I had the pleasure of building and living in a dome (a Cathedralite Dome kit from Aptos, California) in Georgetown, California in the late 1970's. In addition to just being a great space to be in, since we left quite a bit of our floor plan open, the acoustics were quite interesting, too! A neighbor (and long time mentor, Floyd Edwards who started the Creative Dynamics program (Leadership and Human Relations) my ex-wife and I enjoyed teaching in nearby adult schools for several years) had made a custom battery-operated clock with his airbrushed art, which hung on the wall downstairs next to the woodstove. At the time, we had a slant-board in the upstairs loft (looking up at the top 5 triangles of the dome) for meditation. One day, I realized the loud "tick-tick" I kept hearing was the minuscule sound of this little clock bouncing around the interior surface of the 39' diameter dome... and converging back at a point where my head was... amazingly, one could barely hear the clock standing next to it!
Another fond memory of the dome was the day our generous friends and neighbors spent most of a day helping us raise the 60 plywood-over-beveled-2x4-triangles into place. After hoisting 5 pentagons (all made of triangles) atop a 5' riser wall, then linking them together with 5 hexagons (also made of similar trianges) so we could now remove the supports and (after raising the scaffolding to get to the 21' peak), we finally put the last top 5 triangles of the dome into place. The second to the last triangle was fitted with a sturdy eye bolt, through which a long rope was tied. I got to hop up onto the now-sturdy roof with a sledge hammer and sequentially tap the 3 corners until the last triangle fit perfectly snug and the whole structure (just like Bucky professed) went from a loose wobbly thing to rock 'solid' (not accounting for the vast emptiness of quantum space, of course!
To help visualize this 3/8 sphere
dome, check out Poly from Pedagoguery
Software.
and animate the 3-Frequency Icosahedral Geodesic
Sphere (and imagine 5 pentagons (defaulting to red
color) resting on a 'cylinder'. Here's a "bird's
eye view" of the dome we built and lived in, using
a screen snap from Poly with appropriate triangles
grayed out and more dome
resources.
=====
Hi Bruce ...What does the star mean in sacred geometry?
This might depend somewhat on the specific geometry involved... In particular, are we talking about 5 or 6 (or some other number) of points on the star? Hexagonal (6-fold) stars (a.k.a. hexagrams) relate to the Flower of Life, Seed of Life, Fruit of Life, 2D matrix which occurs in a myriad of forms in the various kingdoms of the natural world (basalt column cross-sections in the mineral kingdom, cloverleaf and cellular structures in the plant kingdom, honeycomb in the animal kingdom, etc. just to name a few.
I am wondering if you have any idea what the star on the bottom of each blueberry would mean?
A little gem I learned from Michael Schneider is that the blossom of every edible fruit has 5-sided (pentagonal) geometry. The five-pointed star (pentagram) was the symbol allegedly drawn on the hands of the Pythagorean initiates (perhaps because the notion of interconnectedness leading to the awareness of all-encompassing oneness is just as "threatening" now as it was to the predominant culture then
There is also a wealth of other
examples in my book:
as well as quite a few on the tutorial on my website (I imagine you've already read that?)
and the links on the resources page:
I am doing food research and it seems like the star would mean something. Doesn’t it look like a star at the bottom of a blueberry?
You got it! It is indeed the guiding archetype for this form, as well as so many others in nature!
Here's a static image of some of her engaging animation:
I have fond memories of staying after hours in my high school electronics lab in Livermore, California, hooking up every oscillator in the lab to the horizontal and vertical inputs of a 'scope and creating endless variations of patterns like these. Judy uses interesting (close to Phi-based) harmonic ratios and elegant transitions to show how many of the complex patterns we're familiar with are simply the communion of number within the mirage of space time.
Glad you enjoyed my abstract - feel free to post it - or selections thereof - on your blog.
