#epistemology #rationality #physic # [[Epistemic status]] #shower-thought # Simplicity >Above all, our theory explains why **simplicity** is so highly desirable. To understand this there is no need for us to assume a 'principle of economy of thought' or anything of the kind. Simple statements, if knowledge is our object, are to be prized more highly than less simple ones because they tell us more; because their empirical content is greater; and because they are better testable. >~ [[Karl Popper]] In science, simple theories are usually preferred over complex ones, we can also notice this pattern in other area such as [[Programming|programming]], we tend to simplify as much as possible. It is almost law-like, the tendency of the [[Philosophy/Rationality/Models/Lindy Effect|Lindy Effect]] to preserve simple theories alive. >assertions can be better understood if we assume that **when speaking about simplicity they sometimes had testability in mind**. This elucidates even some of [[Poincare|Poincaré’s]] examples, though it clashes with his views. Today I should stress two further points: (1) We can compare theories with respect to testability only if at least some of the problems they are supposed to solve coincide. (2) Ad ho hypotheses cannot be compared in this way. >~ [[Karl Popper]] How does simplicity relates to [[Truth|truth]]? [[Karl Popper]] makes the analogy of lower and higher dimensions for this, and it seems to make sense. [[Simplicity does not necessarily mean truth]], but lower dimension theories are more [[Philosophy/Epistemology/Falsifiability|falsifiable]], therefore encoding more [[Philosophy/Epistemology/Knowledge|knowledge]]? ## Invariance and equivariance role in multidimensional theories [[Deep learning]] seems to go toward [[Graph neural networks]] which seems more prone to capture the [[Symmetry]] of nature. [[Geometric deep learning]] paper aims to aggregate and simplify the thousands of theories into a unified one # External links - #todo explore [[Hermann Weyl]], he seems to have thought about simplicity (quoted by [[Karl Popper]] and [[Deep learning]] guys) - [[Occam razor]] - [[Via Negativa|Less is more]]