John Baez's post explains that the common notion of black holes shrinking due to Hawking radiation is a simplification. While Hawking radiation exists, it's emitted by the hot "quantum atmosphere" surrounding the black hole, not the singularity itself. This atmosphere is formed from infalling matter interacting with intense spacetime curvature. The black hole's mass, contained within its event horizon, only decreases because this infalling matter effectively loses some energy as Hawking radiation before crossing the horizon. Therefore, it's more accurate to say the black hole's atmosphere radiates and shrinks as it loses energy, indirectly causing the enclosed black hole to shrink over vast timescales.
Entropy, in the context of information theory, quantifies uncertainty. A high-entropy system, like a fair coin flip, is unpredictable, as all outcomes are equally likely. A low-entropy system, like a weighted coin always landing on heads, is highly predictable. This uncertainty is measured in bits, representing the minimum number of yes/no questions needed to determine the outcome. Entropy also relates to compressibility: high-entropy data is difficult to compress because it lacks predictable patterns, while low-entropy data, with its inherent redundancy, can be compressed significantly. Ultimately, entropy provides a fundamental way to measure information content and randomness within a system.
Hacker News users generally praised the article for its clear explanation of entropy, particularly its focus on the "volume of surprise" and use of visual aids. Some commenters offered alternative analogies or further clarifications, such as relating entropy to the number of microstates corresponding to a macrostate, or explaining its connection to lossless compression. A few pointed out minor perceived issues, like the potential confusion between thermodynamic and information entropy, and questioned the accuracy of describing entropy as "disorder." One commenter suggested a more precise phrasing involving "indistinguishable microstates", while another highlighted the significance of Boltzmann's constant in relating information entropy to physical systems. Overall, the discussion demonstrates a positive reception of the article's attempt to demystify a complex concept.
Cross-entropy and KL divergence are closely related measures of difference between probability distributions. While cross-entropy quantifies the average number of bits needed to encode events drawn from a true distribution p using a coding scheme optimized for a predicted distribution q, KL divergence measures how much more information is needed on average when using q instead of p. Specifically, KL divergence is the difference between cross-entropy and the entropy of the true distribution p. Therefore, minimizing cross-entropy with respect to q is equivalent to minimizing the KL divergence, as the entropy of p is constant. While both can measure the dissimilarity between distributions, KL divergence is a true "distance" metric (though asymmetric), whereas cross-entropy is not. The post illustrates these concepts with detailed numerical examples and explains their significance in machine learning, particularly for tasks like classification where the goal is to match a predicted distribution to the true data distribution.
Hacker News users generally praised the clarity and helpfulness of the article explaining cross-entropy and KL divergence. Several commenters pointed out the value of the concrete code examples and visualizations provided. One user appreciated the explanation of the difference between minimizing cross-entropy and maximizing likelihood, while another highlighted the article's effective use of simple language to explain complex concepts. A few comments focused on practical applications, including how cross-entropy helps in model selection and its relation to log loss. Some users shared additional resources and alternative explanations, further enriching the discussion.
The blog post "Entropy Attacks" argues against blindly trusting entropy sources, particularly in cryptographic contexts. It emphasizes that measuring entropy based solely on observed outputs, like those from /dev/random, is insufficient for security. An attacker might manipulate or partially control the supposedly random source, leading to predictable outputs despite seemingly high entropy. The post uses the example of an attacker influencing the timing of network packets to illustrate how seemingly unpredictable data can still be exploited. It concludes by advocating for robust key-derivation functions and avoiding reliance on potentially compromised entropy sources, suggesting deterministic random bit generators (DRBGs) seeded with a high-quality initial seed as a preferable alternative.
The Hacker News comments discuss the practicality and effectiveness of entropy-reduction attacks, particularly in the context of Bernstein's blog post. Some users debate the real-world impact, pointing out that while theoretically interesting, such attacks often rely on unrealistic assumptions like attackers having precise timing information or access to specific hardware. Others highlight the importance of considering these attacks when designing security systems, emphasizing defense-in-depth strategies. Several comments delve into the technical details of entropy estimation and the challenges of accurately measuring it. A few users also mention specific examples of vulnerabilities related to insufficient entropy, like Debian's OpenSSL bug. The overall sentiment suggests that while these attacks aren't always easily exploitable, understanding and mitigating them is crucial for robust security.
