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Mathematicians discover new class of shape seen throughout nature
- eh_why_not 2y agoLooking past Nature magazine's unnecessarily fancy/clickbait title, the original work's [0] title is "Soft cells and the geometry of seashells". [0] https://academic.oup.com/pnasnexus/article/3/9/pgae311/7754698?login=false https://academic.oup.com/pnasnexus/article/3/9/pgae311/77546...
- crazygringo 2y agoIt's also funny that while the title uses the baity word "discover", the very first paragraph merely claims the mathematicians "described" the shapes. I know that in newspapers and magazines, editors write headlines rather than authors to get clicks, regardless of accuracy. I would have thought Nature would try to be better though...
- excalibur 2y agoReminds me of those stupid Lipozene ads circa 2012: "Researchers have now discovered a capsule that helps reduce this 'body fat', and control your weight."
- chairmansteve 2y agoThe Nature empire is just another click bait factory.
- dotancohen 2y agoHonestly, the observation seems novel enough to me that the term discovery is appropriate. We say that Darwin discovered evolution and Newton discovered gravity. Both these phenomenon were previously observed but it took a genius to consider what they were in essence. Same with this work - look at the photographs of the mollusk, river, and onion. I would have never connected those dots.
- atworkc 2y agoMaybe a tad philosophical/pedantic but many mathematicians follow the "Mathematical realism" approach and would say that any new mathematics be it simply describing existing shapes is actually a form of discovery in the world of mathematics
- A_D_E_P_T 2y agoIt's pretty egregious clickbait for Nature -- more along the lines of what I'd expect from Forbes or a similar outfit. I mean, the title is saying that they "discovered" the "new class of shape" featured in this old kitchen tile: https://www.contemporist.com/reasons-why-you-should-get-creative-with-fish-scale-tiles/ https://www.contemporist.com/reasons-why-you-should-get-crea... Come on, now. The Egyptians, Greeks, and Romans were surely aware of it, and used similar pointed/curved and lenticular shapes in art and design.
- JackFr 2y ago>Domokos and colleagues devised an algorithm for smoothly converting geometric tiles — either 2D polygons or 3D polyhedra, like the bubbles of a foam — into soft cells, and explored the range of possible shapes these rules permit. In 2D, the options are fairly limited: all tiles must have at least two cusp-like corners. (Emphasis mine) Am I reading that wrong or are the kitchen tiles in the images impossible based on the statement above
- A_D_E_P_T 2y agoThat shape has three cusp-like corners -- one at each sharp point, with smooth curves (convex/concave) between them. This satisfies the "at least two" condition. The even simpler "lemon" is an even more egregious example, as it satisfies the conditions in two and three dimensions and yet is rather old and well-defined: https://mathworld.wolfram.com/LemonSurface.html https://mathworld.wolfram.com/LemonSurface.html
- mhandley 2y agoI think that tile shape has one cusp-like corner and two ~90-degree corners. Thus it's not a complete transformation of a polygon into a soft cell, and hence the "at least two" rule doesn't apply.
- A_D_E_P_T 2y agoThey aren't 90° corners -- and in any case it would be simple to modify the angle of those corners and keep the shape basically (or nearly) the same. Also the plain 2D lemon/lozenge/lentil satisfies all conditions.
- gradschoolfail 2y agoThe actual discovery seems to be buried in the midsection >…suspected that the actual 3D chamber had no corners at all. “That sounded unbelievable,” says Domokos. “But later we found that she was right.” Fwiw its also not obvious from the main paper, you have to look at fig 7 d-e for an idea So in this case, i’d place some of the blame on the mathematicians themselves for failure to properly follow up on the bait. (But nature shall not be absolved from holding them to a higher standard)
- kalium-xyz 2y agoI was thinking about how incredibly funny it would be if it was something mundane like the cube.
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- PaulDavisThe1st 2y agoTaken from the ancient tongue twister: soft cells and seashells by the sea shore.
- mmooss 2y ago> The Heydar Aliyev Center in Baku was designed architect Zaha Hadid, whose buildings use soft cells to avoid or minimize corners. Its large glass front formed by the concrete 'soft cell' is tiled, sadly, with rectangles.
