This blog post presents a different perspective on deriving Shannon entropy, distinct from the traditional axiomatic approach. Instead of starting with desired properties and deducing the entropy formula, it begins with a fundamental problem: quantifying the average number of bits needed to optimally represent outcomes from a probabilistic source. The author argues this approach provides a more intuitive and grounded understanding of why the entropy formula takes the shape it does.
The post meticulously constructs this derivation. It starts by considering a source emitting symbols from a finite alphabet, each with an associated probability. The core idea is to group these symbols into sets based on their probabilities, specifically targeting sets where the cumulative probability is a power of two. This allows for efficient representation using binary codes, as each set can be uniquely identified by a binary prefix.
The process begins with the most probable symbol and continues iteratively, grouping less probable symbols into progressively larger sets until all symbols are assigned. The author demonstrates how this grouping mirrors the process of building a Huffman code, a well-known algorithm for creating optimal prefix-free codes.
The post then carefully analyzes the expected number of bits required to encode a symbol using this method. This expectation involves summing the product of the number of bits assigned to a set (which relates to the negative logarithm of the cumulative probability of that set) and the cumulative probability of the symbols within that set.
Through a series of mathematical manipulations and approximations, leveraging the properties of logarithms and the behavior of probabilities as the number of samples increases, the author shows that this expected number of bits converges to the familiar Shannon entropy formula: the negative sum of each symbol's probability multiplied by the logarithm base 2 of that probability.
Crucially, the derivation highlights the relationship between optimal coding and entropy. It demonstrates that Shannon entropy represents the theoretical lower bound on the average number of bits needed to encode messages from a given source, achievable through optimal coding schemes like Huffman coding. This construction emphasizes that entropy is not just a measure of uncertainty or information content, but intrinsically linked to efficient data compression and representation. The post concludes by suggesting this alternative construction offers a more concrete and less abstract understanding of Shannon entropy's significance in information theory.
Researchers at the University of Pittsburgh have made significant advancements in the field of fuzzy logic hardware, potentially revolutionizing edge computing. They have developed a novel transistor design, dubbed the reconfigurable ferroelectric transistor (RFET), that allows for the direct implementation of fuzzy logic operations within hardware itself. This breakthrough promises to greatly enhance the efficiency and performance of edge devices, particularly in applications demanding complex decision-making in resource-constrained environments.
Traditional computing systems rely on Boolean logic, which operates on absolute true or false values (represented as 1s and 0s). Fuzzy logic, in contrast, embraces the inherent ambiguity and uncertainty of real-world scenarios, allowing for degrees of truth or falsehood. This makes it particularly well-suited for tasks like pattern recognition, control systems, and artificial intelligence, where precise measurements and definitive answers are not always available. However, implementing fuzzy logic in traditional hardware is complex and inefficient, requiring significant processing power and memory.
The RFET addresses this challenge by incorporating ferroelectric materials, which exhibit spontaneous electric polarization that can be switched between multiple stable states. This multi-state capability allows the transistor to directly represent and manipulate fuzzy logic variables, eliminating the need for complex digital circuits typically used to emulate fuzzy logic behavior. Furthermore, the polarization states of the RFET can be dynamically reconfigured, enabling the implementation of different fuzzy logic functions within the same hardware, offering unprecedented flexibility and adaptability.
This dynamic reconfigurability is a key advantage of the RFET. It means that a single hardware unit can be adapted to perform various fuzzy logic operations on demand, optimizing resource utilization and reducing the overall system complexity. This adaptability is especially crucial for edge computing devices, which often operate with limited power and processing capabilities.
The research team has demonstrated the functionality of the RFET by constructing basic fuzzy logic gates and implementing simple fuzzy inference systems. While still in its early stages, this work showcases the potential of RFETs to pave the way for more efficient and powerful edge computing devices. By directly incorporating fuzzy logic into hardware, these transistors can significantly reduce the processing overhead and power consumption associated with fuzzy logic computations, enabling more sophisticated AI capabilities to be deployed on resource-constrained edge devices, like those used in the Internet of Things (IoT), robotics, and autonomous vehicles. This development could ultimately lead to more responsive, intelligent, and autonomous systems that can operate effectively even in complex and unpredictable environments.
