1208: "Footnote Labyrinths"

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Quicksilver
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1208: "Footnote Labyrinths"

Postby Quicksilver » Mon May 06, 2013 4:03 am UTC

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http://xkcd.com/1208/
Alt Text:"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)."
Footnoteception?
Image

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Re: 1208: "Footnote Labyrinths"

Postby rhomboidal » Mon May 06, 2013 4:05 am UTC

My cable, phone, and internet contracts are crawling with hidden minotaurs.

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Marios101Cool
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Re: 1208: "Footnote Labyrinths"

Postby Marios101Cool » Mon May 06, 2013 4:06 am UTC

My head really hurts from trying to follow these footnotes. I seem to be able to get to all the footnotes if I interpret them as footnotes of footnotes, but I end up on an infinite loop between 5, 2, and 6.
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Re: 1208: "Footnote Labyrinths"

Postby Draco18s » Mon May 06, 2013 4:19 am UTC

I'm reminded of the Footnoterphone from the Thursday Next novels.

There was a not-insignificant amount of plot that happened inside the footnotes in one book.

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Re: 1208: "Footnote Labyrinths"

Postby HAL9000 » Mon May 06, 2013 4:31 am UTC

I'm probably just missing something obvious, but what does 'increment by 2 before following' mean?
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Re: 1208: "Footnote Labyrinths"

Postby blowfishhootie » Mon May 06, 2013 4:57 am UTC

HAL9000 wrote:I'm probably just missing something obvious, but what does 'increment by 2 before following' mean?


Increment as a verb means to increase something slightly. So it means add two to this footnote number before following it.

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BAReFOOt
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Re: 1208: "Footnote Labyrinths"

Postby BAReFOOt » Mon May 06, 2013 5:01 am UTC

The solution:

It just gives a infinitely repeating (the part between the 《 》) pattern of…

[math]no^{notTrue《^{2^{6^{notTrue^{true》《}}}}》}[/math]
where 6 resolves to “actually a …”, where the “…” is a ignored “ignore this”,
and 2 makes no sense since you cannot increment a boolean statement by two.

A simple RPN or Haskell parser has no trouble in automatically resolving it (and hence ending in an infinite loop).

EDIT: If anyone knows why the above doesn’t show as math even though I used the [math] bbcode tag, please tell me…
Last edited by BAReFOOt on Mon May 06, 2013 5:20 am UTC, edited 1 time in total.

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Re: 1208: "Footnote Labyrinths"

Postby PM 2Ring » Mon May 06, 2013 5:12 am UTC

BAReFOOt wrote:EDIT: If anyone knows why the above doesn’t show as math even though I used the [math] bbcode tag, please tell me…

Sorry, math tags stopped working across the fora some time ago.

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Re: 1208: "Footnote Labyrinths"

Postby da Doctah » Mon May 06, 2013 5:13 am UTC

It's just a shame the toggling mentioned in the mouseover text couldn't be accomplished without resorting to the person reading it.

(And to the Javascript lunatics, that is not intended as a challenge!)

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Re: 1208: "Footnote Labyrinths"

Postby BAReFOOt » Mon May 06, 2013 5:23 am UTC

da Doctah wrote:(And to the Javascript lunatics, that is not intended as a challenge!)


Programmatically doing it would also be an act of reading it. As would any method of measurement.

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Re: 1208: "Footnote Labyrinths"

Postby oryhara » Mon May 06, 2013 6:21 am UTC

I'm pretty sure
3: Not true
5: True
gives a consistent state. Since 6 resolves to effectively 1^3, the 2^(6^3) tower in 5 resolves to 2^((1^3)^3), which resolves to 2^1. So 5 just resolves to True^(2^1), so it's true.

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Re: 1208: "Footnote Labyrinths"

Postby Flotter » Mon May 06, 2013 6:37 am UTC

To me, this is a sign that Randall reads (or at least is aware of) the discussions in the Topic1 for Time2. Complex footnote constructions have been used there for a while now, this can't be a coincidence.

