[HN Gopher] Dubious Math in Infinite Jest (2009)
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Dubious Math in Infinite Jest (2009)
Author : rafaepta
Score : 75 points
Date : 2025-06-10 15:04 UTC (7 hours ago)
(HTM) web link (www.thehowlingfantods.com)
(TXT) w3m dump (www.thehowlingfantods.com)
| lou1306 wrote:
| > the Mean Value Theorem for integrals is a theoretical tool for
| proving the existence of this particular x'. It does not,
| however, offer any method of finding the value of x'. Therefore,
| it is difficult to imagine how the Mean Value Theorem for
| integrals could be employed in Pemulis' Eschaton calculations.
|
| Knowing the character, at least this one could be explained as
| yet another parlour trick from Michael Pemulis. God knows how he
| actually calculated those values.
| thaumasiotes wrote:
| > Intentional math errors in David Foster Wallace's work
|
| The actual title of this piece is "Dubious Math in _Infinite
| Jest_ ". There is no suggestion, in the title or the contents,
| that the errors are intentional. In the author's words:
|
| > As I have said, I have no theories to explain the existence of
| these errors.
| caminanteblanco wrote:
| Yes, the title entered here on HN is misleading and
| misrepresents the actual article.
| rafaepta wrote:
| You're right. I've just changed the title of the article adding
| "(un)" to the beginning. I can't prove the errors are
| intentional, but given the author's reputation it would
| surprise me if they weren't.
| Jtsummers wrote:
| Instead of editing the title, the guidelines have this to
| say:
|
| > Otherwise please use the original title, unless it is
| misleading or linkbait; don't editorialize.
|
| https://news.ycombinator.com/newsguidelines.html
|
| Edited titles (without a reason, like abbreviating them to
| fit or removing elements suggested by the guidelines for
| elimination) just get reverted, you're creating work for the
| mods by not submitting the original title.
| FL33TW00D wrote:
| I look forward to the day another book makes me feel like IJ -
| even with the mathematical flaws :)
| lemonberry wrote:
| Have you read "Gravity's Rainbow" by Thomas Pynchon? If not,
| it's worth checking out.
| chamomeal wrote:
| Inherent Vice is such a fun whacky read too. I kinda wanted
| to read Gravity's Rainbow but my friend (who also recommended
| Inherent Vice) said I probably wouldn't have the patience for
| it lol. He's usually right
| spondylosaurus wrote:
| Bleeding Edge is another fun, (relatively) short read if
| you want to go back for more Pynchon.
| lemonberry wrote:
| Inherent Vice was great too. Gravity's Rainbow took me a
| few times to get into but it was a wild ride.
|
| His early book "The Crying of Lot 49" was also really good.
| igor47 wrote:
| As detective Blanc says in Glass Onion, "nobody has read"
| Gravity's Rainbow
| Boogie_Man wrote:
| What race is Hal?
| sanderjd wrote:
| Agreed. It was really a revelation to me. Looking back now,
| it's clear that I started reading it as a status seeking thing.
| I thought my intellectual friends (and especially girlfriends)
| would think it was cool that I actually read the whole thing
| (which nobody else in our circle had actually managed yet). But
| then it turned out to really affect me deeply.
|
| I read it again about a decade later after all those games were
| over for me, just for myself, and loved it even more that time.
|
| For some people, it just really does hit a nerve!
| gowld wrote:
| > I thought my intellectual friends (and especially
| girlfriends) would think it was cool that I actually read the
| whole thing
|
| Interesting though, considering the popular meme among women,
| that men think reading IJ makes them look smart.
|
| https://reductress.com/post/why-im-waiting-for-the-right-
| man...
|
| https://www.reddit.com/r/davidfosterwallace/comments/evsylv/.
| ..
| scyzoryk_xyz wrote:
| It's a Bildungsroman for the 90's Americana age.
|
| Whoever is reading it is eager to come of age, but is
| likely super obnoxious because they're not there yet. At
| least that's how I think of myself reading it at 25.
| sanderjd wrote:
| ha, well put!
