0688: "Self-Description"

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0688: "Self-Description"

Postby lingomaniac88 » Wed Jan 13, 2010 5:06 am UTC

Permanent Link: http://xkcd.com/688

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Alt-text: 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.

Hmm... it actually is 242 characters long. Nice.
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Re: "Self-Description" Discussion

Postby Duban » Wed Jan 13, 2010 5:07 am UTC

That's kind of cool. What kind of algorithm or system was used to create the images?
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Re: "Self-Description" Discussion

Postby Rofler » Wed Jan 13, 2010 5:07 am UTC

love it, but it also kinda does my head in.
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Re: "Self-Description" Discussion

Postby BlazeOrangeDeer » Wed Jan 13, 2010 5:07 am UTC

I am in awe. At first I didn't see the purpose of it, then I said ooohhhh that's actually pretty complicated.
edit: also I think he should make it a program for this that procedurally draws itself, so looking at the last graph would be the same as looking at the whole comic. that would be even more interesting.
Last edited by BlazeOrangeDeer on Wed Jan 13, 2010 5:11 am UTC, edited 1 time in total.
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Re: "Self-Description" Discussion

Postby Kain » Wed Jan 13, 2010 5:09 am UTC

good thing about numbers is that one + two + six, four + five + nine, etc all make nice little groups, so it isnt entirely too hard to get one of those sentences to work.

This Line Has Thirty Nine Non Space Characters.
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Re: "Self-Description" Discussion

Postby phlip » Wed Jan 13, 2010 5:11 am UTC

The graphs look pretty accurate to me.

But yeah, with a bit of work, once you've sketched how the whole thing will look, you can find equations for the amount of black in each of the three panels based on the amount in the others - then you have three equations (which I'm pretty sure would be linear) in three unknowns, not too hard to solve. Then from that you can draw each panel. Looks impressive, though.
Last edited by phlip on Wed Jan 13, 2010 5:14 am UTC, edited 2 times in total.
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Re: "Self-Description" Discussion

Postby cprocjr » Wed Jan 13, 2010 5:11 am UTC

"Location of black ink in this image" was the best one. I wonder how accurate the other two panels are. Knowing Randall they're probably very accurate.
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Re: "Self-Description" Discussion

Postby GodShapedBullet » Wed Jan 13, 2010 5:12 am UTC

Duban wrote:That's kind of cool. What kind of algorithm or system was used to create the images?


I suppose something fancy could have been done, but it could have just been an easy copy and paste job. I mean, there's only so many pixels.
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Re: "Self-Description" Discussion

Postby Ghandi 2 » Wed Jan 13, 2010 5:12 am UTC

Demitri Martin lite.
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Re: "Self-Description" Discussion

Postby halcyon1234 » Wed Jan 13, 2010 5:13 am UTC

This is the ninth reply, and was ninjad thrice.
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Re: "Self-Description" Discussion

Postby Omegaton » Wed Jan 13, 2010 5:13 am UTC

If this were anyone else, I'd assume that these were just drawn down. But knowing Randall, he probably made it a point to make this at least approximately correct. Of course, that might just be what he wants us to think...
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Re: "Self-Description" Discussion

Postby mattflaschen » Wed Jan 13, 2010 5:20 am UTC

At first I didn't see how the first panel depended on the others ("The contents of any one panel are dependent on the contents of every panel including itself."). That's because I thought the pie chart panel was just a variant on the old pie chart joke (e.g. Percentage of Chart Which Resembles Pac-man, Pie I Have not Yet Eaten, etc.). Now that I get that the pie chart is actually valid for the whole comic (not just the pie chart itself), and misinterpretable as a pie chart joke, I am considerably more impressed.
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Re: "Self-Description" Discussion

Postby lihan161051 » Wed Jan 13, 2010 5:27 am UTC

This is actually not the first time today that I've been reminded of Edward Tufte ..
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Re: "Self-Description" Discussion

Postby Tyr_oathkeeper » Wed Jan 13, 2010 5:31 am UTC

*Mind asplodes*
It's note helping that I read it late at night while waiting for openoffice to download on our netbook cause it seems to be the only computer that can see the printer right now and I need to print my summative report for auto.
And I played too much Achron(http://achrongame.com/) while procrastinating and my mind is still a big boggled.
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Re: "Self-Description" Discussion

