12 ms·
Knuth changes his mind on Bernoulli number B_1
- iaw 4y agoKnuth and Cliff Stoll are some of the people that I feel like are amazing treasures of our generation.
- glandium 4y agoOne of them hangs out on this site, too.
- svat 4y agoRelated tweet from Russ Cox: https://twitter.com/_rsc/status/1483899960684863493 https://twitter.com/_rsc/status/1483899960684863493 > Knuth is making backwards incompatible changes to fix bugs in something he wrote 54 years ago (TAOCP volume 1, 1968)! And mine: Apart from the care Knuth takes, what's remarkable is that he has basically put out a permanent invitation to a DDoS on his time and attention—everyone in the world is invited to contact him about every word he has ever written—and somehow still continues to produce new material. From Wilf's toast/roast of Knuth (https://www2.math.upenn.edu/~wilf/website/dek.pdf https://www2.math.upenn.edu/~wilf/website/dek.pdf): “[…]your letter will be placed on a stack that already has 5,379 letters that reached him before yours did,[…] while he completes his latest additions to 47 new manuscripts and 311 revisions of already existing books.”
- tambourine_man 4y agoI think the secret is he uses letters. Try that invitation to a DDoS on his life with Twitter or email. If you’re willing to post a physical letter, chances of the content being worth reading are a lot higher.
- ReactiveJelly 4y agoIt's hashcash! But the hash is literal cash of about 50 cents
- femto 4y agoWith a further optimisation in the batch handling of snail mail: "I have a wonderful secretary who looks at the incoming postal mail and separates out anything that she knows I've been looking forward to seeing urgently. Everything else goes into a buffer storage area, which I empty periodically." from: https://www-cs-faculty.stanford.edu/~knuth/email.html https://www-cs-faculty.stanford.edu/~knuth/email.html
- svat 4y agoJust to clarify, you can email him to report errors in any of his books (and I have done so, several times). It's only for other general communication that he insists you use physical email.
- krisrm 4y agoThat is a fantastic and highly amusing speech, thank you for linking it.
- svat 4y agoYou may also like this other speech by the same author (Herb Wilf) that I love too (on an unrelated topic): • Epsilon Sandwiches https://www2.math.upenn.edu/~wilf/website/MAASpeech https://www2.math.upenn.edu/~wilf/website/MAASpeech In fact everything by Wilf that I've read is lovely: the paper "Recounting the rationals" (https://www2.math.upenn.edu/~wilf/website/recounting.pdf https://www2.math.upenn.edu/~wilf/website/recounting.pdf with Neil Calkin), and the book generatingfunctionology https://www2.math.upenn.edu/~wilf/DownldGF.html https://www2.math.upenn.edu/~wilf/DownldGF.html
- JadeNB 4y agoEpsilon sandwiches is a great speech, with advice that I wish I could follow—but it pre-supposes students for whom the referenced very easy proofs are indeed very easy conceptually, and the struggle is only to put those concepts into words. I can believe that this is true of students in a UPenn first analysis course, but it is not true at the less prestigious university where I teach students who are encountering proofs for the first time (well before analysis)—and I have long struggled with how to break down this two-step complication into separate manageable steps with students for whom, say, it is still a real challenge to understand (in the context of proving facts about sums and products of even numbers) why 2(x + y) = 2x + 2y is true, but 2(xy) = (2x)(2y) is not. If anyone knows how to adapt Wilf's advice to such students, then I—and they, in my fall class!—will be grateful to hear it!
- dento 4y agoI case it helps, this is how it was taught to me when introducing proofs. For your example case, it's simply the matter of seeing multiplication as repeated addition. So, 2x is x+x, and from this follows: 2(x+y) = (x+y)+(x+y) = x+y+x+y = x+x+y+y = 2x+2y However, for the other case, when we convert the multiplication by 2 to an addition and back: 2(xy) = (xy)+(xy) = xy+xy = 2xy Now we can show that this works for n instead of two: n(x+y) = (x+y)+..[n times]..+(x+y) = x+..[n times]..+x + y+..[n times]..+y = nx+ny And for multiplication: n(xy) = xy+..[n times]..+xy = nxy
- lou1306 4y ago> Apart from the care Knuth takes, what's remarkable is that he has basically put out a permanent invitation to a DDoS on his time and attention—everyone in the world is invited to contact him about every word he has ever written—and somehow still continues to produce new material. I mean, this is just a best practice among academics -- every paper has at least one corresponding author to whom you should write for all inquiries about it. Of course, Knuth's immense popularity and the chance you may get a reward [0] contribute to the intensity of the DDoS. [0]: https://en.wikipedia.org/wiki/Knuth_reward_check https://en.wikipedia.org/wiki/Knuth_reward_check (of course, the "reward" is not really the money, but rather getting recognition from Don Knuth himself)
- smitty1e 4y ago> everyone in the world is invited to contact him about every word he has ever written But not by email.
