explain xkcd - User contributions [en]

Talk:2042: Rolle's Theorem

2018-09-08T05:53:28Z

198.41.238.64: What goes up must come down.

Now we wait for https://en.wikipedia.org/wiki/Munroes_theorem. [[Special:Contributions/172.69.54.165|172.69.54.165]] 15:51, 5 September 2018 (UTC)
:Can't wait to see how long it takes to remove the article. [[User:Linker|Linker]] ([[User talk:Linker|talk]]) 17:05, 5 September 2018 (UTC)

:Proposed ideas for Munroe's Law:
::- Any seemingly simple idea will be difficult to prove; the simpler it seems, the harder the proof.
::- Any proof which is discovered by a layperson will have been previously discovered by an expert (or an "expert") in the field.
:[[User:Rajakiit|Raj-a-Kiit]] ([[User talk:Rajakiit|talk]]) 17:57, 5 September 2018 (UTC)
:I do not have the time to do it good, so here a suggestion: Would someone go to the wikipedia page of Rolle's theorem and add a "in popular culture" section? may be a first? Not even "Nash equilibrum" has that :-) [[Special:Contributions/162.158.234.16|162.158.234.16]] 08:13, 6 September 2018 (UTC)
::Speaking of popular culture, there's a (moderately) well known Ballad of Rolle's theorem [https://www.youtube.com/watch?v=S0BXv90MlhA Balada o vete Rolleovej] ("moderately" meaning some people who studied at Faculty of mathematics in Bratislava might have heard (of) it) --[[User:Kventin|Kventin]] ([[User talk:Kventin|talk]]) 07:41, 7 September 2018 (UTC)

I feel like Euclid beat Randall to the punch here, a couple millennia. [[Special:Contributions/162.158.155.146|162.158.155.146]] 16:54, 5 September 2018 (UTC)

I don't see that Thales has proven Randall's theorem. Do not to be confused with {{w|Thales's theorem}}, that's about right angles. Maybe I'm blind or just dumb, but if so it has to be explained with more traceable background. I just believe that this diagonal is so trivial that even the ancient Greeks weren't engaged on a proof. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 21:38, 5 September 2018 (UTC)
* From {{w|Thales|Wikipedia}}: Other quotes from Proclus list more of Thales' mathematical achievements: "They say that Thales was the first to demonstrate that the circle is bisected by the diameter, the cause of the bisection being the unimpeded passage of the straight line through the centre." [[User:Alexei Kopylov|Alexei Kopylov]] ([[User talk:Alexei Kopylov|talk]]) 05:39, 6 September 2018 (UTC)
* On the other hand not all historian believe Proclus. But van der Waerden does: [https://books.google.com/books?id=HK3vCAAAQBAJ&pg=PA88#v=onepage&q&f=false]. [[User:Alexei Kopylov|Alexei Kopylov]] ([[User talk:Alexei Kopylov|talk]]) 05:49, 6 September 2018 (UTC)

'''Rolle's Theorem counterexample?'''

Isn't the TAN(x) function a counterexample to this? Starting at a given point, it rises to infinity, then returns from negative infinity to the same point without ever having a slope of zero. [[Special:Contributions/172.68.58.89|172.68.58.89]] 06:58, 6 September 2018 (UTC)
:TAN(x) isn't differentiable at pi/2, hence the theorem doesn't apply--[[Special:Contributions/162.158.92.40|162.158.92.40]] 07:48, 6 September 2018 (UTC)
::And tan(x) has a slope of 0 at pi, so even if it applied, it wouldn't prove it wrong. A better example would be 1/x, but still invalid. [[User:Fabian42|Fabian42]] ([[User talk:Fabian42|talk]]) 08:01, 6 September 2018 (UTC)
:::Nope: tan(x) has a slope of 1 at pi, and its slope is never less than 1. Of course, that doesn't make it a counterexample. Zetfr 09:17, 6 September 2018 (UTC)

'''Clueless Museum Visitor'''