| sanderjd wrote:
| I hoped it was clear from my comment that this was a
| youthful indiscretion and should not be used as any
| indication that I was _right_ about any of my motivations
| for this at the time :)
|
| Though I dunno, this was a long time ago, much closer to
| the publication date of the book (like a decade and a half
| before either of these articles were published), and I'm
| not sure this cynicism had quite taken off yet.
|
| Also, I'm a bit skeptical of the gender lens on this, at
| least at that time period. From reading these articles, I
| think the girls I was trying to impress were likely
| themselves "typical DFW asshole[s]" by the judgement of
| these authors. Men don't actually have a monopoly on "I am
| so smart" vanity (though I'd agree we seem more prone to
| it).
| 11101010001100 wrote:
| Yes, once you read IJ, it is very hard to find another book
| like it. It is almost as if IJ refers to itself.
| jrm4 wrote:
| House of Leaves, perhaps?
| npilk wrote:
| I've seen a theory that the mistakes Pemulis makes are
| intentional, and signal that he isn't as smart as he thinks and
| that he doesn't really have everything in control.
|
| I'm not sure; clearly DFW had some math aptitude but these also
| could have been honest mistakes. Presumably it would have been
| harder for editors to check these things in the 90s.
|
| The probability error seems harder to explain and likely just a
| mistake.
|
| Edit - While searching a bit more about this, I found an
| interesting perspective on a message board:
|
| > The main thing that I think argues for Pemulis not being as
| smart as he thinks he is, is that he is the analogue of Polonious
| from Hamlet. In Hamlet, the court jester (the "fool") is actually
| really wise and always speaks the truth (=Mario), while the
| King's supposedly "wise" counselor, Polonious, actually gets
| everything wrong.
|
| I find that pretty compelling. I hadn't really thought about
| deeper correspondences with Hamlet beyond Hal and his parents.
|
| https://infinitesummer.org/forums/viewtopic.php?f=12&t=471
| dbtc wrote:
| And the title
| spondylosaurus wrote:
| Would Pemulis be Polonius though? If he were the advisor to the
| king, then the king would more likely be Tavis, not Hal.
|
| I do like the idea of Mario as a court jester though.
| npilk wrote:
| Good point. Although the book isn't any sort of adaptation,
| so I could see including an allusion to the Polonius
| character even in a slightly different role.
|
| (I'd also forgotten about the janitors, who are clearly a
| reference to Rosencrantz and Guildenstern)
| eszed wrote:
| I associated Pemulis with Polonius based on the phonemic
| similarity of the names. I don't have the maths background to
| evaluate the mistakes, but agree that if intentional they
| "match" with the character's presentation in Hamlet.
| kolbe wrote:
| Maybe a phonetic similarity with "pretentious" as well
| RunSet wrote:
| Perhaps my favorite deliberate error in arithmetic is from
| Winston Groom's Forrest Gump, during the protagonist's tour in
| Vietnam:
|
| > I am the machine gun ammo bearer, cause they figger I can
| carry a lot of shit on account of my size. Before we lef, a
| couple of other fellers axed if I would mind carryin some of
| their han grenades so's they could carry more orations, an I
| agreed. It didn't hurt me none. Also, Sergeant Kranz made me
| carry a ten-gallon water can that weighed about fifty pounds.
|
| Unlike Forrest, the reader knows a gallon of water weighs
| roughly eight pounds and is not spared the extent of his
| burden.
| gowld wrote:
| Eighty pounds is "about fifty pounds", especially considering
| that a water can worth carrying at all is often not full, and
| insofar as nothing else in the paragraph is given a specific
| weight so the precise number doesn't really matter.
| ofalkaed wrote:
| They are purposeful, I don't think Pemulis ever gets one thing
| right in the novel. His explanation of Annular Fusion is a good
| example, unless you also want to make the case that Wallace got
| the made up science wrong as well. Pemulis grew up in a place
| where he was generally the smartest person around and was able
| to bluff his way through life without much effort. Then he got
| a scholarship to somewhere with actual expectations and
| standards but Pemulis kept on with his lazy ways. Pemulis is
| probably smart but his laziness and arrogance keep him from
| ever achieving his own intelligence, he is forever lobbing but
| is a bit too slow to get to the net in time.
