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mathematikal_arts_2011 [2011-07-13 13:02] – nik | mathematickal_arts_2011 [2011-08-06 19:16] – davegriffiths | ||
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- | ==== Mathematikal | + | ===== Mathematickal |
- | Part of Splinterfields. | ||
- | |||
- | To me the simple act of tying a knot is an adventure in unlimited space. A bit of string affords the dimensional latitude that is unique among the entities. For an uncomplicated strand is a palpable object that, for all practical purposes, possesses one dimension only. If we move a single strand out of the plane, interlacing at will, actual objects of beauty result in what is practically two dimensions; and if we choose to direct our strand out of this plane, another dimension is added which provides an opportunity that is limited only by the scope of our own imagery and the length of a ropemakers coil. | ||
+ | "To me the simple act of tying a knot is an adventure in unlimited space. A bit of string affords the dimensional latitude that is unique among the entities. For an uncomplicated strand is a palpable object that, for all practical purposes, possesses one dimension only. If we move a single strand out of the plane, interlacing at will, actual objects of beauty result in what is practically two dimensions; and if we choose to direct our strand out of this plane, another dimension is added which provides an opportunity that is limited only by the scope of our own imagery and the length of a ropemakers coil." | ||
-The Book of Knots, Clifford W Ashley | -The Book of Knots, Clifford W Ashley | ||
+ | |||
+ | Mathematickal arts workshop is organised by FoAM, as a part of Resilients (http:// | ||
+ | |||
+ | {{http:// | ||
+ | |||
+ | The workshop is designed and lead by Carole Collet, coming from textile education and sustainable design, together with Tim Boykett, a mathematician, | ||
+ | |||
+ | Workshop leaders: | ||
+ | * Carole Collet (CSM Textile Futures, http:// | ||
+ | * Tim Boykett (Time' | ||
+ | |||
+ | Workshop participants: | ||
+ | * Martaque | ||
+ | * Pieter Slock | ||
+ | * Eugenie Poste | ||
+ | * Wendy van Wynsberghe | ||
+ | * Fabian Feraux | ||
+ | * Stephanie Vilayphiou | ||
+ | * Miska Knapek | ||
+ | * Dave Griffiths | ||
+ | * Cocky Eek | ||
+ | |||
+ | Organisers/ | ||
+ | * Nik Gaffney | ||
+ | * Lina Kusaite | ||
+ | * Maja Kuzmanovic | ||
+ | |||
+ | Cook/ | ||
+ | * Annabel Meuleman | ||
+ | |||
+ | |||
+ | ==== Day 1: 20110723 ==== | ||
+ | |||
+ | |||
+ | After the introductions to the workshop and its wider context of cultural resilience, the participants were invited to warm up by playing a human knot game - randomly joining all hands and trying to unknot to a loop or a twist without letting go (http:// | ||
+ | |||
+ | Slides from the presentation: | ||
+ | |||
+ | The presentation showed a broad range of possibilities that the workshop could unfold into, but its final direction depends on the participants and their interests. For example: | ||
+ | * group theory and different types of symmetries (http:// | ||
+ | * tesselation, | ||
+ | * knotting, such as the Turk's Head (http:// | ||
+ | * braiding (http:// | ||
+ | * short intro into continuous deformations (homotopy) of doughnuts into teacups in topology (http:// | ||
+ | * weaving cellular automata (http:// | ||
+ | * the hairy ball theorem (http:// | ||
+ | |||
+ | |||
+ | === Dissecting a Moebius strip === | ||
+ | |||
+ | The first practical exercise took one of the seemingly simple mathematical phenomena - the Moebius strip, and attempted to intuitively predict what will happen when one begins cutting it. What will be the lengths, twists, knots? How would you explain what happen to someone who'd like to try it themselves? | ||
+ | |||
+ | {{http:// | ||
+ | {{http:// | ||
+ | |||
+ | |||
+ | After proceeding to cut, count and get entangled in strips of paper, the group came together to look at each other' | ||
+ | |||
+ | Conjecture: When the length is twice as long it has twice as many twists; odd number of twists - you go around the loop twice, so you double the length and you double the twists - you can never get more than double the original length. | ||
+ | |||
+ | * odd number of twists --> 1/2 cut --> double length, double twist | ||
+ | * odd number of twists --> 1/3 cut --> double length double twist + same length, same twist | ||
+ | |||
+ | Evidence: | ||
