Infinite Proofs: The Effects of Mathematics on David Foster Wallace (2012)(lareviewofbooks.org)
lareviewofbooks.org
Infinite Proofs: The Effects of Mathematics on David Foster Wallace (2012)
https://lareviewofbooks.org/article/infinite-proofs-the-effects-of-mathematics-on-david-foster-wallace/
45 comments
Here is the book on Infinity DFW penned: https://www.amazon.com/Everything-More-Compact-History-Infin...
I want to note for the HN crowd that the book is in the "just technical enough to inform yet not scare off the layman, but not technical enough for the practitioner" nonfiction subgenre. Critically, there are a number of finer details that DFW gets wrong; if you're mathematically inclined and intend to read this, I suggest pairing it with a printed copy of Prabhakar Ragde's errata document hosted by the DFW fansite The Howling Fantods ([1]).
[1] https://www.thehowlingfantods.com/dfw/images/enmerrata.pdf
[1] https://www.thehowlingfantods.com/dfw/images/enmerrata.pdf
This. He tries to do a few epsilon delta proofs and completely gets the concept wrong. I’m surprised an editor did not stop this.
If he can’t understand a limit it really puts a question mark on whether it’s worth reading his insight into the subject.
If he can’t understand a limit it really puts a question mark on whether it’s worth reading his insight into the subject.
Why would his editor know any more about it than he did?
I would expect them to have someone with at least an undergrad in math look over the math. Editor would help identify that
Maybe everyone that worked with DFW found him to be as insufferable and arrogant as I did and simply refused to help even when the need was clear.
Would you care to elaborate on this? Sounds like there is an interesting story here...
I'm surprised by the mathematician's critiques of this book. I have a PhD in math and I read this book about 10 years ago now. I loved it. I'm sure there are some inaccuracies, but he gets the overall story correct. There's enough math in the book to be engaging for someone mathematically trained. There's also a lot more history than if you read a math book that just has proofs. And the book is entertaining in the way that DFW's books usually are. As a former mathematician I highly recommend.
I agree. The inaccuracies listed are like, once every few pages the author makes a statement like "P implies Q" without mentioning some minor condition, like, "only if you assume the axiom of choice". Yes, this is annoying for mathematicians, but there's just a fundamental compromise that has to be made. If you spell out every single detail then you will create a book that is not engaging enough to read straight through.
I think you will really enjoy this book if, like me, you:
1. Enjoy David Foster Wallace's literary style
2. Have a good mathematical understanding of set theory
Unfortunately, the intersection of these two conditions might make for a very small target audience!
I think you will really enjoy this book if, like me, you:
1. Enjoy David Foster Wallace's literary style
2. Have a good mathematical understanding of set theory
Unfortunately, the intersection of these two conditions might make for a very small target audience!
The axiom of choice isn't exactly some minor condition.
That’s why you don’t have to explicitly add it as a qualifier at every instance in which it’s implied in your work of non fiction for a general audience.
I think if you aren't deeply concerned with the axiom of choice in your work about infinity for a general audience, then the entire affair is rather farcical. Most of the "weird" stuff about infinity derives from the axiom, after all. A book about infinity, for the lay person in particular, must be in large part a book about the axiom of choice.
This should be read in parallel with the review by Michael Harris in the AMS Notices: "A Sometimes Funny Book Supposedly about Infinity" https://www.ams.org/notices/200406/rev-harris.pdf
As a DFW lover whose day job is as a mathematician... that book's a clunker.
As a DFW lover whose day job is as a mathematician... that book's a clunker.
Michael Harris is a great mathematician (number theory, let's go!!), but that review to me is pretty rambling and doesn't point out many inaccuracies in DFW's book, but takes issue with DFW's approach and style or writing. I did just skim the review and am a DFW fanboy, but Harris seems to have issues with books about infinity and math for lay people, which is fine, that's driving his opinions here.
I'd imagine there will also be a gap between what mathematician's think of novelists writing and what novelists think of real math. So there's that too.
I'd imagine there will also be a gap between what mathematician's think of novelists writing and what novelists think of real math. So there's that too.
I feel less-bad about not having finished it now.
I was doing fine until formulas started showing up more than very-occasionally. I’m basically dyslexic when equations enter the picture.
I was doing fine until formulas started showing up more than very-occasionally. I’m basically dyslexic when equations enter the picture.
