https://www.explainxkcd.com/wiki/api.php?action=feedcontributions&user=70.72.16.171&feedformat=atomexplain xkcd - User contributions [en]2024-03-19T08:02:04ZUser contributionsMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=Talk:1208:_Footnote_Labyrinths&diff=36543Talk:1208: Footnote Labyrinths2013-05-06T23:18:15Z<p>70.72.16.171: </p>
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<div>Way to nerd-snipe me, Randall. [[User:Alpha|Alpha]] ([[User talk:Alpha|talk]]) 04:52, 6 May 2013 (UTC)<br />
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In the nested-footnotes interpretation, 5 has to be ignored: The 6 must be true, and the 6 says that it’s “actually a 1”, but with footnote 2+2 which says “ibid.” and thus equals footnote 3, which is true. So 6 really ''does mean'' actually a 1, which leaves 5 to be ignored. --[[Special:Contributions/77.186.8.191|77.186.8.191]] 10:47, 6 May 2013 (UTC)<br />
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The footnote for 6 is actually 1 to the 2 to the 2 [[User:Schmammel|Schmammel]] ([[User talk:Schmammel|talk]]) 12:36, 6 May 2013 (UTC)<br />
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Explaination is wrong : a<sup>b<sup>c</sup></sup> = a<sup>(b<sup>c</sup>)</sup> = a<sup>b^c</sup> (confer the definition of a gogol = 10^100 = 10<sup>10<sup>2</sup></sup>, and a gogolplex = 10^gogol = 10<sup>(10<sup>100</sup>)</sup>, not 10^110. So since 1^2= 1, No<sup>1<sup>2</sup></sup> really means No<sup>1</sup>. {{unsigned ip|192.54.145.66}}<br />
:Yes, so "no<sup>1</sup>" means to ignore the "no" and the answer for the second explanation is "we found evidence for the data." By the way, it's spelled "googol." [[User:Alpha|Alpha]] ([[User talk:Alpha|talk]]) 17:51, 6 May 2013 (UTC)<br />
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;Question, alternative explination<br />
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I wasn't really satisfied with the whole discarding of the infinite loop, so I worked through the problem seperately using the nested footnotes. Then, when we hit the infinite loop I split between the two possible answers (either the infinite loop ends on true or false). As I read it, they both get the same answer:<br />
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no (3) <br />
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no (not true (5)) <br />
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no (not true (true (2 < 6 < 3)) <br />
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no (not true (true (2 < 6 < (not true)))) <br />
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no (not true (true (2 < (actually 1 < 2 < 2 (not true 3 < 2))))) <br />
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no (not true (true (2 < (actually 1 < 2 < 2 (not true (5))))) <br />
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Split! <br />
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If 6 is false (infinite loop possibility) <br />
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no (3 < 5 < 2) <br />
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no (not true (7)) - meaningless, so discard <br />
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no (not true) <br />
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If 6 is true (infinite loop possibility) <br />
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no (3 < 5 < 1 < 2 < 2) <br />
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no (3 < 5 < 1 < 4) <br />
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no (3 < 5 < 1) <br />
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no (3) <br />
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no (not true) <br />
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Both lead to the answer "... experiments to observe this and we found evidence for it in our data". {{unsigned|Urah}}<br />
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:Yes, but at each stage you may "''toggle between interpreting nested footnotes as footnotes on footnotes and interpreting them as exponents (minus one, modulo 6, plus 1).''" That is, a<sup>2<sup>3</sup></sup> may ''either'' be read as "apply note 8 (=2mod6) to text ''a''", or as "apply note 3 to text "2", then the result to text ''a''". {{unsigned ip|192.54.145.66}}<br />
:There are differences in interpretation here. If we write "foo<sup>3<sup>6</sup></sup>", is it equal to "foo<sup>1<sup>1<sup>2</sup></sup></sup>" or "foo<sup>3<sup>1<sup>1<sup>2</sup></sup></sup></sup>"? I assumed the former and you assumed the latter. My reasoning is that footnotes modify their arguments and not themselves. [[User:Alpha|Alpha]] ([[User talk:Alpha|talk]]) 17:44, 6 May 2013 (UTC)<br />
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Shouldn't 5 be true (because 6 is actually 1<sup>3</sup>; therefore 5 is true<sup>2<sup>1<sup>3<sup>3</sup></sup></sup></sup>; so the 2 is ignored regardless the truth of 3) and 3 is not true? Sebastian --[[Special:Contributions/178.26.118.249|178.26.118.249]] 18:35, 6 May 2013 (UTC)<br />
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'''Yet another alternative solution:''' Footnotes should be evaluated from top to bottom, so "no<sup>1<sup>2</sup></sup>" = "no<sup>1 + 2</sup>" = "no<sup>3</sup>". We turn to the definition of <sup>3</sup>, which is "not true<sup>3<sup>2</sup></sup>" = "not true<sup>3 + 2</sup>" = "not true<sup>5</sup>".<br />
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Now <sup>5</sup> is "true<sup>2<sup>6<sup>3</sup></sup></sup>". The 6 says that the 2 footnote is really 1<sup>2<sup>2</sup></sup> = 1<sup>(4. ibid.)</sup> = 1<sup>3</sup>, but the 3 tells us that the 6 is "not true<sup>5</sup>", getting us into an infinite loop. However, 2<sup>6<sup>3</sup></sup> must evaluate to 1, because otherwise we're incrementing "true" by 2, which is meaningless. This means that 3 must be equal "not true". 6<sup>3</sup> = "actually a 1"<sup>3<sup>3</sup></sup> = "actually a 1". 5 becomes true<sup>1</sup> which just says to ignore this footnote altogether and we can confirm that 3 is indeed not true (not true<sup>5</sup> = not true). So the answer is that the "no" is not true, and the correct statement is "we found ''some'' evidence for it in our data." Phew. [[User:Ciamej|Ciamej]] ([[User talk:Ciamej|talk]]) 22:40, 6 May 2013 (UTC)<br />
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I'm not discouraging anyone from coming up with more alternate solutions, but would it be fair to say that part of the point is that there are multiple equally legit ways to run this labyrinth, and that some exit where you ignore the 'no', others exit on the other side where you don't ignore it. and then there's those who won't exit because they're busy making a map. - [[Special:Contributions/70.72.16.171|70.72.16.171]] 23:18, 6 May 2013 (UTC)</div>70.72.16.171https://www.explainxkcd.com/wiki/index.php?title=Talk:277:_Long_Light&diff=35143Talk:277: Long Light2013-04-25T13:42:00Z<p>70.72.16.171: /* another perspective */ new section</p>
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<div>The driver seems to know that the light always takes forever and yet there he is. Sometimes people get what they deserve. {{unsigned|99.234.144.69}}<br />
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== another perspective ==<br />
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when I'm at a long light like this, I don't blame the engineer of that light, I blame the city planner who decided to put that light at that intersection when a different system would have worked better (one that adjusts to time of day and/or uses sensors to notice that someone's waiting and there's no traffic). just sayin' [[Special:Contributions/70.72.16.171|70.72.16.171]] 13:42, 25 April 2013 (UTC)</div>70.72.16.171