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Posted: Wed Jan 13, 2010 3:58 pm UTC
two hundred and forty-two? should be two hundred forty-two (but of course that would be incorrect)

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 4:15 pm UTC
Very fun comic. Douglas R Hofstadter has some excellent discussions of mathematical, visual, and linguistic self reference in his books, Metamagical Memas and Goedel Escher Bach, for anyone interested in the subject.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 4:31 pm UTC
The comic reminds me of this:

Only the fool would take trouble to verify that this sentence was composed of ten a's, three b's, four c's, four d's, forty-six e's, sixteen f's, four g's, thirteen h's, fifteen i's, two k's, nine l's, four m's, twenty-five n's, twenty-four o's, five p's, sixteen r's, forty-one s's, thirty-seven t's, ten u's, eight v's, eight w's, four x's, eleven y's, twenty-seven commas, twenty-three apostrophes, seven hyphens, and, last but not least, a single !

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 4:51 pm UTC
I remember when I was younger, I made a machine out of lego that turned itself off....

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 5:00 pm UTC
Ah, reminds me of this...

How many letters are in the ANSWER to this question?

Just a few of the correct responses:
0
Four
Exactly ten
42: it's the answer to life, the universe, and everything.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 5:05 pm UTC
Agentstinky wrote:Anyone else reminded of Douglas Hofstadter? I'm working my way through "Godel, Escher, Bach" right now.

That was the first thing I thought once I realized where the comic was going. GEB is great, but do not skip the dialogues, even though he says they aren't mandatory reading, they really should be (in later chapters he will outright reference them). I Am a Strange Loop is a pretty good follow up as well, explains some of the stuff about cognition in a much clearer way with less math/logic (I mean this in that it is less confusing of a read) and virtually no music theory.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 5:36 pm UTC
tzvibish wrote:OK, after an hour or so of picking out brain chunks from the wall behind me, I have a serious question. In the last panel, for the recursion, take the pie chart. It says: "Amount of Black in the Image". Not just the panel, but the entire strip, correct? So, once you take the final recursion into account, the actual amount of black in the pie chart will be the value of limit (as a percentage) as the summation approaches infinity? I think I'm right so far. Let me know if not.

Now, in the last panel, we have a series of pie charts that get proportionally smaller ever time, but the relative size of the pie slices remain the same. So, if they are the same percentage every time, then they all must equal the final value of the limit of summation as it approaches infinity (and it's around 10%). Am I looking at this right?

An easy way to answer this is to ask how much ink is in the image. Is it 100% black? No. Even if it was, that would not be infinite, just all of it. So we know it's not approaching infinity. Each repeated image is smaller than the next. So you can add it up like "10 + 9 + 8..." and so on. As we are dealling with pixels, we eventually get one last pixel, which is black, or white. If we could divide up a pixel infinitely then we could still only reach 100% ( which would be 3million pixels on a 3MP picture etc). We don't reach infinite pixels, because we are fixed in how many we can use.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 5:52 pm UTC
Technical Ben wrote:
tzvibish wrote:OK, after an hour or so of picking out brain chunks from the wall behind me, I have a serious question. In the last panel, for the recursion, take the pie chart. It says: "Amount of Black in the Image". Not just the panel, but the entire strip, correct? So, once you take the final recursion into account, the actual amount of black in the pie chart will be the value of limit (as a percentage) as the summation approaches infinity? I think I'm right so far. Let me know if not.

Now, in the last panel, we have a series of pie charts that get proportionally smaller ever time, but the relative size of the pie slices remain the same. So, if they are the same percentage every time, then they all must equal the final value of the limit of summation as it approaches infinity (and it's around 10%). Am I looking at this right?

An easy way to answer this is to ask how much ink is in the image. Is it 100% black? No. Even if it was, that would not be infinite, just all of it. So we know it's not approaching infinity. Each repeated image is smaller than the next. So you can add it up like "10 + 9 + 8..." and so on. As we are dealling with pixels, we eventually get one last pixel, which is black, or white. If we could divide up a pixel infinitely then we could still only reach 100% ( which would be 3million pixels on a 3MP picture etc). We don't reach infinite pixels, because we are fixed in how many we can use.

I think you misunderstood me. What I mean is that the limit of the summation as it approaches infinity = the amount of black in the comic. The amount of black in each recursion gets closer and closer to 1/infinity every time.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 6:11 pm UTC
Pxtl wrote:At first I thought they were describing themselves - that is, "this much of the chart is black" and "this much of this bar is black", making it recursive but extremely trivial.

Then I saw the 3rd panel and dawn broke.
I thought this too. Very nicely done, Randall.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 6:20 pm UTC
I was initially thrilled by this one, then greatly disappointed. On close examination, I noticed that the values given weren't even approximately correct. I mentioned this to a co-worker who printed out a copy to confirm my observation, which he did: the amount of black ink was nowhere near correct.

This is where it gets freaky though.

We told another co-worker and when she printed out a copy, we could all see that the values were reasonably accurate (certainly close enough for a web comic).