- lou1306 4y agoWell, as others have pointed out, at his scale this is likely a necessary rate-limiting countermeasure. Even relatively obscure academics easily end raking up hundreds of emails in their inboxes once they are senior enough. With someone as popular as Knuth, it would be madness.
- svat 4y agoYes by email (search the posted page for "@" or look under "Rewards" at https://cs.stanford.edu/~knuth/taocp.html#:~:text=Rewards https://cs.stanford.edu/~knuth/taocp.html#:~:text=Rewards ) And when I said "invited" I meant "strongly incentivized": by offering cash rewards (initially) and those highly prized "Knuth checks", he surely gets orders of magnitude more scrutiny and error reports than a typical academic.
- macintux 4y agoI had not realized there’s now an estimated release date for 4B of this October. I think it may finally be time (after 4B) to buy the box set and leave it lying around in hopes that by 2030 I’ll get up the courage to start it.
- macintux 4y agoWorth noting: there’s currently a discount available via a code displayed prominently on the Pearson site, so preordering it came to about $210 USD for me. https://www.informit.com/store/art-of-computer-programming-volume-4b-combinatorial-9780201038064 https://www.informit.com/store/art-of-computer-programming-v...
- EddySchauHai 4y agoI bought it, got stuck on the maths in chapter 1 of volume 1, and it's now in my friends Attic in another country. Maybe one day! But not yet.
- currymj 4y agojust skip ahead!
- JadeNB 4y agoThis is such great advice at least for reading mathematics, and I assume for reading most science. Skip the introductory part you don't understand, which is almost certainly explanatory throat-clearing, and get to the part that interests you. Now you won't understand it! But you'll see the reason you don't understand it, and you can go back to the introduction with the mission specifically of understanding that part. It is consistently amazing to me how the same sentence that was baffling when you had no context in which to put it becomes enlightening when you have a problem to which to apply it. (That is also, if I may air a personal pet peeve here, why, though I am always delighted to see people understanding a concept, I get defensive as a teacher when later-life learners say "why didn't my teacher just say that?" Because the answer is often some combination of (1) even if they had said that exact thing, it wouldn't have reached you then, because you weren't then in the head space that you are now; and (2) they probably did say that, or something like it, and, because of (1), it seemed so far from relevant that you don't even remember it.)
- hprotagonist 4y agoas a side note, publishing errata and pages is such a lovely practice and i wish it was more widely applicable and used.
- biorach 4y agolet's just get some perspective here HE'S 84 YEARS OLD AND STILL DEFINING COMPUTER SCIENCE
- biorach 4y agoI'd stopped checking for updates a few years back and just assumed that TAOCP was done because he'd run out of steam... boy was I wrong
- eointierney 4y agoYup, this individual is epochally awesome, and he still lets us try and correct him. So humble, so calm, so happy.
- stephencanon 4y agoI don’t get it. We certainly wouldn’t let someone younger do so.
- iam-TJ 4y agoPuts into perspective the behaviour of companies developing reputations for firing older staff in favour of fresh graduates, doesn't it?
- baltimore 4y agoEmail is a wonderful thing for people whose role in life is to be on top of things. But not for me; my role is to be on the bottom of things. Source: "Knuth versus Email" https://www-cs-faculty.stanford.edu/~knuth/email.html https://www-cs-faculty.stanford.edu/~knuth/email.html
- ozim 4y agoI think more developers should be like that. Too much energy is wasted for being on top of new framework of the month.
- jodrellblank 4y ago> "A digraph is weakly connected if and only if cannot be divided into two nonempty parts" Is there an "it" missing here? (I wouldn't normally, but this is the closest I'll ever come to finding a Professor Knuth mistake!)
- klyrs 4y agoEmail him. I got a check for noticing some macro barf in a preprint.
- orlp 4y agoHe doesn't have an email address. He accepts letters though: https://www-cs-faculty.stanford.edu/~knuth/email.html https://www-cs-faculty.stanford.edu/~knuth/email.html
- jhncls 4y agoWell, the article that is being discussed [0], mentions an "address for bug reports (taocp@cs.stanford.edu)". [0]: https://www-cs-faculty.stanford.edu/~knuth/news22.html https://www-cs-faculty.stanford.edu/~knuth/news22.html
- password4321 4y agoNot quite. From that very page: > Email is a no-no EXCEPT for reporting errors in books.