|
| Vast majority of character's are well explained and the answers
| are all in the novel, just need to look at their childhood and
| upbringing.
| mathgradthrow wrote:
| Maybe DFW wasn't as smart as he thought he was.
| ajkjk wrote:
| No one of any level of math skill would mistake the the
| derivative of x^n as nx + x^n-1. There's no way DFW messed that
| up, but it's also a pretty bizarre mistake to have a character
| make if they're supposed to be making mistakes.
| evanjrowley wrote:
| Wouldn't Pemulis' mathematical errors be consistent with how
| Infinite Jest begins? I.e., he has some sort of degenerative
| condition directly or indirectly associated with exposure to
| strange mold found in the basement of his childhood home?
| andy_xor_andrew wrote:
| > Again, Mike Pemulis is lecturing Hal, but this time he is
| helping Hal prepare for the college board exams. Pemulis states
| that for the function x^n, the derivative is nx + x^(n-1). In
| fact, the correct expression is nx^(n-1). This, too, may be a
| typographical error.
|
| Another possibility is that Pemulis is simply bad at math :D
| lacker wrote:
| Reading the DFW biography, Every Love Story Is a Ghost Story,
| it said that there were hundreds of cases where the editor
| claimed something was a typographical error, and DFW insisted
| that actually it was precisely how he meant it to be. They went
| back and forth for months, with the publisher eventually
| charging DFW a fee for all the extra labor involved.
|
| So... we can't know for sure, but there's a strong case that
| any particular little weird error, DFW intended it to be this
| way. Especially for a "basic calculus" issue like this, for
| someone who wrote a whole book on the mathematical history of
| infinity. (Which arguably has its own errors, but those tend to
| fall more in the category of simplifications for the lay
| reader, IMO.)
| spondylosaurus wrote:
| I've definitely noticed some of those odd one-off typos, like
| misspelling the NIKKEI stock exchange as NIKEI, but I had
| always just assumed some of those were bound to slip through
| in such a long, dense novel, even with an astute editor :P It
| sounds like that may not be the case after all...
| gowld wrote:
| > (Which arguably has its own errors, but those tend to fall
| more in the category of simplifications for the lay reader,
| IMO.)
|
| They were more mis-simplifications by the lay writer.
| crystal_revenge wrote:
| What's interesting about this is that it used to be far more
| common for most technical people to be pretty well versed in
| basic calculus. A frightening number of software engineers
| don't really understand calculus. But back in the 90s most
| engineers, even software folks who may likely have come from an
| EE background, would have had the basics down pretty well. DFW
| was writing for an audience with a potentially much higher
| mathematical literacy than today.
|
| The probability that this "mistake" is intentional is related
| to how likely an informed reader would be to recognize this
| mistake.
| griffzhowl wrote:
| Yeah, that looks to me far more likely to be deliberate. The
| obvious comedy of the situation is someone taking himself to be
| well-versed enough to be giving a lecture while in fact being
| an incompetent buffoon.
| arh68 wrote:
| Maybe he "just" got it wrong. Maybe they're typos, and the
| manuscript was correct. Or...
|
| Maybe Pemulis gave Hal an obviously wrong derivative, and when
| uncorrected, drove Pemulis to abruptly end the tutoring. Maybe
| Pemulis _said_ it right but Hal _heard_ it wrong. Or...
|
| Maybe it's "just" another sign they're in an alternate universe
| where even the math is different. That's pretty much how I feel
| about it
| feoren wrote:
| > Maybe it's "just" another sign they're in an alternate
| universe where even the math is different
|
| Unlike physics, there are no conceivable alternate universes
| with different math. That's what's so cool about math: it could
| not possibly be any different. There could be alternate
| universes where they've discovered different amounts of it, or
| named the discoveries different things, but everything that is
| "wrong" in math in our universe is universally (multiversally?)
| wrong.
| LegionMammal978 wrote:
| > That's what's so cool about math: it could not possibly be
| any different.
|
| Why not? There's not much tethering our axioms-on-paper to
| what is necessarily true, past what we can empirically
| observe. For instance, a universe that is "exactly like ours,
| except the truth of the continuum hypothesis is flipped"
| seems no less conceivable than our own universe, given that
| we don't even have any solid evidence for its truth or
| falsehood in the first place.