You can find my abstract online here:
http://www.asdreams.org/2007/abstracts/abstracts_a-h.htm
Scroll down about halfway below Rita Dwyer, who chaired the "Cosmic Dreaming" session.
You can also find the abstract for my dream healing workshop here:
http://www.asdreams.org/2007/abstracts/abstracts_i-r.htm
Scroll down to Kellogg.
They recorded two of my sessions, "Cosmic Dream Connections" (#306) and "Exploring Inner Space "(#321.)
http://www.conferencerecording.com/aaaListTapes.asp?CID=ASD27
"Trans-Personal Dreaming Beyond Time and Space."
Short Abstract: Mystics through the ages have taught that although humans have separate personalities, that at a deeper level we share the same greater Self. The validation of psi-dreaming supports this idea, and has demonstrated that through dreams we can connect with people, places, and times unrelated to our waking lives.
Summary: Some models of consciousness posit that although humans have separate personalities, that at the deepest level we all share the same greater Self. As a metaphor think of our waking selves as leaves upon a tree - although the leaves differ from one another, they all belong to the same Tree and share the same trunk and roots. In this model, telepathy would not involve transfer of information over a distance between separate minds, but of simply accessing information by going within to find what the ‘Greater You’ already knows. This "Tree of Life" model of creation has found support in the writings and experiences of mystics through the ages. In recent years, scientific research under controlled conditions has demonstrated that through psi-dreaming we can connect with people, places, and times unrelated to our waking lives.
How might this manifest in our dreams? I've noticed over the years that while many people often dream of themselves in ways that closely match their waking physical reality experiences, that these people report also dreams in which they become someone else, or even something else, and experience the world from a very different perspective than in their waking lives. In my own case, I've experienced myself in dreams as many different beings - age, sex, race, etc. Often not only does my dreambody differ from its waking physical reality counterpart, but so does my dream personality and memories. However, through all this, my essential sense of self somehow remains the same - "I" remain "me", my dreambody, personality and memories seem no more "me" than does the clothing I wear or the car that I drive. I’d estimate that in 80% of dreams my dream self differs significantly in some way from my waking physical reality self.
Although I believe that although some dreams of this type may have to do with personality "aspects", that for most of them this explanation proves inadequate. Instead I favor different interpretations, in that I experience while dreaming parallel selves, past lives, future lives, and even other dimensional lives, and that tuning into different locations and different beings throughout the Multiverse just seems a routine and normal activity for my dreaming Self. And after many years of such experiences, I've finally come up with an answer to the perennial "Why do we dream?" question that rings true for me. Dreams provide "food for the soul", reconnecting us to our greater Selves and allowing a therapeutic release from the constraints of a time-space bound existence that reminds us, if only unconsciously, of the illusion of separateness.
Richard Feather Anderson will be giving a slideshow "The Eight Patterns of Nature" on July 25, another slideshow "Geometry That Matters: Power of Creation, Laws of Harmony" on July 27, and a weekend workshop "Exploring the Symbolic Language of Geometry" July 28-29, 2007 (Friday evening through Sunday) in Ashland, Oregon. I had the pleasure of meeting Richard while attending a recent (MARVELOUS!) evening talk on labyrinths in Medford, following on the heels of the local regional labyrinth gathering here a few weeks ago featuring Jean Houston. Based on the enthusiastic response, this will be a more intensive follow-on workshop exploring labyrinths, sacred geometry, regional geomancy and much more. Since Richard and I complement each other's work, I will be assisting at this weekend workshop giving short multimedia presentations on topics that emphasize 3D and higher dimensional geometries. If you are interested, or would like to reserve a place in upcoming slideshow or workshops, contact Bonnie Bayard at 541-773-4286. The short presentations I give this weekend will be "samplers" of expanded workshops I'll be conducting in the southern Oregon area (or your vicinity!); contact me for details.
Here's more details from Richard:
What is Sacred Geometry all about and why should we care?