1here3
2here4
3The One True Topic
4The One True Comic
5Random unreferenced footnote6
6An act of Blasphemy7 in the One True Topic1
7Punishable by the Inquisition with comfy chairs and layers of chocolate

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Re: 1208: "Footnote Labyrinths"

Postby snowyowl » Mon May 06, 2013 7:05 am UTC

I like having fun with complicated systems that people take for granted1.

1like footnotes23
3there is no footnote number 2
The preceding comment is an automated response.

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Re: 1208: "Footnote Labyrinths"

Postby Ekaros » Mon May 06, 2013 8:54 am UTC

Pratchett isn't that bad...

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Re: 1208: "Footnote Labyrinths"

Postby J L » Mon May 06, 2013 10:20 am UTC

Well, if you increment everything footnoted with a 2 by 2 before following it (and disregard the meaningless and anyhow "corrected" 2 in footnote [5]), doesn't that give you:

"... and we found no3 evidence for it in our data"

3 not true5

5 true5 (the last statement being marked as "not true" by the upmost 3)

So the asserted "trueness" of footnote [5] is ultimately cancelled, which cancels the "not true" of footnote [3], so they indeed found no evidence in their data ... or did they?

Maybe I should note I'd like to invoke an Alternate Timelines approach to the upmost 3 in footnote [5] to prevent it from being self-cancelling ... just in case.

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Re: 1208: "Footnote Labyrinths"

Postby waidh » Mon May 06, 2013 10:27 am UTC

Flotter wrote:To me, this is a sign that Randall reads (or at least is aware of) the discussions in the Topic1 for Time2. Complex footnote constructions have been used there for a while now, this can't be a coincidence.

Or maybe he was already playing with footnotes before Time.

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Re: 1208: "Footnote Labyrinths"

Postby Diadem » Mon May 06, 2013 10:38 am UTC

We start with "No^1^2".
The outer 2 tells us the 1 should be a three.
So we look at 3, which says "not true^3^2" which is "not true^5".
So we look at 5, which reads "True^2^6^3". This is the hard part. The 6 tells us that the footnotes should actually be "1^2^2" but the 3 says this is not true^3^2.
So now we're in an endless loop of footnote 3 and 5, which read 'true' and 'not true'. Is the resulting expression true or not true? If the result is not t rue, that means that the 6 footnote referenced in 5 never happens, meaning that in 5 we are left with "true^2" which is a syntax error. If it's true, then the 6 happens, and 5 is reduced to "True^1^4^4" which is "True^1^4" which is true^ignore this^ibid which just invalidates the entire footnote. Meaning we collapse all the way back to our original "not true". So the claim in the text is false, and we did find evidence in our data.
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Re: 1208: "Footnote Labyrinths"

Postby Klear » Mon May 06, 2013 11:13 am UTC

What is is with Randall and footnotes lately?

Anyway, I had no problem - since incrementing numbers is not a valid way to be directed by footnotes, I never got directed to footnotes 3 and above, which didn't worry me, since the previous two footnotes were devoid of information and the trend didn't show signs of stopping.

What I'm saying here, I guess, us who actually care about footnote usage won't get nerdsniped by this. These footnotes are worthless, that's it.

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Re: 1208: "Footnote Labyrinths"

Postby J L » Mon May 06, 2013 12:17 pm UTC

Diadem wrote:We start with "No^1^2".
If it's true, then the 6 happens, and 5 is reduced to "True^1^4^4" which is "True^1^4" which is true^ignore this^ibid which just invalidates the entire footnote. Meaning we collapse all the way back to our original "not true". So the claim in the text is false, and we did find evidence in our data.

All right, I shouldn't have incremented the 1 in [6], since it's no footnote. I already wondered how to get to footnote [4] at all.

Klear wrote:What I'm saying here, I guess, us who actually care about footnote usage won't get nerdsniped by this. These footnotes are worthless, that's it.

Well, true enough ... that's what I would put on a term paper if a student handed me something like this :)

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Re: 1208: "Footnote Labyrinths"

Postby corsairmark » Mon May 06, 2013 12:33 pm UTC

This is a slight tangent, but...
As a result of 1208: "Footnote Labyrinths", I stumbled upon two novels (Ibid: A Life and Pale Fire) that use footnotes instead of (or in the case of Pale Fire, in addition to) prose to tell the story
I have not read them, but the concept sounds interesting
Has anyone read them, or other, similar works?