|
| If we're willing to treat mathematical and logical ideas as
| physically contingent, then it's only a few further steps to
| "the concepts of identity and discreteness and measure in
| this universe are different than ours, so all our
| mathematical axioms are not applicable". Though it would be
| very difficult to translate any stories from such a universe
| into our own ideas.
| thaumasiotes wrote:
| > For instance, a universe that is "exactly like ours,
| except the truth of the continuum hypothesis is flipped"
| seems no less conceivable than our own universe
|
| Really? For that to be possible, the continuum hypothesis
| would have to be either true or false in our universe,
| which does not appear to be the case.
| mtizim wrote:
| Why not? Exactly because there is nothing tethering our
| axioms on paper to what is necessarily true. You could
| formulate something wildly different from
| ZF+-C/Peano/whatever normal axiom system, but we wouldn't
| call it "math", and what we currently call "math" will work
| under any conditions
| feoren wrote:
| > "exactly like ours, except the truth of the continuum
| hypothesis is flipped"
|
| We can and do create two alternate models of math with CH
| and ~CH as axioms, in this universe, right now. No need for
| alternate universes. There's no reason to think the CH is
| either true or false in the natural laws of our universe --
| what would that even mean?
|
| I suppose it's distantly possible that models where CH is
| true happen to represent our own universe much better than
| models where CH is false, and that there are other
| universes that are better represented by models where CH is
| false. Even if that were true, all the math is still the
| same, we're just preferring some models over others.
| NewsaHackO wrote:
| I haven't read IJ in a while, but I don't think I agree with the
| first one. Unless he specifically said that each player has an
| equal chance of winning, I would not assume that to be the case.
| sanderjd wrote:
| Interesting! But then it seems like he would have said it a bit
| differently, that the odds of _that particular_ tournament with
| those specific players ending in a tie were much lower.
| trefoiled wrote:
| This isn't the only example of a debate over intentionality in
| mistakes in Infinite Jest. The book's french is also littered
| with errors so egregious that most think they could only have
| been intentional [1].
|
| [1] https://ask.metafilter.com/116066/French-language-in-
| Infinit...
| A_D_E_P_T wrote:
| DFW also wrote _Everything and More: A Compact History of
| Infinity_ -- an uncritical review of Cantor 's work, which was
| absolutely loaded with errors.
|
| Rudy Rucker wrote a scathing review here:
| https://www.rudyrucker.com/oldhomepage/wallace_review.pdf
|
| I actually read _Everything and More_ and it 's probably even
| worse than that. Though I'll admit that I'm a little bit biased;
| I'm a sort of Aristotelian Realist or even a Finitist when it
| comes to mathematics, and I view Cantor's hierarchy of infinities
| as... well... schizo _at best_.
| lacker wrote:
| Personally I don't agree with that review at all, and I loved
| _Everything and More_. I 'm even somewhat of a "finitist"
| myself mathematically, but I think you can just view the whole
| hierarchy of infinities as a finite mode of description, and
| get utility from it without worrying about the "reality" of the
| whole thing. But that's a bit of an aside.
|
| The review-writer clearly hates the book before he even gets to
| the mathematics. The whole book is striking a middle ground
| between expressing every step of mathematical rigor, and
| describing in a more literary way how to feel about these
| concepts. All of these "errors" are just the author passing
| over a point in less detail than you would want from a text on
| set theory. I thought it was great, and for anyone who enjoys
| both set theory and Infinite Jest, I would strongly recommend
| the book.
|
| I understand that some people don't like it, but it should be
| viewed as "controversial" rather than "everyone agrees that
| it's riddled with errors".
| A_D_E_P_T wrote:
| > _" He incorrectly suggests that the axiom of choice is used
| for Cantor's diagonal argument"_
|
| This alone is a pretty substantial, even foundational, error.
|
| The author of the review, Rudy Rucker, is a sort of
| cult/underground author of math-heavy science fiction. I
| don't think he's opposed to framing things in a literary way,
| so long as it's not misleading or falsely dramatized. Like,
| e.g., Godel ending his days in some sort of forced
| confinement, as DFW seems to have suggested?