The Eight Patterns of Nature
Is it really true that Nature needs only eight patterns to create and sustain all life? Learn how spirals, meanders, and other dynamic patterns work for plants, animals, and the human body, and how free-flowing water purifies itself. The world will never look the same after viewing these astounding images and acquiring the ability to recognize cosmic patterns in ordinary things!
“Richard is the first person to explain the golden mean in a way I could understand.” – Jillian Brorby, feng shui consultant
The Geometry That Matters:
Power of Creation, Laws of Harmony
A visual introduction to the themes of the weekend workshop.
View a multitude of awe-inspiring images and awaken to the staggering recognition of the order and harmony of the universe. Learn about the essential role geometry plays in the continual creation of our universe. It is one of the greatest reservoirs of Nature’s laws of harmony. Sacred Geometry has the unique ability to depict the essence of a thing (by revealing its true underlying vibrational quality), rather than merely represent it metaphorically. Understand why knowledge of sacred geometry is crucial to be able to create beauty and ecologically sustainable culture, and design environments in harmony with Nature so they feed the human soul.
“You
gave the best presentation of the whole conference! I
learned more about sacred geometry from you in one
hour than from any other talk.” — Ursula Rabe, feng
shui consultant/astrologer and fine artist, Grass
Valley, CA
Exploring the Symbolic Language of Geometry
Geometry is the universe’s secret way to turn energy
into matter, and guide the growth of all forms of
life. It holds the real key to the identity of DNA, a
molecule, or an organism, and enables Nature to
implant intention and form harmonious, life-enhancing
relationships.
Learn about the benefits of tapping into this body of
knowledge, including the ability:
* To recognize spatial patterns more quickly and
accurately
* To read the geometry of a building as a language
that may reveal the symbolic message the original
builders wanted the edifice to embody and convey.
This seminar will be a rare opportunity to
re-discover geometry as a rich, universal, symbolic
language, which illuminates the core teachings of the
world’s spiritual traditions in a pure, non-dogmatic
way. (This obviously bears little resemblance to high
school geometry or math!) Richard's use of a
hands-on, visual, kinesthetic, Mystery School
approach restores geometry to its ancient sacred
function as a portal into meditation, soul-work, and
timeless wisdom.
•
Understand
proportions, like the golden ratio, that guide the
growth of organisms.
•
Relive
the initiation into the laws of manifestation that
our cells received during embryonic development.
•
Discover
the intriguing geometrical symbols hidden within
cosmological mandalas.
•
Glimpse
how to apply the laws of harmony to create art and
architecture in which all the parts relate
harmoniously to each other and the whole like a
well-tuned orchestra.
•
Join
us for a visual tour of Chartres, the most glorious
French Gothic Cathedral, and witness how to decode
the hidden messages in its geometry, to gain clues
about its potential mystical uses and cosmological
story.
“You
helped me get all the connections, including the
surprise of how geometry applies to group process.
When I’m with a teacher who loves what he’s doing, I
understand it in my body.” – Gail Gardener, massage
therapist
Evening
Talks start
promptly @ 7:00 pm; Q & A from 9-9:30 pm
Suggested
Donation:
$10-20 in advance or at door
Sat-Sun.
Workshop Fee: $225
- $325 sliding scale. If paid by July 20, Friday
night slide show is included in seminar fee. Please
register by July 20 to help make workshop happen.
Locations
and materials list
will be sent when payment is received.
For Questions on Content: Contact
Richard at 707.544.8203
For
Registration Information: Call
Bonnie at 541-773-4286 between 9 am - 8 pm.
Space is limited to maximize personal attention.
To Register: Call
first to reserve space, then confirm by mailing your
non-refundable check, made payable to Richard
Anderson, to Bonnie Bayard, POB 1691, Medford, OR
97501. Please write on your check which programs you
have registered for.
...