+ | * 1 twist 1/2 cut = two pieces of twice the length, 2 twists | ||
+ | * 1 twist, 1/4 cut = 1 same length, 1 twist + 1 2 lengths, 2 twists | ||
+ | |||
+ | Observations: | ||
+ | * counting twists is hard | ||
+ | * when you bring patterns in your cuts, it gives you more headaches, but becomes a creative exercise | ||
+ | |||
+ | |||
+ | Summary of experiments (i.e. "what did we do"): | ||
+ | * We have taken a simple piece of material and done a series of experiments, | ||
+ | |||
+ | * We got into trouble quite quickly (intuition was contrary to empirical evidence). Mathematician Trevor Evans said that if maths contributed anything to the world it was to put common sense in a box on a top shelf, just next to a box with nonsense (paraphrasing Tim). Maths keeps messing with our intuitions (common sense), in a repeatable way. | ||
+ | |||
+ | * We started with hands-on experiments, | ||
+ | |||
+ | {{http:// | ||
+ | |||
+ | " | ||
+ | http:// | ||
+ | |||
+ | |||
+ | |||
+ | === On hyperbolic geometry === | ||
+ | |||
+ | Example of non-euclidean geometry challenging Euclid' | ||
+ | |||
+ | * Euclid' | ||
+ | * Circular geometry - there is always one point where two lines will meet | ||
+ | * Hyperbolic geometry - there are at least two parallel lines diverging | ||
+ | (More: http:// | ||
+ | |||
+ | After a short demonstration of FoAM's stitched hyperbolic surfaces (http:// | ||
+ | |||
+ | {{http:// | ||
+ | {{http:// | ||
+ | |||
+ | In addition to stitching and knotting, folding flat square pieces of paper (i.e. origami) was a third technique used at the workshop to explore hyperbolic geometry. The participants began with single hyperbolic paraboloids (http:// | ||
+ | |||
+ | Movie suggestion: | ||
+ | * Between the folds (http:// | ||
+ | |||
+ | Software: Computational origami | ||
+ | * treemaker origami http:// | ||
+ | * http:// | ||
+ | * anarchiste origami > http:// | ||
+ | * http:// | ||
+ | * http:// | ||
+ | |||
+ | References to practical exercises: | ||
+ | * Cutting Moebius strips (how to: http:// | ||
+ | * Crocheting hyperbolic surfaces (http:// | ||
+ | * Using origami folding to create hyperbolic paraboloids (http:// | ||
+ | |||
+ | Ideas for day 2: Macram� to find out about different knot theories. Japanese bondage technique to avoid knots, installation with ropes. Remixing folds and knots, weaving the space, turning scribbles into weaves, weaves into knots... | ||
+ | |||
+ | |||
+ | ==== Day 2: 20110724 ==== | ||
+ | |||
+ | Pieter - one of the participants at the workshop - recently graduated by developing software to parametrically design foldable architecture. He demonstrated two models of origami-like architectural structures, that he used to test his software. The structures begin as a flat plane, with a textile sandwiched between two layers of wooden panels, combined in such a way that when lifted up in a third dimension, the shape will form folds through mountains and valleys held together by waterproof textile ' | ||
+ | |||
+ | "An organism is so complex a thing, and growth so complex a phenomenon, that for growth to be so uniform and constant in all the parts as to keep the whole shape unchanged would indeed be an unlikely and an unusual circumstance. Rates vary, proportions change, and the whole configuration alters accordingly." | ||
+ | |||
+ | === Spatial Weaving === | ||
+ | |||
+ | The first exercise was an oversized demonstration of weaving a geometrical pattern using a black and white rope. The participants tied a loop of a weft around their waste and followed instructions to lift or lower their ropes, so the warp could pass through them, creating a woven pattern. After a short period of time, it became physically apparent why Jacquard designed | ||
+ | * each individual could be given a set of instructions, | ||
+ | * the instructions could be relative to their immediate neighbours (e.g mirror your neighbour) | ||
+ | * the instructions could be relative to the previous action (stay/ | ||
+ | * ... | ||
+ | |||
+ | |||
+ | {{http:// | ||
+ | {{http:// | ||
+ | |||
+ | === Groups and repeats === | ||
+ | From weaving to printing, the participants got their heads around group theory and making patterns for printing textiles, by exploring symmetry (http:// | ||
+ | |||
+ | * links http:// | ||
+ | * how to make a seamless pattern using square cuts: http:// | ||
+ | |||
+ | |||
+ | === Knotted dough === | ||