The Hacker News post "Transistor for fuzzy logic hardware: promise for better edge computing" linking to a TechXplore article about a new transistor design for fuzzy logic hardware, has generated a modest discussion with a few interesting points.
One commenter highlights the potential benefits of this technology for edge computing, particularly in situations with limited power and resources. They point out that traditional binary logic can be computationally expensive, while fuzzy logic, with its ability to handle uncertainty and imprecise data, might be more efficient for certain edge computing tasks. This comment emphasizes the potential power savings and improved performance that fuzzy logic hardware could offer in resource-constrained environments.
Another commenter expresses skepticism about the practical applications of fuzzy logic, questioning whether it truly offers advantages over other approaches. They seem to imply that while fuzzy logic might be conceptually interesting, its real-world usefulness remains to be proven, especially in the context of the specific transistor design discussed in the article. This comment serves as a counterpoint to the more optimistic views, injecting a note of caution about the technology's potential.
Further discussion revolves around the specific design of the transistor and its implications. One commenter questions the novelty of the approach, suggesting that similar concepts have been explored before. They ask for clarification on what distinguishes this particular transistor design from previous attempts at implementing fuzzy logic in hardware. This comment adds a layer of technical scrutiny, prompting further investigation into the actual innovation presented in the linked article.
Finally, a commenter raises the important point about the developmental stage of this technology. They acknowledge the potential of fuzzy logic hardware but emphasize that it's still in its early stages. They caution against overhyping the technology before its practical viability and scalability have been thoroughly demonstrated. This comment provides a grounded perspective, reminding readers that the transition from a promising concept to a widely adopted technology can be a long and challenging process.
This GitHub project, titled "obsidian-textgrams," introduces a novel approach to managing and displaying ASCII diagrams within Obsidian, a popular note-taking and knowledge management application. The plugin specifically addresses the challenge of storing and rendering these text-based diagrams, which are often used for visualizations, technical illustrations, and quick sketches. Instead of relying on image embedding, which can be cumbersome and inflexible, obsidian-textgrams allows users to store these diagrams directly within their Markdown files as code blocks. This maintains the inherent portability and editability of plain text.
The plugin leverages a custom code block language identifier, likely textgram or similar, to delineate these diagrams within the Markdown document. This allows Obsidian, with the plugin installed, to distinguish them from standard code blocks. Upon encountering a textgram code block, the plugin intercepts the rendering process. Instead of displaying the raw ASCII text, it parses the content and dynamically generates a visual representation of the diagram. This rendering is likely achieved using a JavaScript library capable of interpreting and visualizing ASCII characters as graphical elements, connecting lines, and forming shapes based on the provided input.
This approach offers several advantages. Firstly, it keeps the diagrams within the text file itself, promoting version control friendliness and avoiding the need to manage separate image files. Secondly, it facilitates easier editing. Users can directly modify the ASCII text within the code block, and the rendered diagram will update accordingly, streamlining the iterative design process. Finally, this method likely preserves the semantic meaning of the diagram, as the underlying ASCII text remains accessible and searchable within Obsidian. This stands in contrast to raster image-based diagrams where the underlying information is lost in the pixel data. In essence, obsidian-textgrams transforms Obsidian into a more powerful tool for working with ASCII diagrams, offering a more integrated and streamlined workflow compared to traditional image-based approaches.
The Hacker News post "Show HN: Store and render ASCII diagrams in Obsidian" at https://news.ycombinator.com/item?id=42112168 generated several comments discussing various aspects of the project.
Several commenters appreciated the utility of the tool, particularly for quickly sketching out diagrams within Obsidian. One user pointed out the advantage of having diagrams rendered directly within the note-taking application, rather than relying on external tools or image uploads. They specifically mentioned the convenience this offers for quick brainstorming and idea capture. This sentiment was echoed by another user who highlighted the speed and ease of use compared to traditional diagramming software.
