Wednesday, May 27, 2009

Class 4 and 5

These two classes were devoted to a specific topic each. Class 4 was mostly dedicated to the topic of Geometry in Nature (as a continuation of class 3), while class 5 was focused on Geometry in the Man-made World. In general, we learned that Sacred Geometry deals with both, and that in fact the principles are correlated, showing precisely the connection between the work of humans and their inspiration from nature, as being part of one unifying principle: that of "Heaven on Earth."

In the "Geometry in Nature" class, we made many connections between our drawing surface and the world around us. After looking at the seemingly familiar world of plants, we saw examples of geometry found in nature that were beyond what our own senses can perceive, looking at images both microscopic and telescopic. We saw galaxies, clusters, planetary orbits and rings, down to river banks, craters, clouds and huracanes, down to animal skeletons, seashells and even further down and inside, to organs, arteries, cells, atom collisions and Quanta! (just kidding, we didn't get that tiny, but we did see atom collisions!). All of these forms shared many of the familiar geometries we have been studying, and the concepts and symbols associated with these patterns seemed to make sense across scales. For example, we talked about the spiral being sometimes associated with the notion of "growth" and experienced precisely this sense when looking at examples in the natural world, at many different scales. Galaxies, plants and seashells are spiral because of their growth, no matter their size. We also experienced some curious connections, such as learning that the eye of a bee is made of a hexagonal matrix, very similar to the pattern of a beehive.

These connections are inumerable and they give us a sense of wonder. Is it all random, or is it all connected?
This question led us to deeper terrains and we explored, for example, the idea of a connection existing between animate and innanimate matter. We saw that, at least according to the forms of sacred geometry, living and dead matter are very much connected by the notion of pattern.

We briefly looked at one the first books proposing this idea, and even though now many of the postulates in this book are obsolete, we found some very valid points. The book is called "Of Growth and Form" by D'Arcy Thompson. This was one of the first books of this kind, and it reformed the way biology is conducted and understood. In a nutshell, Thompson argued that the patterns and forms of living beings were the direct material imprint of physical and chemical processes. He argued that organic form was a result of the same innanimate processes one could study in the lab. In class, we conducted one of the experiments described in the book, that of simply releasing a drop of ink in a container of water. I didn't want to bias the class, so instead of saying much, after I released the drop I asked: "What do you see?" One of the students spontaneously replied: "Jelly fish!" It was fascinating for the class to see that in his book, D'Arcy Thompson had the drawings of the ink drop experiment inmediately along side jellyfish. His point was made.
But is there a deeper connection between animate and inanimate matter, other than pattern? Ok, so, the sun is not alive and it is round and an eye is live tissue and it is round too, so they are connected. Big deal. Blood vessels and river beds look exactly alike, one is giant one is tiny, one is live the other is dead, they are connected by pattern... big deal.
We learned about another interesting idea to promote the notion of wholeness, or interconnection between all things (in this case live and innert matter). This is a reocurring theme in our study of Sacred Geometry, because remember, a big part of our definition involves the idea of a connecting principle, one that relates things across scales, disciplines and philosophies. It is a theory proposed by James Lovelock and Lynn Margulis called GAIA theory.

Unlike popular belief, Gaia theory is not a hippie or new-age idea relating to the Goddess Mother Earth being alive. This is, rather, just a convenient metaphor to describe the theory in a few words! Gaia theory is an actual scientific development, and one that is crucial to our survival in this planet (the planet itself is fine, it is US who are in danger!)
Gaia theory proposes that, instead of thinking of the Earth as a dead planet, made of rock, ocean and atmosphere, merely inhabited by life on its surface, that planet Earth is a self-regulating system, and all of its elements and components actively participate in the continuation of the entire system. The planet is thus considered to be closer to a living organism than it is to a rock, in that it can self-organize and regulate itself. This is not to say that Earth is intelligent (at least not in the antropomorphic sense) but it is to say that every rock, bug, cloud, tree and person, ALL play a huge roll in the development and continuation of life on this planet. Water is not alive(I'm not even sure about this :)), and yet without it life is not possible. I can't go too in depth here, since that is the point of taking the class, but we did cover one good example used by Lovelock and Margulis to support and explain their theory in easy terms. It is the cycle of CO2 as described by GAIA theory. I will just direct you to an awesome book by Fritjoff Capra called "The web of Life". In this book, he describes the cycle of CO2 as a good example of the collaboration between animate and innanimate matter to sustain life on Earth. He also describes Gaia theory, and covers very digestable explanations of systems theory, cybernetics, quantum physics, self organization, genetics, mysticism and many other things which are key to a new understanding of the universe. WOW! Just get the book...

In our "Geometry in the Man-made World" class, we talked about humans deriving inspiration from nature to create sacred sites and buildings, monuments, designs, icons, symbols and even everyday products! We discussed how the same principles found in nature such as the Golden Ratio, the circle, the polygons, proportions, etc, were used as the basic structures for creating objects. In this sense, we entertained the ancient idea that using these principles can create a bridge between the material, physical world and the realm of the Heavens.

We looked at architecture, and how sacred geometry plays a central role in creating every part of a building, from its floor plan to its elevation, through all its details and ornaments.

We looked at art, tiling and tesselation, mandalas and mechanisms, all as examples of the use of mathematics, geometry and pattern, for the creation of beautiful, spiritual, or efficient objects.

So we discussed "Biomimicry", which literally means "imitating life", as a widely used principle in art, engineering, architecture and science. I want to share here a video we watched in class about artist/inventor Theo Jansen and his "animals". This is a great example of biomimicry, and all the more related to our class since he mentions the use of "eleven holy numbers", which are totally mysterious to me. I've heard someone say, very matter of factly: "Its most likely the Fibonacci sequence" but this makes absolutely no sense, since by the time you get to the eleventh digit, 89, the difference in measure would be so radical to the first digit, 1, that you could not make this mechanism work. Anyway...

I also wanted to share this beautiful drawing by Architect Louis Sullivan. I wanted to show, on one hand, his enourmous understanding of how to describe organic forms with drawing tools, but mostly because it came up in our class that asymmetry is as beautiful as any form of symmetry, which is something that became an important topic in our fractal and Li discussions.


  1. It's nice to see teachers teaching. Can I come to your class? :)

    You write good articles, you should do more often. Information (knowledge) is the future: spread a little more please.

  2. Awesome info...