Fibonacci hashing offers a faster alternative to the typical modulo operator (%) for distributing items into hash tables, especially when the table size is a power of two. It leverages the golden ratio's properties by multiplying the hash key by a large constant derived from the golden ratio and then bit-shifting the result, effectively achieving a modulo operation without the expensive division. This method produces a more even distribution compared to modulo with prime table sizes, particularly when dealing with keys exhibiting sequential patterns, thus reducing collisions and improving performance. While theoretically superior, its benefits may be negligible in modern systems due to compiler optimizations and branch prediction for modulo with powers of two.
The blog post explores the interconnectedness of various measurement systems and mathematical concepts, examining potential historical links that are likely coincidental. The author notes the near equivalence of a meter to a royal cubit times the golden ratio, and how this relates to the dimensions of the Great Pyramid of Giza. While acknowledging the established historical definition of the meter based on Earth's circumference, the post speculates on whether ancient Egyptians might have possessed a sophisticated understanding of these relationships, potentially incorporating the golden ratio and Earth's dimensions into their construction. However, the author ultimately concludes that the observed connections are likely due to mathematical happenstance rather than deliberate design.
HN commenters largely dismiss the linked article as numerology and pseudoscience. Several point out the arbitrary nature of choosing specific measurements and units (meters, cubits) to force connections. One commenter notes that the golden ratio shows up frequently in geometric constructions, making its presence in the pyramids unsurprising and not necessarily indicative of intentional design. Others criticize the article's lack of rigor and its reliance on coincidences rather than evidence-based arguments. The general consensus is that the article presents a flawed and unconvincing argument for a relationship between these different elements.
Rafael Araujo creates stunning hand-drawn geometrical illustrations of nature, blending art, mathematics, and biology. His intricate works meticulously depict the Golden Ratio and Fibonacci sequence found in natural forms like butterflies, shells, and flowers. Using only compass, ruler, and pencil, Araujo spends hundreds of hours on each piece, resulting in mesmerizing visualizations of complex mathematical principles within the beauty of the natural world. His work showcases both the inherent order and aesthetic elegance found in nature's design.
HN users were generally impressed with Araujo's work, describing it as "stunning," "beautiful," and "mind-blowing." Some questioned the practicality of the golden ratio's influence, suggesting it's overstated and a form of "sacred geometry" pseudoscience. Others countered, emphasizing the golden ratio's genuine mathematical properties and its aesthetic appeal, regardless of deeper meaning. A few comments focused on the tools and techniques Araujo might have used, mentioning potential software like Cinderella and GeoGebra, and appreciating the dedication required for such intricate hand-drawn pieces. There was also discussion of the intersection of art, mathematics, and nature, with some users drawing connections to biological forms and patterns.
Summary of Comments ( 10 )
https://news.ycombinator.com/item?id=43677122
HN commenters generally praise the article for clearly explaining Fibonacci hashing and its benefits over modulo. Some point out that the technique is not forgotten, being used in game development and hash table implementations within popular languages like Java. A few commenters discuss the nuances of the golden ratio's properties and its suitability for hashing, with one noting the importance of good hash functions over minor speed differences in the hashing algorithm itself. Others shared alternative hashing methods like "Multiply-with-carry" and "SplitMix64", along with links to resources on hash table performance testing. A recurring theme is that Fibonacci hashing shines with power-of-two table sizes, losing its advantages (and potentially becoming worse) with prime table sizes.
The Hacker News post titled "Fibonacci Hashing: The Optimization That the World Forgot" (https://news.ycombinator.com/item?id=43677122) has a moderate number of comments, generating a discussion around the merits and applicability of Fibonacci hashing.
Several commenters delve into the practicalities of Fibonacci hashing, questioning its supposed superiority over simpler modulo methods. One recurring point is the potential performance impact of multiplication on various architectures. While the article champions multiplication as faster than modulo, some commenters argue that this isn't universally true. Modern CPUs, they point out, often have efficient modulo instructions, especially when dealing with powers of two. One commenter specifically mentions that modulo by a power of two can be as simple as a bitwise AND operation, which is extremely fast. Therefore, the supposed speed advantage of Fibonacci hashing becomes less clear-cut and highly dependent on the specific hardware.
Another key discussion thread centers around the quality of hash distribution. Some commenters express skepticism about Fibonacci hashing consistently outperforming modulo, especially when dealing with real-world data that might not be uniformly distributed. Concerns are raised about potential clustering or patterns in the hashed values that could negatively impact performance. One commenter highlights the importance of benchmarking with realistic datasets to demonstrate any tangible benefits over traditional methods. They also mention Knuth's multiplicative hashing method as a strong contender, suggesting it often provides a good balance between speed and distribution quality.
A few commenters provide valuable context by linking to related resources and discussions. One link points to a Stack Overflow post discussing the choice of the multiplier in multiplicative hashing. Another commenter shares a link to a paper analyzing different hashing methods. These external resources add depth to the conversation and provide alternative perspectives on the topic.
Finally, some commenters offer practical advice and considerations. One commenter suggests that the choice of hashing method should depend on the specific application and its performance requirements. They emphasize the need to profile and measure the impact of different hashing strategies rather than relying on theoretical assumptions. Another commenter points out the potential complexity of implementing Fibonacci hashing correctly, which could outweigh its theoretical benefits in some cases.
In summary, the comments section provides a balanced perspective on Fibonacci hashing, challenging the article's claim of it being a forgotten optimization. The discussion highlights the importance of considering hardware specifics, data distribution, and practical implementation challenges when evaluating any hashing method.