Talk:2781: The Six Platonic Solids

Does he know about Homestar Runner? 172.70.131.137 06:02, 27 May 2023 (UTC)

Yes. http://www.hrwiki.org/wiki/Webcomic_Sightings#xkcd Trogdor147 (talk) 01:07, 29 May 2023 (UTC)

Why Jorb? Only thing I can find is Jorb on wikitionary just meaning spelling of bad pronunciation of Job. And yes the episode of Homestar Runner A Jorb Well Done comes up. Also this episode that is the top meaning of jorb on Urban dictionary. Would really like there to a better idea than that Plato did a great Jorb making a sixth solid to rule the mathematicians. --Kynde (talk) 07:18, 27 May 2023 (UTC)

I agree. We should ask for our money back. -- Dtgriscom (talk) 17:19, 27 May 2023 (UTC)

What if there're much more of them, like a Ď̩̰odec̭ähedron, but our minds can't properly comprehend their shape?

There are a bunch of other regular polyhedra besides the Platonic solids. Most notable are the triangular, square, and hexagonal tilings (which are planar and infinite) and the four Kepler-Poinsot polyedra (which are nonconvex). And there are dozens more if you don't require faces to be planar. 172.70.178.234 09:44, 27 May 2023 (UTC)

See https://youtu.be/_hjRvZYkAgA for an overview of every regular polyhedron in Euclidean 3-space. 162.158.146.40 09:59, 27 May 2023 (UTC)

I had never seen this channel before, and I'd very much like to thank you for introducing it to me. 162.158.167.8 21:39, 29 May 2023 (UTC)

Some of the proofs of the theorem that there are exactly five platonic solids do not require our minds to "comprehend their shape", because they only rely on their algebrical properties. In fact, the Group theory proof works in any dimension (≥3), despite our minds being very bad at picturing what stuff looks like in higher dimensions. In fact, it's a bit of the opposite: lower dimensions (2 and 3) are "special cases", because all other dimensions have exactly 6 such platonic solids. Jthulhu (talk) 15:41, 27 May 2023 (UTC)

I think this is a reference to how the Utah Teapot is nicknamed “the sixth Platonic solid” due to its presence beside real Platonic solids in demonstrations of 33D rendering. 172.68.118.133 08:52, 27 May 2023 (UTC)

...yeah, but you need to render that 33D shape on a proper 32D monitor, ideally, because even on a 31D monitor the two different forced perspectives/projections you need to collapse the extra dimensions down tend to look confusing. 172.70.162.229 10:46, 27 May 2023 (UTC) *insert winky-face as necessary*

Thanks, that predates my claim in https://arxiv.org/abs/2103.00090, so I won’t claim priority:

‘By this conception, the claim that there is a Russell Set is simply wishful thinking, analogous to wanting the phrase “sixth Platonic solid” to have a referent, while not actually intuiting which shape this might be.’

— FlashSheridan (talk) 12:33, 31 May 2023 (UTC)

Should we think about Jorb, perhaps, as "J orb," which might lead us to think about (i,j) coordinates, i.e. notational systems where j is the square root of minus 1? (blah blah engineering vs. mathematics, what does i mean, &c., &c., &c.) Maybe not! JohnHawkinson (talk) 10:41, 27 May 2023 (UTC)

When I naively imagine further platonic solids, my approach to cheating is usually to imagine arbitrarily non-euclidean space. It’s somewhat pleasant that the jorb looks a little like that —- it’s only platonic if the coordinate system it’s in bends and stretches to make it so. I imagine the name and depiction are simply to be intentionslkynvague or confusing about what it actually is. It’s a lot harder to do real innovation nowadays and tasks like inventing a jorb can readily crop up to nerds (the nerd snipe kind) who are looking for sufficiently hard and harmless puzzles. A sixth platonic solid seems to mostly happen outside the norms of what people usually consider in a pretty significant way. 162.158.155.99 02:30, 28 May 2023 (UTC)

I asked GPT-4, "Why could Sauron control the Nazgûl when not in possession of the One Ring?" The response:

Sauron was able to control the Nazgûl even when he didn't possess the One Ring because of the nature of the rings they received and the relationship these rings had with the One Ring.

Sauron, disguised as Annatar, the "Lord of Gifts," helped the Elven smiths of Eregion, led by Celebrimbor, forge the Rings of Power. Unknown to the Elves, Sauron had instructed them to forge the rings in such a way that they could be controlled by one master ring - the One Ring. He secretly forged the One Ring in the fires of Mount Doom, uttering the famous verse: "One ring to rule them all, one ring to find them, one ring to bring them all and in the darkness bind them."