So what was up with that? The only thing we could figure was that, even though the image is black and white her colour printer was somehow giving a more accurate rendition of the original than my monitor or Eddie's laser printer, especially in regards to the amount of back ink used. This may be a good thing to keep in mind as a benchmark the next time you are printer (or monitor) shopping.

-- MarkusQ

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 6:32 pm UTC
Just another self referencial riddle:

There is three errers in this sentence.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 6:45 pm UTC
ok about the first panel, according to it, X% is black ink, now as he added up the total used to write the statement + the amount in the graph, the graph should continuously grow because as you add up the percentages, more ink has to be used to state how much, so the number should grow even more.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 6:52 pm UTC
...

(did you hear that? that was my brain imploding just now)

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 6:59 pm UTC
I applaud this strip.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 7:01 pm UTC
BlazeOrangeDeer wrote:I am in awe. At first I didn't see the purpose of it, then I said ooohhhh that's actually pretty complicated.

Wait, IS there any purpose? That is, other than to make the reader feel smart?

(I actually thought the purposelessness, the pointlessness and the extreme absurdity of it were the joke. The comic would be hilarious if it were a mockery of nerd mentality, but apparently it's unintentional self-parody)

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 7:10 pm UTC
cheeseheadtotherescue wrote:Just another self referential riddle:

There is three errers in this sentence.

Wait a second. The errors I see are "is" and "errers", but that's only two, which means that sentence is false, making three, but then it would be true, as- *sinuses detonate*

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 7:15 pm UTC
On a similar topic. One of the more evil self references out there.

http://consc.net/misc/moser.html

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 7:29 pm UTC
RockoTDF wrote:
Agentstinky wrote:Anyone else reminded of Douglas Hofstadter? I'm working my way through "Godel, Escher, Bach" right now.

That was the first thing I thought once I realized where the comic was going. GEB is great, but do not skip the dialogues, even though he says they aren't mandatory reading, they really should be (in later chapters he will outright reference them). I Am a Strange Loop is a pretty good follow up as well, explains some of the stuff about cognition in a much clearer way with less math/logic (I mean this in that it is less confusing of a read) and virtually no music theory.

I'm a fan of Hofstadter's work, but for me he sorta jumped the shark with I Am a Strange Loop. All the mathy/sciency stuff is great, but he rather lost me with the metaphysical "my wife isn't dead" material in the second half of the book. I ended up returning it (library book) before I finished the last chapter.

His other work is fascinating, though!

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 7:31 pm UTC
Maltheos wrote:On a similar topic. One of the more evil self references out there.

http://consc.net/misc/moser.html

That is amazing.

Edit: beaten to it.

Haha I was also going for it. :S

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 7:48 pm UTC
It occurs to me that this may be the first forum thread in the history of web comics where a reader could have posted the word, "First!" as the first posting and it would have been both topical and witty.

Perhaps that's why it didn't happen.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 7:57 pm UTC
The obvious question is whether this comic is inconsistent or incomplete. Or if it's just insufficiently expressive to encode a GĂ¶del sentence. I suppose the world will never know.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 8:04 pm UTC
dawigwam wrote:ok about the first panel, according to it, X% is black ink, now as he added up the total used to write the statement + the amount in the graph, the graph should continuously grow because as you add up the percentages, more ink has to be used to state how much, so the number should grow even more.

Yes, but it doesn't grow to infinity, it approaches a finite number.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 8:36 pm UTC
tzvibish wrote:
I think you misunderstood me. What I mean is that the limit of the summation as it approaches infinity = the amount of black in the comic. The amount of black in each recursion gets closer and closer to 1/infinity every time.

Oh, sorry. I totally agree on that one. But my brain also says it must be able to reach an equilibrium.
 What the above poster said.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 8:54 pm UTC
SunDawg wrote:Only the fool would take trouble to verify that this sentence was composed of ten a's, three b's, four c's, four d's, forty-six e's, sixteen f's, four g's, thirteen h's, fifteen i's, two k's, nine l's, four m's, twenty-five n's, twenty-four o's, five p's, sixteen r's, forty-one s's, thirty-seven t's, ten u's, eight v's, eight w's, four x's, eleven y's, twenty-seven commas, twenty-three apostrophes, seven hyphens, and, last but not least, a single !
This fool sadly notes that the above sentence is incorrect on two counts :(

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 9:23 pm UTC
I would very much like to see a version of this comic where panel 3 shows "Location of WHITE ink in this image"

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 9:31 pm UTC
All right, clearly in panel 3 of the mini-comic in panel 3 there's another comic...and you can make it out well enough in that mini-comic...but what's in that mini-comic? We're getting close to the resolution, so is it just an approximation? It looks like kind of a grey smudge...

tmjdisorder wrote:two hundred and forty-two? should be two hundred forty-two (but of course that would be incorrect)

Why? (Why should it be, not why would it be incorrect.)

