科学发现的困难是结构性的,无法通过更好工具彻底解决。
The Existential Theory of Research: Why Discovery Is Hard
- 提出存在性研究理论,从表示、观测、计算三方面建模发现难题
- 证明三者无法同时优化,存在不可克服的发现瓶颈
- 适合对科研本质、算法局限感兴趣的学者阅读
科学发现能否通过选择合适表示、收集足够数据、使用强大算法而变得任意简单?本文认为答案是否定的。我们提出存在性研究理论(ETR),将发现建模为在表示、观测与计算约束下恢复结构化解释的过程。在此框架中,我们证明三者无法同时优化:任何方法都无法保证普遍简单的解释、任意压缩的观测以及高效的精确推断。这一限制并非模型特定,而是源于稀疏表示中的不确定性原理、高维恢复的样本复杂度边界以及精确推断的计算难度。此外,仅表示不匹配就可能将内在简单性转化为表观复杂性,使原本可解的问题在观测与计算上变得不可行。为此,我们引入一个不确定性泛函,量化发现的联合难度。结果表明,科学难度并非偶然,而是推断几何与复杂性的结构性后果。
原文摘要 · Abstract (English)
Can scientific discovery be made arbitrarily easy by choosing the right representation, collecting enough data, and deploying sufficiently powerful algorithms? This paper argues that the answer is fundamentally negative. We introduce the Existential Theory of Research (ETR), a formal framework that models discovery as the recovery of structured explanations under constraints of representation, observation, and computation. Within this framework, we show that these three components cannot be simultaneously optimized: no method can guarantee universally simple explanations, arbitrarily compressed observations, and efficient exact inference. This limitation is not model-specific, but arises from a synthesis of uncertainty principles in sparse representation, sample complexity bounds in high-dimensional recovery, and the computational hardness of exact inference. We further show that representation mismatch alone can inflate intrinsic simplicity into apparent complexity, rendering otherwise tractable problems observationally and computationally prohibitive. To quantify these effects, we introduce an uncertainty functional that captures the joint difficulty of discovery. The results suggest that scientific difficulty is not accidental, but a structural consequence of the geometry and complexity of inference.
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