Editing 688: Self-Description

{{comic
| number    = 688
| date      = January 13, 2010
| title     = Self-Description
| image     = self_description.png
| titletext = The contents of any one panel are dependent on the contents of every panel including itself. The graph of panel dependencies is complete and bidirectional, and each node has a loop. The mouseover text has two hundred and forty-two characters.
}}

==Explanation==
This comic is {{w|Self-reference|self-referential}} because every graph is dependent on the whole comic. If you were to change anything in the comic, you would change the ink distribution, and would therefore have to update all three graphs. This would result in further changes that would have to be considered. This comic might be inspired by [https://www.smbc-comics.com/comic/2007-07-05 SMBC].

In the first panel's {{w|pie chart}}, "this image" refers to the entire comic image, the one that can be downloaded from xkcd (and the entire comic as displayed here above). This is a little confusing as it would be easy to misunderstand this meaning, and believe that the first panel only refers to itself. The title text though makes it clear that it is the entire comic that is called image here. The image size is 740x180 or 133200 pixels. Out of those, 14228 pixels are black (gray pixels are accounted based on their brightness). The ratio of black pixels to the size of the image is 0.1068, so the pie chart segment describing black part should be about 38.5 degrees wide, which is indeed true for the pie chart in the image.

In the second panel the amount of black used in each panel is displayed in a {{w|bar chart}}. This actually makes this panel the one that uses most black. First panel (including the border) has 4944 black pixels, second 6180 and the third 3103. First bar is about 70 pixels high, second about 87 and the third about 43, which roughly checks out. It is hard to measure exact height of the bars as the axis and bars themselves are not straight.

The third panel features a {{w|scatter plot}} labeled "Location of black ink in this image." It is the first {{w|Quadrant (plane geometry)|quadrant}} of a {{w|Cartesian coordinate system|cartesian plane}} with the zeroes marked. The graph is the whole comic scaled proportionally to fit the axes, so the last panel also has to contain an image of itself having an image of itself ad infinitum thus displaying the {{w|Droste effect}}, a type of visual {{w|recursion}}.

The title text refers to the comic's own self-reference, but it is also self-referencing because of the character count in it. It would be difficult to write this sentence, as just one more character would not be solved by writing 243, as "three" has two more characters than "two", and "four" has only one more character...

"The graph of panel dependencies is complete and bidirectional, and every node has a loop." This means that if we draw a dot corresponding to each panel, and then we draw arrows connecting the dots to indicate dependencies, the resulting {{w|Graph (discrete mathematics)|graph}} is {{w|complete graph|complete}} (meaning that all the points are connected to one another) and bidirectional (meaning that if point A has an arrow to point B, then point B also has an arrow to point A). "Every node has a loop" means that each point also has an arrow connecting to itself.

This is an observation of the interdependent relationship between description and creation that pertains to all things perceived by humans, including the concept of "Self".

Self-reference was used very early for instance in [[33: Self-reference]], but never so famously as here. See [[:Category:Self-reference|other self-references here]].

==Transcript==
:[A pie chart which is mainly white with a black slice of about 30 degree towards the bottom left. The two sections are labeled with a line going from the label to the sections. The line going into the black section turns white in this last part.]
:Fraction of this image which is white
:Fraction of this image which is black

:[A bar graph labeled with a label over the Y-axis. There are three black bars with a label below each bar. Bar 1 is of medium height, bar 2 highest and bar 3 the lowest.]
:Amount of black ink by panel:
:1 2 3

:[A scatter-plot with a label over the Y-axis. In the bottom left corner of the graph, the two axis has a tick just away from the origo, and these are labeled with zeros. The graph shows the whole comic scaled proportionally to fit the axes. The scale is too small to actually read any of the text in this representation, which would of course be the same as that noted here for the two previous panel and for this panel here below:]
:Location of black ink in this image:
:0
:0

==Trivia==
* This comic has seen interest from several computer programmers who have [https://mathematica.stackexchange.com/questions/121160/reproducing-the-xkcd-self-description-comic  taken up on the challenge] to recreate this comic. Jon McLoone of the Wolfram blog [https://blog.wolfram.com/2010/09/07/self-description/ seems to have done it] quite well.
* The {{w|Mathematical Association of America}} [https://www.maa.org/press/periodicals/math-horizons/the-mathematics-behind-xkcd-a-conversation-with-randall-munroe-0 interviewed] [[Randall Munroe|Randall]] about this topic.
* This is one of the six [[Footer comics|footer comics]] featured in the bottom segment of [https://xkcd.com xkcd.com].
* This comic used to be [https://web.archive.org/web/20211215183603/https://store.xkcd.com/products/self-reference available as a T-shirt] and [https://web.archive.org/web/20220125023401/https://store.xkcd.com/products/signed-prints as a signed print] in the xkcd store before it was [[Store|shut down]].

{{comic discussion}}

[[Category:Pie charts]]
[[Category:Bar charts]]
[[Category:Scatter plots]]
[[Category:Logic]]
[[Category:Footer comics]]
[[Category:Self-reference]]
[[Category:Comics with xkcd store products]]
[[Category:Recursion]]