Update (11Mar2008) from Richard Feather Anderson:
RECORDINGS
AND BOOKLETS BY RICHARD FEATHER ANDERSON
___ Booklet — The Patterns of Life — Description of
the eight patterns that Nature uses to create and
sustain all life on planet Earth. Each pattern allows
Nature to function efficiently, using the least
amount of energy and matter, thus conserving its
resources. Examples are given of how the patterns
manifest in the forms and dynamic forces of Nature.
Knowing these patterns enables you to see the world
more fully, understand the basis of feng shui, and
recognize the archetypal power of single-path
labyrinths. 5 pp.
$5.00+ .80
To place an order, Please print out and use order
form below to calculate sales tax and shipping
charges.
Total PRICE of ordered items
(Do not include postage on this line.) >
__________
Add HANDLING CHARGE > __$2.00 ___
SUBTOTAL > __________
Calif. Residents: add 8%
SALES TAX based on Subtotal > __________
add total POSTAGE > __________
Payment enclosed for GRAND TOTAL> __________
Make checks payable to: Richard Feather Anderson.
We accept checks from U.S. Banks or International
Money Orders.
Sorry, no credit cards.
Please mail orders with check to:
Richard Feather Anderson, 1570 North St. #17, Santa
Rosa, CA 95404
Information: 707.544.8203
Customer Info /Shipping Label:
Name _______________________________________
Address _______________________________________
City/State/Zip
_______________________________________
Phone: Day ________________ Eve ______________
Richard Feather Anderson
American School of Geomancy
1570 North St. #17
Santa Rosa, CA 95404
www.richardfeatheranderson.com
707.544.8203
Bathsheba Grossman has created another lovely crystal in her array of exquisite art... this one is a 3D model of Johannes Kepler's diagram of the inner planets, first published in his 1596 book Mysterium Cosmographicum. I'd love to see this first hand....
I created a POV-Ray model a while ago entitled "Homage to Kepler" which incorporates both the inner and outer solar system models.
Even at smaller print sizes you can see both the inner and outer models fairly easily. If you want a really close view, the print is available all the way up to 36" x 27". This early POV-Ray model was a precursor to my Martineau Solar System Series now being exhibited in at least 3 different venues on this planet.
MAJOR website changes today! Intent.com has moved to geometrycode.com and brucerawles.com...
Intent.com has a new steward/owner! We've had a number of offers over the years to buy our domain,
and recently 3 at one time! However, until now, none had the intent we wanted to go forward with that idea.
The new owner plans to create a website with new content for intent.com soon:
"a community site based on the ideas of exchanging information on wellness, helping the planet,
personal development, and other topics related to health, the environment, and personal expression."
Please explore our new websites! We'd love feedback. (See section 2 about our new email addresses for this.)
Also, PLEASE fix any links you might have on YOUR websites to intent.com. I have redirect pages in place
which should be around for a year, but now's the time to fix the links... THANKS! Thanks particularly to those
of you who have linked to our websites over the years. I'll be adding even more links to our new sites soon,
so please continue to send suggestions for sites that complement the work we're doing.
Here's the result of the "cattle drive" (still in progress) of moving about 12 years of web content to 2 newer sites:
I've moved all of the geometric (and related) content (from intent.com) to:
http://www.geometrycode.com/
Hopefully this new website will be much more accessible and navigable; you might even discover content
that has been there for a dozen years you just never realized was there!
This new format (featuring
CSS and SSI) will make it MUCH easier for me to maintain and enhance, so look forward to much more frequent
updates and additions going forward...
I'm moving everything else, such as my favorite books, movies, music, webcasts/radio, etc. and all the
New Frontiers of the Gold Country event archives (from intent.com) to:
http://www.brucerawles.com/
This latter effort is still in progress (just barely started, but I'll finish it ASAP, and I wanted to let everyone know early.
