https://www.explainxkcd.com/wiki/api.php?action=feedcontributions&feedformat=atom&user=Bradnemitz explain xkcd - User contributions [en] 2026-04-30T18:37:21Z User contributions MediaWiki 1.30.0 https://www.explainxkcd.com/wiki/index.php?title=1208:_Footnote_Labyrinths&diff=36482 1208: Footnote Labyrinths 2013-05-06T11:43:35Z <p>Bradnemitz: /* Removed superscript tags on the 1 in the sixth footnote to match formatting in the comic*/</p> <hr /> <div>{{comic<br /> | number = 1208<br /> | date = May 6, 2013<br /> | title = Footnote Labyrinths<br /> | image = footnote_labyrinths.png<br /> | titletext = Every time you read this mouseover, toggle between interpreting nested footnotes as footnotes on footnotes and interpreting them as exponents (minus one, modulo 6, plus 1).<br /> }}<br /> <br /> ==Explanation==<br /> <br /> This is a logic puzzle where the reader has to follow a confusing network of footnotes to determine whether the word &quot;no&quot; is to be ignored or not. The title text references comic [[1184]], playing on the typographical similarity between footnotes and exponents.<br /> <br /> '''Solution:''' Footnotes should be evaluated from top to bottom, so &quot;no&lt;sup&gt;1&lt;sup&gt;2&lt;/sup&gt;&lt;/sup&gt;&quot; = &quot;no&lt;sup&gt;1 + 2&lt;/sup&gt;&quot; = &quot;no&lt;sup&gt;3&lt;/sup&gt;&quot;. We turn to the definition of &lt;sup&gt;3&lt;/sup&gt;, which is &quot;not true&lt;sup&gt;3&lt;sup&gt;2&lt;/sup&gt;&lt;/sup&gt;&quot; = &quot;not true&lt;sup&gt;3 + 2&lt;/sup&gt;&quot; = &quot;not true&lt;sup&gt;5&lt;/sup&gt;&quot;.<br /> <br /> Now &lt;sup&gt;5&lt;/sup&gt; is &quot;true&lt;sup&gt;2&lt;sup&gt;6&lt;sup&gt;3&lt;/sup&gt;&lt;/sup&gt;&lt;/sup&gt;&quot;. The 6 says that the footnote is really 1&lt;sup&gt;1&lt;sup&gt;2&lt;/sup&gt;&lt;/sup&gt;, but the 3 tells us that the 6 is &quot;not true&lt;sup&gt;5&lt;/sup&gt;&quot;, getting us into an infinite loop. However, the 6 must be true because otherwise we're incrementing &quot;not true&quot; by 2, which is meaningless. This means that 3 = &quot;true&quot; (and 5 = &quot;not true&quot;). So the answer is that the &quot;no&quot; should not be ignored, and the correct statement is &quot;we found ''no'' evidence for the data.&quot; Phew.<br /> <br /> '''Solution (exponents):''' &quot;no&lt;sup&gt;1&lt;sup&gt;2&lt;/sup&gt;&lt;/sup&gt;&quot; = &quot;no&lt;sup&gt;1&lt;/sup&gt;&quot;, so we ignore the &quot;no&quot; and the correct statement is &quot;we found evidence for the data.&quot; &lt;sup&gt;3&lt;/sup&gt; becomes &quot;not true&lt;sup&gt;3&lt;/sup&gt;&quot;, the {{w|liar's paradox}}. Since 2&lt;sup&gt;6&lt;sup&gt;3&lt;/sup&gt;&lt;/sup&gt; is 4 mod 6, we just get &quot;ibid&quot; and the 5 refers back to the 3.<br /> <br /> ==Transcript==<br /> :[Excerpt from what appears to be an academic paper with footnotes.]<br /> :experiments to observe this and we found no&lt;sup&gt;1&lt;sup&gt;2&lt;/sup&gt;&lt;/sup&gt; evidence for it in our data.<br /> <br /> :&lt;sup&gt;1&lt;/sup&gt;Ignore this<br /> :&lt;sup&gt;2&lt;/sup&gt;Increment by 2 before following<br /> :&lt;sup&gt;3&lt;/sup&gt;Not true&lt;sup&gt;3&lt;sup&gt;2&lt;/sup&gt;&lt;/sup&gt;<br /> :&lt;sup&gt;4&lt;/sup&gt;Ibid.<br /> :&lt;sup&gt;5&lt;/sup&gt;True&lt;sup&gt;2&lt;sup&gt;6&lt;sup&gt;3&lt;/sup&gt;&lt;/sup&gt;&lt;/sup&gt;<br /> :&lt;sup&gt;6&lt;/sup&gt;Actually a 1&lt;sup&gt;2&lt;sup&gt;2&lt;/sup&gt;&lt;/sup&gt;<br /> <br /> {{comic discussion}}<br /> [[Category:My Hobby]]</div> Bradnemitz