Researchers at the University of Surrey have theoretically demonstrated that two opposing arrows of time can emerge within specific quantum systems. By examining the evolution of entanglement within these systems, they found that while one subsystem experiences time flowing forward as entropy increases, another subsystem can simultaneously experience time flowing backward, with entropy decreasing. This doesn't violate the second law of thermodynamics, as the overall combined system still sees entropy increase. This discovery offers new insights into the foundations of quantum mechanics and its relationship with thermodynamics, particularly in understanding the flow of time at the quantum level.
HN users express skepticism about the press release's interpretation of the research, questioning whether the "two arrows of time" are a genuine phenomenon or simply an artifact of the chosen model. Some suggest the description is sensationalized and oversimplifies complex quantum behavior. Several commenters call for access to the actual paper rather than relying on the university's press release, emphasizing the need to examine the methodology and mathematical framework to understand the true implications of the findings. A few commenters delve into the specifics of microscopic reversibility and entropy, highlighting the challenges in reconciling these concepts with the claims made in the article. There's a general consensus that the headline is attention-grabbing but potentially misleading without deeper analysis of the underlying research.
The blog post "Fat Rand: How Many Lines Do You Need to Generate a Random Number?" explores the surprising complexity hidden within seemingly simple random number generation. It dissects the code behind Python's random.randint() function, revealing a multi-layered process involving system-level entropy sources, hashing, and bit manipulation to ultimately produce a seemingly simple random integer. The post highlights the extensive effort required to achieve statistically sound randomness, demonstrating that generating even a single random number relies on a significant amount of code and underlying system functionality. This complexity is necessary to ensure unpredictability and avoid biases, which are crucial for security, simulations, and various other applications.
Hacker News users discussed the surprising complexity of generating truly random numbers, agreeing with the article's premise. Some commenters highlighted the difficulty in seeding pseudo-random number generators (PRNGs) effectively, with suggestions like using /dev/random, hardware sources, or even mixing multiple sources. Others pointed out that the article focuses on uniformly distributed random numbers, and that generating other distributions introduces additional complexity. A few users mentioned specific use cases where simple PRNGs are sufficient, like games or simulations, while others emphasized the critical importance of robust randomness in cryptography and security. The discussion also touched upon the trade-offs between performance and security when choosing a random number generation method, and the value of having different "grades" of randomness for various applications.
Klarity is an open-source Python library designed to analyze uncertainty and entropy in large language model (LLM) outputs. It provides various metrics and visualization tools to help users understand how confident an LLM is in its generated text. This can be used to identify potential errors, biases, or areas where the model is struggling, ultimately enabling better prompt engineering and more reliable LLM application development. Klarity supports different uncertainty estimation methods and integrates with popular LLM frameworks like Hugging Face Transformers.
Hacker News users discussed Klarity's potential usefulness, but also expressed skepticism and pointed out limitations. Some questioned the practical applications, wondering if uncertainty analysis is truly valuable for most LLM use cases. Others noted that Klarity focuses primarily on token-level entropy, which may not accurately reflect higher-level semantic uncertainty. The reliance on temperature scaling as the primary uncertainty control mechanism was also criticized. Some commenters suggested alternative approaches to uncertainty quantification, such as Bayesian methods or ensembles, might be more informative. There was interest in seeing Klarity applied to different models and tasks to better understand its capabilities and limitations. Finally, the need for better visualization and integration with existing LLM workflows was highlighted.
This post provides a high-level overview of compression algorithms, categorizing them into lossless and lossy methods. Lossless compression, suitable for text and code, reconstructs the original data perfectly using techniques like Huffman coding and LZ77. Lossy compression, often used for multimedia like images and audio, achieves higher compression ratios by discarding less perceptible data, employing methods such as discrete cosine transform (DCT) and quantization. The post briefly explains the core concepts behind these techniques and illustrates how they reduce data size by exploiting redundancy and irrelevancy. It emphasizes the trade-off between compression ratio and data fidelity, with lossy compression prioritizing smaller file sizes at the expense of some information loss.
Hacker News users discussed various aspects of compression, prompted by a blog post overviewing different algorithms. Several commenters highlighted the importance of understanding data characteristics when choosing a compression method, emphasizing that no single algorithm is universally superior. Some pointed out the trade-offs between compression ratio, speed, and memory usage, with specific examples like LZ77 being fast for decompression but slower for compression. Others discussed more niche compression techniques like ANS and its use in modern codecs, as well as the role of entropy coding. A few users mentioned practical applications and tools, like using zstd for backups and mentioning the utility of brotli. The complexities of lossy compression, particularly for images, were also touched upon.
