[HN Gopher] First shape found that can't pass through itself
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       First shape found that can't pass through itself
        
       Author : fleahunter
       Score  : 154 points
       Date   : 2025-10-24 14:12 UTC (8 hours ago)
        
 (HTM) web link (www.quantamagazine.org)
 (TXT) w3m dump (www.quantamagazine.org)
        
       | ratelimitsteve wrote:
       | it intuitively feels impossible because it sounds like the
       | definition of "can pass through itself" is really "has at least
       | one orientation where all of the sides of one instance are at
       | most as long as all of the sides of the other instance" and then
       | however you define an orientation an instance of a shape in
       | orientation X should be able to pass through an instance of the
       | same shape and size in the same orientation
        
         | hyperhello wrote:
         | Yes, and when you think of it that way, it sounds like a
         | partial ordering with a base case. If angle A can pass through
         | angle B, and angle B can pass through angle C...
        
         | strbean wrote:
         | The criteria is "pass through itself without cutting in half".
         | Presumably that extends to "without deleting the object
         | entirely", which is what would happen to pass through in the
         | same orientation.
        
           | jibal wrote:
           | Notably, a sphere is non-Rupert (but a soccer ball is not ...
           | it can pass through a tiny fringe).
        
         | jibal wrote:
         | My intuition is very different (and happens to fit reality).
         | Note that convex polyhedra can have asymmetries.
        
       | king_geedorah wrote:
       | Rather interesting solution to the problem. You can't test every
       | possibility, so you pick one and get to rule out a bunch of other
       | ones in the same region provided you can determine some other
       | quality of that (non) solution.
       | 
       | I watched a pretty neat video[0] on the topic of ruperts /
       | noperts a few weeks ago, which is a rather fun coincidence ahead
       | of this advancement.
       | 
       | [0] https://www.youtube.com/watch?v=QH4MviUE0_s
        
         | anyfoo wrote:
         | Not _that_ coincidental. tom7 is mentioned in the article
         | itself, and in his video 's heartbreaking conclusion, he
         | mentions the work presented in the article at the end. tom7 was
         | working on proving the same thing!
        
       | moralestapia wrote:
       | >Prince Rupert of the Rhine, a 17th-century army officer, naval
       | commander, colonial governor and gentleman scientist, won a bet
       | about whether it's possible to pass a cube through another.
       | 
       | Based.
        
         | greenchair wrote:
         | I aspire to be a gentleman scientist!
        
           | dinkblam wrote:
           | I conspire to be a colonial governor!
        
             | AaronAPU wrote:
             | I'd be happy just winning a bet!
        
       | mrguyorama wrote:
       | Fans of "Tom7" should be very recently familiar with this!
       | 
       | He released a video about the Ruperts problems and his attempt to
       | find a Nopert on just Sept 16th!
       | 
       | https://www.youtube.com/watch?v=QH4MviUE0_s
       | 
       | With this and the Knotting conjecture being disproven, there are
       | have some really interesting math developments just recently!
       | 
       | Tom regularly releases wonderful videos to go with SIGBOVIK
       | papers about fun and interesting topics, or even just interesting
       | narratives of personal projects. He has that weird kind of
       | computer comedy that you also get from like Foone, the kind where
       | making computers do weird things that don't make sense is fun,
       | the kind where a waterproof RJ45 to HDMI adapter (passive)
       | tickles that odd part of your brain.
        
         | chaps wrote:
         | His videos are some of the best out there. Super funny, depth
         | that's _rarely_ seen elsewhere, and a refreshingly scrappy
         | academic approach. His video on kerning being an incomputable
         | problem is filled with rigor and worth a watch.
         | 
         | Highly recommend all of his videos!
        
       | biot wrote:
       | Presumably a simple sphere would trivially qualify as being
       | unable to pass through itself.
        
         | smokel wrote:
         | The puzzle applies only to convex polyhedra.
        
         | LostMyLogin wrote:
         | A sphere is not a convex polyhedron
        
           | guelo wrote:
           | At the limit of faces they are.
        
