Discovering errors in Donald Knuth's TAOCP(glthr.com)
glthr.com
Discovering errors in Donald Knuth's TAOCP
https://glthr.com/discovering-errors-in-donald-knuths-taocp
67 comments
> he makes the same kinds and the same frequency of errors as anyone else
Putting this here because I don’t know where else to tell this story and I simply have to share:
I flew into Munich a few months ago, and since I have an EU passport I was able to use the shorter self-scan line for EU citizens at passport control. In front of me was an older couple who was having trouble with getting their passports to scan. I noticed they had US passports, so I politely informed the gentleman that he was in the wrong line. He turned around and thanked me, and that’s when I noticed the guy looked exactly like Donald Knuth! Before I could compose myself enough to say anything though, he and his wife had left to find the correct line. Obviously I couldn’t be sure it was him, but I checked Knuth’s public schedule and he was apparently speaking at some conference in Venice about two weeks later, so I’m guessing he decided to come a bit early and enjoy a vacation before the conference.
So yeah, I’m like 99% sure I technically corrected an error by Donald Knuth, but unfortunately I missed out on my reward check. Didn’t even get a selfie with him.
Putting this here because I don’t know where else to tell this story and I simply have to share:
I flew into Munich a few months ago, and since I have an EU passport I was able to use the shorter self-scan line for EU citizens at passport control. In front of me was an older couple who was having trouble with getting their passports to scan. I noticed they had US passports, so I politely informed the gentleman that he was in the wrong line. He turned around and thanked me, and that’s when I noticed the guy looked exactly like Donald Knuth! Before I could compose myself enough to say anything though, he and his wife had left to find the correct line. Obviously I couldn’t be sure it was him, but I checked Knuth’s public schedule and he was apparently speaking at some conference in Venice about two weeks later, so I’m guessing he decided to come a bit early and enjoy a vacation before the conference.
So yeah, I’m like 99% sure I technically corrected an error by Donald Knuth, but unfortunately I missed out on my reward check. Didn’t even get a selfie with him.
I have mentioned this elsewhere online but I was once attending a talk in the computer history museum for which I had turned up early. An elderly gentleman took his seat right before me - it took me a while to process that it was Knuth (in reality, it was less to do with processing and more with accepting!).
Somewhat recently we spotted him at a Hitchcock movie festival at Palo Alto, which my wife and I were attending.
Random run-ins are surreal :-)
Somewhat recently we spotted him at a Hitchcock movie festival at Palo Alto, which my wife and I were attending.
Random run-ins are surreal :-)
I attended one of his MMIX lectures in Munich two decades ago and he mentioned that he was going to visit a friend later, so I guess he might have contacts in Munich.
Speaking of errors, in the lecture he once forgot to save a file in Emacs and was confused about the compilation result briefly. Made him very relatable.
Speaking of errors, in the lecture he once forgot to save a file in Emacs and was confused about the compilation result briefly. Made him very relatable.
At risk of sounding negative, I'm glad you didn't get to pester old man with a selfie.
I wouldn’t have seriously asked him for a selfie while we were both trying to get through passport control after a 12-hour flight. It’s just a little bit of a bummer that I have no way of confirming that I actually did randomly run into Donald-Freaking-Knuth in the Munich airport. Doubly so because most people who I relate this story to have absolutely no clue who Donald-Freaking-Knuth even is, so it’s just completely lost on them.
Great post. Some general takeaways for people who want Knuth checks:
1. You are unlikely to find errors in the algorithms themselves, especially if they've been officially published. You might find some infelicities, but these are not counted as full errors. For example, the author here found some confusing-but-not-wrong comments about local variables and unused registers. These are counted as "suggestions" (worth 0x20¢) rather than "errors" (worth 0x$1.00).
2. Knuth is pretty generous with credit -- if your suggestion leads him to find an error, you get credit for the error. The author here said that some defined variables went unused. Knuth pointed out that those variables were in fact used in an exercise. However, in looking this up he noticed a variable-related error in that exercise. Author is credited with 0x$1.00!
3. Exercises are more likely to contain errors and infelicities than the main text. And there are an awful lot of exercises.
