While implementing algorithms from Donald Knuth's "The Art of Computer Programming" (TAOCP), the author uncovered a few discrepancies. One involved an incorrect formula for calculating index values in a tree-like structure, leading to crashes when implemented directly. Another error related to the analysis of an algorithm's performance, where a specific case was overlooked, potentially impacting the efficiency calculations. The author reported these findings to Knuth, who confirmed the issues and issued corrections, highlighting the ongoing evolution and collaborative nature of perfecting even such a revered work. The experience underscores the value of practical implementation in verifying theoretical computer science concepts.
This blog post by Gustavo L. Tharrington recounts the author's experience discovering and reporting a potential error in Donald Knuth's seminal work, The Art of Computer Programming (TAOCP), specifically within Volume 4A, Combinatorial Algorithms, Part 1. Tharrington, a self-described admirer of Knuth and his meticulous approach to accuracy, meticulously details his journey, emphasizing the reverence he holds for the work and the cautious approach he took to ensure his findings were indeed valid.
The story begins with Tharrington's exploration of Algorithm X, a technique for solving exact cover problems. While studying the accompanying exercises in TAOCP, he encountered exercise 251, which proposed a specific problem instance and asserted a particular solution. However, when Tharrington implemented Algorithm X and applied it to the exercise, his solution differed from Knuth's. This discrepancy prompted a period of intensive self-doubt and re-examination of his code and understanding of the algorithm. He meticulously checked for bugs, considering the much higher probability of his own error compared to a mistake in Knuth's meticulously crafted text.
After exhaustive verification, Tharrington remained convinced of a genuine discrepancy. He proceeded to formally document his findings, compiling a comprehensive report that included not just his differing solution but also the precise steps he took, his code, and the logic behind his conclusions. Cognizant of Knuth's reputation for rewarding those who discover errors in his works, Tharrington sent his report to Knuth, hoping it would be deemed a legitimate find.
The blog post then shifts to the anticipation Tharrington experienced while awaiting a response from Knuth. This period of waiting is depicted as a mix of excitement and anxiety, reflecting the respect and almost reverence the author holds for Knuth. Finally, Tharrington received a reply. Knuth acknowledged the discrepancy, confirming it as a genuine error in the text. He further explained the origin of the mistake, attributing it to a misinterpretation of the problem statement during the process of translating the exercise from its original context to the format presented in the book.
The post culminates with Tharrington expressing his elation at having contributed to the improvement of such an influential work in computer science. The experience not only validated his understanding of the material but also afforded him a direct interaction with a figure he deeply admires. The narrative emphasizes the thoroughness and meticulous approach both Knuth and Tharrington took, highlighting the significance of accuracy and rigor in the field of computer science. The author's carefulness in verifying his findings and his respect for Knuth's work are central themes throughout the narrative.
Summary of Comments ( 49 )
https://news.ycombinator.com/item?id=43301342
Hacker News commenters generally express admiration for both Knuth and the detailed errata-finding process described in the linked article. Several discuss the value of meticulous proofreading and the inevitability of errors, even in highly regarded works like The Art of Computer Programming. Some commenters point out the impressive depth of analysis involved in uncovering these errors, noting the specialized knowledge and effort required. A few lament the declining emphasis on rigorous proofreading in modern publishing, contrasting it with Knuth's dedication to accuracy and his reward system for finding errors. The overall tone is one of respect for Knuth's work and appreciation for the effort put into maintaining its quality.
The Hacker News post titled "Discovering errors in Donald Knuth's TAOCP" (linking to an article on glthr.com) has generated several comments discussing the process of finding and reporting errors in Knuth's seminal work, The Art of Computer Programming (TAOCP).
Several commenters express admiration for Knuth's dedication to accuracy and his reward system for finding errors. They highlight the meticulous nature of his work and the challenge involved in identifying even minor inaccuracies. One commenter mentions the existence of a website dedicated to cataloging errata in TAOCP, emphasizing the ongoing community effort to refine and perfect the books.
Some comments delve into the specific types of errors found, noting that they are often subtle and don't detract significantly from the overall value of the work. One commenter points out the distinction between typographical errors and more substantive errors in algorithms or analysis. The discussion touches on the concept of "check digits" within TAOCP, suggesting that even these safeguards are not foolproof.
The reward offered by Knuth for finding errors is also a topic of conversation. Commenters discuss the symbolic value of the reward checks, more than their monetary worth, viewing them as a unique collectible. The system itself is praised as a clever way to incentivize careful reading and contribute to the ongoing improvement of the books.
A few comments express surprise at the number of errors still being found, given the work's reputation for rigor. However, others counter that the complexity and depth of TAOCP make some errors inevitable, and the ongoing errata process is a testament to Knuth's commitment to continuous improvement. One commenter points out the difficulty of maintaining perfection in such a comprehensive and technically demanding work.
The overall sentiment in the comments is one of respect for Knuth's work and the community effort involved in maintaining its accuracy. The discussion highlights the importance of meticulous attention to detail in computer science and the value of collaborative error correction in advancing the field.