The discussion also delved into the technical aspects of the project. One commenter inquired about the rendering process, specifically whether it was client-side or server-side. The project creator clarified that rendering is handled client-side using JavaScript within Obsidian. This prompted further discussion about potential performance implications for complex diagrams.
The choice of using Mermaid.js for rendering was also a topic of conversation. One commenter suggested PlantUML as an alternative, praising its flexibility and extensive feature set. They also pointed out PlantUML's wider adoption and the availability of server-side rendering options. This led to a discussion about the trade-offs between different rendering engines, considering factors like ease of use, feature richness, and performance.
Some commenters expressed interest in extending the plugin's functionality. One suggestion involved integrating with other Obsidian plugins, specifically those focused on graph visualization. Another user proposed adding support for other diagram formats beyond Mermaid.js, such as Graphviz.
Overall, the comments reflect a positive reception of the project, with users acknowledging its practicality and potential for enhancing the Obsidian note-taking experience. The discussion also highlighted areas for potential improvement and expansion, including exploring alternative rendering engines and integrating with other Obsidian plugins. There was a definite interest in the technical aspects of implementation and a healthy discussion regarding the chosen technical stack as well as some alternatives.
Eli Bendersky's blog post, "ML in Go with a Python Sidecar," explores a practical approach to integrating machine learning (ML) models, typically developed and trained in Python, into applications written in Go. Bendersky acknowledges the strengths of Go for building robust and performant backend systems while simultaneously recognizing Python's dominance in the ML ecosystem, particularly with libraries like TensorFlow, PyTorch, and scikit-learn. Instead of attempting to replicate the extensive ML capabilities of Python within Go, which could prove complex and less efficient, he advocates for a "sidecar" architecture.
This architecture involves running a separate Python process alongside the main Go application. The Go application interacts with the Python ML service through inter-process communication (IPC), specifically using gRPC. This allows the Go application to leverage the strengths of both languages: Go handles the core application logic, networking, and other backend tasks, while Python focuses solely on executing the ML model.
Bendersky meticulously details the implementation of this sidecar pattern. He provides comprehensive code examples demonstrating how to define the gRPC service in Protocol Buffers, implement the Python server utilizing TensorFlow to load and execute a pre-trained model, and create the corresponding Go client to communicate with the Python server. The example focuses on a simple image classification task, where the Go application sends an image to the Python sidecar, which then returns the predicted classification label.
The post highlights several advantages of this approach. Firstly, it enables clear separation of concerns. The Go and Python components remain independent, simplifying development, testing, and deployment. Secondly, it allows leveraging existing Python ML code and expertise without requiring extensive Go ML libraries. Thirdly, it provides flexibility for scaling the ML component independently from the main application. For example, the Python sidecar could be deployed on separate hardware optimized for ML tasks.
Bendersky also discusses the performance implications of this architecture, acknowledging the overhead introduced by IPC. He mentions potential optimizations, like batching requests to the Python sidecar to minimize communication overhead. He also suggests exploring alternative IPC mechanisms besides gRPC if performance becomes a critical bottleneck.
In summary, the blog post presents a pragmatic solution for incorporating ML models into Go applications by leveraging a Python sidecar. The provided code examples and detailed explanations offer a valuable starting point for developers seeking to implement a similar architecture in their own projects. While acknowledging the inherent performance trade-offs of IPC, the post emphasizes the significant benefits of this approach in terms of development simplicity, flexibility, and the ability to leverage the strengths of both Go and Python.
The Hacker News post titled "ML in Go with a Python Sidecar" (https://news.ycombinator.com/item?id=42108933) elicited a modest number of comments, generally focusing on the practicality and trade-offs of the proposed approach of using Python for machine learning tasks within a Go application.
