Terence Tao has released "A Lean Companion to Analysis I," a streamlined version of his Analysis I text. This new edition focuses on the core essentials of single-variable real analysis, omitting more advanced or specialized topics like Fourier analysis, complex analysis, and Lebesgue theory. Intended for a faster-paced course or independent study, it retains the rigorous approach and problem-solving emphasis of the original while being more concise and accessible. The companion text is freely available online and is designed to be adaptable, allowing instructors to supplement with additional material as needed based on their specific course requirements.
A Reddit user mathematically investigated Kellogg's claim that their frosted Pop-Tarts have "more frosting" than unfrosted ones. By meticulously measuring frosted and unfrosted Pop-Tarts and calculating their respective surface areas, they determined that the total surface area of a frosted Pop-Tart is actually less than that of an unfrosted one due to the frosting filling in the pastry's nooks and crannies. Therefore, even if the volume of frosting added equals the volume of pastry lost, the claim of "more" based on surface area is demonstrably false. The user concluded that Kellogg's should phrase their claim differently, perhaps focusing on volume or weight, to be technically accurate.
Hacker News users discuss the methodology and conclusions of the Reddit post analyzing Frosted Mini-Wheats' frosting coverage. Several commenters point out flaws in the original analysis, particularly the assumption of uniform frosting distribution and the limited sample size. Some suggest more robust statistical methods, like analyzing a larger sample and considering the variability in frosting application. Others debate the practical significance of the findings, questioning whether a slightly lower frosting percentage truly constitutes false advertising. A few find humor in the meticulous mathematical approach to a seemingly trivial issue. The overall sentiment is one of mild amusement and skepticism towards the original post's claims.
Driven by curiosity during a vacation, the author reverse-engineered the World Sudoku Championship (WSC) app to understand its puzzle generation and difficulty rating system. This deep dive, though intellectually stimulating, consumed a significant portion of their vacation time and ultimately detracted from the relaxation and enjoyment they had planned. They discovered the app used a fairly standard constraint solver for generation and a simplistic difficulty rating based on solving techniques, neither of which were particularly sophisticated. While the author gained a deeper understanding of the app's inner workings, the project ultimately proved to be a bittersweet experience, highlighting the trade-off between intellectual curiosity and vacation relaxation.
Several commenters on Hacker News discussed the author's approach and the ethics of reverse engineering a closed system, even one as seemingly innocuous as a water park's wristband system. Some questioned the wisdom of dedicating vacation time to such a project, while others praised the author's curiosity and technical skill. A few pointed out potential security flaws inherent in the system, highlighting the risks of using RFID technology without sufficient security measures. Others suggested alternative approaches the author could have taken, such as contacting the water park directly with their concerns. The overall sentiment was a mixture of amusement, admiration, and concern for the potential implications of reverse engineering such systems. Some also debated the legal gray area of such activities, with some arguing that the author's actions might be considered a violation of terms of service or even illegal in some jurisdictions.
Mathematicians have finally proven the Kakeya conjecture, a century-old problem concerning the smallest area required to rotate a unit line segment 180 degrees in a plane. The collaborative work, spearheaded by Nets Katz and Joshua Zahl, builds upon previous partial solutions and introduces a novel geometric argument. While their proof technically addresses the finite field version of the conjecture, it's considered a significant breakthrough with strong implications for the original Euclidean plane problem. The techniques developed for this proof are anticipated to have far-reaching consequences across various mathematical fields, including harmonic analysis and additive combinatorics.
HN commenters generally express excitement and appreciation for the breakthrough proof of the Kakeya conjecture, with several noting its accessibility even to non-mathematicians. Some discuss the implications of the proof and its reliance on additive combinatorics, a relatively new field. A few commenters delve into the history of the problem and the contributions of various mathematicians. The top comment highlights the fascinating connection between the conjecture and seemingly disparate areas like harmonic analysis and extractors for randomness. Others discuss the "once-in-a-century" claim, questioning its accuracy while acknowledging the significance of the achievement. A recurring theme is the beauty and elegance of the proof, reflecting a shared sense of awe at the power of mathematical reasoning.