| lacker wrote:
| The DFW style is not just "literary", it's dense, full of
| self-referential hints, critical footnotes, invented
| acronyms, retellings of the same events from multiple
| perspectives. I like Rudy Rucker a lot but his work is
| nothing like it.
|
| The core problem with this book is that it is a great book
| for people who love both math and Infinite Jest. But, that
| might be an audience of nobody. Or almost nobody, because
| it does include me.
| dkarl wrote:
| > The whole book is striking a middle ground between
| expressing every step of mathematical rigor, and describing
| in a more literary way how to feel about these concepts
|
| I really hate this. If you don't care to understand
| something, why would you want to absorb the feelings that
| somebody else thinks you should have from understanding it?
| It reminds me of all the cringey posturing that undergrads
| engage in because their English professor mentioned a couple
| of philosophers during lectures and it totally changed their
| wardrobe.
| jknoepfler wrote:
| Why would you hate a book exploring mathematics and
| reflecting on your relationship with it? What a weird thing
| to hate. Wouldn't you rather celebrate intellectual
| curiosity?
|
| Like... I hate journalism that profits off of xenophobic
| fear mongering. A book from a genuinely curious and
| interesting author who did some moonlighting in more formal
| subjects, though? That seems harmless and kind of cute at
| worst. Maybe a little misguided, maybe not.
|
| It's a weird energy to bring to a relatively innoccuous
| corner of the world.
| sfpotter wrote:
| I read it and it made me pretty upset... Wallace clearly got
| way out over his skis and simply shouldn't have been writing
| about the topic. There were way too many moments interspersed
| throughout the book where it was obvious that he didn't
| understand what he was talking about or trying to prove. I
| think one of the key lessons to be learned from the study of
| mathematics is intellectual honestly and humility. It felt
| like Wallace hadn't learnt that lesson and had something
| to... ahem... prove?
| gowld wrote:
| The problem with Everything and More is not because it is
| "uncritical"; it's that DFW didn't understand it and was "not
| even wrong" when explaining it. Even if you choose not to
| engage with Cantor's hierarchy of infinities because you don't
| find it interesting or relevant to the (finite or smaller
| infinite) sets you care about, there's nothing wrong with it as
| mathematics.
| ks2048 wrote:
| Yeah, I like DFW (although mainly from essays and interviews)
| and thought this book was not good. Tangentially, I didn't
| really like Rucker's book on infinity either. I can't remember
| why exactly, but it didn't match up with other math
| popularizers (eg, Strogatz, Nahin).
| neuroelectron wrote:
| Has anyone actually read Infinite Jest in its entirety? I got
| about 50 pages in and I'm pretty sure I got the _jist_ of it from
| that. The constant slog into minutia and clunky grammar made it
| very slow reading for me. There were some funny parts but overall
| the effort didn 't feel worth it.
|
| I tore through Gravity's Rainbow (mentioned in another thread).
| dilap wrote:
| Yeah definitely, multiple times. But I feel you! The first time
| I read it it took me months to make it past the first couple
| hundred pages. But once you get far enough in everything starts
| to gel and it gets really fun.
| kolbe wrote:
| Cool. We care. Keep talking.
| rurp wrote:
| I totally agree, IJ might be the single most disappointing book
| I've read given the extreme hype around it. The writing style
| felt very self-indulgent and annoying. The funny/clever parts
| rarely seemed amusing to me.
|
| Enough people say they love the book that it's probably just a
| style thing that didn't click for me, but I regret how much
| time I spent slogging through the book and never bothered to
| finish it.
| jquaint wrote:
| I enjoyed Infinite Jest.
|
| I think it's good book if you are someone who HAS to know all
| the details.
|
| The book itself criticizes this way of thinking, while letting
| you in the all the details you could want. (the footnotes
| especially)
|
| I get the sense that the writing style is a metaphor and part
| of it for sure.
|
| I also really like many of the subtle ideas the book presents.
|
| Though like many "post modern novels", it's not for everyone.
| If intentionally dull parts are not your thing, that's
| perfectly fine IMO.
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