Showing papers on "Naturalness published in 1971"

Topology and Transformations in High School Geometry.

Abstract: There is a simple and natural way of regarding Euclidean geometry that has been largely ignored in the teaching of geometry. This is the view that Euclidean geometry is the mathematical study of the size and shape attributes of physical objects. The motivation of the study is that such attributes are intrinsically interesting and also that the information obtained is useful. It is my belief that this functional approach to the subject not only provides a natural dynamics to the development but leads to surprisingly sophisticated and vital mathematical concepts. Though I shall sketch the basis for only the innovative topics, topology and transformations, the view I am advocating leads with equal naturalness to other aspects of the subject, such as vectors or analytic geometry.

Synchronic grammars’, reconstruction, and the selection problem

Abstract: There are in principle infinitely many descriptions to fit the data of language, whether synchronic or diachronic. Although in practice one is seldom confronted with more than a few alternatives within any one descriptive system, the difficulty of choosing between these alternatives in a principled way has been well recognized since Chao. Two sorts of criteria have traditionally been and continue to be invoked more or less explicitly, criteria which may be subsumed under the headings of simplicity and naturalness. Historical linguists have long had to cope with certain sets of data for which neither type of criterion could dictate unique solutions. There is now a growing list of similar dilemmas in generative descriptions. The present paper presents a case where non-unique generative and reconstructional accounts