Such a great book. Do you know if he there is any other DFW math-ish writings to be found? All my searches thus far have turned up naught.
I'm not aware of any, but maybe somebody else is. A more general question is are there any other DFW-ish math-ish writings to be found? Against The Day (Pynchon) is not really math-ish, but it does have a good bit of math (more than GR at least), and a DFW fan would probably like it. Stella Maris (McCarthy) is perhaps neither DFW-ish nor math-ish, but it is Serious Fiction centered on a mathematician and is probably the best work of fiction to feature Alexander Grothendieck. I have heard that Solenoid (Cartarescu) has some math in it, though I fear it's still sitting on my shelf. Every Arc Bends Its Radian (due in a couple months from Sergio De La Pava) has a math-ish title but I doubt it will actually contain much math.
Michael Harris -- a mathematician who wrote a review of the DFW Infinity book -- has a book called "Mathematics Without Apologies", which I liked, though it's non-fiction. There is also "Birth of a Theorem" by Fields medalist Cedric Villani which is an interesting read -- not fiction, but it is experimental in many respects and I would say worth a read.
Michael Harris -- a mathematician who wrote a review of the DFW Infinity book -- has a book called "Mathematics Without Apologies", which I liked, though it's non-fiction. There is also "Birth of a Theorem" by Fields medalist Cedric Villani which is an interesting read -- not fiction, but it is experimental in many respects and I would say worth a read.
Endnote 123 in Infinite Jest
There's quite a lot of mathematical mistakes (obvious ones, even) in DFWs work. I'm not sure whether it's intentional or not, but given that he also makes mistakes in his nonfiction it might just be that he's not a great mathematician.
Like in TPK, 0/0 is Infinity and in IJ, Pemulis explains differentiation completely incorrectly, also that stuff about the mean value theorem is irrelevant?!?
Still one of the greatest authors; deep technical correctness is more of a Pynchon thing.
Like in TPK, 0/0 is Infinity and in IJ, Pemulis explains differentiation completely incorrectly, also that stuff about the mean value theorem is irrelevant?!?
Still one of the greatest authors; deep technical correctness is more of a Pynchon thing.
Pemulis’ absolutely worthless and wrong but also completely self-assured descriptions of calculus are part of his character
Given that proofs must be finite (or it's easy to prove falsehoods), maybe the title is appropriate then.
I haven't read the The Pale King, but I absolutely love the reading of this excerpt from the book. The protagonist recalls a speech by his substitute teacher in the Advanced Tax course - https://youtu.be/sJXrXf-0yoQ (10mins. no math). I do hope to tackle the book one day.
Amazing delivery! Thank you for sharing this, I started The Pale King many years ago but got sidetracked - this video inspired me greatly to try to finish it again.
I loved the movie "The end of the tour"
https://www.imdb.com/title/tt3416744/
Would like to read but I dont know math.
I am also too addicted. I have had a book on my shelf for 2 years unread.
I listen to 1h of audio book and I love it and then I stop and loose the plot.
oh well.
Would like to read but I dont know math.
I am also too addicted. I have had a book on my shelf for 2 years unread.
I listen to 1h of audio book and I love it and then I stop and loose the plot.
oh well.
Small suggestion from a DFW fan, read the extremely brief book This Is Water, and then try to take on Infinite Jest - just make sure to read the foreword by Dave Eggers before you start, it will light a guiding torch for the journey and what to expect coming out of it.
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while I haven't read DFW, it was because I was suspicious of his motives even in the 90s. the article leads with how he studied "modal logic," as an undergrad, which I only know of as a tool from a theorist named Kripke to reason about systems of logic that don't need external consistency or to produce arithmetic. it was taught in cultural studies programs as a justifying rhetorical "what-aboutism" for neutralizing appeals to logic, a kind of critical theory of math to unmoor people from the authority of math or anything objective, and to guide them to adopting subjectivity. What made me suspicious of DFW was he seemed to be doing just another variation of what L. Ron Hubbard, Richard Wagner, Karl Marx, Osho, Nietzche, and other attempted inventors of religions were up to, and Kripke's modal logics are a tool for producing these logics-of-ideas, a way of writing new pop-ideologies the way we write songs. DFW seemed like a hipster demagogue to me.
