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.
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.
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.
In terms of 'meeting the reader where they are,' you would want to telegraph the math mistakes pretty hard, or they would fly past everyone. Making them obvious and dumb is the only way they'll get attributed to the character, rather than the author.
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.
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.
> the reader knows a gallon of water weighs roughly eight pounds
Haha, you have to love those quaint, backwards Americans and their “freedom units”. Meanwhile, in the rest of the world, we can peacefully enjoy the fact that 3.785 litres of water weighs exactly 3.785 kg.
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.
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)
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?
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.
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".
> "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?
> 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.
As a mathematician, I think it is very hard to write popular expositions of mathematics. It is acceptable and even necessary to skip the technical details and replace rigorous definitions with intuitive explanations, but it should be done with great care to avoid statements that are plainly wrong and only introduce more confusion. I think the majority of texts on complicated mathematics that target the general audience suffer from this issue.
The review mentions some very unfortunate errors that are not "passing over a point in less detail": suggesting that Cantor's diagonal argument depends on the AC and that CH is equivalent to c = 2^ℵ₀.
I wasn't familiar with the book and had just read the review; I wouldn't blame the author, but the publisher should have contacted someone for proofreading.
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?
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.
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).
About half way through the book he tries to do an epsilon delta proof and completely gets the logic wrong. Ignoring any philosophical outlook, this is not a great math book.
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
> 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.
> 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.
> 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.
> 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
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.
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.)
> 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.
You'd have to assume that every time he got called out on an obvious error and insisted he'd meant it all along, he was telling the truth.
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...
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.
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.
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
Mathematically, the odds of getting exactly N heads after flipping a fair coin 2N times is surprisingly high - it asymptotically approaches 1/sqrt(pi * N) as N becomes large. For the problem in IJ, this comes out to 1/(3.14 * 54) which is 0.076776 - not far from the exact value of 0.076599. As another example, if you flip a fair coin 1000 times, you’ll get exactly 500 heads about 2.5% of the time.
The proof is also similarly easy: it’s a straightforward application of Stirling’s approximation to the formula (2N!)/(N!*N!)/2^(2N).
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).
Yes the writing style is def a metaphor for the book's subject and why i feel like I already get it without having to read the whole thing. 1080 pages of that does feel like infinity.
I had a very easy/boring job and where during last few month I spent most of my time reading infinite jest after finishing the days work. I really loved it but I probably won't read it again anytime soon, there's a pretty substantial upfront time investment you have to make before it starts getting enjoyable to read.
Though once you lock in with the world and flow of infinite jest it gets pretty amazing, I wish I had more people to talk to about it without coming off as a pretentious jackass. Also it's far more enjoyable to read it as an ebook where you can jump instantly from the text to footnotes and look up unfamiliar words. Reading the physical copy seems torturous to me.
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.
For the 20th birthday of the book's publication, there was an article in the Guardian that ended on this beautiful quote that captured the experience of reading the book perfectly for me:
"
It’ll be a slog, but around the point where it starts making sense, you will read these words:
'But you never know when the magic will descend on you. You never know when the grooves will open up. And once the magic descends you don’t want to change even the smallest detail. You don’t know what concordance of factors and variables yields that calibrated can’t-miss feeling, and you don’t want to soil the magic by trying to figure it out, but you don’t want to change your grip, your stick, your side of the court, your angle of incidence to the sun.'
"
I am curious... what's up with your "What race is Hal?" questions throughout this thread? Unless I'm super unobservant I legitimately don't remember it being made explicit in the novel. Avril is obviously French-Canadian[1], so she's presumably white, which would also make Hal at least half white, but I don't remember any description of JOI's appearance (when he was alive lol) or ethnicity beyond him being very tall.
I feel like a more definitive question could be "Which ETA student is missing several fingers?" or "How did Bruce Green's mom die?" or "What's the call sign for Joelle's radio station?" or "What roams the Great Concavity?"[2]
[1] I can't remember if CT is a true Quebecker or not, but if he is, I could at least say that Mario is 100% French-Canadian, lol.
[2] Or I just thought of another... "Which ETA student has an ironically apt disease?"
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.
Readit News
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
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.
> 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.
Maybe at the time. Presumably that gets an explanatory footnote in modern editions?
Haha, you have to love those quaint, backwards Americans and their “freedom units”. Meanwhile, in the rest of the world, we can peacefully enjoy the fact that 3.785 litres of water weighs exactly 3.785 kg.
I do like the idea of Mario as a court jester though.
(I'd also forgotten about the janitors, who are clearly a reference to Rosencrantz and Guildenstern)
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.
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".
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?
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.
The review mentions some very unfortunate errors that are not "passing over a point in less detail": suggesting that Cantor's diagonal argument depends on the AC and that CH is equivalent to c = 2^ℵ₀.
I wasn't familiar with the book and had just read the review; I wouldn't blame the author, but the publisher should have contacted someone for proofreading.
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
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.
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.
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.
Another possibility is that Pemulis is simply bad at math :D
The probability that this “mistake” is intentional is related to how likely an informed reader would be to recognize this mistake.
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.)
> 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.
You'd have to assume that every time he got called out on an obvious error and insisted he'd meant it all along, he was telling the truth.
They were more mis-simplifications by the lay writer.
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!
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/...
Dead Comment
The proof is also similarly easy: it’s a straightforward application of Stirling’s approximation to the formula (2N!)/(N!*N!)/2^(2N).
I tore through Gravity's Rainbow (mentioned in another thread).
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.
Though once you lock in with the world and flow of infinite jest it gets pretty amazing, I wish I had more people to talk to about it without coming off as a pretentious jackass. Also it's far more enjoyable to read it as an ebook where you can jump instantly from the text to footnotes and look up unfamiliar words. Reading the physical copy seems torturous to me.
" It’ll be a slog, but around the point where it starts making sense, you will read these words:
'But you never know when the magic will descend on you. You never know when the grooves will open up. And once the magic descends you don’t want to change even the smallest detail. You don’t know what concordance of factors and variables yields that calibrated can’t-miss feeling, and you don’t want to soil the magic by trying to figure it out, but you don’t want to change your grip, your stick, your side of the court, your angle of incidence to the sun.' "
(/s - I have read and enjoyed Infinite Jest. It's very reasonable for someone to not enjoy it though)
I feel like a more definitive question could be "Which ETA student is missing several fingers?" or "How did Bruce Green's mom die?" or "What's the call sign for Joelle's radio station?" or "What roams the Great Concavity?"[2]
[1] I can't remember if CT is a true Quebecker or not, but if he is, I could at least say that Mario is 100% French-Canadian, lol.
[2] Or I just thought of another... "Which ETA student has an ironically apt disease?"
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.