- orlp 4y agoI can't read apparently...
- gerdesj 4y agoOK manchestercalling it seems you've caught a pretty major grammatical error unprotected in the wild. Now, do you replace the second if with it or add an it post second if? "if and only if" is a standard and well understood term in our rather wooly language, so we will probably need your missing "it" to complete the sentence. Note that nothing was lost anyway - both you and I could see what was going on. English is pretty close to stripped to the waist and holding both fists up already. There isn't much left to remove for conciseness with clarity and unambiguity. I think we need to keep the pronouns but they can often be dropped with minimal loss of clarity. If we lost pronouns wholesale, we'd have to get pretty weird on suffixes or the like. Before you know it - you are speaking German or Dutch instead of our unholy brew of pretty much every language that has been seen on the continent and cuddled up to nearly every other language in the world. (The last time I saw JB in the flesh was 1977 when I was seven and lived in Wythenshawe for a year in between parental postings to exotic lands like W Germany - it looked like science fiction to me then and it still looks rather impressive now)
- paulhodge 4y agoWelp, time to throw my set of AOCP in the trash.
- j7ake 4y agoI feel like this man is as close to being a monk for computer science as one could ever be. I envy his daily routines and discipline that keeps him going well beyond typical retirement age. I can only hope to have a sliver of his discipline to lead my daily life.
- skissane 4y ago> I feel like this man is as close to being a monk for computer science as one could ever be. He has a wife, two grown kids, and some grandkids too. He’s a believing, practising Lutheran [0] (some have even said a “devout” one) and published a book on the Bible [1]. He plays piano and organ - he sometimes plays the organ at his church, and he and his wife even have a pipe organ in their house [2], and he has composed an original work for it [3]. Calling him a “monk for computer science” makes him sound very one-dimensional, when he isn’t. [0] https://www.livinglutheran.org/2018/12/im-a-lutheran-don-knuth/ https://www.livinglutheran.org/2018/12/im-a-lutheran-don-knu... [1] https://www-cs-faculty.stanford.edu/~knuth/316.html https://www-cs-faculty.stanford.edu/~knuth/316.html [2] https://www-cs-faculty.stanford.edu/~knuth/organ.html https://www-cs-faculty.stanford.edu/~knuth/organ.html [3] https://www-cs-faculty.stanford.edu/~knuth/fant.html https://www-cs-faculty.stanford.edu/~knuth/fant.html
- manquer 4y agoReal life monks aren't one dimensional either. Buddhism in its essence is about balance and right path not extreme focus on one thing
- eru 4y agoReal life Christian monks weren't / aren't one dimensional either.
- naniwaduni 4y agoOther than the "has a wife and kids" part, that sounds a lot like a monk?
- acjohnson55 4y agoI wonder if we can get him on Team Tau: https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto
- djmips 4y agoVery unlikely. I think that one you've become accustomed to using 2π everywhere there isn't a big technical reason to change. I love tau though and I use and promote it at work.
- djbusby 4y agoWild link. That's a well reasoned argument and a good geometry mind bender. Thanks.
- gunnihinn 4y agoI’m a mathematician. Tau is bikeshedding. It’s far removed from being either interesting or useful. But it is a useful litmus test for whether a person’s options on math are worth listening to or not.
