Much research has linked surprise to violation of expectations, but it has been less clear how one can be surprised when one has no particular expectation. This paper discusses a computational theory based on Algorithmic Information Theory, which can account for surprises in which one initially expects randomness but then notices a pattern in stimuli. The authors present evidence that a “randomness deficiency” heuristic leads to surprise in such cases.

This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of Lp-computable functions with a size notion, by introducing Lp-computable Baire categories. We show that Lp-computable Baire categories satisfy the following three basic properties. Singleton sets {f } are meager, suitable infinite unions of meager sets are meager, and the whole space of Lp-computable functions is not meager. We give an alternative characterization of meager sets via Banach-Mazur games. We (...) study the convergence of Fourier series for Lp-computable functions and show that whereas for every p > 1, the Fourier series of every Lp-computable function f converges to f in the Lp norm, the set of L1-computable functions whose Fourier series does not diverge almost everywhere is meager. (shrink)