The HYTRADBOI 2025 conference, focused on hybrid traditional/digital back-office infrastructure, was deemed a moderate success. While attendance was lower than projected and the venue presented some A/V challenges, attendees generally found the sessions valuable and networking opportunities fruitful. The organizer highlighted successful experiments like the "hallway track" and unconference sessions, but acknowledged areas for improvement, including earlier promotion, clearer session descriptions, and a more robust A/V setup. Despite the shortcomings, positive feedback and a renewed sense of community suggest a strong foundation for future HYTRADBOI events.
HN commenters largely praised the HYTRADBOI postmortem for its humor and satirical take on tech conference culture. Several appreciated the specific details that made the satire resonate, like the obsession with "engagement," the meaningless jargon, and the over-the-top branding exercises. Some debated whether the piece was too cynical or accurately reflected current trends, while others pointed out parallels with existing events and marketing strategies. A few commenters focused on the writing style, praising its wit and clarity. One commenter suggested the fictional conference's premise—hybrid traditional boy—perfectly captured the tech industry's struggle to reconcile old and new ways of working. Others offered humorous additions to the fictional world, such as potential sponsors or session titles.
Troubleshooting is a perpetually valuable skill applicable across various domains, from software development to everyday life. It involves a systematic approach of identifying the root cause of a problem, not just treating symptoms. This process relies on observation, critical thinking, research, and testing potential solutions, often involving a cyclical process of refining hypotheses based on results. Mastering troubleshooting empowers individuals to solve problems independently, fostering resilience and adaptability in a constantly evolving world. It's a crucial skill for learning effectively, especially in self-directed learning, by encouraging active engagement with challenges and promoting deeper understanding through the process of overcoming them.
HN users largely praised the article for its clear and concise explanation of troubleshooting methodology. Several commenters highlighted the importance of the "binary search" approach to isolating problems, while others emphasized the value of understanding the system you're working with. Some users shared personal anecdotes about troubleshooting challenges they'd faced, reinforcing the article's points. A few commenters also mentioned the importance of documentation and logging for effective troubleshooting, and the article's brief touch on "pre-mortem" analysis was also appreciated. One compelling comment suggested the article should be required reading for all engineers. Another highlighted the critical skill of translating user complaints into actionable troubleshooting steps.
Posh, a YC W22 startup, is hiring an Energy Analysis & Modeling Engineer. This role will involve building and maintaining energy models to optimize battery performance and efficiency within their virtual power plant (VPP) software platform. The ideal candidate has experience in energy systems modeling, optimization algorithms, and data analysis, preferably with a background in electrical engineering, mechanical engineering, or a related field. They are looking for someone proficient in Python and comfortable working in a fast-paced startup environment.
The Hacker News comments express skepticism and concern about Posh's business model and the specific job posting. Several commenters question the viability of Posh's approach to automating customer service for banks, citing the complexity of financial transactions and the potential for errors. Others express concerns about the low salary offered for the required skillset, particularly given the location (Boston). Some speculate about the high turnover hinted at by the constant hiring and question the long-term prospects of the company. The general sentiment seems to be one of caution and doubt about Posh's potential for success.
An analysis of top researchers across various disciplines revealed that approximately 10% publish at incredibly high rates, likely unsustainable without questionable practices. These researchers produced papers at a pace suggesting a new publication every five days, raising concerns about potential shortcuts like salami slicing, honorary authorship, and insufficient peer review. While some researchers naturally produce more work, the study suggests this extreme output level hints at systemic issues within academia, incentivizing quantity over quality and potentially impacting research integrity.
