I'm working on an origami representation of the "Council of Giants", a name given by someone to our dozen or so nearest-neighbor large galaxies, in the so-called Local Sheet. This sheet has little to do with origami, or the "dark-matter sheet" that is relevant physically, but is just called a sheet that because the nearest galaxies, instead of filling out a full 3-dimensional space as they could, are roughly coplanar. I'm using Robert Lang's Tessellatica software, http://www.langorigami.com/article/tessellatica It's really amazing that he so generously put all that great code up there! Note: it does require Mathematica to run it.
Anyway, it seems that the network of nodes I was feeding it wasn't quite "spiderweb" enough for a simple algorithm known as "shrink-rotate" to work everywhere (see the unfortunately paywalled http://www.crcnetbase.com/doi/abs/10.1201/b10971-40). In the picture below, the pink dashed lines (upper right) are supposed to be creases hidden under folds, but they aren't. (The stick figure represents the Milky Way)! Anyway, the design needs revision; I will either find the nearest-approximation "spiderweb" graph, or do something more manually ...
Also I wanted to point out a cool mathematical/geometrical art app that I just found, called iOrnament,
I just downloaded it myself so I can't endorse it fully yet, but it seems quite powerful, making it rather easy to make kaleidoscopic things somewhat like mandalas I discussed last week. Here's something from their Facebook page:
...and here's something I quickly tried out (completely unrelated to cosmology, but with a 4-quadrant symmetry)
Anyway, more next week!
Mark and I both worked on a folded paper model of the Council of Giants this week. Our hope is that this piece will create a stepping stone for folks to get from structures visible and familiar to us, such as the Milky Way and nearby Andromeda galaxies, to large-scale structures like galaxy clusters and voids, through the similarity of their forms. He mentioned briefly in our chat this week that the model might not actually fold properly, but I went in full steam ahead anyway.
I took a trip to my local art supply store looking for paper. I came away with some sheets of mulberry paper from the scrapbooking section, and a pack of “paper” branded for origami folding that is really rayon fabric mesh! In the spirit of Ron Resch (see first post) I examined the mesh paper, folded some parts to see how it would take the folds, and then simply crumpled the piece into my fist and let it go. In the film “Paper and Stick,” Resch describes his process of crumpling and unfolding paper to find and refine expandable folding patterns. The un-crumpled piece of rayon mesh looks familiar!
Right: crumpled rayon mesh. Left: detail of “Origami-Universe-4.png” from python source code for the “Fold Your Own Universe” NASA SpaceApp hackathon project, 2014.
I look forward to seeing where this material takes me...
Here is my folded model of the Council of Giants, created by Mark using Robert Lang’s Tessellatica software.
I think we both came to the conclusion that something is amiss, the twist folds are not quite there. Nevertheless, I got a nice close-up shot.
This pattern is quite literally an abstraction of reality. Abstract art, if I may. It’s expressive nature (how it makes the viewer feel) can be altered through the materials with which it is made and the context within which is is seen. Arguably, it is a bit underwhelming in its current form of folded-computer-paper-photo-taken-with-phone-camera-viewed-in-a-blog-post. It may be inexplicably more amazing in a refined material and context. It may also offer drastically new meanings if it were to be shown beside a piece of text… just some thoughts on the creation and exhibition of artwork inspired by scientific research.
And, last but not least, here are photos of my experiments with this mulberry paper. It’s a bit too soft to have the active twist-folding effect that I was hoping to see (and video or stop-motion capture) although it did fold up nicely without showing creases everywhere, and I do appreciate the decorative element that the fibers provide.
One of the tricks to good paper for folding is long fibers within the paper. These prevent the paper from ripping when folds are stressing it from stretching and compressing. Computer paper has short fibers, which you can actually see in the backlit closeup. This mulberry paper has long fibers criss-crossing throughout, making it uniformly strong. Folds made in any direction on this type of paper will not have the tendency to rip, and there will be less creasing. Paper differs from the Dark Matter Sheet in that way. The DMS is modeled as stretching in void areas and compressing in dense areas, eliminating the concept of ripping. Inspired by the engineers in my life, I wonder what the sheer stress of the fabric of spacetime would be, if there were one? In other words, at what point would the fabric of spacetime rip, due to gravity or otherwise? Maybe a pointless thought experiment. It turns out, a quick internet search will give you some answers: The Mechanics of Spacetime - A Solid Mechanics Perspective on the Theory of General Relativity, T. G. Tenev and M. F. Horstemeyer. (link will download PDF file of manuscript.) This leads me to wonder how to bring in a stretchy sheet of material, like a stretchy fabric or a metal screen, to these visualizations… and I’m off to fill my blog (which I will share shortly) with links to these inspirations and musings.
