The blog post "The Cultural Divide Between Mathematics and AI" explores the differing approaches to knowledge and validation between mathematicians and AI researchers. Mathematicians prioritize rigorous proofs and deductive reasoning, building upon established theorems and valuing elegance and simplicity. AI, conversely, focuses on empirical results and inductive reasoning, driven by performance on benchmarks and real-world applications, often prioritizing scale and complexity over theoretical guarantees. This divergence manifests in communication styles, publication venues, and even the perceived importance of explainability, creating a cultural gap that hinders potential collaboration and mutual understanding. Bridging this divide requires recognizing the strengths of both approaches, fostering interdisciplinary communication, and developing shared goals.
The blog post explores the potential of applying "quantitative mereology," the study of parts and wholes with numerical measures, to complex systems. It argues that traditional physics, focusing on fundamental particles and forces, struggles to capture the emergent properties of complex systems. Instead, a mereological approach could offer a complementary perspective by quantifying relationships between parts and wholes across different scales, providing insights into how these systems function and evolve. This involves defining measures of "wholeness" based on concepts like integration, differentiation, and organization, potentially leading to new mathematical tools and models for understanding emergent phenomena in areas like biology, economics, and social systems. The author uses the example of entropy to illustrate how a mereological view might reinterpret existing physical concepts, suggesting entropy as a measure of the distribution of energy across a system's parts rather than purely as disorder.
HN users discussed the practicality and philosophical implications of applying mereology (the study of parts and wholes) to complex systems. Some expressed skepticism about quantifying mereology, questioning the usefulness of assigning numerical values to part-whole relationships, especially in fields like biology. Others were more receptive, suggesting potential applications in areas like network analysis and systems engineering. The debate touched on the inherent complexity of defining "parts" and "wholes" in different contexts, and whether a purely reductionist approach using mereology could capture emergent properties. Some commenters also drew parallels to other frameworks like category theory and information theory as potentially more suitable tools for understanding complex systems. Finally, there was discussion of the challenge of reconciling discrete, measurable components with the continuous nature of many real-world phenomena.
The author argues that science has always been intertwined with politics, using historical examples like the Manhattan Project and Lysenkoism to illustrate how scientific research is shaped by political agendas and funding priorities. They contend that the notion of "pure" science separate from political influence is a myth, and that acknowledging this inherent connection is crucial for understanding how science operates and its impact on society. The post emphasizes that recognizing the political dimension of science doesn't invalidate scientific findings, but rather provides a more complete understanding of the context in which scientific knowledge is produced and utilized.
Hacker News users discuss the inherent link between science and politics, largely agreeing with the article's premise. Several commenters point out that funding, research direction, and the application of scientific discoveries are inevitably influenced by political forces. Some highlight historical examples like the Manhattan Project and the space race as clear demonstrations of science driven by political agendas. Others caution against conflating the process of science (ideally objective) with the uses of science, which are often political. A recurring theme is the concern over politicization of specific scientific fields, like climate change and medicine, where powerful interests can manipulate or suppress research for political gain. A few express worry that acknowledging the political nature of science might further erode public trust, while others argue that transparency about these influences is crucial for maintaining scientific integrity.
Summary of Comments ( 49 )
https://news.ycombinator.com/item?id=43344703
HN commenters largely agree with the author's premise of a cultural divide between mathematics and AI. Several highlighted the differing goals, with mathematics prioritizing provable theorems and elegant abstractions, while AI focuses on empirical performance and practical applications. Some pointed out that AI often uses mathematical tools without necessarily needing a deep theoretical understanding, leading to a "cargo cult" analogy. Others discussed the differing incentive structures, with academia rewarding theoretical contributions and industry favoring impactful results. A few comments pushed back, arguing that theoretical advancements in areas like optimization and statistics are driven by AI research. The lack of formal proofs in AI was a recurring theme, with some suggesting that this limits the field's long-term potential. Finally, the role of hype and marketing in AI, contrasting with the relative obscurity of pure mathematics, was also noted.
The Hacker News post titled "The Cultural Divide Between Mathematics and AI" (linking to an article on sugaku.net) has generated a moderate number of comments, exploring various facets of the perceived cultural differences between the two fields.
Several commenters discuss the contrasting emphases on proof versus empirical results. One commenter highlights that mathematics prioritizes rigorous proof and deductive reasoning, while AI often focuses on empirical validation and inductive reasoning based on experimental outcomes. This difference in approach is further elaborated upon by another commenter who suggests that mathematicians are primarily concerned with establishing absolute truths, whereas AI practitioners are more interested in building systems that perform effectively, even if their inner workings aren't fully understood. The idea that AI is more results-oriented is echoed in another comment mentioning the importance of benchmarks and practical applications in the field.
Another line of discussion revolves around the different communities and their values. One commenter observes that the mathematical community values elegance and conciseness in their proofs and solutions, whereas the AI community, influenced by engineering principles, often prioritizes performance and scalability. This difference in values is attributed to the distinct goals of each field – uncovering fundamental truths versus building practical applications.
The role of theory is also debated. One commenter argues that despite the empirical focus, theoretical underpinnings are becoming increasingly important in AI as the field matures, exemplified by the growing interest in explainable AI (XAI). Another comment suggests that AI, being a relatively young field, still lacks the deep theoretical foundation that mathematics possesses. This difference in theoretical maturity is linked to the historical development of the fields, with mathematics having centuries of established theory compared to the nascent stages of AI.
The discussion also touches upon the different tools and techniques used in each field. One commenter mentions the prevalence of probabilistic methods and statistical analysis in AI, contrasting it with the deterministic and logical approaches favored in mathematics. This distinction is highlighted by another comment pointing out the reliance on large datasets and computational power in AI, which is less common in traditional mathematical research.
Finally, some commenters express skepticism about the framing of a "cultural divide." One commenter argues that the two fields are complementary, with mathematical insights informing AI advancements and AI challenges prompting new mathematical research. Another comment suggests that the perceived divide is more of a difference in emphasis and methodology rather than a fundamental clash of cultures.