Postby tpow » Wed Jan 13, 2010 5:33 am UTC

:shock: my head asplode...
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Re: "Self-Description" Discussion

Postby CorruptUser » Wed Jan 13, 2010 5:34 am UTC

My head asplode

Edit: beaten to it.
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Re: "Self-Description" Discussion

Postby Kailen » Wed Jan 13, 2010 5:41 am UTC

I think the best part is that he could have pulled the figures out of Uranus and people will still believe they were close because, hey, "It's Randall".
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Re: "Self-Description" Discussion

Postby westrim » Wed Jan 13, 2010 5:44 am UTC

I'm not quite getting the third panel.
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Re: "Self-Description" Discussion

Postby Lazar » Wed Jan 13, 2010 5:45 am UTC

westrim wrote:I'm not quite getting the third panel.

I think it's just a scaled-down representation of the strip itself. Which means that there's an infinite recursion of the third panel.
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Re: "Self-Description" Discussion

Postby yuwtze » Wed Jan 13, 2010 5:48 am UTC

Kailen wrote:I think the best part is that he could have pulled the figures out of Uranus and people will still believe they were close because, hey, "It's Randall".


True, but this being xkcd, you know that there will be someone who will actually do the math and verify it.
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Re: "Self-Description" Discussion

Postby v1ND » Wed Jan 13, 2010 5:53 am UTC

tbh, I thought it was pretty lame. :?
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Re: "Self-Description" Discussion

Postby Gamaliel » Wed Jan 13, 2010 5:57 am UTC

I find it interesting that the height of the middle bar in the second panel primarily only affects itself, as the only thing that is significantly changing is the amount of ink in the second panel.

However, since both the first and the third panel would change slightly if you increased/decreased the size of the second bar in the second panel, it's not a completely closed system.

Still, it means you can pretty much increase or decrease the size of the second bar in the second panel at will, and as long as you make the correct small adjustments to the pie chart in the first panel and the mini-comic in the third panel, the math will still be accurate.


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Re: "Self-Description" Discussion

Postby Raptor Jesus » Wed Jan 13, 2010 6:00 am UTC

Edit: I was ninja'd, feel free to skip this post

Wait, isn't the middle one impossible? Because to show the amount of ink that were in the first two, you would have to add more ink. Adding more ink would cause you to have to add even more ink to the #2 comic, therefore increasing the size of the bar, adding more ink, and repeating the loop....

Or am I just over thinking this? :mrgreen:
Last edited by Raptor Jesus on Wed Jan 13, 2010 6:04 am UTC, edited 2 times in total.
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Re: "Self-Description" Discussion

Postby Someursault » Wed Jan 13, 2010 6:02 am UTC

Somebody thinks about self-reference a lot.
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Re: "Self-Description" Discussion

Postby MotorToad » Wed Jan 13, 2010 6:05 am UTC

Raptor Jesus wrote:Edit: I was ninja'd

Wait, isn't the middle one impossible? Because to show the amount of ink that were in the first two, you would have to add more ink. Adding more ink would cause you to have to add even more ink to the #2 comic, therefore increasing the size of the bar, adding more ink, and repeating the loop....

Or am I just over thinking this? :mrgreen:

It's just a comparison, it'll balance out eventually. :)

I'm more interested in exploding the strip and seeing how many levels the third panel attains.
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Re: "Self-Description" Discussion

Postby piesquared88 » Wed Jan 13, 2010 6:06 am UTC

Raptor Jesus wrote:Wait, isn't the middle one impossible? Because to show the amount of ink that were in the first two, you would have to add more ink. Adding more ink would cause you to have to add even more ink to the #2 comic, therefore increasing the size of the bar, adding more ink, and repeating the loop....