Still inspired by last week’s themes of Tantric diagrams, or yantras, I was led to a site that offers research into a commonly used and popular yantra known as the Sri Yantra called simply, “Sri Yantra Research Center” linked here. The Sri Yantra consists of 9 overlapping triangles and creates an interesting collection of angles and shapes. There has been some mathematical research into the form and a publication which claims to identify the specific angles that make an ‘optimal” Sri Yantra, which can be found on the site’s homepage. I'm interested in these geometric relationships, and I think they would make good raw material for further dark matter sheet simulation patterns.
What interests me initially about yantras in conjunction with the scientific visualization of the early universe, or large scale structure in the universe, is the definition of a yantra as a diagram, a tool, or a figure used to illustrate a conception of cosmology or reality. Quoted from the page titled “Yantras,”
In its first meaning, 'yantra' may refer to any kind of mechanical contrivance which is harnessed to aid an enterprise. A yantra in this sense, therefore, is any sort of machine or instrument such as is used in architecture, astronomy, alchemy, chemistry, warfare or recreation…
They are, first of all, believed to reveal the inner basis of the forms and shapes abounding in the universe. Just as, whatever the outer structure, all matter is made of an intrinsic basic unity, the atom, so each aspect of the world can be seen in its structural form as a yantra. As the scientist sees the final picture of the world in the orderly, simple, atomic structures in which certain primal shapes appear as a harmonized 'whole', so the Indian shilpi-yogins (makers of ritual art) seek to identify the innermost structure of the universe by concentrating the variegated picture of world-appearances through intense yogic vision into simple form-equations. A yantra, then, can be considered an ultimate form-equation of a specific energy manifesting in the world. These simple form-equations are held to epitomize the real nature of the cosmos as abstracted from the concrete. [emphasis mine]
I am not surprised by the analogy, from the standpoint of the spiritual, between scientist and makers of ritual art. (They even use the word “equation”!) I am more surprised by scientists’ seemingly unwillingness to examine how spiritualists conceive of the nature of reality and cosmology. Is it seen as a distraction? Perhaps. Perhaps it is only Western science that has broken completely from spirituality, a result of the Church denying the scientific truths discovered during the scientific revolution. Perhaps it is just my personal experience with staunchly atheist scientists.
And yet, in recent years, popular science has come forth to the masses, such as in the form of television series like “Cosmos” and “Through the Wormhole”, with language and image that draw a direct connection between science and spirituality. For example, in a segment from “Through the Wormhole”, scientist Garrett Lisi is described by the narrator as having a “vision’ that led him to develop the algebraic Li group called E8, which purports to offer a unified theory of particle physics all the way through to gravity and force carriers. The segment can be viewed on YouTube here. “To us, it is just a mind-bending pattern, but to Garrett Lisi…” the narrator goes on describing the scientist’s “Ah-ha” moment. The video shows a beachside surf scene overlapping the scientist’s mathematical notebook (surf culture is very spiritual, and Lisi himself is an avid surfer). Lisi is quoted on video, “You know, seeing how gravity could be combined with these other Li groups during this unification was one of the greatest moments of my life [emphasis mine].” What is it that he saw, was it a mathematical vision? A pictorial vision? Was it a literal visual process aided by the geometric visualization shown in the segment? A combination of all of these? “Vision” and “seeing” seem to be ways of describing a (modern?) thought process or mental conclusion with no English word to truly define it. Instead, these ways of describing a discovery are borrowed from spirituality.
The Sri Yantra Research Center homepage links to a video on E8 geometry. Would you expect to find an analogous link on a scientist's’ research page?
There is still so much more to consider in this exploration of yantras and scientific visualization. Color plays an enormous symbolic role in spiritual diagrams, as do specific angle relationships and geometry. Could visualizations be made more refined as tools of science if they were to use color in a symbolic or otherwise meaningful manner? Mark has done this in some of his visualizations, perhaps intuitively choosing the contrasting colors of blue and orange because they visually support each other (I haven’t yet asked how he chooses colors! Hey Mark, how do you choose your colors?) Could visualizations be translated more easily to the general public if they used familiar color or geometric relationships? Two very different questions. Quite frankly, I think it is important for high-science research to be shared with the public due to the massive investment in this field through space exploration and particle research. Science is rather new. Spiritual practices and models could represent an ancient gateway for approaching science’s questions and answers that appeals to the world’s Godly masses. Dalí did it in his 1954 oil painting Crucifixion (Corpus Hypercubus)
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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.