- keithalewis 4y agoI believe you just empirically verified this. :-)
- jiggawatts 4y agoDisclaimer: I'm not a mathematician, and I only have a bachelor degree in science. With respect: It's not bikeshedding. Pi is wrong, and you know it, it's just that you (likely) feel that it is too late to change it, so why fight against history? One of the best quotes I've ever heard is: "The standard you walk past is the standard you accept." There are several problems with simply letting things remain as they are. I'm sure you've heard them already, but allow me to reiterate them for the benefit of the non-mathematicians here: 1. Pedagogical: I never "got" radians, or had a really firm grasp on trigonometry until I had heard of tau-vs-pi. Suddenly, everything just clicked. Sure, once you know it, it's a trivial mental substitution to replace every instance of pi with tau/2, but... only if you know to do this. I'm not the only one. Persisting on using pi is doing millions of students a disservice. A tau is one turn. A pi is half a turn! Wat? Do you buy bread half a loaf at a time and tell everyone that this is fine because you just need to by two half-loafs and it all works out? 2. Theoretical: Something that opened my eyes about physical theories is that it's easy to confuse oneself by cancelling small constants... such as when making the tau -> 2 pi substitution. The '2' gets cancelled all over the place, making other integer constants "wrong", and not always in an obvious way. They then get hand-waved away because they stop making sense, and so important things can be missed. 3. Boundary pushing: Most endeavours are limited by physics. Mathematics is unique in that it is limited only by human brain capacity. Ergo, the cutting edge of mathematics is bounded by how far a single human brain can go, but no further. Progress is achievable only through efficiency of thought, via shortcuts, elegance, abstraction, consistency, simplicity, and other similar means. Unnecessary complexity at the bottom is unnecessary and should be dropped to make room at the top. I could go on and on, but better articles have been written on the topic. The point is, if you see someone turning right three times to turn left, you immediately, indistinctively think less of them. You're saying that no-no-no-no... the triple turners are just fine the way the are, and nobody should listen to those strange people in the minority who insist on turning directly towards the intended destination. Sure, it's faster, but we've never done it that way...
- pdpi 4y ago> It was their well-intentioned but ultimately poor choice that had led to what I'd been taught in the 1950s. (...) Yet Luschny convinced me that we have all been wrong, and that it's high time to change back to the correct definition before the situation gets even worse. I have no doubts that Knuth's ability to keep producing novel material is strongly related to this willingness to be proven wrong on ideas he's held for almost seventy years. I can only hope I get to his age and still have the flexibility to do that.
- djbusby 4y agoAnother older fella in the game I know says: "strong opinions, loosely held".
- eslaught 4y agoThis phrase bothers me. It's sort of a contradiction in terms: what does it mean to hold a "strong" opinion "loosely"? In my experience, those tend to be highly correlated. The people who have strong opinions hold them firmly, and the people who have weak opinions (or more charitably, for whom having opinions---whether strong or weak---is not important to their identity) are much more able to accept reality as it exists rather than as they'd like it to be. I think the phrase ends up getting used to justify arguing for things (opinions) passionately, but then (supposedly) being able to turn around when proven wrong. I say "supposedly" because again my experience is that this is more wishful thinking than reality, and that in practice the correlation I identified above holds the vast majority of the time. Does anyone else feel this way?
- quickthrower2 4y agoSince the best we can hope for for an opinion is evidence based, experience based and from deductive reasoning, and new evidence and experience is always being uncovered (in science and elsewhere) let alone the amount of material a person has been exposed to, you can have a strong opinion but be willing to change your mind if you see new evidence.
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- cvoss 4y ago> These changes to Concrete Mathematics are too numerous to incorporate into the online errata. Therefore I've prepared replacement pages for anybody who wants to upgrade their copy of the second edition. I have a beloved copy of CM displayed in a prominent place on my living room bookcase. Do I just stuff the replacement pages in between the old ones? Is there actually a proper procedure to replace pages and rebind a book like that?
- lake_vincent 4y agoYes, but it is an art. I would recommend taking it to a reputable used book store. They will sometimes have traditional bookbinding skills, if they carry lots of old books.
- eru 4y agoA library might also have people with the right skills?
- hugey010 4y agoThere are book binders that will do one offs, and the binding will probably be better than the original if you get it sowed & glued correctly!
- kevinpet 4y agoThe conventional way to add a page to a book is to glue it along the inside edge. https://en.wikipedia.org/wiki/Tipped-in_page https://en.wikipedia.org/wiki/Tipped-in_page There are several versions of this article floating around the web showing the process if you happen to have bookbinding equipment laying around https://www.lineco.com/book-repair-3/ https://www.lineco.com/book-repair-3/
- jhncls 4y agoFor anyone interested in a magical introduction to Bernoulli numbers, there is Mathologer's video [0]. [0]: https://youtu.be/fw1kRz83Fj0 https://youtu.be/fw1kRz83Fj0
- ceautery 4y agoThis reminds me somewhat of Nicod redefining Sheffer's Stroke as NAND instead of NOR. (edit: Use the correct name)
- bartkappenburg 4y agoOn a side note: Bernoulli was born in my home town Groningen (NL). Brilliant mathematician.
- rurban 4y ago
- smitty1e 4y ago> It would be nice to believe that I actually got the details right in my first attempt. But that seems unlikely, because I had hundreds of chances to make mistakes. So I fear that the most probable hypothesis is that nobody has been sufficiently motivated to check these things out carefully as yet. Even the pros have woes.