The math in the comic is well explained, but shouldn't there be something about the "math equivalent of the clueless art museum visitor..." part? Zetfr 09:17, 6 September 2018 (UTC)
: Seconded, all the argument here is about math that isn't even *in* the comic, whereas the bit that confuses me is the cultural metaphor... [[Special:Contributions/162.158.154.235|162.158.154.235]] 07:16, 7 September 2018 (UTC)
: I had a go.[[Special:Contributions/162.158.154.103|162.158.154.103]] 08:35, 7 September 2018 (UTC)

Just so we're on the same page, while the proof of Rolle's theorem is not completely trivial, neither is it difficult by any means. Proving it seems to be a pretty common homework assignment in undergrad math classes, for example, so one might legitimately ask why it deserved to be named. Perhaps it's simply that it's old enough that the methods at the time were crappy, and so modern proofs are much easier. [[Special:Contributions/172.69.22.140|172.69.22.140]]
: It is named because it's a very important theorem in calculus, used to prove many other theorems or results. So when you need to prove something using this property, instead of re-demonstrating it or merely saying "it is well known that..." (which often raises alarm bells in the mind of the reader/corrector), all you have to do is reference Rolle's theorem.[[Special:Contributions/162.158.155.158|162.158.155.158]] 11:08, 6 September 2018 (UTC)
:: It could almost be called "Rolle's lemma". [[Special:Contributions/162.158.154.103|162.158.154.103]] 12:28, 6 September 2018 (UTC)
: When I am teaching Rolle's theorem, I always make it a point to draw the link to reals. Rolle's theorem fails when the output is complex valued. Then you can see for yourself how non-trivial this is. [[Special:Contributions/162.158.165.124|162.158.165.124]] 04:40, 7 September 2018 (UTC)

Has anyone else noted the irony of having a wiki page to explain a comic whose subject is how some things are self-evident? [[User:JamesCurran|JamesCurran]] ([[User talk:JamesCurran|talk]]) 20:13, 6 September 2018 (UTC)

Does the Kepler Conjecture actually belong on that list at the end? Most of the others are "derp" level intuitively obvious and/or essentially tautological on a very basic level, but the Kepler Conjecture couldn't actually be exhaustively proven until machine computation, nor is it intuitively definitive--if you've ever stacked round things into a box you've noticed that it feels like you're wasting a lot of space at the edges. So...? [[User:AtrumMessor|AtrumMessor]] ([[User talk:AtrumMessor|talk]]) 21:37, 6 September 2018 (UTC)
:I would also argue against most of the other examples. Neither the isoperimetric inequality nor the hairy ball theorem are obviously true and their proof is quite a bit more involved than the one of Rolle's theorem. The Jordan curve theorem sounds obvious but then the proof definitely isn't. The parallel postulate isn't even a theorem. The only real good example in the list is the pigeonhole principle.[[Special:Contributions/162.158.91.155|162.158.91.155]] 12:35, 7 September 2018 (UTC)
:I have removed all but that, as it is the only one comparable to Rolle's in simplicity to understand without understanding math. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 14:04, 7 September 2018 (UTC)
::I agree, Randall mentions nothing like that and a simple parallel is enough. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 14:25, 7 September 2018 (UTC)

I also suggest that Fundamental Theorem of Calculus be removed from this list. Firstly, the beginner student, just introduced to derivatives and antiderivatives, will not easily see that antiderivatives are the same as finding areas under curves. Instead, it is only obvious upon hindsight, after instruction. More importantly, a restriction of the FTC to better-behaved spaces shows a far greater insanity: the restricted FTC is a consequence of generalised Stokes's theorem '''applied twice'''. This operation is so highly unintuitive, that one simply cannot claim that this is in any way, shape, or form, trivial. I think that trying to pretend that anything in beginning calculus is obvious to students is just going to alienate them rather than soothe their worries. [[Special:Contributions/162.158.165.124|162.158.165.124]] 04:40, 7 September 2018 (UTC)

