The Existential Theory of Research: Why Discovery Is Hard
This addresses a foundational problem for researchers in AI and science, as it provides a formal theory explaining why discovery is inherently hard, though it is incremental in synthesizing existing principles.
The paper tackles the problem of whether scientific discovery can be made arbitrarily easy through optimal representation, data, and algorithms, and shows that it is fundamentally impossible due to inherent limitations in representation, observation, and computation.
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.