The blog post explores using entropy as a measure of the predictability and "surprise" of Large Language Model (LLM) outputs. It explains how to calculate entropy character-by-character and demonstrates that higher entropy generally corresponds to more creative or unexpected text. The author argues that while tools like perplexity exist, entropy offers a more granular and interpretable way to analyze LLM behavior, potentially revealing insights into the model's internal workings and helping identify areas for improvement, such as reducing repetitive or predictable outputs. They provide Python code examples for calculating entropy and showcase its application in evaluating different LLM prompts and outputs.
Hacker News users discussed the relationship between LLM output entropy and interestingness/creativity, generally agreeing with the article's premise. Some debated the best metrics for measuring "interestingness," suggesting alternatives like perplexity or considering audience-specific novelty. Others pointed out the limitations of entropy alone, highlighting the importance of semantic coherence and relevance. Several commenters offered practical applications, like using entropy for prompt engineering and filtering outputs, or combining it with other metrics for better evaluation. There was also discussion on the potential for LLMs to maximize entropy for "clickbait" generation and the ethical implications of manipulating these metrics.
This blog post presents a different way to derive Shannon entropy, focusing on its property as a unique measure of information content. Instead of starting with desired properties like additivity and then finding a formula that satisfies them, the author begins with a core idea: measuring the average number of binary questions needed to pinpoint a specific outcome from a probability distribution. By formalizing this concept using a binary tree representation of the questioning process and leveraging Kraft's inequality, they demonstrate that -∑pᵢlog₂(pᵢ) emerges naturally as the optimal average question length, thus establishing it as the entropy. This construction emphasizes the intuitive link between entropy and the efficient encoding of information.
Hacker News users discuss the alternative construction of Shannon entropy presented in the linked article. Some express appreciation for the clear explanation and visualizations, finding the geometric approach insightful and offering a fresh perspective on a familiar concept. Others debate the pedagogical value of the approach, questioning whether it truly simplifies understanding for those unfamiliar with entropy, or merely offers a different lens for those already versed in the subject. A few commenters note the connection to cross-entropy and Kullback-Leibler divergence, suggesting the geometric interpretation could be extended to these related concepts. There's also a brief discussion on the practical implications and potential applications of this alternative construction, although no concrete examples are provided. Overall, the comments reflect a mix of appreciation for the novel approach and a pragmatic assessment of its usefulness in teaching and application.
Summary of Comments ( 79 )
https://news.ycombinator.com/item?id=44015872
Hacker News users discuss the surprising assertion that dead stars don't radiate, focusing on the definition of "dead" in this context. Several point out that even black dwarfs, the theoretical endpoint of stellar evolution, would still emit some radiation due to Hawking radiation, though at an incredibly low temperature and over vast timescales. The discussion also touches on the complexities of heat death, the challenges of simulating such long-term processes, and the limitations of current scientific understanding regarding proton decay and other long-term phenomena. Some users highlight the immense timescales involved, emphasizing the difference between theoretical predictions and observable reality. Others express fascination with the concept and appreciate the thought-provoking nature of the article.
The Hacker News post titled "Dead Stars Don’t Radiate" generated a moderate amount of discussion, with several commenters engaging with the premise and its implications.
One of the most compelling threads revolved around the definition of "dead" in the context of stars. A commenter pointed out that even black holes, often considered the ultimate dead stars, emit Hawking radiation, albeit at incredibly low levels. This sparked a discussion about the timescale over which this radiation would lead to complete evaporation, highlighting the immense durations involved in cosmological processes. Another user added to this by explaining that while a true black dwarf (a hypothetical, fully cooled white dwarf) wouldn't radiate, the universe isn't old enough for any to have formed yet. This clarification helped contextualize the article's claim within the current understanding of stellar evolution.
Several comments focused on the idea of heat death, the theoretical state where the universe reaches maximum entropy. Users discussed the implications of a universe where no temperature differences exist, and whether this truly represents a "dead" state. One comment explored the possibility of quantum fluctuations allowing for localized pockets of energy even in a heat-dead universe, leaving a glimmer of potential for activity even in such an extreme scenario.
A more technical discussion branched off, delving into the thermodynamics of black holes. Users debated the nature of the information paradox and the role of entropy in black hole evaporation. This conversation touched on complex theoretical concepts, showcasing the depth of understanding some commenters brought to the discussion.
A few commenters expressed their appreciation for the article's clarity and its ability to explain complex physics concepts in an accessible manner. This sentiment highlighted the value of clear scientific communication and the article's success in achieving this goal.
Finally, a couple of comments offered additional resources, such as links to relevant Wikipedia articles and other scientific papers, further enriching the conversation and providing avenues for deeper exploration of the topic.