Footnote Labyrinths
Footnote Labyrinths
[Excerpt from what appears to be an academic paper with footnotes.] experiments to observe this and we found no 1 2 evidence for it in our data.
1 Ignore this 2 Increment by 2 before following 3 Not true 3 2 4 Ibid. 5 True 2 6 3 6 Actually a 1 2 2

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.
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 6 ) 3 is left-associative, and 2 (6 3 ) is right-associative).
The term "ibid." is short for "ibidem", or "at the same place", meaning the reference was noted on the same page just before.
Interpreting nested footnotes as footnotes on footnotes, left-associative no 1 2 = (no 1 ) 2 = "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 1 2 " = "no 1 + 2 " = "no 3 ". We turn to the definition of 3 , which is "not true 3 2 " = "not true 3 + 2 " = "not true 5 ". Now 5 is "true 2 6 3 ". The 6 says that the 2 footnote is really 1 2 2 = 1 (4. ibid.) = 1 3 , but the 3 tells us that the 6 is "not true 5 ", getting us into an infinite loop, meaning there is no solution.
The title text suggests interpreting footnotes as exponents (minus one, modulo 6, plus 1). Because applying the operations "minus one, modulo 6, plus 1" to an integer always results in an integer between one and six (inclusive), no sequence of integer exponents will ever end up referencing a footnote that does not exist. In mathematics, nested exponents are exclusively right-associative. "no 1 2 " = "no 1 ", so we ignore the "no" and the correct statement is "we found evidence for the data." Meanwhile, 3 becomes "not true 3 ", an infinite recursion , and since 2 6 3 mod 6 = 4, we just get "ibid" and the 5 refers back to the 3. Footnote 6 is equivalent to 1 4 = 1 = "ignore this".
The comic 1184: Circumference Formula is also playing on the typographical similarity between footnotes and exponents, as well as adding even more ridiculous rules.
[Excerpt from what appears to be an academic paper with footnotes.] experiments to observe this and we found no 1 2 evidence for it in our data.
1 Ignore this 2 Increment by 2 before following 3 Not true 3 2 4 Ibid. 5 True 2 6 3 6 Actually a 1 2 2