4. Knuth includes a whole bunch of stuff in his books that is not related to CS. Lots of weird trivia and references. This stuff is more likely to be wrong than the main text. For example, Knuth mentions "icosahedral objects inscribed with Greek letters" and includes a reference to an article in the Bulletin de l’Institut français du Caire. But the author points out that the article is actually in the Bulletin de l’Institut français d’archéologie orientale. Whoops! 0x$1.00 for you!
1. You are unlikely to find errors in the algorithms themselves, especially if they've been officially published. You might find some infelicities, but these are not counted as full errors. For example, the author here found some confusing-but-not-wrong comments about local variables and unused registers. These are counted as "suggestions" (worth 0x20¢) rather than "errors" (worth 0x$1.00).
2. Knuth is pretty generous with credit -- if your suggestion leads him to find an error, you get credit for the error. The author here said that some defined variables went unused. Knuth pointed out that those variables were in fact used in an exercise. However, in looking this up he noticed a variable-related error in that exercise. Author is credited with 0x$1.00!
3. Exercises are more likely to contain errors and infelicities than the main text. And there are an awful lot of exercises.
4. Knuth includes a whole bunch of stuff in his books that is not related to CS. Lots of weird trivia and references. This stuff is more likely to be wrong than the main text. For example, Knuth mentions "icosahedral objects inscribed with Greek letters" and includes a reference to an article in the Bulletin de l’Institut français du Caire. But the author points out that the article is actually in the Bulletin de l’Institut français d’archéologie orientale. Whoops! 0x$1.00 for you!
I found an error in a published version of TAOCP, 2nd edition I think, with improvements on Sieve of Eratosthenes. I was so excited, then found it was already listed in the errata.
I later got a check for identifying a minor issue with the early history of superimposed coding. I happen to have copies of the relevant patent case containing examples predating Mooers' randomized superimposed coding.
("Happened to" because I had visited the Mooers archive at the Charles Babbage Institute in Minnesota to research some of the early history of chemical information management. Mooers is one of the "fathers" of information retrieval, and in fact coined the term "information retrieval" at a chemistry conference.)
I later got a check for identifying a minor issue with the early history of superimposed coding. I happen to have copies of the relevant patent case containing examples predating Mooers' randomized superimposed coding.
("Happened to" because I had visited the Mooers archive at the Charles Babbage Institute in Minnesota to research some of the early history of chemical information management. Mooers is one of the "fathers" of information retrieval, and in fact coined the term "information retrieval" at a chemistry conference.)
Don't make assumptions about what parts must have been combed through so much that there is no chance of finding annerror.
I found one and got my cheque on page Arabic one in one of his books. Paragraph one. First sentence. The very first word.
I found one and got my cheque on page Arabic one in one of his books. Paragraph one. First sentence. The very first word.
Was it the word “the” instead of “a”? Trying to think what else it could even be.
It's amusing that the same two commenters have essentially the same two comments side-by-side in both threads, years apart.
For the lazy, the word is: "infinitely"
Knuth has the Pablo Picasso’s Dinner Bill “Problem” and so can afford to be generous.
Picasso used to dine and dash as it were by drawing a doodle on the back of his check when the bill came due, and often enough the owner would choose to frame the check instead of cash it.
For a long time most of the cost of writing checks to Knuth is the writing of the checks, not the cashing of them. He’s paying for X00 checks at a time and the energy to fill them out. And anyone who had gotten their first check from him would not cash it.
Though these days I can cash a check via a phone app and so I don’t need to forfeit the check to get the money.
Picasso used to dine and dash as it were by drawing a doodle on the back of his check when the bill came due, and often enough the owner would choose to frame the check instead of cash it.
For a long time most of the cost of writing checks to Knuth is the writing of the checks, not the cashing of them. He’s paying for X00 checks at a time and the energy to fill them out. And anyone who had gotten their first check from him would not cash it.
Though these days I can cash a check via a phone app and so I don’t need to forfeit the check to get the money.
>Though these days I can cash a check via a phone app and so I don’t need to forfeit the check to get the money.
Its incredible that both of these technologies is in active use at the same time.
Its incredible that both of these technologies is in active use at the same time.
They’re not “real” checks anymore (unless you insist) because of check fraud issues. Bank of San Serif isn’t a real bank.
My bank knows where I live and if I start cashing fake checks they know where to send the FBI.
