Terence Tao's blog post explores how "landscape functions," a mathematical tool from optimization and computer science, could improve energy efficiency in buildings. He explains how these functions can model the complex interplay of factors affecting energy consumption, such as appliance usage, weather conditions, and occupancy patterns. By finding the "minimum" of the landscape function, one can identify the most energy-efficient operating strategy for a given building. Tao suggests that while practical implementation presents challenges like data acquisition and model complexity, landscape functions offer a promising theoretical framework for bridging the "green gap" – the disparity between predicted and actual energy savings in buildings – and ultimately reducing electricity costs for consumers.
The paper "Tensor evolution" introduces a novel framework for accelerating tensor computations, particularly focusing on deep learning operations. It leverages the inherent recurrence structures present in many tensor operations, expressing them as tensor recurrence equations (TREs). By representing these operations with TREs, the framework enables optimized code generation that exploits data reuse and minimizes memory accesses. This leads to significant performance improvements compared to traditional implementations, especially for large tensors and complex operations like convolutions and matrix multiplications. The framework offers automated transformation and optimization of TREs, allowing users to express tensor computations at a high level of abstraction while achieving near-optimal performance. Ultimately, tensor evolution aims to simplify and accelerate the development and deployment of high-performance tensor computations across diverse hardware architectures.
Hacker News users discuss the potential performance benefits of tensor evolution, expressing interest in seeing benchmarks against established libraries like PyTorch. Some question the novelty, suggesting the technique resembles existing dynamic programming approaches for tensor computations. Others highlight the complexity of implementing such a system, particularly the challenge of automatically generating efficient code for diverse hardware. Several commenters point out the paper's focus on solving recurrences with tensors, which could be useful for specific applications but may not be a general-purpose tensor computation framework. A desire for clarity on the practical implications and broader applicability of the method is a recurring theme.
This video demonstrates a project-based learning approach to teaching math concepts, specifically using real-world examples from aerospace engineering. It showcases how principles of trigonometry and calculus can be applied to calculate things like rocket trajectories and orbital mechanics, making the math more engaging and relatable for students. The video emphasizes the practical application of these mathematical concepts within the context of exciting aerospace projects, aiming to inspire students and demonstrate the relevance of math in solving real-world problems.
HN users generally praised the video for its engaging approach to teaching math through real-world aerospace applications. Several commenters appreciated the clear explanations and the focus on practical examples, making complex concepts more accessible. Some discussed the presenter's effectiveness and charisma, while others highlighted the importance of connecting theoretical knowledge to tangible projects. A few users mentioned specific examples from the video that resonated with them, like the explanation of quaternions. There was also discussion around the broader educational implications of project-based learning and the value of making math more relevant to students.
Summary of Comments ( 7 )
https://news.ycombinator.com/item?id=43164499
HN commenters are skeptical of the practicality of applying the landscape function to energy optimization. Several doubt the computational feasibility, pointing out the complexity and scale of the power grid. Others question the focus on mathematical optimization, suggesting that more fundamental issues like transmission capacity and storage are the real bottlenecks. Some express concerns about the idealized assumptions in the model, and the lack of consideration for real-world constraints. One commenter notes the difficulty of applying abstract mathematical tools to complex real-world systems, and another suggests exploring simpler, more robust approaches. There's a general sentiment that while the math is interesting, its impact on lowering electricity costs is likely minimal.
The Hacker News post "Closing the 'green gap': energy savings from the math of the landscape function," linking to a blog post by Terence Tao, generated a moderate amount of discussion, with several commenters engaging with the core ideas presented.
A significant portion of the discussion revolves around the practical applicability and scalability of the ideas presented by Tao. One commenter expresses skepticism about the real-world impact, questioning whether the theoretical gains outlined will translate into tangible reductions in energy consumption, particularly given the complexities and inefficiencies inherent in real-world power grids. This skepticism is echoed by another commenter who highlights the existing sophisticated optimization efforts employed by grid operators, suggesting that any further improvements through the proposed method might be marginal.
Another thread of discussion focuses on the computational complexity of the landscape function. One commenter points out the potential difficulties in computing this function for large and complex systems, which could limit its practical use. Relatedly, the discussion touches upon the challenge of integrating intermittent renewable energy sources into the grid, with one commenter noting the existing research and development efforts focused on addressing this specific issue.
Some commenters delve into specific aspects of Tao's proposal, including the role of convex optimization and its limitations in this context. The discussion also explores the potential for using machine learning techniques to approximate the landscape function, acknowledging both the potential benefits and the challenges associated with this approach.
A few commenters express general enthusiasm for Tao's work and the potential of applying mathematical tools to solve real-world energy problems. However, the overall tone remains cautiously optimistic, with several commenters emphasizing the need for further research and practical experimentation to validate the theoretical claims. Notably, there isn't a strongly dissenting viewpoint; the skepticism expressed is primarily focused on the practical challenges rather than the underlying mathematical concepts.