# Explain to me the latest xkcd **URL:** \ **Category:** Cafe Society\ **Created:** [August 29, 2008, 2:59am UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642 "2008-08-29T02:59:23Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Risha](https://avatars.discourse-cdn.com/v4/letter/r/5fc32e/32.png) [@Risha](https://boards.straightdope.com/u/Risha)\ **Post date:** [August 29, 2008, 2:59am UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/1 "2008-08-29T02:59:23Z")
I get the general joke about “[anything not on your list](http://xkcd.com/468/)”, but the rest of it eludes me. I skimmed Wikipedia’s article about whom I assume to be the correct [Godel](http://en.wikipedia.org/wiki/Godel), but remain unenlightened. Thanks in advance! ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 29, 2008, 3:05am UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/2 "2008-08-29T03:05:28Z")
Maybe you don’t get the joke about “anything not on your list”? The “anything not on your list” is a reference to Russell’s paradox in logic/mathematics, that engendered by asking whether (the set of all sets which do not contain themselves) contains itself or not. This kind of “strange” self-reference is an instance of a technique known as “diagonalization”. Goedel is famed for having proved Goedel’s Incompleteness Theorem in mathematical logic (not actually a paradox in the sense of yielding an inconsistency, but to many, for some reason, a surprising and undesirable result nonetheless), using a diagonalization proof along similar lines, by constructing a sentence S whose meaning, in some sense, is “S is not provable [within formal system X]”. Similarly, the reference to Cantor in the alt-text is because of Cantor’s Theorem, the canonical diagonalization proof within set theory, which leads straightforwardly to the discovery of Russell’s paradox. [Though, I’d say, I’m not a huge fan of this comic. It falls within a large swath of xkcd comics a friend of mine is constantly denouncing as “Not funny; just geeky ‘name-dropping’”; while I often disagree with that assessment, in this case, it seems spot-on] ---
**Author:** ![Terrifel](https://avatars.discourse-cdn.com/v4/letter/t/c68b51/32.png) [@Terrifel](https://boards.straightdope.com/u/Terrifel)\ **Post date:** [August 29, 2008, 3:15am UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/3 "2008-08-29T03:15:33Z")
That doesn’t look anything like Russell. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [August 29, 2008, 3:27am UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/4 "2008-08-29T03:27:59Z")
But Whitehead’s representation is spot-on. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 29, 2008, 3:31am UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/5 "2008-08-29T03:31:54Z")
Also, being very nitpicky, the comic just doesn’t seem to hold together conceptually for me. Russell’s paradox didn’t damage Russell and Whitehead’s work (Principia Mathematica); rather, it damaged (aspects of) Frege’s previous work, with Principia Mathematica specifically being a response to this in order to avoid such paradox (and, as far as avoiding inconsistency goes, it certainly seems to have pulled that off). Also, what would be the problem with the list containing a fetish of “Anything not on the list”? [For example, if the list is meant to be truly comprehensive, then this can work out just fine; there won’t be anything not on the list, Goedel isn’t turned on by anything, whatever, done. No problems.] And in the alt-text, what’s the “everything-in-the-fetish-book-twice” result of Cantor’s supposed to allude to? Or is that just silliness with no substantial reference? [Yeah, I know. Way too nitpicky. Well, I actually think the depiction of Russell is pretty accurate; in his older years, white-haired and pipe-smoking, and, most importantly, facing to the viewer’s right. Everyone knows that [Russell](http://ecx.images-amazon.com/images/I/417JQ0JYGRL._SS500_.jpg) turned more and more towards the viewer’s right as the years went on.] ---
**Author:** ![Freudian\_Slit](https://avatars.discourse-cdn.com/v4/letter/f/5daacb/32.png) [@Freudian\_Slit](https://boards.straightdope.com/u/Freudian_Slit)\ **Post date:** [August 29, 2008, 3:54am UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/6 "2008-08-29T03:54:19Z")
Um. I’m just going to smile and nod and accept the fact that some xkcd comics are just too geeky for me… ---
**Author:** ![Risha](https://avatars.discourse-cdn.com/v4/letter/r/5fc32e/32.png) [@Risha](https://boards.straightdope.com/u/Risha)\ **Post date:** [August 29, 2008, 4:15am UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/7 "2008-08-29T04:15:14Z")
[QUOTE=Freudian Slit] Um. I’m just going to smile and nod and accept the fact that some xkcd comics are just too geeky for me… [/QUOTE] Er. Sorry, **Indistinguishable** , but despite your efforts I’m going to have to go with **Freudian Slit** with that. Obviously Calc I failed to prepare me for your explanation. 😃 (As you noted, I didn’t even realize that the “anything not on your list” was part of the math reference - I had interpreted it as a straightforward joke about throwing the survey off by giving an answer that can never be added to the list of answers.) ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [August 29, 2008, 4:24am UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/8 "2008-08-29T04:24:13Z")