:Ehh what? No, FTC restricted to smooth functions is simply a special-case of Stokes' Theorem. This is explained [https://en.wikipedia.org/wiki/Stokes%27_theorem#Introduction here]. I don't even know what you could possibly mean by applying Stokes' theorem twice, in any context. [[User:Zmatt|Zmatt]] ([[User talk:Zmatt|talk]]) 13:23, 7 September 2018 (UTC)

"Munroe's theorem" should definitely refer to the circle thing in the alt text {{unsigned ip|162.158.62.57}}

Since I'm half a mathematician, I did the math. I looked up Rolle's theorem and it uses the theorem of Weierstraß. I looked up the theorem of Weierstraß (better known as extreme value theorem) and it uses the theorem of Bolzano-Weierstraß. I looked up...why am I suddenly reminded of https://xkcd.com/609 ? :-) [[Special:Contributions/141.101.104.71|141.101.104.71]] 08:36, 7 September 2018 (UTC)

What goes up must come down. [[Special:Contributions/198.41.238.64|198.41.238.64]] 05:53, 8 September 2018 (UTC)

Talk:1484: Apollo Speeches

2018-06-18T18:41:52Z

198.41.238.64:

[http://watergate.info/1969/07/20/an-undelivered-nixon-speech.html Speech] for reference[[User:Blawho|Blawho]] ([[User talk:Blawho|talk]]) 06:40, 9 February 2015 (UTC)

Any chance the scenario with extra astronauts coming back is a reference to Scott Card's Xenocide, in the book they find a way for FTL travel but some odd things happen on the first voyage including extra people coming back ([http://en.wikipedia.org/wiki/Xenocide#Outside click if you're not afraid of spoilers])? {{unsigned ip|188.114.98.29}}

The scenario that the spacecraft was sold for scrap might be a reference to the apolo having a fire during a training and trapping the asyronauts inside. {{unsigned ip|173.245.52.127}}

Probably it could also be a reference to Tarkowski's movie "Solaris"? {{unsigned ip|141.101.92.93}}

:: It's also similar to the premise of the comic ''[https://en.wikipedia.org/wiki/The_Chimpanzee_Complex The Chimpanzee Complex]''. Probably just a coincidence, though. – [[User:PhantomLimbic|PhantomLimbic]] ([[User talk:PhantomLimbic|talk]]) 17:06, 9 February 2015 (UTC)

Anyone remember the Saturday Night Live skit with Dana Carvey as Tom Brokaw recording contingency broadcasts reporting on Gerald Ford's death from more and more unlikely circumstances (including one where Brokaw was told to add, "and also, I'm gay", because "If that happens, you don't want another reporter to get the scoop!") [[User:Mwburden|mwburden]] ([[User talk:Mwburden|talk]]) 17:55, 9 February 2015 (UTC)

"there is some corner of another world that is forever mankind" has to be a reference to the Rupert Brooke poem ''The Soldier'', which Safire no doubt knew. It begins "If I should die, think only this of me:/That there's some corner of a foreign field/That is forever England." {{unsigned ip|108.162.246.219}}
:Maybe, but that would not be a reference in the context of the comic, since the first two pages are from the actual speech. -Pennpenn [[Special:Contributions/108.162.250.155|108.162.250.155]] 23:19, 9 February 2015 (UTC)
::Exactly, it's a reference that Safire was making in writing the speech.[[User:Silverpie|Silverpie]] ([[User talk:Silverpie|talk]]) 18:15, 12 February 2015 (UTC)