Even in the old paper days banks where a little hesitant to let me come into your bank with a check from you and cash it without me also being a customer of that same bank. In theory you could do it, but sometimes if you tried you got the runaround.
Even in the old paper days banks where a little hesitant to let me come into your bank with a check from you and cash it without me also being a customer of that same bank. In theory you could do it, but sometimes if you tried you got the runaround.
You can still wreak havoc with the account and routing numbers if you want to - it gets reversed when noticed which is why people still do it - sometimes it’s not noticed.
> ... includes a reference to an article in the Bulletin de l’Institut français du Caire. But the author points out that the article is actually in the Bulletin de l’Institut français d’archéologie orientale. Whoops! 0x$1.00 for you!
I do wonder whether this is more likely to be a case where the journal actually changed its name over time (perhaps because the Institut itself did) and then made the older papers available under the new name - which would mean both references are ultimately correct.
I do wonder whether this is more likely to be a case where the journal actually changed its name over time (perhaps because the Institut itself did) and then made the older papers available under the new name - which would mean both references are ultimately correct.
I don't think so. The article links to an image of the 1930 journal article – https://gallica.bnf.fr/ark:/12148/btv1b53180372w – it doesn't look like it has been republished, it looks like something close to the original publication
I don't completely know what is going on here, but I guess it is something like this: the institute has since 1898 officially been called Institut français d'archéologie orientale, and its journal has always officially been called Bulletin de l'Institut français d'archéologie orientale. However, historically, people would sometimes add du Caire (in Cairo) to the institute's name (to specify its location) – this habit was supported by the history that, prior to 1898, the institute (or its predecessor) was called École française du Caire (French School of Cairo) – and then unofficially abbreviate it from Institut français d'archéologie orientale du Caire to Institut français d'archéologie du Caire or even Institut français du Caire. And since the journal is named for the institution, once people got in the habit of unofficially abbreviating the name of the institution, they applied the same habit to the journal.
So Bulletin de l’Institut français d’archéologie orientale has always been the official name of the journal, but Bulletin de l’Institut français du Caire is a historical unofficial alternative name.
As I said, I'm just speculating, I don't really know. But this seems more plausible to me than the journal or institute changing its name, because I can't find any evidence of any name change since 1898, which was long before the publication of the 1930 article.
I don't completely know what is going on here, but I guess it is something like this: the institute has since 1898 officially been called Institut français d'archéologie orientale, and its journal has always officially been called Bulletin de l'Institut français d'archéologie orientale. However, historically, people would sometimes add du Caire (in Cairo) to the institute's name (to specify its location) – this habit was supported by the history that, prior to 1898, the institute (or its predecessor) was called École française du Caire (French School of Cairo) – and then unofficially abbreviate it from Institut français d'archéologie orientale du Caire to Institut français d'archéologie du Caire or even Institut français du Caire. And since the journal is named for the institution, once people got in the habit of unofficially abbreviating the name of the institution, they applied the same habit to the journal.
So Bulletin de l’Institut français d’archéologie orientale has always been the official name of the journal, but Bulletin de l’Institut français du Caire is a historical unofficial alternative name.
As I said, I'm just speculating, I don't really know. But this seems more plausible to me than the journal or institute changing its name, because I can't find any evidence of any name change since 1898, which was long before the publication of the 1930 article.
I've emailed DEK to point out that the first person to break Enigma was not actually Alan M. Turing (as stated in one of the recent pre-fascicles) but the Polish mathematician Marian Rejewski (Turing's contribution was to automate the task, which was important because the rotors/settings were reconfigured by the German Wehrmacht every morning).
Bletchley Park now has a prominent bust of Rejewski that credits his accomplishment. The Polish wisely passed on their knowledge to the British to keep the intel safe, because they expected a German invasion.
On another note, I hope Professor Knuth has a continuity plan in place that ensures that his book series gets completed despite his advanced age (I'm worried about that, but tact prohibited me from asking, of course).
Bletchley Park now has a prominent bust of Rejewski that credits his accomplishment. The Polish wisely passed on their knowledge to the British to keep the intel safe, because they expected a German invasion.
On another note, I hope Professor Knuth has a continuity plan in place that ensures that his book series gets completed despite his advanced age (I'm worried about that, but tact prohibited me from asking, of course).