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Re: 1208: "Footnote Labyrinths"

Postby iChef » Mon May 06, 2013 12:44 pm UTC

Mark Danielewski will forever be the master at this art form.
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Re: 1208: "Footnote Labyrinths"

Postby cellocgw » Mon May 06, 2013 12:51 pm UTC

BAReFOOt wrote:
da Doctah wrote:(And to the Javascript lunatics, that is not intended as a challenge!)


Programmatically doing it would also be an act of reading it. As would any method of measurement.


Yep, reading is a form of observing. And we all know what observations do to quantum footnotes.
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Re: 1208: "Footnote Labyrinths"

Postby rogerhere » Mon May 06, 2013 12:55 pm UTC

Reminds me about "CLOG" - The Computer Linograph, an Ada package for automatic footnote generation.
Communications of the ACM, April 1984.

:D

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Re: 1208: "Footnote Labyrinths"

Postby philsov » Mon May 06, 2013 1:31 pm UTC

aaaand there go the horrible/lovely House flashbacks...
The time and seasons go on, but all the rhymes and reasons are wrong
I know I'll discover after its all said and done I should've been a nun.

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Re: 1208: "Footnote Labyrinths"

Postby jgh » Mon May 06, 2013 1:49 pm UTC

I'm caught in an infinite loop of twisty little passages, all alike.

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Re: 1208: "Footnote Labyrinths"

Postby Someguy945 » Mon May 06, 2013 2:15 pm UTC

Flotter wrote:To me, this is a sign that Randall reads (or at least is aware of) the discussions in the Topic1 for Time2. Complex footnote constructions have been used there for a while now, this can't be a coincidence.


Look, in the end Randall is a human (I know it's fun to pretend he is superhuman, but lets real talk for a minute).

There is no way that he could put THAT much effort into "Time" and spawn a 500+ page thread and not read any of it. He is aware of it, and he probably reads or at least skims it on a regular basis.

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Re: 1208: "Footnote Labyrinths"

Postby Istaro » Mon May 06, 2013 2:32 pm UTC

Since nested footnotes are right-associative for the same reason that exponentiation is right-associative, note that footnote 6 says "actually a 1^4", i.e. "actually a 1^3". Also note that since 3 relates to truth, not numerical value, it must be applying to the entire preceding string, not just the 1: "(actually a 1)^3", not "actually a (1^3)".

Now, take a look at footnote 5: "true^(2^(6^3))".

We know that the 6^3 applied to the 2 must change said 2 somehow, because if the 2 were left as is, we'd end up having to apply it to the "true" at the bottom, and true^2 is a syntax error.

Looking at all the footnotes, there are only two conceivable ways in which 6^3 could change 2 (because there are only two footnote effects that can change numbers): increment it, or make it actually a 1.

But 6^3 can't increment 2, because 6^3 doesn't ever take us to the incrementing footnote (footnote 2). See my first line if you're unsure about that. (Specifically, 6^3 only involves the statement "actually a 1" and the stuff pertaining to truth or the lack thereof.)

So that leaves us with one option: 6^3 must equal "actually a 1"—that's the only way in which 6^3 can safely dispose of the 2 under it, preventing that 2 from illegally applying to "true".

If 6 is "actually a 1", that means that "(actually a 1)^(2^2)" = "(actually a 1)^4" = "(actually a 1)^3" is equal to "actually a 1"; i.e., 3 is "true".

If 3 is "true", the original text says "no^true", i.e. "no". No evidence was found in the data.

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Re: 1208: "Footnote Labyrinths"

Postby orangedragonfire » Mon May 06, 2013 3:04 pm UTC

Ah, this reminds me of the forum story1.


1Which could just as well have been called Footnotes: The Game2
2This game is quite popluar with young4 vegetables in the fruitsphere3
3See footnote number 22 in forum story1
4You know, probably. It's not polite to ask a vegetable about it's age.

