Stories with Tag mnemonics

• Spaced repetition can allow for infinite recall (2022)

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  Posted: 2025-02-02 11:42:06

  Verbose tl;dr

  Spaced repetition, a learning technique that schedules reviews at increasing intervals, can theoretically lead to near-perfect, long-term retention. By strategically timing repetitions just before forgetting occurs, the memory trace is strengthened, making recall progressively easier and extending the retention period indefinitely. The article argues against the common misconception of a "forgetting curve" with inevitable decay, proposing instead a model where each successful recall flattens the curve and increases the time until the next necessary review. This allows for efficient long-term learning by minimizing the number of reviews required to maintain information in memory, effectively making "infinite recall" achievable.

  The blog post "Spaced repetition can allow for infinite recall (2022)" on efavdb.com delves into the concept of achieving near-perfect, long-term retention of information through the strategic implementation of spaced repetition systems (SRS). The author posits that while true "infinite" recall might be a theoretical ideal, leveraging the principles of spaced repetition can drastically extend the lifespan of memories, effectively making forgetting a non-issue for practical purposes.

  The core premise revolves around the scientifically established forgetting curve, which dictates that newly acquired information rapidly decays over time unless actively recalled. Spaced repetition combats this decay by prompting the learner to retrieve the information at increasing intervals. Each successful retrieval strengthens the memory trace, pushing the next review further into the future. The post emphasizes that the timing of these reviews is crucial and that optimized algorithms, like those employed by popular SRS software such as Anki, are designed to maximize retention while minimizing review effort.

  The author elaborates on the mechanics of these algorithms, explaining how they factor in the perceived difficulty of an item and the learner's individual performance history to dynamically adjust the review schedule. A correct recall extends the interval, while a failure shortens it, ensuring that the learner is consistently challenged just before forgetting is likely to occur. This "sweet spot" of retrieval difficulty is key to the effectiveness of spaced repetition.

  Furthermore, the post discusses the practical benefits of incorporating spaced repetition into various learning endeavors, including language acquisition, technical skill development, and general knowledge retention. It highlights the efficiency of SRS compared to traditional rote memorization techniques, arguing that spaced repetition allows learners to achieve a higher level of mastery with significantly less overall study time.

  The author acknowledges potential downsides, such as the initial setup time required to create flashcards or other learning materials, and the ongoing commitment needed to maintain the review schedule. However, they argue that the long-term benefits of near-perfect recall far outweigh these initial investments. The post concludes with a strong endorsement of spaced repetition as a powerful tool for lifelong learning, capable of transforming how we acquire and retain information. It encourages readers to explore and experiment with available SRS tools to experience the transformative potential of this learning technique firsthand.

  • spaced repetition
  • Memory
  • recall
  • learning
  • retention
  • mnemonics
  • Cognitive Science
  • memory palace
  • long-term memory
  • study techniques
  • anki
  • 2022

  Summary of Comments ( 121 )
  https://news.ycombinator.com/item?id=42908041

  Verbose tl;dr

  Hacker News users discussed the effectiveness and practicality of spaced repetition, referencing personal experiences and variations in implementation. Some commenters highlighted the importance of understanding the underlying cognitive science, advocating for adjusting repetition schedules based on individual needs rather than blindly following algorithms. Others debated the difference between recognition and recall, and the article's conflation of the two. A few pointed out potential downsides of spaced repetition, such as the time commitment required and the possibility of over-optimizing for memorization at the expense of deeper understanding. Several users shared their preferred spaced repetition software and techniques.

  The Hacker News post "Spaced repetition can allow for infinite recall (2022)" linking to an article on efavdb.com has generated several comments discussing the merits and nuances of spaced repetition as a learning technique.

  Several commenters agree with the premise, sharing their positive experiences with spaced repetition systems (SRS) like Anki. They highlight the effectiveness of SRS for memorizing vast amounts of information, ranging from vocabulary and medical facts to programming languages and historical dates. One commenter points out the importance of creating high-quality flashcards with clear context and meaningful connections to maximize retention. Another emphasizes the psychological benefit of the "investment" made in crafting good flashcards, leading to a stronger commitment to the learning process. The ease of integrating spaced repetition into daily routines is also mentioned as a significant advantage.

  However, some commenters express more nuanced perspectives. One individual argues that while spaced repetition excels at rote memorization, it might not be as effective for deeper understanding or the ability to apply knowledge creatively. They suggest that other learning methods might be more suitable for these goals. This point sparks a discussion about the difference between remembering and understanding, with some arguing that robust memorization forms a solid foundation for deeper comprehension.

  Another commenter raises the issue of the time commitment required for spaced repetition, acknowledging its effectiveness but questioning its practicality for individuals with limited time or those who struggle with maintaining consistent study habits. They propose alternative learning strategies that might be less demanding but potentially less powerful for long-term retention.

  A few commenters delve into the technical aspects of spaced repetition algorithms, discussing the importance of parameters like the forgetting curve and the spacing intervals. They also mention the potential for customizing these parameters to optimize individual learning styles and preferences.

  One commenter introduces the concept of "elaborative encoding," which involves actively relating new information to existing knowledge to enhance memorization. They suggest combining spaced repetition with elaborative encoding techniques for optimal results.

  Finally, some comments address the limitations of spaced repetition. One commenter points out that while it can facilitate recall, it doesn't necessarily guarantee comprehension or the ability to use the recalled information effectively. Another raises the possibility of "illusory fluency," where the ease of recall within the SRS environment might not translate to real-world application.