Given his quite healthy lifestyle, I believe that we should be okay on that latter front --- I certainly hope so.
It's not his lifestyle I'm worried about. There was a healthy youtuber who made videos about wilderness survival who was killed when he was rear ended by a drunk driver while stopped at a red light (the drunk driver, of course, survived). It's all the morons around Knuth I'm worried about.
I hate to be morbid and I wish him a long life, but at age 87, I don’t think drunk drivers are his biggest risk.
The book series will never be completed, and wouldn't be if Knuth lives to 120.
And that's perfectly fine.
And that's perfectly fine.
I have a Knuth cheque from back when he sent out real cheques. Or at least I did; for some reason I decided that cashing it was a good idea and so I have his note back to me and a photocopy of the actual cheque.
I have one for $7.68 ($2.56*3). Alas, it was for some minor typos and grammatical errors in SPOCS [1], not "real" math errors in TAOCP. Never plan on cashing it in though. And I can't remember where I stashed it, so there's that too... :)
[1] https://www-cs-faculty.stanford.edu/~knuth/cs.html
[1] https://www-cs-faculty.stanford.edu/~knuth/cs.html
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lol I'm a bit curious about the thought process that led you to decide you wanted to cash it.
Aren't the cheques for $2.56?
What error did you find?
A long while back I wrote an answer on Stack Overflow to a question that asked "How to read TAOCP?" my answer looked something like this:
- don't read them
- get all the books, put them in a bin bag and shake vigorously with some lumps of coal, to give them that "used" look
- go through the books, underline things at random and make notes (also at random) in the margin such as "how true", or even better "wrong!"
- put books on shelf in office - never look at them again
This has worked for me, though I must admit that Searching & Sorting and stuff about random numbers are pretty good.
I got my copies free from Addison Wesley for doing some book reviews for them - not reviewing Knuth, needless to say!
- don't read them
- get all the books, put them in a bin bag and shake vigorously with some lumps of coal, to give them that "used" look
- go through the books, underline things at random and make notes (also at random) in the margin such as "how true", or even better "wrong!"
- put books on shelf in office - never look at them again
This has worked for me, though I must admit that Searching & Sorting and stuff about random numbers are pretty good.
I got my copies free from Addison Wesley for doing some book reviews for them - not reviewing Knuth, needless to say!
I have worked with two programmers who had well-thumbed copies of TAoCP on their shelves which each had actually read (one was the only other person I've met outside of a TeX conference who had a reward check) --- to this day, I've not worked with better devs.
Ah nothing like a DEK post to pull out the old TeX folks on HN.
When I bought the first volume in about 1969, I vowed to read that one, and then each one that followed.
However, that is yet to come to pass.
However, when we at Mark Williams Company writing the floating point routines for the C compiler (https://winworldpc.com/product/mark-williams-letsc/3x), we were heavily reading Chapter 4, particularly on long division.
Also did spend some time in the Random Number generation chapter.
An interesting difference between my 1965 version and the ones published today is that long multi-page foldout in Sorting and Searching showing tape-based merge sort is no longer part of the book.
However, that is yet to come to pass.
However, when we at Mark Williams Company writing the floating point routines for the C compiler (https://winworldpc.com/product/mark-williams-letsc/3x), we were heavily reading Chapter 4, particularly on long division.
Also did spend some time in the Random Number generation chapter.
An interesting difference between my 1965 version and the ones published today is that long multi-page foldout in Sorting and Searching showing tape-based merge sort is no longer part of the book.
Hey, I have a question about the Mark Williams Company. I understand it was founded by Aaron Swartz's father. Did he work on the programming? Did Aaron spend time around the office? I'm curious how Aaron first got involved in programming, which I think was probably long after the company.
I was gifted the new set this last Christmas after losing my old versions in a fire, the fold out pages are there in the latest release.
Edited to add: Amazon often has fake or at least printed with lower quality/cost versions. It was hard to find a real copy of his concrete math book when I was searching. The 'i18n' edition is printed on the cheapest of cheap paper for that book. I suspect that is related. But the fan-out pages are in the sorting volume.
#2 Vol 3 is on the second edition, with the tape merge fanout between pages 338 and 339. So it would be a particular printing that didn't have it.