A couple of minor corrections on that page:
Geometry literally means “the measure of the earth" ... adding 'sacred' just adds the meaning and significance of that word
Also, on that same page, the author/artist refers to the square root of 3 as transcendental. In mathematical terms (to be technically correct), I believe that number is just irrational. However, Pi, (the circumference/diameter proportion of any circle) which is almost always "nearby" or present whenever the square root of three is involved geometrically (either with the vesica piscis made from two circles, or the diagonal of a cube which can be perfectly inscribed or circumscribed by a sphere containing an infinity of circles) IS a transcendental number. In my presentations, I often share the metaphor that an irrational number (like the square roots of 2, 3, or 5) is not resolvable by our conscious 'rational' minds; however a transcendental number (like Pi) is not only irrational, it also transcends this 'dimension', since it can't be expressed even as a polynomial fraction (a fraction made of whole number polynomials, or numbers raised to higher powers or 'dimensions' metaphorically.)
Here's a link to the MathWorld reference on transcendental numbers. Along with Pi, Euler's number, e (the base of natural logarithms) is perhaps also commonly known to many.
Here is a link to
"E8" research
and
a "string art"
visualization.
to some of the "insectogram" (or spider) crop circles of a few years ago, such as these few quick finds:
Scroll down on this page to find "Fish/Eye Formation at Silbury Hill, near Avebury, Wiltshire, 9 July 2005"
with a similar link (and overlapping content) here: note the 2nd and 3rd images past this line of text:
"This one appears in 13th July last year at West Kenet Long Barrow". Scroll down on this page to find
"The Star Nation peoples have sent similar messages in other formations"
and a more zoomed out view showing the nexus above the Giza longitude crowning the Nile Delta ...
When you zoom out, you'll see lovely images of the Earth surrounded by the grid.
Thanks also to lucid dream researcher and forum host Ed Kellogg for showing me an interesting book by Shafica Karragula (author of Breakthrough to Creativity: Your Higher Sense Perception which I read a bit of decades ago) and Viola Petitt Neal entitled "Through the Curtain" which contains references to the diamond and other geometric shapes as appropriate for meditation and spiritual resonance. This reminded me of the significance of the diamond (rhombus) shape and the appearance of the Golden Rhombus (the diamond shape you get when you connect the midpoints of the sides of a golden rectangle) in the Rhombic Triacontahedron, also known as Kepler's Solid; I have a fold-up pattern for it on my website here. The conversation Ed & I had about the diamond/rhombus shape also lead to talking about Eric Weisstein's fabulous magnum opus, Eric's Treasure Troves of Math (and Physics and ...) which evolved into his Encyclopedia of Mathematics and the online version, a collaboration with Wolfram which I seem to refer to constantly. Kudos to Eric and all the other contributors which make this such an exemplary gift to humankind's understanding!
Thanks to Luke G. and Michael H. for this neat visual progression from R.W. Gray about dodecahedron/tetrahedron nesting relationships.
(looks like a great update for this interesting looking software; another enticement to get an Intel-based Mac, I suppose
===============================================
I just released version 4.0 of Stella, plus a new product called Stella4D. It includes everything from Great Stella, but also includes
support for 4D polytopes! Watch a tesseract (4D cube) undergoing 4D rotation. Watch 3D cross-sections of 4D polytopes animating as the slicing hyperplane cuts deeper and deeper. All 1849 known uniform 4D polychora are included, plus more!
I attach a photo of a paper model I made of a 4D polytope using nets created and printed from Stella4D (the cantellated tesseract).
Home page: http://web.aanet.com.au/robertw/Stella.html
Get the demo of Stella4D here: http://web.aanet.com.au/robertw/Downloads.html
See a bunch of screenshots, including animated ones, here: http://web.aanet.com.au/robertw/ScreenShots.html
=================================
Hi Julian:
Many thanks for your inquiry. I got so involved with the reply, that I've decided to post it on my blog for today, as well as in this email; I'm grateful that you asked the question, so now I can answer it for the world
On 30 Jan 2007, at 6:54 AM, Julian wrote:
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.
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 photocopies 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 links page
at http://www.intent.com/bruce/links.html), 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