+ | Bugnes, sweet French dough fritters are a wonderful way to explore knots, strips, planes, weaves and other forms in action. Stretching the dough and creating the form, then dipping it in boiling oil shows what happens when the form is subjected to a continuous transformation - a raw tea-cup becomes a fried doughnut, for example. The results were deliciously sweet and greasy afternoon snacks, happily eaten during the afternoon break. | ||
+ | |||
+ | {{http:// | ||
+ | {{http:// | ||
+ | |||
+ | Traditional Bugnes recipe: http:// | ||
+ | |||
+ | |||
+ | === Complicating knots === | ||
+ | |||
+ | Once the simple dough knots were digested, the group proceeded to complicate the matter with braiding the Turk's Head (http:// | ||
+ | |||
+ | === Suspensions === | ||
+ | |||
+ | Knots are often used to hold things in place. How about using knots to hold things in space, in mid-air? | ||
+ | |||
+ | Using ropes and knots a series of cubes and hyper-cubes was suspended in the space, seeing how to deform the shapes through tension. | ||
+ | |||
+ | Fabian explored elegant Japanese bondage (http:// | ||
+ | |||
+ | {{http:// | ||
+ | {{http:// | ||
+ | |||
+ | |||
+ | === Steaming origami fabric === | ||
+ | |||
+ | Polyester organza is easy to pleat by simple applying heat using the iron, oven or steaming it in the pressure cooker | ||
+ | |||
+ | Heat-setting synthetic textiles: http:// | ||
+ | |||
+ | Origami in textile: http:// | ||
+ | |||
+ | {{http:// | ||
+ | {{http:// | ||
+ | |||
+ | ==== Day 3: 20110725 ==== | ||
+ | |||
+ | The third day of the workshop began with a recap of things learned and tried out the previous day. A parade of repeats, textile origami, knotted suspended cubes and other mathematical textiles was observed with interest. | ||
+ | |||
+ | To bring a bit of ' | ||
+ | |||
+ | {{http:// | ||
+ | |||
+ | The last hours of Mathematickal Arts were reserved to deeper explore ideas discovered in the first two days, especially ideas that the participants find most applicable in their practice. The participants proceeded to develop their experiments in smaller groups: textile origami, knotted suspensions, | ||
+ | |||
+ | The workshop leaders re-introduced the question of the workshop - whether bringing mathematics and textiles together increases the resilience of both practices. One hypothesis is that by combining the two, a better balance can be found between a heuristic | ||
+ | |||
+ | One of the examples was the experiment with suspending a cube made out of rope. T participants began making the sculpture by intuitively cutting and assembling pieces of rope, which used a lot of material and many knots. After using mathematics to understand the more optimal way of building the cube, much less rope was used and a different knot, that allowed for easy adjustments. This combination of techniques made the suspended cube more adaptive and in a way more resilient. Another example was that applying mathematics to textiles makes the craft of mathematics understandable and applicable to non-experts and therefore more embedded in common understanding. | ||
+ | |||
+ | As a possible future reunion, Carole suggested a visit to Calais to look at the complexity of lace looms (http:// | ||
+ | |||
+ | Finally, Tim's last experiment was to create a Moebius Turks head, and the group felt that something' | ||
+ | |||
+ | |||
+ | === Workshop Outcomes === | ||
+ | |||
+ | |||
+ | == Tour de France fish net == | ||
+ | |||
+ | Martaque designed a net based on historical tour de France scores. She mapped out the progress of individual riders and relationship with other riders, using them as netting points. Every point in the net was determined by the position of two riders in the netting. In this way it was possible to tangibly visualise the speed of different riders at various points in the race. Martaque will use the learnings from this experiment to develop a netted artwork using the results of 2011 Tour de France. | ||
+ | |||
+ | {{http:// | ||
+ | |||
+ | == Suspensions == | ||
+ | |||
+ | Fabian Feraux used the suspended cube as a geometrical shape to enhance the suspensions of humans in space. The cube functions as an etherial aquarium, that changes shape as it is tensed by the elevation of the human body into it. He explored how much weight one can put on what angle of the cube, looking at tension on attachment points. He experimented with Japanese bondage, where knots are only made at the beginning of a new rope. After that, he uses only twists to restrict and suspend a body or an object. In Japanese bondage, a strictly codified system, knots are considered offensive and ugly, in addition to the practical consideration that they take too long to untie if something goes wrong. | ||