[QUOTE=Risha] Er. Sorry, **Indistinguishable** , but despite your efforts I’m going to have to go with **Freudian Slit** with that. Obviously Calc I failed to prepare me for your explanation. 😃 [/QUOTE] Alas. Though, I didn’t really explain any of the math, either; I just expanded on the name-dropping of the strip by pointing out the history it was alluding to. If you’d really care to know, I (and/or others, of course) could take the time to actually explain the math instead of merely mentioning it, though I don’t think it would actually enhance your enjoyment of the strip that much, and might even detract from it. 🙂 [QUOTE=Risha] (As you noted, I didn’t even realize that the “anything not on your list” was part of the math reference - I had interpreted it as a straightforward joke about throwing the survey off by giving an answer that can never be added to the list of answers.) [/QUOTE] Well, it is that too; it’s just that _that_ itself is part of the math reference. (And, like I said, I don’t see how this actually works out; why _couldn’t_ you add that answer to the list?) ---
**Author:** ![mr.jp](https://avatars.discourse-cdn.com/v4/letter/m/48db29/32.png) [@mr.jp](https://boards.straightdope.com/u/mr.jp)\ **Post date:** [August 29, 2008, 10:36am UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/9 "2008-08-29T10:36:54Z")
I think he had another truly remarkable punch-line in mind to this comic, but there wasn’t enough space in the the alt text. ---
**Author:** ![HMS\_Irruncible](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hms_irruncible/32/7394_2.png) [@HMS\_Irruncible](https://boards.straightdope.com/u/HMS_Irruncible)\ **Post date:** [August 29, 2008, 10:49am UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/10 "2008-08-29T10:49:40Z")
[QUOTE=Indistinguishable] [Though, I’d say, I’m not a huge fan of this comic. It falls within a large swath of xkcd comics a friend of mine is constantly denouncing as “Not funny; just geeky ‘name-dropping’”; while I often disagree with that assessment, in this case, it seems spot-on] [/QUOTE] Agreed. It’s like Wired magazine (and its readers), they want to look smarter than they actually are. ---
**Author:** ![Terrifel](https://avatars.discourse-cdn.com/v4/letter/t/c68b51/32.png) [@Terrifel](https://boards.straightdope.com/u/Terrifel)\ **Post date:** [August 29, 2008, 10:52am UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/11 "2008-08-29T10:52:30Z")
I think it’s a bet to see how many college math professors will post the cartoon on their office doors. ---
**Author:** ![Risha](https://avatars.discourse-cdn.com/v4/letter/r/5fc32e/32.png) [@Risha](https://boards.straightdope.com/u/Risha)\ **Post date:** [August 29, 2008, 12:09pm UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/12 "2008-08-29T12:09:30Z")
[QUOTE=Indistinguishable] Alas. Though, I didn’t really explain any of the math, either; I just expanded on the name-dropping of the strip by pointing out the history it was alluding to. If you’d really care to know, I (and/or others, of course) could take the time to actually explain the math instead of merely mentioning it, though I don’t think it would actually enhance your enjoyment of the strip that much, and might even detract from it. 🙂 [/QUOTE] I think that I’ll skip (but thanks!). My brain power is low this close to a holiday weekend. _insert zombie smiley_ ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [September 2, 2008, 6:11pm UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/13 "2008-09-02T18:11:41Z")
Here’s what someone on the xkcd forums says: > [@](#): > > Edit: Okay, basically, math up until the 1920s or so was a struggle for completeness - take a small number of axioms, extend them as far as is possible, and try to hit everything that the system has reason to consider. It was generally believed that this was possible. Bertrand Russell and Alfred North Whitehead were two guys fairly well known for a book called the Principia Mathematica(no, not that one). It was published just before WW1, and tried to push completeness farther than it had ever gone before, by some fairly ingenious methods of trying to prevent recursive paradoxes(a well-known failing point). > > Kurt Godel saw this, and about a decade later published a little paper that absolutely demolished Russel and Whitehead’s entire thesis, by proving that completeness was not merely difficult, but completely impossible for any system of any real complexity. It was an absolutely beautiful argument - the short version is that he figured out a way to make the statement “This statement cannot be proven in this system” a viable theorem in any system. This statement can be proven neither true nor false, and is therefore undecidable. Given one unprovable statement, the system is incomplete, and Russell and Whitehead’s work, brilliant as it was, collapses entirely as regards their original goal. > > The mouseover text is based around an entirely different issue - specifically, counting infinities. There are many “levels” of infinities, and Georg Cantor did a lot of interesting work defining and delimiting them. It’s a bit more technical, and the best place to look is probably links off the Cantor article. For what it’s worth, take it or leave it. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 2, 2008, 6:16pm UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/14 "2008-09-02T18:16:52Z")