- griffzhowl 2y agoThe glaziers cut corners by not cutting the corners off
- adolph 2y agoWould it shatter your hypothesis to reframe the problem as extrusion limitations?
- mmooss 2y agoI should know this in order to post on HN, but I hope someone will explain: In mathematics, what is the difference between a grid, tiling, packing, and tessellation? I've read several sources without forming a precise answer. My best guess is that a grid is about the lines formed by and forming tiling polygons; tiling is about polygons (assuming 2-d) filling a space; packing is filling a space with a defined polygon (again if 2-d) whether or not it's filled completely; and tessellation is a form of tiling that requires some kind of periodicity? Edit: I forgot 'packing'!
- thechao 2y agoA grid is a set of points, described by a basis. A tiling is like puzzle pieces, but with a fixed number of piece "shapes". A packing is a way to stuff a set of things into a space. Tilings and packings are related, but the subfields are asking different questions.
- smokel 2y agoYou may also like: lattice.
- mmooss 2y agoThank you! I do. https://mathworld.wolfram.com/PointLattice.html https://mathworld.wolfram.com/PointLattice.html
- dexwiz 2y agoTilings cover an entire plane with no gaps or overlaps. Opposed to packings which may leave gaps.
- itronitron 2y agoI may be wrong but I think 'packing' may allow the shapes to vary in size.
- abetusk 2y agoSome of these terms are pretty general and their usage will depend on the user and context. I'll try to define what I think are the most appropriate and common usages of each. Grid - usually a regular D-dimensional boxes that are packed, axis aligned. Sometimes used synonymously with a set of points that are also regularly placed and axis aligned. I've used this to describe a (finite) rectangular cuboid (in 3D) but could just as easily be used to describe an infinite set of boxes. As in "Label each cell in the grid an alternating color of red or blue". Tiling - A covering of some D-dimensional space from a (finite) set of smaller tiles, with no overlap and no gaps. I've used this to describe higher dimensional spaces but is often used for 2D. As in "A set of Penrose tiles can be used in a plane tiling". Packing - Placing a (finite) set of smaller geometric elements into a large area such that the geometry doesn't overlap but gaps are allow. The larger area that can be be finite or infinite. The dimension can be arbitrary. This is often used in context of trying to minimize the gaps within the area being packed. As in "Randomely placing 3D oblong spheroids (aka 'M&Ms') in a box of side length L will yield a sub-optimal packing. Introducing gravity, friction and 'shaking' the box for some amount of time will yield a better packing" Tesselation - A synonym for tiling. A grid is a tiling. For example a 2d grid is a tiling/tesselation of the plane by boxes.
- jedisct1 2y agoCould that have applications to 3D printing?
- OutOfHere 2y agoIn 3D printing you need pieces that can fit together into each other, not merely tile together. It should however be quite interesting to extend the soft cell shapes to also fit together while preserving softness. Perhaps it is possible that the shown saddle-like shape in Fig 6, Panel 4 of the PNAS Nexus article can serve this purpose, but it is not clear how.
- rinvi 2y agojunji ito uzumaki
- latexr 2y agoComments on HN are expected to have a bit more substance. Most people will have no idea what you’re on about. An alternative: > This reminded me of Junji Ito’s Uzumaki, a horror manga where a town is cursed by spirals. It can get gruesome. A short anime adaptation is about to come out. > https://en.wikipedia.org/wiki/Uzumaki https://en.wikipedia.org/wiki/Uzumaki
- imp0cat 2y agoTrailer: https://www.youtube.com/watch?v=2ivmweJQaco https://www.youtube.com/watch?v=2ivmweJQaco
- flembat 2y agoI would like to see this new knowlege used to generate tiled desktop wallpaper. Also does this tiling seem like a form of compression?
- CRConrad 2y agoNot that this is all that new, IIRC. Didn't StandUpMaths on YouTube have a video on this months (at least) ago?
- Alifatisk 2y agoYeah, but he was covering a new shaped called Scutoid.