+ | |||
+ | {{http:// | ||
+ | |||
+ | == Simulation of elastic rope structures == | ||
+ | |||
+ | Miska Knapek made a simulation of flexible structures, using physics of elastic bands. He creates attachment points and uses them as anchors, the program calculates the ideal distance for the elastics and keeps the structures in dynamic balance. Miska was inspired by varying elasticity of rope (hemp to nylon) and used parametric design to simulate the poetry of physical structures inherent in their emergent dynamics. The result was a small prototype of algoritmic graphics generated from varying relationships in a system, examining the properties of physically inspired pseudo/ | ||
+ | |||
+ | {{http:// | ||
+ | |||
+ | == Textile origami == | ||
+ | |||
+ | Cocky, Pieter, Wendy, Stephanie explored different origami patterns in textiles. One of the approaches was to sandwich polyester organza in-between a paper mould using paperclips. The textile and the mould were placed for 1 hr in the high pressure steamer. When the paper is taken away, the folds stay - polyester keeps the memory of the shape. A mix of polyester and metal proved not to be as successful. The pleats created in this way are permanent until the textile is heated to the same temperature. | ||
+ | |||
+ | The group looked at changing scales for origami textiles - using the same technique to design the textile for the body and textile for architecture. The challenge for the future is to see if larger structures can be made out of one material only (e.g. textile, rather than textile and wood). This has proven more challenging, | ||
+ | |||
+ | {{http:// | ||
+ | |||
+ | Wendy, Stephanie and Eug�nie explored creating origami patterns by knotting textiles - building a vocabulary of dots, lines, squares, triangles | ||
+ | |||
+ | The group observed the difference in dimensionality between different materials - sown fabric produced 2 1/2 D, fabric and wood can be reversed from 2d to 3d and back again, while steamed organza patterns always stay 3D. | ||
+ | |||
+ | In addition to origami textiles, Wendy and Stephanie created crocheted hyperbolic sausages that they saw as inspirations for folding and origami books, both in paper and in textile. | ||
+ | |||
+ | Eug�nie works together with dancers and is interested in making folds that can follow joints. Wendy will joing her from a Dance & Technology angle - thinking about making completely fabric sensors. The origami folds might help creating a third dimension in a fabric that moves on the body of a dancer. They will continue exploring different materials and colours to exaggerate the movement. | ||
+ | |||
+ | == Ascii weaving == | ||
+ | |||
+ | |||
+ | Dave Griffiths created little programs to create patterns that he would weave in textiles. The program starts with a rule and makes a sequence: e.g. when you encounter a yellow yarn, replace it with a sequence green, yellow, yellow, green. While Dave was weaving from command line, the computer was predicting what the pattern would look like in ascii code. The challenge was to see if the real weave matched with the ascii weave. The first prototype was made in plain weave, but adding more rules would help make something approaching a jacquard. | ||
+ | |||
+ | {{http:// | ||
+ | {{http:// | ||
+ | |||
+ | See more detail here: | ||
+ | [[http:// | ||
+ | [[http:// | ||
+ | |||
+ | ==== Conclusion: what happens when you bring maths & textiles together? ==== | ||
+ | |||
+ | |||
+ | == A few reactions from participants == | ||
+ | |||
+ | * The combination of textile and mathematics is very relevant - it clarifies some of the more abstract ideas in science and programming | ||
+ | * Learning how to make the turk's head was a revelation | ||
+ | * It was valuable to look at braiding more in detail and understand topological complexity in the real world (e.g.), rather than just abstractions | ||
+ | * Putting the code in textile - creating information inside the weaves, rather than on it. I'm reminded of threads and fibres as communication systems of the ancient Inkas: | ||
+ | * Self referential weaves as educational materials - showing what the rule set was that created them. | ||