             | jibal wrote:
             | A sphere has no faces so it's not a convex poloyhedron.
        
             | teraflop wrote:
             | Sure, and pi is the limit of a sequence of rational
             | numbers, but lots of properties that hold for rational
             | numbers don't hold for pi.
        
               | guelo wrote:
               | As you approach sphere you lose Rupertness.
        
       | jmkd wrote:
       | Layperson question: aren't the nopert candidates just
       | increasingly close to being spheres, which cannot have Rupert
       | tunnels?
        
         | tmiku wrote:
         | Yes, they get visually more sphere-like as more faces are
         | added. But spheres are obviously/trivially non-Rupert, while
         | the question of whether a convex polyhedron can be non-Rupert
         | is more interesting.
        
         | gitaarik wrote:
         | Would be interesting to see how much sides you can keep adding
         | before the shape can't pass through itself. Or maybe you can
         | indefinely keep passing them through, occasionally encountering
         | noperts. Or maybe the noperts gradually increase, eventually
         | making the no-nopperts harder to find. Who knows, let's find
         | out.
        
         | maplant wrote:
         | But importantly, they're NOT!
        
       | dnw wrote:
       | > Noperthedron (after "Nopert," a coinage by Murphy that combines
       | "Rupert" and "nope").
       | 
       | A good sense of humor to go with the math.
        
         | 867-5309 wrote:
         | this logical falsehood annoyed me since _nopert_ is no+Rupert,
         | whereas nope+Rupert would in fact be _nopepert_
        
           | strbean wrote:
           | That's not how portmanteaus work.
        
             | gary_0 wrote:
             | https://xkcd.com/739/
        
             | stephenlf wrote:
             | Tom7 also has a couple of videos about portmanteaus
        
           | pharrington wrote:
           | Portmanton't.
        
           | burkaman wrote:
           | The coiner gets to pick the combination that sounds the best,
           | there is no correct choice. We could have gotten breakfunch
           | and mototel, but some person or collection of people decided
           | that brunch and motel work better.
        
           | jibal wrote:
           | Perhaps you should review what "logical falsehood" means,
           | because that's not one.
        
         | pinkmuffinere wrote:
         | Tom7 is one of my favorite people, he is hilarious, has an
         | amazing technical depth, and so much whimsy to go along with
         | it. I'll proselytize for him all day!
         | 
         | relevant video: https://www.youtube.com/watch?v=QH4MviUE0_s
         | 
         | less relevant, but I think my favorite:
         | https://www.youtube.com/watch?v=ar9WRwCiSr0
        
       | tempestn wrote:
       | I really like the level of detail in this article. It was enough
       | that I felt like I could get an actual understanding of the work
       | done, but not into such mathematical detail that it was difficult
       | to follow.
        
       | teo_zero wrote:
       | Misleading title. Other shapes have been well known for years,
       | like a sphere. The novelty here is the first _polyhedron_ that
       | can 't pass through itself.
        
         | jibal wrote:
         | _convex_ polyhedron
         | 
         | (but your point about the title is valid)
        
         | cluckindan wrote:
         | A sphere can be approximated by a polyhedron. Somewhat
         | obviously, all such polyhedra would seem to have the Rupert
         | property. This new Nopert seems to differ in one key detail:
         | some of the vertices near the flat top/bottom are at a
         | shallower angle to the vertical axis than the vertices
         | below/above them.
         | 
         | Can you pass the T-shaped tetromino through itself?
        
           | mkl wrote:
           | The T-shaped tetromino is not convex, so not part of the
           | conjecture. There are many nonconvex shapes that don't have
           | the Rupert property.
        
       | stephenlf wrote:
       | He did it!!
        
       | cyode wrote:
       | I'd love to have an in-print magazine with articles of this
       | subject matter and level of detail. Especially for older
       | kids...accessible and interesting content without all the
       | internet's distractions.
       | 
       | Googling says Quanta is online only. Anyone know of similar
       | publications that print?
        
       | TheOtherHobbes wrote:
       | Prince Rupert was an incredibly interesting character. This
       | problem was a minor footnote in an impressively rich life.
        
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