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 9:57 pm UTC
SocialSceneRepairman wrote:All right, clearly in panel 3 of the mini-comic in panel 3 there's another comic...and you can make it out well enough in that mini-comic...but what's in that mini-comic? We're getting close to the resolution, so is it just an approximation? It looks like kind of a grey smudge...

tmjdisorder wrote:two hundred and forty-two? should be two hundred forty-two (but of course that would be incorrect)

Why? (Why should it be, not why would it be incorrect.)

In British English use "and" when saying numbers in the hundreds.
Example: seven hundred AND twenty seven.

In American English do NOT use "and" when saying numbers in the hundreds.
Example: seven hundred twenty seven.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 10:09 pm UTC
Jackpot wrote:Dude, stop. Making fun of recursion sucks. It's not even funny.

Dude, stop. Making fun of recursion sucks. It's not even funny.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 10:15 pm UTC
Splarka wrote:When is "This sentence is spoken with [0-9]* syllables" true?

This sentence is spoken with (five plus five plus five) syllables.

"five plus five plus five" does not match "[0-9]*"

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 10:16 pm UTC
Jackpot wrote:
Jackpot wrote:Dude, stop. Making fun of recursion sucks. It's not even funny.

Dude, stop. Making fun of recursion sucks. It's not even funny.

Oh, an Epimenides joke. Brilliant.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 10:21 pm UTC
Splarka wrote:When is "This sentence is spoken with [0-9]* syllables" true?

"This sentence is spoken with syllables"

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 10:31 pm UTC
jacog wrote:Okay, colour me stupid, but if we're counting pixels, and the image is anti-aliased, isn't a fair portion of the pixels some shade of grey* ?

( or possibly "gray", depending on where you live )

I used a threshold, anything <= 128,128,128 = black

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 10:32 pm UTC
I think some of you are over-thinking the comic: there are a finite number of pixel, so infinite recursion is not required.

Some have pointed out he image is gray-scale, not black & white. That contradiction is easy enough to solve: Posterize the comic such that each 8-bit gray-scale pixel is replaced by a 16x16 grid of black & white pixels. The number of darkened pixels in the grid should correspond to the gray-scale value.

Another way to think of it: the comic is using sub-pixel rendering to approximate a higher resolution black & white image on your colour display.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 10:55 pm UTC
Seriously?...

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 11:09 pm UTC
This sentence contains exactly thirteen syllables.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 11:31 pm UTC

Code: Select all

`phlip@boris:~/self_description\$ ./check.pyFor the first panel to be accurate, these two numbers should match:10.6820467526 10.9279725709For the second panel to be accurate, these three numbers should match:16.3532095773 16.1707719189 16.134083246`

Seems pretty accurate to me. Within measurement error, at least.

For reference: the first two numbers are the percentage of black in the image and the percentage of black in the pie chart, respectively. If these numbers match, the pie chart is accurate.

For the bar graph, we don't have a vertical scale, but what we can do is use one to figure out the scale, and check the other two match that scale. Or, more simply, use all three to figure out the scale, and check that those scales agree. So that's what they are - the numbers are the proportion of black in the appropriate panel, divided by the height of the respective bar in the graph. The number actually represents what the value should be at the very top of the graph - that is, the vertical scale is such that a bar that reached to the top of the graph (that is, the top of the axis on the left) would represent the respective panel being just over 16% black. Because all three numbers agree, the relative heights in the graph are correct.

That the third panel is accurate can be done by inspection.

(This is using weighting, so that, say, a 50%-grey pixel counts as half a black pixel. Since that's what the antialiasing represents anyway.)

So yeah, the comic is accurate.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 11:35 pm UTC
I agree that panel 2 needs to be changed. It could be a percentage of black ink by panel and be correct.

As it stands, if it's just the true amount by panel, the node for panel 2 wouldn't (always) have a loop. This is the case iff you add the black to the top of bar 2 in panel 2 because in that case it would not require a further update to its own panel (meaning no loop).

If it were a percentage, then an addition to the top of bar 2 in panel 2 would require a slight decrease in the height of bars 1 and 3. That's the only way I see the node for panel 2 always having a loop.

synthesis77 wrote:
Splarka wrote:When is "This sentence is spoken with [0-9]* syllables" true?

"This sentence is spoken with syllables"

Ah, you tricky guy. Change it to [0-9]+ for your regex gurus.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 11:45 pm UTC
This sentence is spoken with exactly fifteen syllables.

### Re: "Self-Description" Discussion

Posted: Wed Jan 13, 2010 11:45 pm UTC
Maltheos wrote:On a similar topic. One of the more evil self references out there.

http://consc.net/misc/moser.html

I have read this and conclude that most people do not need to read it but will after they read this synopsis:
neoliminal wrote:I have read this and conclude that most people do not need to read it but will after they read this synopsis:
neoliminal wrote:I have read this and conclude that most people do not need to read it but will after they read this synopsis:
neoliminal wrote:I have read this and conclude that most people do not need to read it but will after they read this synopsis:

### Re: "Self-Description" Discussion

Posted: Thu Jan 14, 2010 12:14 am UTC
I registered on this forum, a somewhat laborious process, simply so I could say that this comic might be the worst xkcd comic ever. And it has some competition.