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Re: 1208: "Footnote Labyrinths"

Postby Dwedit » Mon May 06, 2013 3:17 pm UTC

I tried to parse it, but my brain ended up getting a stack overflow error.

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Re: 1208: "Footnote Labyrinths"

Postby O-Deka-K » Mon May 06, 2013 3:22 pm UTC

There are only two possible end results from the footnotes: True or Not True. Thus, the sentence is equivalent to:

"...we didn't find no evidence for it in our data."

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Re: 1208: "Footnote Labyrinths"

Postby HAL9000 » Mon May 06, 2013 3:36 pm UTC

O-Deka-K wrote:There are only two possible end results from the footnotes: True or Not True. Thus, the sentence is equivalent to:

"...we didn't find no evidence for it in our data."

*cringe*
The grammar...

The grammar...
HAL9000 wrote:I find it simultaneously fascinating and disturbing that the most profound things I've read in the past months I have encountered in or been led to by an internet forum thread about a webcomic.

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Re: 1208: "Footnote Labyrinths"

Postby Markster » Mon May 06, 2013 3:48 pm UTC

The original footnote number is 1 squared, which is just 1. I took the footnote IGNORE THIS to mean to ignore the footnoted word, rather than the footnote itself, so there IS EVIDENCE. The first footnote is not footnoted, so there is no labyrinth.

You don't footnote a footnote number directly, which means the footnote number is a mathematical expression that resolves to a footnote number.

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Re: 1208: "Footnote Labyrinths"

Postby Markster » Mon May 06, 2013 3:53 pm UTC

J L wrote:3 not true5

5 true5 (the last statement being marked as "not true" by the upmost 3)

So the asserted "trueness" of footnote [5] is ultimately cancelled, which cancels the "not true" of footnote [3], so they indeed found no evidence in their data ... or did they?


Nope - footnote 5 just says that footnote 3 is true.

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Re: 1208: "Footnote Labyrinths"

Postby pdxxkcdfan » Mon May 06, 2013 4:09 pm UTC

This comic reminded my of the book "House of Leaves".

The book starts off with mild footnotes, which gradually increase in frequency and complexity, with footnotes on top of footnotes ad nauseum, until the footnotes become the main story. This happens several times, and it became (for me) almost impossible to track what story I was reading.

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Re: 1208: "Footnote Labyrinths"

Postby eran_rathan » Mon May 06, 2013 5:53 pm UTC

i'm so glad there are other House of Leaves fans out there.
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Re: 1208: "Footnote Labyrinths"

Postby oryhara » Mon May 06, 2013 6:18 pm UTC

Istaro wrote:If 6 is "actually a 1", that means that "(actually a 1)^(2^2)" = "(actually a 1)^4" = "(actually a 1)^3" is equal to "actually a 1"; i.e., 3 is "true".

If 3 is "true", the original text says "no^true", i.e. "no". No evidence was found in the data.

But 3=true leads to a contradiction, because it would imply 5=true^(2^(6^3))=true^(2^6)=true^(2^(1^3))=true^(2^1)=true. But then that makes 3=(not true)^(3^2)=(not true)^5=not true.

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Re: 1208: "Footnote Labyrinths"

Postby Blake » Mon May 06, 2013 7:54 pm UTC

I think there's a pretty decent chance this is at least partially intended as a House of Leaves reference, given that work's heavy use of footnotes, and the labyrinth motifs in it.

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Re: 1208: "Footnote Labyrinths"

Postby Klear » Mon May 06, 2013 9:08 pm UTC

But if it is a House of Leaves reference, than it makes it a bit pitiful, since footnotes are emplayed a lot better there. I think I'd enjoy this comic way more if I hadn't read it.

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Re: 1208: "Footnote Labyrinths"

Postby oelbert » Mon May 06, 2013 11:18 pm UTC

This comic is like a David Foster Wallace dream

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Re: 1208: "Footnote Labyrinths"

Postby xatm092 » Mon May 06, 2013 11:25 pm UTC

Am I the only one who assumed that 1^2^2 = 1^4 and not 3^2?


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