- latexr 2y ago6 years ago. https://www.youtube.com/watch?v=2_NZ1ql8B8Y https://www.youtube.com/watch?v=2_NZ1ql8B8Y
- Kunsang 2y ago43 years ago https://www.youtube.com/watch?v=XZVpR3Pk-r8 https://www.youtube.com/watch?v=XZVpR3Pk-r8
- CRConrad 2y agoYeah, I thought that was the shape in question (hadn't read ther article yet). The article -- either OP, or the one linked in one of the first comments (at the time I clicked) -- had a video banner with scutoids across the top.
- ganzuul 2y agoHysteresis.
- wizardforhire 2y agoFwiw and tangent warning: Soft cell is a great band. More pertinent: My niece was asking about my Conus Textile shell last night, which led into an engaging discussion on cellular automata. Going from two dimensions down to one, was able to bring it back to the shell and the lights when on for her! It was great. I hit an impasse when extrapolating to cells which I had to brush over with generalities. This paper couldn’t have come at a better time for the sake of one childs curiosity. I can’t wait to share.
- TomK32 2y agoTook the mathematicians only 43 years to discover Soft Cell...
- vouaobrasil 2y ago[flagged]
- galaxys 2y agoNot the same people
- vouaobrasil 2y agoIt doesn't matter. We are all responsible for propagating a respectful attitude towards nature.
- afro88 2y agoConsider that this work may contribute to us being able to take better care of nature. Live our lives with a lower negative impact. Sometimes study or work tangential to a goal leads to greater discovery in service to the goal.
- vouaobrasil 2y agoWe already know clearly what to do, and we are not doing it.
- the_other 2y agoExtracting energy from the environment is a prerequisite for living. “Extracting” information must be among the lowest energy level consumptions. In many cases it’s a (lossy) copy action rather than a subtraction.
- vouaobrasil 2y agoThe point is not quantitative, but philosophical. The attitude is the problem, not the absolute cost. The attitude is what propagates more serious problems, and that is what engineer types often fail to understand.
- josefritzishere 2y agoMathmatician discovers thing we already know to exist. To quote the meme "I do not think that word means what you think it means."
- aj7 2y agoWould be very interesting to study classical stress analysis in compositions of these shapes subject to external loads. Not to mention vibrational analysis and the forms of wave functions.
- taeric 2y agoI'm somewhat intrigued by the idea that these are fully new. I had thought the general view was that "sharp edges" are not common in nature. The idea being that sharp edges are the result of the simplifications that go into our notation and reasoning tools. Much like how right angles are seen as ideals, not necessarily something that appears in nature.
- OJFord 2y agoThis reminds me of the line in A Beautiful Mind: > You know, there could be a mathematical explanation for how bad that tie is. It's fascinating to me (as a non-mathematician) the breadth of what's interesting in mathematics. e.g. here obviously you could have some equation to describe such a shape if you needed it to model a building roof or something, but more than that it's actually apparently useful to mathematicians to 'learn from nature' etc. in the reverse, drawing inspiration from such things that then have whatever application in some obscure (perhaps, or to me) corner of mathematical research.
- joshmarlow 2y agoI think it's also interesting that we don't always know the applications for mathematical insights. IIRC, Euler invented graph theory (even the traveling salesman problem) and basically wrote that he knew of no applications for it. Now we know that traveling salesman is equivalent to graph-coloring which is crucial for compliers when assigning efficient register allocation in deeply pipe-lined architectures.
- jhedwards 2y agoThis kind of shape reminds me of the "dot" from Chinese calligraphy. It's a surprisingly complicated shape and kind of tricky to get right, and is the foundation for more complicated strokes. Here's an example of someone doing four large dots: https://youtu.be/sotKqmaiggQ?feature=shared&t=36 https://youtu.be/sotKqmaiggQ?feature=shared&t=36
- JKCalhoun 2y agoI'm kind of more curious as to what procedures or forces of nature cause these shapes. Categorizing the resulting shapes is interesting, but more interesting to me is the why.
- reportgunner 2y agoSurely it must have something to do with physics.
- Inviz 2y agoI wonder if tesselated concave octagon shape is seen anywhere in nature. (https://robertlovespi.net/wp-content/uploads/2016/01/tessoct-radial.png https://robertlovespi.net/wp-content/uploads/2016/01/tessoct...) I built my brand on this shape
- Dban1 2y agodefinitely so in the vast universe
- sugarkjube 2y agoPacman packing?