[HN Gopher] Mathematicians discover new class of shape seen thro...
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Mathematicians discover new class of shape seen throughout nature
Author : pseudolus
Score : 242 points
Date : 2024-09-22 17:56 UTC (1 days ago)
(HTM) web link (www.nature.com)
(TXT) w3m dump (www.nature.com)
| eh_why_not wrote:
| Looking 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/pgae311/77546...
| crazygringo wrote:
| It'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 wrote:
| Reminds 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 wrote:
| The Nature empire is just another click bait factory.
| dotancohen wrote:
| Honestly, 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 wrote:
| Maybe 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 wrote:
| It'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-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 wrote:
| >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 wrote:
| That 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
| mhandley wrote:
| I 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 wrote:
| They aren't 90deg 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 wrote:
| The 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 wrote:
| I was thinking about how incredibly funny it would be if it was
| something mundane like the cube.
| PaulDavisThe1st wrote:
| Taken from the ancient tongue twister: soft cells and seashells
| by the sea shore.
| mmooss wrote:
| > 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 wrote:
| The glaziers cut corners by not cutting the corners off
| adolph wrote:
| Would it shatter your hypothesis to reframe the problem as
| extrusion limitations?
| mmooss wrote:
| I 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 wrote:
| A 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 wrote:
| You may also like: lattice.
| mmooss wrote:
| Thank you! I do.
|
| https://mathworld.wolfram.com/PointLattice.html
| dexwiz wrote:
| Tilings cover an entire plane with no gaps or overlaps. Opposed
| to packings which may leave gaps.
| itronitron wrote:
| I may be wrong but I think 'packing' may allow the shapes to
| vary in size.
| abetusk wrote:
| Some 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.
| hinkley wrote:
| Tessellation is more clever tiling. In general you get fairly
| simple concavities in tiling, like darts or deltas, whereas
| tessellation typically has compound inclusions that require
| being assembled from outside the plane.
|
| In the real world you can usually push tiles into place, but
| tessellated objects have to be dropped in place from above,
| like puzzle pieces. Or I suppose grown in place if it's
| organic.
| jedisct1 wrote:
| Could that have applications to 3D printing?
| OutOfHere wrote:
| In 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 wrote:
| junji ito uzumaki
| latexr wrote:
| Comments 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
| imp0cat wrote:
| Trailer: https://www.youtube.com/watch?v=2ivmweJQaco
| flembat wrote:
| I would like to see this new knowlege used to generate tiled
| desktop wallpaper. Also does this tiling seem like a form of
| compression?
| CRConrad wrote:
| Not that this is all that new, IIRC. Didn't StandUpMaths on
| YouTube have a video on this months (at least) ago?
| Alifatisk wrote:
| Yeah, but he was covering a new shaped called Scutoid.
| latexr wrote:
| 6 years ago.
|
| https://www.youtube.com/watch?v=2_NZ1ql8B8Y
| Kunsang wrote:
| 43 years ago https://www.youtube.com/watch?v=XZVpR3Pk-r8
| ganzuul wrote:
| Hysteresis.
| wizardforhire wrote:
| Fwiw 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 wrote:
| Took the mathematicians only 43 years to discover Soft Cell...
| josefritzishere wrote:
| Mathmatician discovers thing we already know to exist. To quote
| the meme "I do not think that word means what you think it
| means."
| aj7 wrote:
| Would 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 wrote:
| I'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 wrote:
| This 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 wrote:
| I 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.
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