You know, technically Apollo 11 probably had enough delta-v to make it into Mars orbit - the service module alone had around 2.8 km/s - although I don't know if there was a point in the actual mission where you could have made this work. Nobody would have survived the trip, of course. [[User:Ijkcomputer|Ijkcomputer]] ([[User talk:Ijkcomputer|talk]]) 15:33, 10 February 2015 (UTC)
:According to [http://upload.wikimedia.org/wikipedia/commons/thumb/7/74/Delta-Vs_for_inner_Solar_System.svg/500px-Delta-Vs_for_inner_Solar_System.svg.png this chart] they could have maybe gotten a Mars intercept, but using simple Hohmann transfers, there is no way the Apollo spacecraft would have been able to make Mars orbit. [[Special:Contributions/198.41.243.249|198.41.243.249]] 18:08, 13 April 2015 (UTC)
::They probaply could have preformed an aerocapture to get into Mars orbit (if they had not died on the way there from lack of food, water, heat and oxygen). The landing, however, would have been unsurivable as the parachutes were designed for the much thicker athmosphere of earth. Landing with the Moon lander would probaly also not be possible, as for once it was designed for the much weaker gravity of the moon, and secondly it probaply would have been destroyed on athmospheric entry. And even if they had somehow surived both the trip and the landing, it would have been a one-way-trip. [[Special:Contributions/162.158.88.146|162.158.88.146]] 14:19, 19 September 2017 (UTC)
So, the contigency speech for the capsule killing the President implies that the astronauts survived - would this be even remotely possible? I'm not sure what order of magnitude of velocity or momentum the capsule would have on impact, but I would think water would be a softer landing than a ship(?), and impact with the ship would not be accounted for... Wouldn't it damage the contents of the capsule (kill the astronauts), if not tear the whole thing apart? -- [[User:Brettpeirce|Brettpeirce]] ([[User talk:Brettpeirce|talk]]) 14:28, 16 February 2015 (UTC)
:I think the astronauts would probably actually survive this. Battered and bruised, certainly, possibly even with a few broken bones. But they would be alive. Descent velocity (from what I could figure out via Google) would be roughly 20 km/h to 25 km/h, and an impact at that speed (shown by a very large number of car crashes) is definitely survivable. [[Special:Contributions/198.41.243.249|198.41.243.249]] 18:08, 13 April 2015 (UTC)

As a side comment, "an unholy zeal for recycling programs" is probably the best phrase I've ever read. [[Special:Contributions/108.162.221.117|108.162.221.117]] 13:49, 23 February 2015 (UTC)

There was an incomplete tag on this comment stating that "more in depth discussion is needed". Without a specific point at which the discussion is incomplete, this struck me as too vague and not really solvable (or clear what is even missing). I removed the tag. If someone wants to put it back, please go ahead, although I'd request that a more specific reason and/or description of what part of the explanation is lacking be given. [[User:Djbrasier|Djbrasier]] ([[User talk:Djbrasier|talk]]) 13:53, 13 March 2015 (UTC)

Regarding being sold for scrap, note that the Eiffel Tower was sold for scrap, not once but twice! ([http://en.wikipedia.org/wiki/Victor_Lustig]) {{unsigned|Jorgbrow}}

I was thinking, maybe the last one is a joke on how notorious Nixon got in the later years? Like, in that alternate universe, he would've been remembered not as the perpetrator of a conspiracy, but rather as a martyr of humanity's advancement? [[Special:Contributions/141.101.81.87|141.101.81.87]] 14:28, 9 February 2016 (UTC)

Could the scenario when the astronauts go to Mars perhaps be a reference to "The Martian"? In the book, the astronauts aboard the Hermes technically mutiny and use Earth's gravity to head back to Mars.

I think the reference to losing Apollo 11 is regarding the lose of signal that actually happened. The 2000 Australian movie 'The Dish' is based the Park's Observery losing the signal leading up to the moon landing.

I believe the title refers to the original Apollo 11 transmission tapes, [https://en.wikipedia.org/wiki/Apollo_11_missing_tapes which were actually recycled].[[Special:Contributions/141.101.77.80|141.101.77.80]] 13:13, 22 March 2018 (UTC)

Re the extra astronauts option - maybe the original astronauts were women disguised, and it was a plot to have the first babies born on the moon American, so they could claim it...which didn't work. [[Special:Contributions/198.41.238.64|198.41.238.64]] 18:41, 18 June 2018 (UTC)