Or am I just over thinking this? :mrgreen:


Zeno's Paradox.
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Re: "Self-Description" Discussion

Postby punto » Wed Jan 13, 2010 6:06 am UTC

good thing the universe is discrete, otherwise the last panel would be out of control
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Re: "Self-Description" Discussion

Postby aterimperator » Wed Jan 13, 2010 6:08 am UTC

What bothers me most is the axes aren't labeled.
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Re: "Self-Description" Discussion

Postby Caffeine » Wed Jan 13, 2010 6:08 am UTC

Basic threshold pixel counting yields the following:

Panel 1 - Black 4962(11%), White 39318(88%), Total 44400 pixels
Panel 2 - Black 6219(14%), White 38241(86%), Total 44400 pixels
Panel 3 - Black 2457(5%), White 42003(94%), Total 44400 pixels
Total - Black 13638(10%), White 119562(89%), Total 133200 pixels

Note that the percentages have some rounding...
Last edited by Caffeine on Wed Jan 13, 2010 6:13 am UTC, edited 1 time in total.
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Re: "Self-Description" Discussion

Postby The_Duck » Wed Jan 13, 2010 6:09 am UTC

At least Randall didn't try to draw an image containing descriptions of all images which do not contain descriptions of themselves.
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Re: "Self-Description" Discussion

Postby Hectamatatortron » Wed Jan 13, 2010 6:10 am UTC

Oh Randall, you tease. Giving us just the third panel of the comic and making us think it was actually the whole thing.
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Re: "Self-Description" Discussion

Postby squareroot » Wed Jan 13, 2010 6:13 am UTC

If they had used an em dash instead of an en dash in the mouseover text, could it have read at the end: "The mouseover text has two hundred and fourty—nine and a half characters." NOTE: I had to change "contains" to "has" to make it work out with the numbers. But then again... this forum post contains three hundred and fourty-four characters.
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Re: "Self-Description" Discussion

Postby RJFerret » Wed Jan 13, 2010 6:16 am UTC

So not surprisingly, 10% of the image is black as per the first pie chart (ironically, about 11% of the first panel itself is black as well). Specifically 10.24% (13638 pixels of 133,200 for the whole and 11.3% or 4962 of 43920 for the panel itself).

There are about 5000 black pixels in the first panel, over 6000 in the second and ~2500 in the third (4962, 6219 and 2457 respectively).

Just because, well, someone had to do the accounting, tax time is right around the corner in the U.S. after all, and we don't want to see any red ink!
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Re: "Self-Description" Discussion

Postby squareroot » Wed Jan 13, 2010 6:23 am UTC

O.o what if it was multicolored?

"Here's a nicely shaded histogram of the hues throughout this image, with a colorwheel legend:"

"Here's a bar graph of how much each pigment was used in creating the other two panels:"

"Here's a plot of the function describing the hue of each pixel within this comic, colored according to height of the function:"

Tooltip: "Due to the yellow of this tooltip and the segment of comic you are most likely to occlude therewith, the correct histogram should be this: (insert ASCII plot here)"
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Re: "Self-Description" Discussion

Postby Covane » Wed Jan 13, 2010 6:28 am UTC

This is one of his (many) strips where it strikes me that the XKCD description ought to actually be "The most intelligent thing you'll read today."
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Re: "Self-Description" Discussion

Postby Okita » Wed Jan 13, 2010 6:29 am UTC

That puts all of Demetri Martin's charts to shame.
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Re: "Self-Description" Discussion

Postby squareroot » Wed Jan 13, 2010 6:33 am UTC

Heheh, I really recommend you all read #33. Totally the same joke... sorta. Or rather, making fun of this joke. Whatever, just read it.
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Re: "Self-Description" Discussion

Postby Galactic Kirby » Wed Jan 13, 2010 6:37 am UTC

Given the fact that recursion in panel 3 is infinite, wouldn't, theoretically, the amount of blank ink used in panel 3 be infinite as well?
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Re: "Self-Description" Discussion

Postby arb246 » Wed Jan 13, 2010 6:38 am UTC

Someone tell me if this is wrong:

Because the third panel involves an infinite recursion, every value represented there has to be indeterminate. As long as we assume the third panel is accurate, it will involve an infinite addition of infinitely small values to the third bar of the bar graph (in drawing an infinity of infinitely small diagrams) and the same would go for the pie, which would involve infinite additions of infinitely small values to the black wedge. If we assume the third panel is just an approximation, then we have to treat the other two as approximations as well.