Hacker News users discuss the implications of a small percentage of researchers publishing an extremely high volume of papers. Some question the validity of the study's methodology, pointing out potential issues like double-counting authors with similar names and the impact of large research groups. Others express skepticism about the value of such prolific publication, suggesting it incentivizes quantity over quality and leads to a flood of incremental or insignificant research. Some commenters highlight the pressures of the academic system, where publishing frequently is essential for career advancement. The discussion also touches on the potential for AI-assisted writing to exacerbate this trend, and the need for alternative metrics to evaluate research impact beyond simple publication counts. A few users provide anecdotal evidence of researchers gaming the system by salami-slicing their work into multiple smaller publications.
Holden Karnofsky examines the question of whether advanced AI will pose an existential threat. He argues that while it's difficult to be certain, the evidence suggests a substantial likelihood of catastrophe. This risk stems from the potential for AI systems to dramatically outperform humans in many domains, combined with misaligned goals or values, leading to unintended and harmful consequences. Karnofsky highlights the rapid pace of AI development, the difficulty of aligning complex systems, and the historical precedent of powerful technologies causing unforeseen disruptions as key factors contributing to the risk. He emphasizes the need for serious consideration and proactive mitigation efforts, arguing that the potential consequences are too significant to ignore.
Hacker News users generally praised the article for its thoroughness and nuanced approach to causal inference. Several commenters highlighted the importance of considering confounding variables and the limitations of observational studies, echoing points made in the article. One compelling comment suggested the piece would be particularly valuable for those working in fields where causal claims are frequently made without sufficient evidence, such as nutrition and social sciences. Another insightful comment discussed the practical challenges of applying Hill's criteria for causality, noting that even with strong evidence, definitively proving causation can be difficult. Some users pointed out the article's length, while others appreciated the depth and detailed examples. A few commenters also shared related resources and tools for causal inference.
A press release by the "Coalition for Independent and Transparent Elections" claims statistical anomalies in Clark County, Nevada's 2024 election results suggest potential manipulation. They cite improbable uniformity in precinct-level vote shares for certain candidates and a suspicious correlation between electronic voting machine usage and outcomes. The group calls for a full audit of the county's election, including hand recounts and forensic analysis of voting machines, to ensure election integrity.
Hacker News users largely dismiss the linked article's claims of election manipulation. Several commenters point out methodological flaws, including comparing dissimilar precincts and drawing conclusions based on cherry-picked data. The lack of transparency in the analysis, particularly the absence of raw data and methodology details, fuels further skepticism. Some users suggest the piece is intentionally misleading, possibly motivated by political agendas. Others highlight the importance of verifiable evidence and rigorous statistical analysis when making such serious allegations. A few commenters engage in more general discussions about election integrity and the spread of misinformation.
The blog post details a teardown and analysis of a SanDisk High Endurance microSDXC card. The author physically de-caps the card to examine the controller and flash memory chips, identifying the controller as a SMI SM2703 and the NAND flash as likely Micron TLC. They then analyze the card's performance using various benchmarking tools, observing consistent write speeds around 30MB/s, significantly lower than the advertised 60MB/s. The author concludes that while the card may provide decent sustained write performance, the marketing claims are inflated and the "high endurance" aspect likely comes from over-provisioning rather than superior hardware. The post also speculates about the internal workings of the pSLC caching mechanism potentially responsible for the consistent write speeds.
Hacker News users discuss the intricacies of the SanDisk High Endurance card and the reverse-engineering process. Several commenters express admiration for the author's deep dive into the card's functionality, particularly the analysis of the wear-leveling algorithm and its pSLC mode. Some discuss the practical implications of the findings, including the limitations of endurance claims and the potential for data recovery even after the card is deemed "dead." One compelling exchange revolves around the trade-offs between endurance and capacity, and whether higher endurance necessitates lower overall storage. Another interesting thread explores the challenges of validating write endurance claims and the lack of standardized testing. A few commenters also share their own experiences with similar cards and offer additional insights into the complexities of flash memory technology.
