible fulfillment of the Universe. All other symbols and geometries reflect various aspects of the profound and consummate perfection of the circle, sphere, and other higher dimensional forms of these we might imagine.
The ratio of the circumference of a circle to its diameter, Pi, is the original transcendental and irrational number. (Pi equals about 3.14159265358979323846264338327950288419716939937511…) It cannot be expressed in terms of the ratio of two whole numbers, or in the language of sacred symbolism, the essence of the circle exists in a dimension that transcends linear rationality. Our holistic perspectives, feelings, and intuitions encompass the finite elements of the ideas within them, yet have a greater wisdom than can be expressed by those ideas alone.
When I was writing my first book (Sacred Geometry Design Sourcebook – Universal Dimensional Patterns), the cover art as well as a majority of the 1300 images (including corner “thumbnail” variations) feature circles, either directly or indirectly, so I made a graphical index, rather than a text-oriented one; the dots that dominate the first column (circles and spheres) in these 2 pages hint at the importance of these primal, archetypal, quintessential symbols: circles and spheres.
When I was writing my second book (The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation) I also used a “Fruit of Life” symbol (6 circles around an inner circle) to represent the interconnectedness and inseparability of all aspects of what is eternally true, reflected in the 7 Hermetic Laws of antiquity. These 7 circle-framed images (along with the other supporting graphics) are all set within a circle which intuitively reminds us of the infinite and eternal in our minds.
On page 62 of the Geometry Code book, I shared an idea that I find increasingly more helpful in both pragmatic and profound ways. Here is the graphic and supporting text for this portion of the chapter “Mentalism: 1st of the 7 Hermetic Laws”:
The Wikipedia definition of scapegoat is “Scapegoating is the practice of singling out one child, employee, member of a group of peers, ethnic or religious group, or country for unmerited negative treatment or blame.”
The biblical story of the scapegoat offers a very helpful clue. It employs the symbol of the circle as a mnemonic for practicing inclusion or exclusion. In historic accounts, the guilt (sins) of the community were projected onto a goat, which was then banished to the realms outside the inner flock – peripheral to the circle of what we’re willing to accept or allow in our minds. Everything within the circle is OK (innocent as lambs), and if you’re outside, tough luck, goat! The problem is that the very premise that divides wholeness into parts is flawed, and even the ‘good’ that remains begins to be suspect because of the inherent lack of trust. The circle closes in and eventually strangles the dualis- tic split mind into oblivion; it becomes a singularity and winks out; but not without a lot of grief and struggle!
Seeing ‘others’ as ‘out there’ throws away the gifts they bring to us each ʻpresentʼ moment that we lucidly bring their symbolic contribution as mirrors of self back into mind. This works for both seemingly positive and negative experiences, until ultimately we realize that any so-called good experience (e.g. pleasure) in the world is no better or worse than any so-called bad experience (e.g. pain) in the world, because those experiences are all projections of a massive dream that we’ve made up to reinforce the belief in separation. Ego can use any excuse to squander the gifts by assigning ‘otherness’ to others and losing the meaning that the intrinsic connection – always in mind – can bring.
Sometimes it’s blatant when we intentionally erect an inner wall and make a fence around those we ‘like’ or agree with and those we’re not so fond of. This has nothing to do with behavior since it would be impossible to physically assist or care for everybody (let alone all the animal, vegetable, and mineral ‘life’ on just this third spheroid helically spinning around our favorite star). However, it has everything to do with inwardly caring for all, equally. This is an egalitarian ideal we probably all pay lip service to in various ways, but then often find ourselves annoyed with certain ‘others’ or internally profiling a group (whether a species, family, region, nation, or galaxy) and then suddenly – Whoops! – there’s that nasty we/they paradigm in action again, begging for our self-forgiveness.
The profound helpfulness of these circle symbols is evident when we consider that a circle of infinite scope – total inclusion – has no one left out, no one excluded, no one denied, and all equally vital to the whole; each mind embracing this idea IS the whole seen holographically. When, on the other hand, we go with the polarizing default of inner/outer, we/they, us/them, no matter where the line is drawn – or whatever shape, for that matter, a circle is just a placeholder for any exclusionary perspective – we’re always at war with the alleged other in our mind. No peace is possible when the foundation for peace (total inclusion) is denied.
The pragmatic benefit of identifying with the “infinite circle” that includes all of us is that – with considerable practice! – we can train our minds to realize that we can truly afford to “Be kind, for everyone you meet is fighting a hard battle.” Even if there’s no instant transformation/manifestation in the surreal world of our space-time dreams, there is always an opportunity to forgive ourselves for dreaming of separation by seeing our shared interest of peace and benefitting from a tranquil mind in the process, regardless of what seems to be happening around us!
Since (in the USA at least) this is an election year, I try to remind myself that we only get to vote every year or so, but we vote for either the infinite (transpersonal) circle of embracing everyone in our gracious consideration – or the finite polarizing (personal) circle which leaves some out; our scapegoats outside the circle become our projected “goat-scape” yet the problem of our dualistic dueling dream has never left our mind.
Affiliates and Archives Galore!
