Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

Earworms ("stuck song syndrome"): towards a natural history of intrusive thoughts

Two studies examine the experience of “earworms”, unwanted catchy tunes that repeat. Survey data show that the experience is widespread but earworms are not generally considered problematic, although those who consider music to be important to them report earworms as longer, and harder to control, than those who consider music as less important. The tunes which produce these experiences vary considerably between individuals but are always familiar to those who experience them. A diary study confirms these findings and also indicates that, although earworm recurrence is relatively uncommon and unlikely to persist for longer than 24 hours, the length of both the earworm and the earworm experience frequently exceed standard estimates of auditory memory capacity. Active attempts to block or eliminate the earworm are less successful than passive acceptance, consistent with Wegner’s (1994) theory of ironic mental control.