  In summary, the comments on the Hacker News post reflect a generally positive view of spaced repetition as a powerful learning tool, particularly for memorization. However, they also acknowledge its limitations and emphasize the importance of considering individual learning styles, time constraints, and the specific learning goals when deciding whether to adopt this technique. The discussion highlights the nuances of spaced repetition and encourages a balanced approach to learning that incorporates various strategies beyond rote memorization.

• Cab Numbers

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  Posted: 2025-01-21 17:37:39

  Verbose tl;dr

  Cab numbers, also known as Ramanujan-Hardy numbers, are positive integers that can be expressed as the sum of two positive cubes in two different ways. The smallest such number is 1729, which is 1³ + 12³ and also 9³ + 10³. The post explores these numbers, providing a formula for generating them and listing the first few examples. It delves into the mathematical underpinnings of these intriguing numbers, discussing their connection to elliptic curves and highlighting the contributions of Srinivasa Ramanujan in identifying their unique property. The author also explores a related concept: numbers expressible as the sum of two cubes in three different ways, offering formulas and examples for these less-common numerical curiosities.

  This article, titled "Cab Numbers," delves into a fascinating mathematical curiosity known as the Hardy-Ramanujan number, also referred to as the "taxi-cab number," specifically 1729. The article begins by recounting the famous anecdote of the mathematician G.H. Hardy visiting his ailing colleague Srinivasa Ramanujan in a taxicab numbered 1729. Hardy remarked that the number seemed rather dull, to which Ramanujan promptly replied that it was, in fact, quite interesting, being the smallest positive integer expressible as the sum of two positive cubes in two distinct ways.

  The article then meticulously elaborates on this property, demonstrating that 1729 can be expressed as both 1³ + 12³ and 9³ + 10³. It emphasizes the significance of the word "distinct," meaning that the pairs of cubes (1, 12) and (9, 10) are different, thus excluding trivial rearrangements like 12³ + 1³.

  Following this initial explanation, the article expands the concept to consider the smallest numbers expressible as the sum of two cubes in three distinct ways, denoted as Taxicab(3), then four distinct ways (Taxicab(4)), and so on. It provides these values, showcasing the rapidly increasing size of these numbers as the number of required representations grows. The article also gives the generalized mathematical notation for Taxicab(n) and explains the computational challenges in finding these numbers as 'n' increases.

  Furthermore, the piece explores a related concept: the smallest number that can be expressed as the sum of two positive nth powers in two different ways. It provides examples for squares, cubes (revisiting the taxicab number), fourth powers, and fifth powers, highlighting the increasing complexity of finding such numbers. It notes how the search for these generalized "taxicab" numbers becomes computationally expensive very quickly.

  Finally, the article briefly touches upon the history of the investigation into these numbers, referencing Leonard Euler's work in the 18th century. It concludes by suggesting that while 1729 might appear mundane at first glance, a deeper exploration reveals its unique mathematical properties, placing it firmly within the realm of interesting numbers.

  • taxicabs
  • taxi numbers
  • telephone numbers
  • mnemonics
  • memory aids
  • phoneword
  • number patterns
  • cognitive psychology
  • human memory

  Summary of Comments ( 3 )
  https://news.ycombinator.com/item?id=42782929

  Verbose tl;dr

  Hacker News users discuss the surprising mathematical properties of "cab numbers" (integers expressible as the sum of two positive cubes in two different ways), focusing on Ramanujan's famous encounter with the number 1729. Several commenters delve into the history and related mathematical concepts, including taxicab numbers of higher order and the significance of 1729 in number theory. Some explore the computational aspects of finding these numbers, referencing algorithms and code examples. Others share anecdotes about Ramanujan and discuss the inherent beauty and elegance of such mathematical discoveries. A few commenters also provide links to further reading on related topics like Fermat's Last Theorem and the sum of cubes problem.

  The Hacker News post titled "Cab Numbers" links to an article exploring the mathematical concept of cab numbers, which are integers expressible as the sum of two positive cubes in two different ways. The discussion in the comments section is brief, but touches on a few interesting points related to the topic.

  One commenter notes the connection between cab numbers and taxicab numbers, pointing out the Ramanujan anecdote about the number 1729 being the smallest number expressible as the sum of two cubes in two different ways. This comment serves as a clarification for those unfamiliar with the mathematical history, reinforcing the main idea of the linked article.

  Another commenter expresses appreciation for the simplicity and clarity of the explanation provided in the article, finding it more accessible than other resources they have encountered. This emphasizes the article's strength in presenting a complex mathematical concept in an understandable way.

  A further comment expands on the mathematical properties of cab numbers, linking to a Wikipedia page about taxicab numbers, and mentioning generalized taxicab numbers (which consider sums of more than two cubes, and more ways of representation). This comment adds depth to the discussion, directing readers towards further exploration of the concept and its generalizations.

  Finally, a short comment mentions the related concept of "taxi-cab" numbers, highlighting the subtle but crucial difference in the terms used and referring to the sequence listed in the Online Encyclopedia of Integer Sequences (OEIS). This contributes to the discussion by clarifying terminology and providing a readily available resource for further investigation.

  While the number of comments is limited, they provide valuable context, clarification, and avenues for further exploration of the concept of cab numbers. They showcase appreciation for the linked article's clarity and contribute to a broader understanding of the topic's mathematical nuances.