Stories with Tag Donald Knuth

• Discovering errors in Donald Knuth's TAOCP

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  Posted: 2025-03-08 16:27:00

  Verbose tl;dr

  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.

  • Donald Knuth
  • TAOCP
  • The Art of Computer Programming
  • Errors
  • Bug Finding
  • algorithm analysis
  • Computer Science
  • programming
  • books
  • Technical Writing
  • Proofreading
  • verification

  Summary of Comments ( 49 )
  https://news.ycombinator.com/item?id=43301342

  Verbose tl;dr

  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.

• The IBM 650: An appreciation from the field (1986) [pdf]

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  Posted: 2025-03-03 10:19:58

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  Donald Knuth's 1986 reflection on the IBM 650 celebrates its profound impact on his formative years as a programmer and computer scientist. He fondly details the machine's quirks, from its rotating magnetic drum memory and bi-quinary arithmetic to its unique assembly language, SOAP. Knuth emphasizes the 650's educational value, arguing that its limitations encouraged creative problem-solving and a deep understanding of computational processes. He contrasts this with the relative "black box" nature of later machines, lamenting the lost art of optimizing code for specific hardware characteristics. Ultimately, the essay is a tribute to the 650's role in fostering a generation of programmers who learned to think deeply about computation at a fundamental level.

  Donald E. Knuth's 1986 reflection, "The IBM 650: An Appreciation from the Field," offers a deeply personal and meticulously detailed account of his formative experiences with the IBM 650 Magnetic Drum Data-Processing Machine. Knuth frames the 650 not merely as a piece of historical computing hardware, but as a pivotal catalyst in his own intellectual development and a representative example of the challenges and triumphs of early computing.

  The article begins by situating the 650 within the broader technological landscape of the mid-1950s, highlighting its relative affordability and accessibility compared to larger mainframe computers of the era. Knuth vividly recounts his initial encounter with the machine at Case Institute of Technology, emphasizing the aura of mystique and excitement that surrounded it. He describes the 650's physical characteristics, including its imposing size, the constantly whirring magnetic drum, and the blinking console lights, evoking a sense of the machine's tangible presence.

  A significant portion of the article is devoted to explaining the intricacies of the 650's architecture and operation. Knuth delves into the specifics of its decimal arithmetic system, the bi-quinary representation of digits, and the concept of "optimally addressed memory," where instructions were strategically placed on the rotating drum to minimize access time. He provides concrete examples of assembly language programming, illustrating the meticulous planning and optimization required to achieve efficient execution. He even describes the process of physically loading programs onto the drum via punched cards and the suspense of waiting for the output.

  Beyond the technical details, Knuth reflects on the impact the 650 had on his thinking and problem-solving approach. He discusses how the limitations of the machine, such as its limited memory and relatively slow processing speed, forced programmers to be resourceful and creative. He argues that these constraints, rather than being hindrances, fostered a deep understanding of computational processes and encouraged the development of elegant and efficient algorithms. He also recounts the thrill of successfully debugging a program and the satisfaction of witnessing the machine execute complex calculations.

  Knuth's narrative is interwoven with anecdotes and personal reflections, adding a human dimension to the technical discussion. He shares stories of late-night programming sessions, the camaraderie among fellow users, and the occasional frustrations of dealing with hardware malfunctions. He mentions specific individuals who influenced his understanding of the 650 and shaped his trajectory in computer science. The article concludes with a nostalgic look back at the 650's legacy, acknowledging its limitations while simultaneously celebrating its significant contribution to the evolution of computing. He expresses gratitude for the opportunity to have learned on such a groundbreaking machine and recognizes the profound impact it had on his intellectual journey.

  • IBM 650
  • computer history
  • Retrocomputing
  • Mainframe Computers
  • 1950s Computers
  • Vacuum Tube Computers
  • Magnetic Drum Memory
  • early computing
  • Donald Knuth
  • knuth
  • PDF
  • Historical Document
  • Computer Architecture
  • vintage computing

  Summary of Comments ( 10 )
  https://news.ycombinator.com/item?id=43240301

  Verbose tl;dr

  HN commenters generally express appreciation for Knuth's historical perspective and the glimpse into early computing. Several share personal anecdotes of using the IBM 650, recalling its quirks like the rotating drum memory and the challenges of programming with SOAP (Symbolic Optimum Assembly Program). Some discuss the significant impact the 650 had despite its limitations, highlighting its role in educating a generation of programmers and paving the way for future advancements. One commenter points out the machine's influence on Knuth's later work, specifically The Art of Computer Programming. Others compare and contrast the 650 with other early computers and discuss the evolution of programming languages and techniques. A few commenters express interest in emulating the 650.

  The Hacker News post titled "The IBM 650: An appreciation from the field (1986) [pdf]" linking to a PDF of Donald Knuth's reflections on the IBM 650 has generated several comments. Many commenters share their own nostalgic experiences and technical insights related to the machine.

  One compelling comment thread discusses the "quirks" of the IBM 650's architecture, particularly its decimal arithmetic and the use of bi-quinary representation. Commenters detail how these design choices, while seemingly unusual today, were logical given the technological constraints of the time and the desire for easy conversion to and from decimal for human operators. They delve into the specific mechanics of bi-quinary, explaining how it facilitated error detection and offered advantages in implementing arithmetic circuits.

  Several commenters reminisce about their personal experiences using the IBM 650 or similar machines, sharing anecdotes about programming with punched cards, the physical presence and sounds of the machine, and the challenges of debugging code in that era. These personal stories provide a vivid illustration of the early days of computing.

  Another commenter highlights the influence of the IBM 650 on the development of symbolic assemblers, specifically SOAP (Symbolic Optimal Assembly Program). They explain how the constraints of the machine's architecture, like its limited memory capacity and the nature of its instruction set, drove innovation in programming tools.

  The discussion also touches on the broader historical context of the IBM 650, its role in the evolution of computer science education, and its impact on subsequent computer architectures. One comment emphasizes the importance of Knuth's writing in preserving the history of computing, allowing modern readers to appreciate the ingenuity and challenges faced by early computer pioneers.

  A few comments focus on the technical details of the IBM 650's magnetic drum memory, including discussions about its capacity, access times, and the techniques used to optimize program performance by strategically placing instructions and data on the drum to minimize latency.

  Finally, several commenters express their appreciation for the opportunity to read Knuth's reflections, praising his clear and engaging writing style and his ability to convey the essence of working with a now-historic machine. The general sentiment reflects a fascination with the history of computing and an acknowledgment of the IBM 650's significant role in its development.