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3D Geometries

Multiplication Tables on Circular String Art lead to Mandelbrot and classic curves

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Thanks to Ed Kellogg for this interesting video link (Times Tables, Mandelbrot and the Heart of Mathematics by Mathologer) and his comments: “This looks like a real treasure trove to me! And not just Mathologer – looks like a lot of other mathematicians or mathematics enthusiasts have put up some great videos since the last time I checked out this area on YouTube! Visually entertaining and illuminating videos illustrating mathematical concepts and processes used to seem almost as rare as hens teeth – nice to see how much that situation has improved.” … I agree, Ed… Looks like I’ll want to spend more time exploring more of his – and related – videos! :-)

Mathologer - String Art Mandelbrot

 

Vibration Station Conversation – What makes Sacred Geometry sacred?

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In this audio recording, Dave Cohen (a.k.a. Davie Crockett), and Bruce Rawles continue their ongoing conversation about the mystical underpinnings of sacred geometry. We spoke about how everything is either sacred … or profane … depending on which thought system – inclusion … or exclusion – we identify with and gave numerous examples, again referring to the Greek philosopher, Plato, who maintained that symbols (including geometric examples in 3 dimensions for which he is justly famous for) are not the same as the ideas they represent.

This conversation was recorded on Sunday, 18 December 2016, on his LA Talk Radio show.

Thanks again to David Cohen for his continued support and enthusiasm for this work and inviting me on his radio program numerous times over the past 2 years. David and I recently concluded a 10-session series of conversations (1 per chapter) talking about the “7 Hermetic Laws” highlighted in the book The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation.

Dave Cohen - Good Vibration Station-LA talk Radio

Vibration Station Conversation – Sacred Geometry, Plato and Symbolism

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Plato (portion of painting by Raphael)In this audio recording, Dave Cohen (a.k.a. Davie Crockett), and Bruce Rawles resume their ongoing conversation about the mystical underpinnings of sacred geometry. The Greek philosopher, Plato, posited that specific examples (including geometric forms as well as people, quarks, quasars, and anything else that represents, or symbolizes an essential ideal) merely serve as reminders to the mind that the spirit behind manifestation is what is important. Plato is credited with 5 regular polyhedra in 3-dimensional space (a.k.a. the “Platonic Solids“) as well as other mystical ideas taught in his academy such as the allegory of the cave. This conversation was recorded on Sunday, 16 October 2016, on his LA Talk Radio show.

Thanks again to David Cohen for his continued support and enthusiasm for this work and inviting me on his radio program numerous times over the past 2 years. David and I recently concluded a 10-session series of conversations (1 per chapter) talking about the “7 Hermetic Laws” highlighted in the book The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation.

Dave Cohen - Good Vibration Station-LA talk Radio

Möbius strips of light … Donald in Mathmagic Land … Golden Ratio Nautilus

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From the backlog of interesting sacred geometry links I’ve been meaning to share, here are three, with thanks to colleagues who shared the links with me so I can pass along to you! :-)

  • Möbius strips of light” … These mathematical structures show up everywhere from M.C. Escher drawings to electrical circuits, but almost never in nature. Now, a team of physicists have shown for the first time that light can be coaxed into a Möbius shape. …” Thanks to Ed Kellogg for emailing these links.
  • Disney Cartoon From 1959 Teaches Sacred Geometry: ” … Donald in Mathmagic Land is a 27-minute educational film featuring the one and only Donald Duck. Released on June 26, 1959, it soon became the most popular educational film ever released by Disney. … ” If you haven’t seen this classic, you might want to watch it – or watch again – even if just for historical reasons; it’s an good very basic introduction (or re-introduction) to the the golden ratio, pentagram proportions, Pythagorean mysticism and a gateway to a more in-depth study of sacred geometry. Thanks to Haines Ely for this link suggestion.
  • Golden Ratio Nautilus: George Hart clarifies common misconceptions about popular spiral shapes (specifically golden ratio spirals) in this interesting video where he sets the record straight … or is that curved? :-)

Golden Ratio Nautilus

 

Cross symbolism, coloring books for adults, vesica piscis and misc. links

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I recently received this inquiry about the symbolic meaning of a cross:

Hi, I love your site. I am learning so much. I don’t see any information about the symbol ‘The Cross’. Is the cross a universal symbol? A sacred symbol? It’s the symbol used in Christianity but does it have wider significance?
Thank you for your time and your knowledge! Thank you, thank you,
– A., California

… and I provided this response:

Thanks for the kind words, and your question.

Yes, the cross can represent a very wide array of symbolic meanings, and its obvious geometric aspects attest to its universality beyond any specific religious or philosophical adoption, but I try to remember that symbolic systems can be simplified to just 2 thought systems:
Inclusion: whatever leads us back to thoughts of sameness, interconnectedness and ultimately Oneness
and
Exclusion: whatever leads us deeper into the metaphoric darkness of separate interests, differences and identification with the ephemeral, dualistic and divisive.

Therefore, seen from the former thought system of Inclusion, a cross can be a reminder that we can find the center (intersection) point where we transcend polarities, find common ground and respond with kindness … or an idol for specialness and ‘win-lose’ tug-of-war battles. It’s always our choice. :-)

I touch on this symbolism in the chapter on the Law of Polarity in my second book, The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation

Book: The Geometry Code: Universal Symbolic Mirrors of Natural Laws Within Us; Friendly Reminders of Inclusion to Forgive the Dreamer of Separation by Bruce Rawles

You might also enjoy listening to this related recent conversation about the Law of Polarity.

Thanks again for your inquiry and support! :-)

I keep finding more indications that the interest in adult coloring books is continuing to rise, such as this Coloring Book Master Class promotion. In addition to the classic reference book that contains over 1300 images suitable for easy photocopying for geometric coloring book use, my German publisher recently released a beautiful hardbound book (with a very nice subset of the images in the larger book) as Bewusst malen – Heilige Geometrie which also has some great quotes on facing pages. Thanks again to fellow author and artist, Jay Goldner, for his work in bringing this second book containing my geometric artwork to Europe and the world.

Here are a few miscellaneous links about sacred geometry and related, interconnected topics that have crossed (pun intended) my path recently that you might find interesting:

The Hourglass Nebula
This is an image of MyCn18, a young planetary nebula located about 8,000 light-years away, taken with the Wide Field and Planetary Camera 2 (WFPC2) aboard the Hubble Space Telescope (HST). This Hubble image reveals the true shape of MyCn18 to be an hourglass with an intricate pattern of ‘etchings’ in its walls. This picture has been composed from three separate images taken in the light of ionized nitrogen (represented by red), hydrogen (green), and doubly-ionized oxygen (blue). The results are of great interest because they shed new light on the poorly understood ejection of stellar matter which accompanies the slow death of Sun-like stars. In previous ground-based images, MyCn18 appears to be a pair of large outer rings with a smaller central one, but the fine details cannot be seen.