The blog post "The Lost Art of Logarithms" argues that logarithms are underappreciated and underutilized in modern mathematics education and programming. While often taught purely as the inverse of exponentiation, logarithms possess unique properties that make them powerful tools for simplifying complex calculations, particularly those involving multiplication, division, powers, and roots. The author emphasizes their practical applications in diverse fields like finance, music theory, and computer science, citing examples such as calculating compound interest and understanding musical intervals. The post advocates for a shift in how logarithms are taught, focusing on their intuitive understanding and practical uses rather than rote memorization of formulas and identities. Ultimately, the author believes that rediscovering the "lost art" of logarithms can unlock a deeper understanding of mathematical relationships and enhance problem-solving skills.
The article, "The Lost Art of Logarithms," laments the decline in practical understanding and utilization of logarithms, particularly within the realm of software engineering. The author posits that while logarithms remain a crucial underpinning of computer science, their direct application in day-to-day programming tasks has diminished, leading to a gap in many developers' intuitive grasp of their power and utility. This "lost art," as the author terms it, is not about rote memorization of logarithmic identities or complex manipulations, but rather a nuanced appreciation for the logarithmic scale and its inherent relationship to phenomena like algorithm complexity and dynamic range.
The author argues that this decline stems from several factors. Firstly, the increasing abstraction layers within modern software development tools and libraries often obscure the underlying mathematical principles. Programmers can manipulate data structures and algorithms without needing to explicitly engage with the logarithmic relationships that govern their efficiency. Secondly, the emphasis in many computer science curricula has shifted towards higher-level concepts, potentially at the expense of a deep dive into fundamental mathematical tools like logarithms. Finally, the sheer power of modern computing hardware can mask inefficiencies that a keen understanding of logarithms would quickly expose. In simpler terms, brute force computation can sometimes compensate for a lack of algorithmic elegance rooted in logarithmic principles.
The article proceeds to illustrate the continued relevance of logarithms through a series of concrete examples. It elucidates how logarithms play a critical role in analyzing algorithm performance, particularly in Big O notation, where logarithmic time complexity represents a highly desirable characteristic. The author further demonstrates how logarithms are intrinsically linked to concepts like binary search, demonstrating their practical utility in optimizing search operations. The piece also touches upon the importance of logarithms in understanding and managing data with vastly varying magnitudes, highlighting their application in areas such as sound processing and computer graphics, where decibels and color representation often rely on logarithmic scales.
Ultimately, the author advocates for a renewed focus on the intuitive understanding of logarithms within the software engineering community. The article concludes with a call to action, urging developers to rediscover the elegance and power of this "lost art" and to integrate a deeper appreciation for logarithmic thinking into their daily practice. This, the author suggests, will lead to more efficient, elegant, and ultimately more effective software solutions.
Summary of Comments ( 166 )
https://news.ycombinator.com/item?id=43356314
Hacker News users generally praised the article for its clear explanation of logarithms and their usefulness, particularly in understanding scaling and exponential growth. Several commenters shared personal anecdotes about how a proper grasp of logarithms helped them in their careers, especially in software engineering and data science. Some pointed out the connection between logarithms and music theory, while others discussed the historical context and the importance of slide rules. A few users wished they had encountered such a clear explanation earlier in their education, highlighting the potential of the article as a valuable learning resource. One commenter offered a practical tip for remembering the relationship between logs and exponents. There was also a short thread discussing the practical applications of logarithms in machine learning and information theory.
The Hacker News post titled "The Lost Art of Logarithms" generated several comments discussing the article's premise and related concepts. Here's a summary of the discussion:
Agreement with the core premise: Several commenters concurred with the author's point about the declining emphasis on logarithmic thinking in modern education and programming. They noted that while logarithms are still taught, their deeper significance and intuitive understanding often get lost. Some attributed this to the increasing abstraction layers in software development, where developers rarely need to grapple with low-level details involving logarithmic scales. One commenter lamented that even computer science graduates often lack a strong grasp of logarithms, despite their importance in various algorithms and data structures.
Logarithms in specific domains: Commenters highlighted areas where logarithmic thinking remains crucial. Examples included understanding complexity analysis (Big O notation), working with databases and indexing, comprehending information theory and entropy, and appreciating the logarithmic nature of human perception (e.g., sound intensity, brightness). One commenter specifically mentioned the importance of logarithms in music theory.
Calculators and the loss of intuition: The discussion touched upon how the readily available calculators might have contributed to the decline of mental estimation skills and a deeper intuitive understanding of logarithms. One commenter argued that while calculators are helpful tools, over-reliance on them can hinder the development of a "feel" for numbers and their relationships.
Historical perspective and slide rules: Some comments reflected on the historical significance of logarithms, particularly their use in slide rules before the advent of electronic calculators. This sparked a brief tangent discussing the elegance and tactile experience of using slide rules, and how they fostered a different kind of numerical literacy.
Teaching approaches and practical examples: Commenters suggested ways to improve the teaching of logarithms, emphasizing the need for more engaging and practical examples that resonate with students. They proposed scenarios involving exponential growth, compound interest, and the Richter scale to illustrate the power and relevance of logarithms.
Alternative explanations of logarithms: A couple of commenters offered their own concise explanations of logarithms, aiming to provide a clearer understanding of the concept. One commenter framed logarithms as a way to express large numbers compactly, while another described them as the inverse of exponentiation.
Beyond base 10 and base e: While the article and most comments focused on base 10 and base e logarithms, one commenter highlighted the importance of base 2 logarithms in computer science, especially in the context of binary representation and bit manipulation.
In summary, the Hacker News discussion largely agreed with the article's observation about the declining appreciation for logarithms. The comments explored the reasons behind this trend, highlighted the continued relevance of logarithms in various fields, and offered suggestions for improving the way logarithms are taught and understood. The thread offered a nuanced perspective on the topic, enriched by the diverse backgrounds and experiences of the commenters.