Edited to add: Amazon often has fake or at least printed with lower quality/cost versions. It was hard to find a real copy of his concrete math book when I was searching. The 'i18n' edition is printed on the cheapest of cheap paper for that book. I suspect that is related. But the fan-out pages are in the sorting volume.
#2 Vol 3 is on the second edition, with the tape merge fanout between pages 338 and 339. So it would be a particular printing that didn't have it.
I double checked my latest volume and it does the foldout. My error
I was mistaken about the foldout. It is in both versions. My error.
I just bought the whole set
and just did chapter one, will probably not keep up with doing all the assignments but I indend to at least skim them and get a rough feel to where I can find stuff if I ever need it.
The inventor of the bug bounty.
TOACP The Art of Computer Programming, Volumes 1~4c
https://en.wikipedia.org/wiki/The_Art_of_Computer_Programmin...
Kudos to everyone who found bugs, and got the bounty. Congrats to everyone who used these to get their PhD-CS
https://en.wikipedia.org/wiki/The_Art_of_Computer_Programmin...
Kudos to everyone who found bugs, and got the bounty. Congrats to everyone who used these to get their PhD-CS
I first read parts of vol 1 in 1975, in my undergrad data structure and algorithm class. And then again in 1980 for my PhD comprehensive exams. That book is highly used. I found a pristine copy a few years in a pile of books on the sidewalk, thanks to someone moving.
They put out a Unicomp clicky keyboard a few days later, picked up that too.
They put out a Unicomp clicky keyboard a few days later, picked up that too.
I haven't read TAOCP myself, but if I recall a lecture that Knuth gave, his algorithm analyses sometimes include cycle counts for his virtual MMIX architecture. He mentioned that these are counted by hand. If I were seeking a reward check, I would write a verifier to look for errors there.
Nice! When I reported an error and a point of improvement in _Digital Typography_ the address was printed and glued on, not hand-written, which somewhat detracts from the display of the check/envelope.
Need to find another error so I can get an account....
Need to find another error so I can get an account....
This makes me feel less bad about also not being able to figure out my printer's address printing function.
Like I know it is capable. I know how to set up the hand feed for it (and I successfully do that for thicker paper). And ostensibly I know the right dimensions and how to line it up in a PDF. But then it's just failure after failure, and I go back to cut and paste or handwrite.
Like I know it is capable. I know how to set up the hand feed for it (and I successfully do that for thicker paper). And ostensibly I know the right dimensions and how to line it up in a PDF. But then it's just failure after failure, and I go back to cut and paste or handwrite.
Really miss poste.app on my NeXT Cube, which was a small app/service which did nothing but print a selected address onto a hand-fed envelope.
"he decided against breaking up Algorithm X between different pages"
He should have used TeX ;) I've heard handles such layout problems automatically.
He should have used TeX ;) I've heard handles such layout problems automatically.
Does the bank really read the amounts as hexadecimal?
He used to send out real cheques for $2.56 but apparently they contained codes that could be used to transfer money out of his account in excess of the sum of the cheque. Now he uses the made-up Bank of San Serriffe, which naturally understands hexadecimal.
https://www-cs-faculty.stanford.edu/~knuth/news08.html
https://www-cs-faculty.stanford.edu/~knuth/news08.html
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would like to read, but the site uses some clownflare alternative, that just like clownflare tries to verify my browser (palemoon), and then comes to the conclusion that my browser isn't a browser.
OT: Will Knuth's lifetime of work be used for learning input in AI systems, and does he control that?
An AI application might make a good search interface for Knuth's opus.
An AI application might make a good search interface for Knuth's opus.
Previously, I had the impression that Knuth was some magical figure of perfection. What I realized was that the truth was more surprising: he makes the same kinds and the same frequency of errors as anyone else (in fact likely more, because every page is packed with a lot of detail); what sets him apart is that he cares so deeply about getting everything right — he has basically invited a DDoS on his time and attention, where every person in the world is strongly encouraged to write to him with errors on every page that he has ever written over several decades — and he does go back and look at all of them carefully (example: https://retrocomputing.stackexchange.com/questions/18117/whi...); and despite all this he somehow continues to function, producing new pages at a nonzero rate. After some experience with his responses (handwritten with pencil on a printout of the emails sent to him), I came away even more impressed.