So the problems of self-reference seem persistent, but I think this could have been avoided (and made the comic less fun to read) if the third panel didn't actually depict the whole comic, though of course it could have involved data about the whole comic. It's fine to say 'This sentence contains five words' but you run into trouble if you want to say "The sentence I am now typing, 'the sentence I am now typing contains X words,' contains X words." Here, either the value of X must be wrong, or the internal reference of the sentence to itself must be wrong.
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Re: "Self-Description" Discussion

Postby 10nitro » Wed Jan 13, 2010 6:47 am UTC

The number on the left is the number of times a pixel with the value on the right appears in the comic
Code: Select all
   8183 0
     36 1
     47 2
    383 3
     44 4
     36 5
     26 6
     43 7
     83 8
     28 10
     35 11
     26 12
     49 13
     39 14
     31 15
     48 16
     32 17
     54 18
     36 19
     35 20
     37 21
     33 22
     43 23
     76 24
     41 26
     41 27
     40 28
     29 29
     43 30
     33 31
     28 32
     35 33
     44 34
    219 35
     29 36
     37 37
     32 38
     45 39
     70 40
     62 42
     41 43
     36 44
     23 45
     36 46
     33 47
     37 48
     20 49
     26 50
     38 51
     27 52
     24 53
     37 54
     29 55
     44 56
     31 58
     22 59
     23 60
     24 61
     34 62
     27 63
     22 64
     36 65
     39 66
     37 67
     24 68
     28 69
     21 70
     23 71
     60 72
     17 74
     21 75
     31 76
     18 77
     25 78
     26 79
     25 80
     14 81
     32 82
     38 83
     25 84
     28 85
     29 86
     18 87
     42 88
     22 90
     24 91
     25 92
     29 93
     23 94
     17 95
     24 96
    214 97
     30 98
     28 99
     23 100
     23 101
     33 102
     17 103
     42 104
     15 106
     39 107
     19 108
     20 109
     23 110
     17 111
     46 112
     19 113
     37 114
     28 115
     20 116
     21 117
     22 118
     23 119
     49 120
     29 122
     25 123
     30 124
     28 125
     26 126
     17 127
    941 128
     55 129
     53 130
     66 131
    949 132
     67 133
     38 134
     53 135
    112 136
    415 138
    241 139
     55 140
     53 141
     61 142
     63 143
     35 160
     35 161
     35 162
     23 163
     29 164
     27 165
     31 166
     67 167
    117 168
     33 170
     27 171
     42 172
     36 173
     38 174
     71 175
     29 176
     27 177
    210 178
     34 179
     80 180
     48 181
     49 182
     37 183
    124 184
     36 186
     46 187
     35 188
     45 189
    214 190
     39 191
     33 192
     89 193
     31 194
     36 195
     40 196
     47 197
    204 198
     46 199
     78 200
     35 202
     51 203
     31 204
     35 205
     36 206
     35 207
     35 208
     50 209
     37 210
     30 211
     40 212
     48 213
     88 214
     87 215
     77 216
     87 218
     46 219
     32 220
     50 221
     68 222
     58 223
     56 224
    235 225
     53 226
     49 227
     38 228
     52 229
    223 230
     46 231
    121 232
     58 234
     73 235
     75 236
    482 237
     66 238
     87 239
     84 240
     76 241
     87 242
     78 243
     80 244
     77 245
    134 246
     81 247
    212 248
    142 250
    113 251
     72 252
    114 253
    137 254
 110689 255

Some simple arithmetic tells us that there are 12729 pixels whose values are 0-127, and 120471 who are 128-255 (for a total of 133200 pixels).
By this calculation roughly 9.6% of the image is `black'. However, this actually means `darker than neutral'. This means that a gray pixel is counted as black. Normally we would call this negligible, since it affects both sides.

However, we're not `normal', we read xkcd.

If we use fractions of pixels (ex 64=.25 white, .75 black):
(30312213/255) white pixels, = 89.2%
(3653787/255) black pixels, = 10.8%
(again, percentages are rounded)

edit: where the hell are you guys getting 13638 black pixels?
Last edited by 10nitro on Wed Jan 13, 2010 7:26 am UTC, edited 3 times in total.
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