"Shades of Blunders" explores the psychology behind chess mistakes, arguing that simply labeling errors as "blunders" is insufficient for improvement. The author, a chess coach, introduces a nuanced categorization of blunders based on the underlying mental processes. These categories include overlooking obvious threats due to inattention ("blind spots"), misjudging positional elements ("positional blindness"), calculation errors stemming from limited depth ("short-sightedness"), and emotionally driven mistakes ("impatience" or "fear"). By understanding the root cause of their errors, chess players can develop more targeted training strategies and avoid repeating the same mistakes. The post emphasizes the importance of honest self-assessment and moving beyond simple move-by-move analysis to understand the why behind suboptimal decisions.
HN users discuss various aspects of blunders in chess. Several highlight the psychological impact, including the tilt and frustration that can follow a mistake, even in casual games. Some commenters delve into the different types of blunders, differentiating between simple oversights and more complex errors in calculation or evaluation. The role of time pressure is also mentioned as a contributing factor. A few users share personal anecdotes of particularly memorable blunders, adding a touch of humor to the discussion. Finally, the value of analyzing blunders for improvement is emphasized by multiple commenters.
The original poster wonders if people can be categorized as primarily "story-based" or "fact-based" thinkers. They observe that some individuals seem to prioritize narratives and emotional resonance, readily accepting information that fits a compelling story, even if evidence is lacking. Conversely, others appear to prioritize factual accuracy and logical consistency, potentially dismissing emotionally resonant stories if they lack evidential support. The author questions whether this distinction is valid, if people fall on a spectrum, or if other factors are at play, and asks if this dichotomy influences communication styles and understanding.
The Hacker News comments discuss the idea of "story-based" vs. "fact-based" people, with many expressing skepticism about such a rigid dichotomy. Several commenters suggest the distinction isn't about accepting facts, but rather how people prioritize and interpret them. Some argue everyone uses narratives to understand the world, with the key difference being the quality of evidence people demand to support their narratives. Others point out the influence of cognitive biases, motivated reasoning, and the difficulty of separating facts from interpretation. The role of emotion and empathy in decision-making is also highlighted, with some arguing "story-based" thinking might simply reflect a greater emphasis on emotional connection. A few commenters mention Myers-Briggs personality types as a potential framework for understanding these differences, though this is met with some skepticism. Overall, the consensus seems to be that the proposed dichotomy is overly simplistic and potentially misleading.
NIST's Standard Reference Material (SRM) 2387, peanut butter, isn't for spreading on sandwiches. It serves as a calibration standard for laboratories analyzing food composition, ensuring accurate measurements of nutrients and contaminants like aflatoxins. This carefully blended and homogenized peanut butter provides a consistent benchmark, allowing labs to verify the accuracy of their equipment and methods, ultimately contributing to food safety and quality. The SRM ensures that different labs get comparable results when testing foods, promoting reliable and consistent data across the food industry.
Hacker News users discuss NIST's standard reference peanut butter (SRMs 2387 and 2388). Several commenters express amusement and mild surprise that such a standard exists, questioning its necessity. Some delve into the practical applications, highlighting its use for calibrating analytical instruments and ensuring consistency in food manufacturing and testing. A few commenters with experience in analytical chemistry explain the importance of reference materials, emphasizing the difficulty in creating homogenous samples like peanut butter. Others discuss the specific challenges of peanut butter analysis, like fat migration and particle size distribution. The rigorous testing procedures NIST uses, including multiple labs analyzing the same batch, are also mentioned. Finally, some commenters joke about the "dream job" of tasting peanut butter for NIST.
Karl Weierstrass’s function revolutionized mathematics by demonstrating a curve that is continuous everywhere but differentiable nowhere. This “monster” function, built from an infinite sum of cosine waves with increasingly higher frequencies and smaller amplitudes, visually appears jagged and chaotic at every scale. Its existence challenged the prevailing assumption that continuous functions were mostly smooth, with only isolated points of non-differentiability. Weierstrass's discovery exposed a deep rift between intuition and mathematical rigor, ushering in a new era of analysis focused on precise definitions and rigorous proofs, impacting fields from calculus to fractal geometry.
