[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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