Technology Category
Knowledge Representation and Reasoning: Computational Complexity of ReasoningReasoning under Uncertainty: Other Foundations of Reasoning under UncertaintySearch and Optimization: Other Foundations of Search & Optimization
The Existential Theory of Research: Why Discovery Is Hard
Technology Category
Application Category
📝 Abstract
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.
Problem
Research questions and friction points this paper is trying to address.
scientific discovery
representation
computational hardness
uncertainty principle
sample complexity
Innovation
Methods, ideas, or system contributions that make the work stand out.
Existential Theory of Research
representation mismatch
uncertainty principle
computational hardness
sample complexity
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