One commenter highlighted the potential benefits of this approach, especially for computationally intensive ML tasks where Go's performance might be a bottleneck. They acknowledged the convenience and rich ecosystem of Python's ML libraries, suggesting that leveraging them while keeping the core application logic in Go could be a sensible compromise. This allows for utilizing the strengths of both languages: Go for its performance and concurrency in handling application logic, and Python for its mature ML ecosystem.
Another commenter questioned the performance implications of the inter-process communication between Go and the Python sidecar, particularly for real-time applications. They raised concerns about the overhead introduced by serialization and deserialization of data being passed between the two processes. This raises the question of whether the benefits of using Python for ML outweigh the performance cost of this communication overhead.
One comment suggested exploring alternatives like using shared memory for communication between Go and Python, as a potential way to mitigate the performance overhead mentioned earlier. This alternative approach aims to optimize the data exchange by avoiding the serialization/deserialization steps, leading to potentially faster processing.
A further comment expanded on the shared memory idea, specifically mentioning Apache Arrow as a suitable technology for this purpose. They argued that Apache Arrow’s columnar data format could further enhance the performance and efficiency of data exchange between the Go and Python processes, specifically highlighting zero-copy reads for improved efficiency.
The discussion also touched upon the complexity introduced by managing two separate processes and the potential challenges in debugging and deployment. One commenter briefly discussed potential deployment complexities with two processes and debugging. This contributes to a more holistic view of the proposed architecture, considering not only its performance characteristics but also the operational aspects.
Another commenter pointed out the maturity and performance improvements in Go's own machine learning libraries, suggesting they might be a viable alternative in some cases, obviating the need for a Python sidecar altogether. This introduces the consideration of whether the proposed approach is necessary in all scenarios, or if native Go libraries are sufficient for certain ML tasks.
Finally, one commenter shared an anecdotal experience, confirming the practicality of the Python sidecar approach. They mentioned successfully using a similar setup in production, lending credibility to the article's proposal. This real-world example provides some validation for the discussed approach and suggests it's not just a theoretical concept but a practical solution.
In a remarkable feat of interstellar communication, NASA's Voyager 1 spacecraft, currently the most distant human-made object from Earth, has re-established contact using a long-dormant radio transmitter, marking a significant development in the ongoing saga of this venerable explorer. Launched in 1977, Voyager 1 has journeyed far beyond the realm of the planets, venturing into the uncharted territories of interstellar space. For over four decades, it has diligently transmitted scientific data back to Earth, providing invaluable insights into the heliosphere, the bubble-like region of space dominated by the Sun's influence, and beyond.
Recently, however, a critical component, the spacecraft’s articulation and control system (AACS), which is responsible for orienting Voyager 1's high-gain antenna towards Earth to ensure efficient communication, began transmitting garbled data. While the antenna itself remained correctly pointed, the telemetry data indicating its orientation was nonsensical, leaving engineers perplexed as to the system's status. To further complicate matters, the AACS had been relying on a backup computer known as the attitude articulation control electronics (AACE) since the primary computer failed years ago.
In an attempt to diagnose the issue without jeopardizing the spacecraft's precarious power budget, mission controllers at NASA's Jet Propulsion Laboratory (JPL) made the bold decision to activate a backup transmitter known as the "tricone assembly." This transmitter had been dormant for an impressive 37 years, unused since its role in Voyager 1's encounter with Saturn in 1981. The reactivation was not without risk; the long period of inactivity raised concerns about its functionality.
The gamble, however, paid off spectacularly. After a suspenseful 19.5-hour wait for the signal to traverse the vast gulf of space separating Voyager 1 from Earth, confirmation arrived: the tricone assembly was functioning flawlessly. While the root cause of the AACS anomaly remains under investigation, the successful reactivation of the backup transmitter provides a critical redundancy, ensuring continued communication with Voyager 1, even as it continues its solitary journey into the cosmic unknown. This remarkable demonstration of engineering ingenuity and resilience underscores the enduring legacy of the Voyager program and its invaluable contribution to our understanding of the universe. The ability to communicate with Voyager 1 through this alternate pathway provides a vital lifeline, buying precious time for engineers to diagnose and potentially rectify the original issue, ensuring that this pioneering spacecraft can continue its groundbreaking exploration for years to come.
