I'm currently on a train back to Durham from London, where I went to a seminar called "Thinking Tantra: On waking up, say a spell backwards ..." It was led by professor Chris Dorsett from Northumbria University. It was quite a stimulating discussion, with about 10 people, set in a gallery, The Drawing Room, and it concerned the exhibition currently there, "Thinking Tantra."
One thing that was of particular interest to our project was how the ideas of time and space in a yantra work. The origin (of the universe? I don't entirely understand) is in the center of the diagram, and one is supposed to meditate on the yantra from the outside in. This reminded me of a node of concentric shapes in a crease pattern producing a galaxy in one of my simulations (occurring in an earlier blog, http://www.sciartcenter.org/uploads/6/0/8/9/6089526/image_2_orig.png) grows from inside out the patch in the center collapses first, and oscillates (falling in through the center, then back out) ... as each patch falls in from the outside, it starts to oscillate as well, with an ever-increasing period.
I've also written before about how the inner structure of these nodes is determined by the pattern of nodes around it -- this reminded someone at the seminar about Indra's net. From Wikipedia, "Indra's net is the net of the Vedic god Indra, whose net hangs over his palace on Mount Meru, the axis mundi of Hindu cosmology and Hindu mythology. Indra's net has a multifaceted jewel at each vertex, and each jewel is reflected in all of the other jewels." Mount Meru, incidentally, is the hill at the very center of one of these yantras. I'm not claiming that this indicates some deep religious truth, but the intellectual link is still fascinating.
Yesterday, at the Victoria & Albert Museum, I saw a captivating miniature version of "Transparent Void of a Tree", a huge installation by Sou Fukimoto in 2009 - this may be a good way to represent the origami of the 3D dark-matter sheet:
I'll end with a piece I saw at Thinking Tantra, by Alex Gorlizki:
Admittedly, I have had a hard time focusing this past week. Between US news headlines and, well… more US news headlines, I’ve been spending time reading and making phone calls.
That doesn’t mean my mind will not wander to dark matter and cosmology! Last week, Mark replied to my blog post with some insights that have kept my imagination churning…
“About the tensile strength, etc. of the dark-matter sheet ... the only thing in principle that can "tear" it is the ultimately discrete nature of the sheet, on the level of particles. The particles seem to be about the mass of a heavy atomic nucleus (such as, evocatively, gold, I seem to recall -- but the mass could range within a couple of orders of magnitude of that, so probably someone was just trying to be evocative there) That's still dozens of orders of magnitude smaller than a particle typically used in a simulation -- that's why the dark matter sheet approach is more accurate than treating the dark matter as a literal particle, typically millions of times the mass of the sun! Another place where "tearing" might happen would be around a black hole, because the sheet would get so wrapped around. That's a scenario that I've wanted to think about more but haven't had a chance to ... black holes are weird, as you know ... actually in some respects, things that enter them stay outside, plastered on the surface, but get "infinitely redshifted" and so effectively disappear.”
I love the way my mind wanders at the above mention of the “discrete nature of the sheet.” ‘Sheet’ generally impliescontinuity. But it follows that if all matter is made up of molecules, atoms, and particles, then no matter is indeed “continuous.” ‘Discrete’ and ‘continuous’ are keywords from calculus that inspire me to examine them as concepts and represent them as paradoxical descriptions of reality, and yet as highly practical models that allow science to advance, let alone exist. The very calculus that lets scientists mathematically describe the strangeness of black holes!
“You may realize this already, but the dark-matter sheet idea is not the same as as the "cosmic fabric" in the "Mechanics of Spacetime" paper -- based on my initial impression, their cosmic fabric is a layer of constant time, which can acquire ripples due to time dilation. As I understand it, the cosmic fabric actually would have overlapped with the dark-matter sheet when the density perturbations were very small, shortly after the big bang, but they become separate after that...”
Oh, Mark. How you know I love to speculate! If Einstein had not speculated on the speed of light, where would we be today? But I digress. It is not always helpful to speculate this way. That just means I have an entire new world in the fabric of spacetime to investigate through fine art!
Mark did some travel this week to attend a conference at Northumbria University on Tantra. Just 15 or 30 seconds of focusing on the Sri Yantra image linked in his update this week (focus on it from the outside, in) has me thinking how much 3-dimensionality the image has, almost as a sort of optical illusion. Specifically, it resembles a spherical half dome from above, to me. My awareness of Hindu temple architecture brings in the layer of knowing that these diagrams were used to determine foundations and sacred building and spacial design, meaning the design of these buildings would reflect and harmonize with the “design” of the universe. “As above, so below…” Interesting points to consider in the creation of artwork inspired by these ideas…
I am so impressed by Mark’s willingness to entertain the concepts drawn from the intersection of art and science. It seemed at the beginning of our collaboration that, while he had thought and worked with origami in a broad, intersectional manner, he had not thought of “fine art” as truly relatable. His musings on the conference “Thinking Tantra…” demonstrate that new avenues of thought are opening up for him! The metaphor of Indra’s Net has an amazing connection to the cosmic web. The core principle is that at each node of Indra’s net, a magical jewel resides that reflects each and every other jewel at every other node, ad infinitum. The net represents the interconnectedness of the universe. As I read his update, it was almost like traveling a well-worn path, like picking up a bicycle for the first time in years and remembering exactly how to use it. Had I thought of this before? Likely, just never wrote it down. The conceptual overlap leads me to thinking about quantum entanglement, and the theory of the Big Bang, and a new addition, the peculiar dark matter sheet simulations that show how each node is influenced by nodes around it. The intellectual nature of Hindu mythology and cosmology is deeply fascinating as it reveals intersecting layers at vast and minuscule scales, offering a paradox here and there to disrupt the mind’s propensity for logic.
This connection to eastern religion has reminded me of the cosmological implications of Catholicism and Christian Mysticism, drawing closer to my own cultural upbringing. In reading Dante Alighieri’s Comedia in a dual liberal arts-studio course in 2012, I was amazed by the sensational descriptions of the heavens and the task of visualizing them as an illustrator. While classmates rendered human forms in varying stages of agony and ecstasy, remarkable pen and ink drawings of light, space, and scenery meant to evoke the mountainous and heavenly Purgatorio and Paradiso, I was stripping away all conventions of representation searching for a minimalist conceptual representation that would take the viewers mind to the “world” of Dante’s poem, a purely conceptual world. The same kind of world in which the concepts of mathematics and physics exist, the world of thought-problems and paradox, the world of reference frames and “ifs.” This is sometimes the only place that these concepts can exist. It was almost as if I was attempting to create something like a yantra for this meditative experience, a visual tool to pique the mind into a certain thought structure, within the context of Dante’s Comedia and medieval Christianity.
On a final note, Mark said he was moved by a piece at the Victoria and Albert Museum that was created as part of an exhibition on the theme of “inside/outside.” The piece is titled “Transparent Void of a Tree” by Sou Fujimoto architects. Mark mentioned that the way this piece is fabricated, by edge-linked triangular sheets of transparent acrylic, might also be a good way to represent the origami of the 3D dark-matter sheet. Even the concept and title of the piece are worth chatting about. I see a project proposal in our future…
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Lizzy Storm is an artist and owner of Lizzy Storm Designs based in Atlanta, Georgia.
Mark Neyrinck is an award-winning astrophysicist and cosmologist, and a postdoctoral researcher at Durham University, United Kingdom.