I was looking through prior posts – I’ve been sharing items of interest about geometry and interconnectedness since 2007! – and realized that there is a lot of content that is still every bit as relevant today as when originally published … Since geometrical principles, archetypes, and so many more topics aren’t seasonal or slaves to style… at least as far as I can tell! So, I’m going to pull a couple of images with links to older posts to encourage exploration of the archives. Here’s one about Intention and Symbols and when I followed the link about Villarceau circles I found an interesting animation that shows a plane intersecting a torus to reveal a Vesica Piscis cross-section; neat! (I also added the animation to the original post.)
Here’s another post from a while ago:
Dodecahedra Origami Luminaria – a timely holiday project, too!
I just updated our Affiliates page since it’s been quite a while; thanks for many years of support! When you use the links on this page, it helps fund our “labor of love” efforts keeping this site going and this is greatly appreciated!
Entangled Minds: Extrasensory Experiences in a Quantum Reality
Amazon description:
Is everything connected? Can we sense what’s happening to loved ones thousands of miles away? Why are we sometimes certain of a caller’s identity the instant the phone rings? Do intuitive hunches contain information about future events? Is it possible to perceive without the use of the ordinary senses?
Many people believe that such “psychic phenomena” are rare talents or divine gifts. Others don’t believe they exist at all. But the latest scientific research shows that these phenomena are both real and widespread, and are an unavoidable consequence of the interconnected, entangled physical reality we live in.
Albert Einstein called entanglement “spooky action at a distance” — the way two objects remain connected through time and space, without communicating in any conventional way, long after their initial interaction has taken place. Could a similar entanglement of minds explain our apparent psychic abilities? Dean Radin, senior scientist at the Institute of Noetic Sciences, believes it might.
In this illuminating book, Radin shows how we know that psychic phenomena such as telepathy, clairvoyance, and psychokinesis are real, based on scientific evidence from thousands of controlled lab tests. Radin surveys the origins of this research and explores, among many topics, the collective premonitions of 9/11. He reveals the physical reality behind our uncanny telepathic experiences and intuitive hunches, and he debunks the skeptical myths surrounding them. Entangled Minds sets the stage for a rational, scientific understanding of psychic experience.
Michael Schneider’s new book! Proportion in Art and Architecture (Wooden Books)
Long-time – as in decades-long – readers of GeometryCode.com and its predecessors (such as the bibliography in Sacred Geometry Design Sourcebook (SGDS)– Universal Dimensional Patterns published in 1997) will recall that I’ve often recommended – more than any other book – A Beginner’s Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art, and Science (released September 29, 1995) by geometer colleague Michael S. Schneider as an ideal companion to SGDS. In that lavishly illustrated journey of imagery and text through number and geometry, he explores – in over 350 pages – as the subtitle suggests: mathematical archetypes on a voyage from 1 to 10. It’s a great book!
Schneider also authored 6 geometric activity books spanning 730 pages plus an animated DVD: Constructing The Universe: A Journey From 1 to 12 – brilliant, very easy to follow, and clearly explained, beginning at the bare basics and culminating in compelling cosmologies. Each of the first 12 counting numbers receives a first-class tour through realms mundane to mystical, deepening our appreciation of numbers and their geometric interconnections from many disciplines, traditions, and perspectives. In addition, he also authored the fascinating DVD Fibonacci Garden: Mathematics in the Plant World.
Michael’s most recent work, another great book – Proportion in Art and Architecture – is among the 60 delightful Wooden Books titles by a variety of authors, published by John Martineau who will also be very familiar to readers of this website. This book, like the Beginner’s Guide to Constructing the Universe book, has wonderful explanations, illustrations, and analyses – and most of the analyses in it are original! The UK version is available now, but it’s inexpensive to ship to the US. The US version will be out in March 2023.
The image below is page 13 of this excellent new book in the chapter entitled: Frozen Music: the geometry of harmony:
The illustrations below are color versions of similar illustrations from the book on pages 30 and 31:
Here are the chapter titles to give one a sense of the depth and breadth that this little gem covers:
- Introduction
- Macro-Meso-Microcosm
- Therapeutic Arts
- Mathematics in Design
- Static and Dynamic
- Proportion
- Frozen Music
- Harmonic Rectangles
- Harmonious Proportions
- Hotspots and Alignments
- Regular Polygons
- Ad Triangulatum
- Triangular Proportions
- Ad Quadratum
- Square Proportions
- Pentagonal Proportions
- Hexagonal Proportions
- Heptagonal Proportions
- Octagonal Proportions
- Ten and Twelve
- Canonical Rectangles
- Rabatment
- The Root-Two Rectangle
- Root-Two Proportions
- The Root-Three Rectangle
- The Root-Four Rectangle
- The Root-Five Rectangle
- The Golden Rectangle
- Golden Proportions
- Proportional Quotations
There’s even a cameo appearance of the Mona Lisa in the book which also had a cameo in the Glass Onion movie!
Check out Michael’s website: ConstructingTheUniverse.com
Aside: I interviewed Michael Schneider for local TV in Grass Valley when he first arrived in CA 25 years ago on FCAT (Foothills Community Access Television) which was great fun!