The Hacker News post discussing the Smithsonian Magazine article about Voyager 1's reactivated transmitter has generated several comments. Many of the commenters express awe and wonder at the longevity and resilience of the Voyager probes, highlighting the impressive feat of engineering that has allowed them to continue functioning so far from Earth for over 45 years. Several commenters discuss the technical details of the transmitter reactivation, including the AACS attitude articulation and control system and the challenges of communicating with a spacecraft so distant.
One compelling comment thread delves into the specifics of the transmitter's role, clarifying that it's not used for scientific data transmission but rather for spacecraft orientation and control. Commenters explain how the AACS uses this transmitter to communicate with Earth about its thruster firings and overall spacecraft health, information vital for keeping Voyager 1 pointed correctly at Earth for data transmission via its primary communication systems. This discussion clarifies a potential misunderstanding stemming from the article's title, emphasizing the critical, albeit less glamorous, function of the reactivated transmitter.
Another interesting discussion revolves around the power limitations on Voyager 1. Commenters discuss the decaying plutonium power source and the ongoing efforts to conserve energy by selectively shutting down instruments. This highlights the difficult decisions facing mission engineers as they strive to extend Voyager 1's operational life as long as possible.
Some commenters also reminisce about the Voyager missions' launch and their historical significance, reflecting on the impact these probes have had on our understanding of the outer solar system. There's a sense of nostalgia and appreciation for the scientific legacy of these missions.
Several comments link to additional resources, such as NASA's Voyager website and articles about the Golden Record, further enriching the discussion and providing context for those interested in learning more. Overall, the comments reflect a mixture of technical expertise, historical perspective, and a shared sense of wonder about the enduring legacy of the Voyager probes.
Summary of Comments ( 11 )
https://news.ycombinator.com/item?id=42127609
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.
The Hacker News post titled "An alternative construction of Shannon entropy," linking to an article exploring a different way to derive Shannon entropy, has generated a moderate discussion with several interesting comments.
One commenter highlights the pedagogical value of the approach presented in the article. They appreciate how it starts with desirable properties for a measure of information and derives the entropy formula from those, contrasting this with the more common axiomatic approach where the formula is presented and then shown to satisfy the properties. They believe this method makes the concept of entropy more intuitive.
Another commenter focuses on the historical context, mentioning that Shannon's original derivation was indeed based on desired properties. They point out that the article's approach is similar to the one Shannon employed, further reinforcing the pedagogical benefit of seeing the formula emerge from its intended properties rather than the other way around. They link to a relevant page within a book on information theory which seemingly discusses Shannon's original derivation.
A third commenter questions the novelty of the approach, suggesting that it seems similar to standard treatments of the topic. They wonder if the author might be overselling the "alternative construction" aspect. This sparks a brief exchange with another user who defends the article, arguing that while the fundamental ideas are indeed standard, the specific presentation and the emphasis on the grouping property could offer a fresh perspective, especially for educational purposes.
Another commenter delves into more technical details, discussing the concept of entropy as a measure of average code length and relating it to Kraft's inequality. They connect this idea to the article's approach, demonstrating how the desired properties lead to a formula that aligns with the coding interpretation of entropy.
Finally, a few comments touch upon related concepts like cross-entropy and Kullback-Leibler divergence, briefly extending the discussion beyond the scope of the original article. One commenter mentions an example of how entropy is useful, by stating how optimizing for log-loss in a neural network can be interpreted as an attempt to make the predicted distribution very similar to the true distribution.
Overall, the comments section provides a valuable supplement to the article, offering different perspectives on its significance, clarifying some technical points, and connecting it to broader concepts in information theory. While not groundbreaking, the discussion reinforces the importance of pedagogical approaches that derive fundamental formulas from their intended properties.