another artist whose work may be more rigorous in representing ideas from math is Arvo Pârt. even though there are more concrete things in his work than DFWs that you can logically decode, derive, and then transform and expand on them, much of what I've read[1] is still a bunch of woo that uses talking about "math" as a kind of mystical jibjab to elevate other ideas. Pärt worked as a sound and radio engineer and there is some reason to believe he used that practical knowledge in composing, because the logic in the music is very explicit. (visible triangles and linear functions, he has provided sketches of, etc)
there's a difference between writing something that is a metaphor for a mathematical idea as a vehicle for something else, and something that directly encodes the idea where you could derive it again from the thing you've produced. Maybe DFW did that with the Sierpinksi gasket, but I don't get the sense from anyone that he did. I am not a mathematician at all, but I do think if the idea is not independent of the language or representation it's made in, it's just another metaphor and a vehicle for the author.
[1] https://www.cambridge.org/core/books/cambridge-companion-to-...
another artist whose work may be more rigorous in representing ideas from math is Arvo Pârt. even though there are more concrete things in his work than DFWs that you can logically decode, derive, and then transform and expand on them, much of what I've read[1] is still a bunch of woo that uses talking about "math" as a kind of mystical jibjab to elevate other ideas. Pärt worked as a sound and radio engineer and there is some reason to believe he used that practical knowledge in composing, because the logic in the music is very explicit. (visible triangles and linear functions, he has provided sketches of, etc)
there's a difference between writing something that is a metaphor for a mathematical idea as a vehicle for something else, and something that directly encodes the idea where you could derive it again from the thing you've produced. Maybe DFW did that with the Sierpinksi gasket, but I don't get the sense from anyone that he did. I am not a mathematician at all, but I do think if the idea is not independent of the language or representation it's made in, it's just another metaphor and a vehicle for the author.
[1] https://www.cambridge.org/core/books/cambridge-companion-to-...
Modal logic is a pretty rigorous branch of logic.
https://plato.stanford.edu/entries/logic-modal/
https://plato.stanford.edu/entries/logic-modal/
it has applications in developing semantics, and I think it's about to get some new attention as a tool for LLMs. it's a system for defining consistent systems of rules about semantic relationships that you can write in a LISP, and I think Kripke's modal logics are about to have a resurgence in interest from AI alignment advocates for that reason.
regarding some of the less thoughtful comments on this thread, I'm sure those were the best they could do, but the original article was way more handwavy, and his appeals to the sophistication of math to elevate other ideas seem pretty consistent with my suspicions. why should anyone be surprised that some people operate on systems of belief as systems the way we do with games and software.
regarding some of the less thoughtful comments on this thread, I'm sure those were the best they could do, but the original article was way more handwavy, and his appeals to the sophistication of math to elevate other ideas seem pretty consistent with my suspicions. why should anyone be surprised that some people operate on systems of belief as systems the way we do with games and software.
This is an eclectic mixture of proper nouns.
What on earth are you talking about Saul Kripke and modal logic being some kind of cultural studies tool for “unmooring people from the authority of math”? And your lumping of Wagner, Marx, and Nietszche with Hubbard and Osho as “inventors of religions” is baffling.
Love DFW's Kenyon College commencement speech, but he wasn't all sunshine and rainbows[0]:
> In the early 1990s, Wallace was in a relationship with writer Mary Karr. She later described Wallace as obsessive about her and said the relationship was volatile, with Wallace once throwing a coffee table at her as well as physically forcing her out of a car, leaving her to walk home. Years later, she claimed that Wallace's biographer D. T. Max underreported Wallace's abuse. Of Max's account of their relationship, she tweeted: "That's about 2% of what happened." She said that Wallace kicked her, climbed up the side of her house at night, and followed her five-year-old son home from school.
Reference: [0] https://en.wikipedia.org/wiki/David_Foster_Wallace#Abuse_all...
> In the early 1990s, Wallace was in a relationship with writer Mary Karr. She later described Wallace as obsessive about her and said the relationship was volatile, with Wallace once throwing a coffee table at her as well as physically forcing her out of a car, leaving her to walk home. Years later, she claimed that Wallace's biographer D. T. Max underreported Wallace's abuse. Of Max's account of their relationship, she tweeted: "That's about 2% of what happened." She said that Wallace kicked her, climbed up the side of her house at night, and followed her five-year-old son home from school.
Reference: [0] https://en.wikipedia.org/wiki/David_Foster_Wallace#Abuse_all...