HN users generally express fascination with the Weierstrass function and its implications for calculus. Several comments dive into the history and significance of the function, appreciating its role in challenging intuitive notions of continuity and differentiability. Some discuss its relation to fractals and Brownian motion, while others highlight the beauty of mathematical discoveries that defy expectations. A few commenters provide additional resources, including links to visualizations and related mathematical concepts like space-filling curves. Some debate the accessibility of the original Quanta article, suggesting ways it could be more easily understood by a broader audience. A recurring theme is the wonder inspired by such counterintuitive mathematical objects.
A seemingly innocuous USB-C to Ethernet adapter, purchased from Amazon, was found to contain a sophisticated implant capable of malicious activity. This implant included a complete system with a processor, memory, and network connectivity, hidden within the adapter's casing. Upon plugging it in, the adapter established communication with a command-and-control server, potentially enabling remote access, data exfiltration, and other unauthorized actions on the connected computer. The author meticulously documented the hardware and software components of the implant, revealing its advanced capabilities and stealthy design, highlighting the potential security risks of seemingly ordinary devices.
Hacker News users discuss the practicality and implications of the "evil" RJ45 dongle detailed in the article. Some question the dongle's true malicious intent, suggesting it might be a poorly designed device for legitimate (though obscure) networking purposes like hotel internet access. Others express fascination with the hardware hacking and reverse-engineering process. Several commenters discuss the potential security risks of such devices, particularly in corporate environments, and the difficulty of detecting them. There's also debate on the ethics of creating and distributing such hardware, with some arguing that even proof-of-concept devices can be misused. A few users share similar experiences encountering unexpected or unexplained network behavior, highlighting the potential for hidden hardware compromises.
Summary of Comments ( 5 )
https://news.ycombinator.com/item?id=44145517
The Hacker News comments on Tao's "A Lean Companion to Analysis I" express appreciation for its accessibility and clarity compared to Rudin's "Principles of Mathematical Analysis." Several commenters highlight the value of Tao's conversational style and emphasis on intuition, making the often-dense subject matter more approachable for beginners. Some note the inclusion of topics like logic and set theory, which are often assumed but not explicitly covered in other analysis texts. A few comments mention potential uses for self-study or as a supplementary resource alongside a more traditional textbook. There's also discussion comparing it to other analysis books and resources like Abbott's "Understanding Analysis."
The Hacker News post discussing Terence Tao's "A Lean Companion to Analysis I" has a modest number of comments, focusing primarily on the book's accessibility and target audience.
Several commenters discuss the intended level of the book. One notes that while Tao mentions it's aimed at advanced high school students and undergraduates, the commenter believes a strong mathematical background is necessary, suggesting it's more suitable for those already familiar with proof-based mathematics. Another commenter agrees, emphasizing that the "lean" aspect refers to the concise presentation, not necessarily the difficulty of the material itself. They suggest that it's better suited for those revisiting analysis rather than encountering it for the first time.
A recurring theme is the comparison to Rudin's "Principles of Mathematical Analysis." One commenter praises Tao's book for its clarity and readability, contrasting it with Rudin's denser style. They find Tao's approach more intuitive and pedagogical. This sentiment is echoed by another who appreciates Tao's gentler introduction to the subject.
One commenter points out the usefulness of Tao's inclusion of exercises and solutions, a feature often lacking in similar texts. They believe this makes the book more practical for self-study.
Finally, there's a short discussion about alternative resources. One commenter recommends Apostol's "Calculus" as a good starting point for those seeking a more gradual introduction to analysis, before tackling Tao's book. Another mentions Pugh's "Real Mathematical Analysis" as a further resource, highlighting its more advanced and in-depth treatment of the subject.
In summary, the comments generally portray Tao's book as a well-written but challenging text suitable for a mathematically mature audience, likely those already possessing some exposure to proof-based mathematics. It is praised for its clarity and pedagogical approach, particularly in comparison to Rudin. The inclusion of exercises and solutions is seen as a valuable asset. While not recommended as a first introduction to analysis, it's viewed as an excellent resource for solidifying understanding or revisiting the subject.