Douglas Hofstadter shows in his hybrid of fiction and mathematical introduction Gödel, Escher, Bach—An Eternal Golden Braid (1979), how the paradoxes inherent in Gödel’s theorem (that “no fixed system, no matter how complicated, could represent the complexity of the whole numbers” (p. 19).), Escher’s complex drawings and Bach’s compositional techniques are isomorphic across disciplines. From La...

This paper is to extend the Poincar’e Lemma for differential forms in a bounded, convex domain [1] in R to a more general domain that, we call, is deformable to every point in itself. Then we extend the homotopy operator T in [1] to the domain defromed to every point of itself.

The purpose of this research is to (a) identify which of recent history's influential figures did and which did not personify moral excellence, and (b) to examine the motives that drove these individuals along such divergent paths. In Study 1, 102 social scientists evaluated the moral qualities of influential figures from Time Magazine's lists. In Study 2, we selected the 15 top ranking of thes...

Integrity is the watch word of science. It is important that as we move to the future that we insure the integrity of our work. Too often, a scientist can become so involved in a particular product or area that the product becomes an area unto itself. This can lead to a sense of loyalty to the product, along with a lack of objectivity. This can be dangerous, because once it is perceived by the ...