Search Results for: nature

A Beginner’s Guide to Constructing the Universe: Mathematical Archetypes of Nature, Art, and Science by Michael S. Schneider

Saturday, 28 September 2019 by

The Universe May Be a Mystery,
But It’s No SecretMichael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, expressed in the symbolic language of folk sayings and fairy tales, myth and religion, art and architecture. This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner’s Guide to Constructing, the Universe shows you:

Why cans, pizza, and manhole covers are round.
Why one and two weren’t considered numbers by the ancient Greeks.
Why squares show up so often in goddess art and board games.
What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies.
How the human body shares the design of a bean plant and the solar system.
How a snowflake is like Stonehenge, and a beehive like a calendar.
How our ten fingers hold the secrets of both a lobster and a cathedral.
And much more.

Nature’s Hidden Messages: conversation with Marc Courtenay

Sunday, 24 September 2017 by Bruce Rawles

Update (Sep. 24, 2017): Here is the audio recording of the conversation about sacred geometry, interconnectedness and much more with Marc Courtenay from Sep. 14, 2017 and also the archive page for this show.

On 14Sep2017 8:30 AM (Pacific Time) I talked about “Nature’s Hidden Messages” – and fun stuff about interconnectedness and sacred geometry – as the guest on Marc Courtenay’s radio show “Finding Happiness and Good Health in Today’s Word” on (KCUP-1230 AM and BOSS 100.7 FM Radio in Newport, Oregon) and streaming on the web. You can listen live or via the archives of Marc’s shows.

I was introduced to Marc via long-time friend and neighbor, Dean Shrock, who also has been a frequent guest on Marc’s radio/streaming program. Dean gave a workshop in Newport on Sep. 16, 2017 entitled “Meet Your Spirit Guide”.

Circle as symbol: Inclusion or exclusion?

Friday, 31 May 2024 by Bruce Rawles

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.

Cactus, spirals, and desert geometries

Monday, 31 July 2023 by Bruce Rawles

This will be a short and mostly visual post as we just moved to (Green Valley) Arizona a week or so ago and are getting settled in. Going for early morning walks affords opportunities to observe spiral patterns (and other geometries) in ubiquitous and numerous varieties of cacti. For fun, I’ve added a shot of a vesica piscis shape formed from intertwined trunks, a triangular spiral on a decorative metal screen and there are plenty of obvious geometric patterns as are always evidenced when looking at nature.

Digital dabbling with Dall-E

Wednesday, 29 March 2023 by Bruce Rawles

After several years of mixed results with Siri (on my iPhone and MacBook Pro) and cylindrical kitchen add-on Alexa, often amusing and sometimes rather useful, I think my current favorite “Jetson” technology still might be our humble shorter cybernetic cylinder, “Rosie” the Roomba – our household vacuuming robot weekly whisking an amazing amount of fur from feline friends in our home.

Out of curiosity, I recently have done some very preliminary explorations with 2 OpenAI artificial intelligence apps; ChatGPT – rather impressive for certain well-defined tasks – and Dall-E 2. Since the latter seems appropriate for the visual nature of geometric imagery, I gave it a few prompts and got the results below within a span of about 45 minutes. Most of that time was spent thinking up a geometric ideas and then reviewing (clicking on the smaller thumbnails to see the zoomed-in) results; the actual time that the application took to generate the images with about 10-20 seconds for each batch of 4 rendered thumbnails! At its present maturity, Dall-E seems to have some limited usefulness if mathematical precision is less important than artistic conceptual prototypes. What do you think? Fun to play with, of course! The text I typed is followed by the output for each experiment:

experiment 1:
golden glowing dodecahedron hovering above a shimmering sea of 144 smaller iridescent silvery icosahedra

experiment 2:
a fleet of 12 toroidal UFOs arranged in a circle beaming light to the apex of the Great Pyramid of Giza, Egypt with a rainbow gradient sky

experiment 3:
Mandelbrot set made of cedar sprigs in the style of M.C. Escher

experiment 4:
(Anthony James mirrored icosahedron variations by Dall-E; I used this image as input)

experiment 5:
Impressionist painting in the style of Vincent Van Gogh of CERN hardware

experiment 6:
A photo of the Eiffel Tower scaled to fit in the middle of Stonehenge with glowing orbs atop each megalith in the style of Salvador Dali

… with 4 more variations requested:

experiment 7:
7 purple Flower of Life disks wrapped around a silver cone reflected in a parabolic mirror by Rene Magritte (and 2 more sets of 4 variations)

experiment 8:
a photorealistic image of Dorothy from the Wizard of Oz holding hands with Alice in Wonderland standing in front of the Great Pyramid at Giza, Egypt.
(If you look closely at the faces, they look rather wonky at best, but zoomed out not too bad… Of course the 2nd, 3rd and 4th images used the 2nd “Kephren” pyramid which still has the capstone casing and not the Great Pyramid, but this is a learning technology, right. I wonder if the next time someone asks for a similar image, Dall-E will incorporate my comments and stick to just the Great Pyramid?)