Yes, that’s the history. But, as I said, the comic may refer to that history, but I don’t think it does so particularly coherently, as presented. The apparent paradox within the comic is not much of a paradox at all (except, as discovered during amnesia weekend, if we take Russell and Whitehead to be perhaps composing, and Goedel to be referring to, a list specifically of Goedel’s fetishes, and not just of people’s fetishes in general) (I still don’t think anyone has actually made sense of the alt-text about Cantor, beyond “Oh, yeah, that kinda sounds like it has to do with infinities, maybe…”) ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [September 2, 2008, 6:21pm UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/15 "2008-09-02T18:21:53Z")
> [@Indistinguishable](#): > > Yes, that’s the history. But, as I said, the comic may refer to that history, but I don’t think it does so particularly coherently, as presented. The apparent paradox within the comic is not much of a paradox at all (except, as discovered during amnesia weekend, if we take Russell and Whitehead to be perhaps composing, and Goedel to be referring to, a list specifically of Goedel’s fetishes, and not just of people’s fetishes in general) > > (I still don’t think anyone has actually made sense of the alt-text about Cantor) I’m guessing it has to do with his “infinity of infinities” thing. Albeit if so it would be poorly executed (since it would be this list unlimited times instead of everything on this list twice). ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 2, 2008, 6:30pm UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/16 "2008-09-02T18:30:16Z")
Incidentally, looking back at my first post in here, and at the comic, I suppose it’s fair to say that, the more I look at it, the comic was never referring to Russell’s Paradox at all, but just to Goedel’s Incompleteness Theorem from the start (suitably “transliterated” as “The list of fetishes cannot be both comprehensive and accurate”). So I am duly chagrined on that point. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [September 2, 2008, 6:32pm UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/17 "2008-09-02T18:32:15Z")
Missed edit: I think it has to do with the cardinality of any set that is the power of an already infinite/exhaustive set. It’s often taken with Russell’s Paradox to shatter… something, I glazed over somewhere in there. > **[Cantor's paradox](https://en.wikipedia.org/wiki/Cantor%27s_paradox)** > > In set theory, Cantor's paradox states that there is no set of all cardinalities. This is derived from the theorem that there is no greatest cardinal number. In informal terms, the paradox is that the collection of all possible "infinite sizes" is not only infinite, but so infinitely large that its own infinite size cannot be any of the infinite sizes in the collection. The difficulty is handled in axiomatic set theory by declaring that this collection is not a set but a proper class; in von Neum... I love how wikipedia is only barely useful if you don’t already know what you’re talking about sometimes. Because I’m not that much of a math geek, and doing this is making me feel dumb. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 2, 2008, 6:44pm UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/18 "2008-09-02T18:44:12Z")
> [@Jragon](#): > > Missed edit: I think it has to do with the cardinality of any set that is the power of an already infinite/exhaustive set. It’s often taken with Russell’s Paradox to shatter… something, I glazed over somewhere in there. Cantor showed that (among other things) no set (of any kind) could surject onto its powerset (i.e., given a set X, there is no function from X to the subsets of X which hits every subset of X). This is naively problematic, because if we consider the set of _everything_ (or perhaps the set of _all sets_, or similar universal collections), it is clear that this must surject onto its powerset (by trivially sending an input to the set of its elements). The mainstream mathematical resolution was to conclude that naive principles of set formation (i.e., of what ksets exist) could not be maintained; only limited principles of formation (i.e., of what sets exist) were accepted, which did not allow for the construction of such universal collections (an alternative approach would be to allow for the construction of such universal collections, but not for the subsets required to let Cantor’s theorem go through). The proof of Cantor’s theorem, when applied to create this paradox, yields exactly Russell’s paradox; the two are not really different. ---
**Author:** ![KneadToKnow](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kneadtoknow/32/3999_2.png) [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)\ **Post date:** [September 2, 2008, 7:28pm UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/19 "2008-09-02T19:28:15Z")
I like sex. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 3, 2008, 6:10pm UTC](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642/20 "2008-09-03T18:10:22Z")
And now the discussion rages on [elsewhere](http://languagelog.ldc.upenn.edu/nll/?p=558#more-558). I note Mark Liberman opening with my same mistake, thinking there is a reference to Russell’s paradox, which I now think is definitely wrong; it’s Prinicipia Mathematica + Goedel’s Incompleteness Theorem all the way. [Next page](https://boards.straightdope.com/t/explain-to-me-the-latest-xkcd/461642.md?page=2)