Editing 1208: Footnote Labyrinths

{{comic
| number    = 1208
| date      = May 6, 2013
| title     = Footnote Labyrinths
| image     = footnote_labyrinths.png
| 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).
}}

==Explanation==

This is a logic puzzle where the reader has to follow a confusing network of footnotes to determine whether the word "no" is to be ignored or not. The title text references comic [[1184]], playing on the typographical similarity between footnotes and exponents, as well as adding even more ridiculous rules.

In the following solutions, "right-associative" means that the footnotes are evaluated from right to left or top to bottom, and left-associative from left to right or bottom to top (e.g. (2<sup>6</sup>)<sup><sup>3</sup></sup> is left-associative, and 2<sup>(6<sup>3</sup>)</sup> is right-associative.


===Interpreting nested footnotes as footnotes on footnotes, left-associative===

no<sup>1<sup>2</sup></sup> = (no<sup>1</sup>)<sup><sup>2</sup></sup> = "ignore this" (it is meaningless to increment a phrase by 2), so the correct statement is "we found evidence for it in our data".

===Interpreting nested footnotes as footnotes on footnotes, right-associative===

"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>".

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, meaning there is no solution.

===Interpreting footnotes as exponents (minus one, modulo 6, plus 1)===

In mathematics, nested exponents are exclusively right-associative. Since there are only six footnotes, the alt-text operation is equivalent to modulo 6. "no<sup>1<sup>2</sup></sup>" = "no<sup>1</sup>", so we ignore the "no" and the correct statement is "we found evidence for the data." 

Meanwhile, <sup>3</sup> becomes "not true<sup>3</sup>", an {{w|infinite recursion}}, and since 2<sup>6<sup>3</sup></sup> mod 6 = 4, we just get "ibid" and the 5 refers back to the 3. Footnote 6 is equivalent to 1<sup>4</sup>, and since 4 is "ibid.", we now get "ignore this<sup>3</sup>", so all roads but the solution lead to an infinite recursion.

"ibid." is short for "ibidem", or "at the same place", meaning the reference was noted on the same page just before.

==Transcript==
:[Excerpt from what appears to be an academic paper with footnotes.]
:experiments to observe this and we found no<sup>1<sup>2</sup></sup> evidence for it in our data.

:<sup>1</sup>Ignore this
:<sup>2</sup>Increment by 2 before following
:<sup>3</sup>Not true<sup>3<sup>2</sup></sup>
:<sup>4</sup>Ibid.
:<sup>5</sup>True<sup>2<sup>6<sup>3</sup></sup></sup>
:<sup>6</sup>Actually a 1<sup>2<sup>2</sup></sup>

{{comic discussion}}
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