When he gave the nine rings to Men, these rings corrupted them over time and turned them into the Nazgûl, also known as the Ringwraiths. Because these nine rings were still under the influence of the One Ring, Sauron was able to control the Nazgûl even when he did not possess the One Ring himself. The One Ring's power was inherent and didn't need physical proximity to exert control. The Nazgûl were bound to the will of Sauron as their wills were dominated by their rings, which were in turn dominated by the One Ring.

The link and dominance were so strong that even when the One Ring was lost, the Nazgûl remained under Sauron's control. It's also worth noting that Sauron held the Nine Rings the Nazgûl originally received, which could also contribute to his ability to control them.

It's a complex network of influence and control established by Sauron, making him a powerful Dark Lord even in the absence of his master ring.

Well. I'm glad someone something understands that. Lol. 172.69.22.145 06:11, 28 May 2023 (UTC)

Looks suspiciously like a bicycle saddle to me.  And as anyone who's parked their backside on one for any distance or time, it is DEFINITELY a solid. RAGBRAIvet (talk) 07:25, 28 May 2023 (UTC)

(Well, there's all kinds of saddles, and the golden era of leather saddles were actually not that bad (that link states a 10 year guarantee for the current output, but I personally know of a couple used regularly for 60+years and were still doing well), though with the advent of more synthesised materials they've had to go creative with the texture/covering to give it back the 'give'. Which no doubt makes more an 'impression' on the more modern saddle purchaser, in more ways than one.)

Reminds me of one of the more abstract 'elemental' Henry Moore pieces, or possibly one of his contemporaries/'inspired-by's. And you could certainly find painters and other art-form creators who have gone into 'abstract blob' shapes, either to represent something real in a novel way or to deliberately represent nothing real at all, and I suspect that's Randall's aim... (Like "xkcd" made to not look enough like anything else, or so intended). It certainly shows no sign of any symmetry at all. 172.70.86.32 12:29, 28 May 2023 (UTC)

Based on the shape, ribbing, and a different definition of "platonic" I think this could be referring to the Roman artefact that was recently re-classified as a dildo. Platonic solid? 172.70.111.111 16:06, 28 May 2023 (UTC)

Not gonna lie, this feels like a Cow Tools comic to me. Sometimes mathematicians discover new things, wouldn't it be weird if they discovered something impossible? End of joke. Everything else regarding the shape and name is an inkblot test (until the title text which is actually a LOTR reference of course). 172.70.82.59 17:04, 28 May 2023 (UTC)

Is it worth mentioning that the dodecahedron and isocahedron have their names switched? C.h.ninnymuggins (talk) 21:00, 28 May 2023 (UTC)

It would be if they were (a common error), but... they aren't. (See here.) 172.69.79.196 21:33, 28 May 2023 (UTC)

Ok whoever added that jan misali link that's super cool of you nice 172.71.82.147 03:50, 29 May 2023 (UTC)Bumpf

I feel that there's a joke missing here, especially with the LOTR connection made in the alt-text. After all, Plato might have gifted the solids to the mathematicians, but thanks to Gary Gygax, it was the gamers who found a use for them.... 172.70.86.7 06:37, 29 May 2023 (UTC)

Plato did a a great jorb ruling the mathematicians by forging the impossible... plato got a gold star at his job review... was that really it?--4til7 (talk) 20:33, 29 May 2023 (UTC)

I kind of feel sorry for the platonic solids. Condemned to the friend zone for eternity; or at least until the end of this universe. These Are Not The Comments You Are Looking For (talk) 22:54, 29 May 2023 (UTC)

You've all been nerd sniped. 172.70.42.43

Also the Gömböc comes to mind from the name, the shape and the novelty of Jorb. 162.158.182.115 18:51, 2 June 2023 (UTC)

Added link to "Gömböc", as that is immediately what I thought of when seeing this comic. Randall's Jorb looks designed to have Gomboc-like properties: if starting on the long thin facet seen on the top edge, it would be gently pulled down by the large round egg-like "end" and then presumably roll onto one side or the other i.e. rotating around its long axis until reaching the position shown. If the Jorb were indeed a mono-monostatic shape, then like the known Gömböc design it would be a "polyhedron" with one (albeit curved) "facet", and like the Platonic solids it can rest on any one of its facets, trivially true as there is only one facet. Mrob27 (talk) 05:50, 12 June 2023 (UTC)

So, I think this explanation is under-focused on the actual joke. The core humor here is the idea that "Platonic Solid" means "Solids Plato made" and not regular polyhedra at all. "Mathmetitions long believed there were five platonic solids, all regular polyhedra" So the jorb is explicitly a platonic solid that is not a regular polyhedra. Our explanation should point out then, things like the fact that the platonic solids predate Plato.

I wonder if this is relevant: http://www.hrwiki.org/wiki/A_Jorb_Well_Done