+ | * Working with textiles informed me to make different forms in generative graphics | ||
+ | |||
+ | |||
+ | == AHA moments == | ||
+ | |||
+ | * memory shape fabrics | ||
+ | * calculation for the cube suspensions - understanding maths does help! | ||
+ | * understanding that variations are not endless and knowing that it is possible to know them all | ||
+ | * using a combination of fabric and wood for shelters, waterproof textile hinges is genious - Pieter' | ||
+ | * i have more of an understanding about algorithmic design - reducing a method to something quite simple - short circuiting trial and error, finding productive directions more quickly and more clearly | ||
+ | * finding a new way of working - not only trial and error, not only abstractions, | ||
+ | * the saussage machine is a curiosity, it was great figuring out how it works | ||
+ | * 3 dimensionality of knots & hyperbolic planes (crocheting: | ||
+ | * Force is not necessarily useful for hyperbolic crocheting | ||
+ | * This was a workshop with a high fun factor, so many things popped up suddenly and surprisingly | ||
+ | * the workshop made me specialise in being Martaque | ||
+ | * i hear a lot of music here, which is good! | ||
+ | * Annabel Meuleman' | ||
+ | |||
+ | {{http:// | ||
+ | {{http:// | ||
+ | |||
+ | ---- | ||
+ | |||
+ | ==== notes & miscellanea ==== | ||
+ | |||
+ | * book: http:// | ||
+ | * book: origami tesselations by Eric Gjerde http:// | ||
+ | * blogpost on knitting and debian > http:// | ||
+ | * on miat > http:// | ||
+ | * computational couture > http:// | ||
+ | * hexagonal paper dress > http:// | ||
+ | * http:// | ||
+ | |||
Ideas: | Ideas: | ||
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* Parametrisation in textiles and sizes (related strongly to notation) | * Parametrisation in textiles and sizes (related strongly to notation) | ||
* Biology and mathematics? | * Biology and mathematics? | ||
- | * Knotting patterns that give emergent 3D structures (including [[hyperbolic geometry]]): e.g. crochet-> | + | * Knotting patterns that give emergent 3D structures (including [[hyperbolic_geometry]]): e.g. crochet-> |
- | * Given a pattern, what is the simplest algorithm to make it -> Kolmogorov [[Complexity]] | + | * Given a pattern, what is the simplest algorithm to make it -> Kolmogorov [[complexity]] |
* Challenge: "How to learn some (nontrivial) mathematics through textiles" | * Challenge: "How to learn some (nontrivial) mathematics through textiles" | ||
* large scale 3D weaving - space filling cords. | * large scale 3D weaving - space filling cords. | ||
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* Moebius Strip knitting | * Moebius Strip knitting | ||
* Question: are Celtic knot patterns related to Turk's Head knots? | * Question: are Celtic knot patterns related to Turk's Head knots? | ||
- | |||
- | Next steps: | ||
- | |||
- | * Tim checks through Bridges conferences for relevant maths / arts / crafts crossover | ||
- | * Lina checks prices of ropes in Brussels | ||
- | * We brainstorm on this page | ||
- | * Need a single paragraph | ||
Resources | Resources | ||
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* The American Mathematical Society has a series of meetings: [[http:// | * The American Mathematical Society has a series of meetings: [[http:// | ||
- | Brainstorm: | + | misc: |
* Brunnian rings: [[http:// | * Brunnian rings: [[http:// | ||
- | === Materials required (as of 20110711) === | + | == Notes from dave == |
- | + | ||
- | * **DONE** 6 coils of ropes different colours and different sizes, for example: http:// | + | |
- | * **DONE** 2 x Nylon Rope - 8mm x 220m http:// | + | |
- | * **DONE** 2 x Nylon Rope - 6mm x 220m http:// | + | |
- | * **DONE** 1 x Nylon Rope - 16mm x 220m http:// | + | |
- | * 6 rolls of large paper ( here I find 10 metre long rolls of 150 width), 220 g if possible | + | |
- | * 10 paint rollers (as in rolls to paint walls, but don’t worry we are not planning to do that!) | + | |
- | * Cutters, metal rulers ( ~1 metre), scissors, pens (we assume you have some of that already?) | + | |
- | * Colored masking tape | + | |
- | * 15 Crochet hooks and crochet yarns. | + | |
- | + | ||
- | === Notes from dave === | + | |
* [[algorithmic_textiles]] & [[http:// | * [[algorithmic_textiles]] & [[http:// | ||
* requests: small frame loom + yarn | * requests: small frame loom + yarn | ||