Showing papers by "King's College, Aberdeen published in 1969"
01 Dec 1969
TL;DR: In this article, it was shown that if S is the union of subsemigroups each of which has an identity element, then any compact non-Abelian group contradicts Lin's result.
Abstract: A semigroup S is said to be normal if aS = Sa for each a in S . Thus the class of normal semigroups includes the class of groups and the class of Abelian semigroups. Given a compact semigroup S we write P(S) for the convolution semigroup of probability regular Borel measures on S. In ( 3 ), Theorem 7, Lin asserts that a compact semigroup S is normal if and only if P(S) is normal. We show in this paper that Lin's result is false. In fact, if S is the union of subsemigroups each of which has an identity element, we show that P(S) is normal if and only if S is Abelian. Thus any compact non-Abelian group contradicts Lin's result. What Lin's argument does establish is that if P(S) is normal then S is normal, and if S is normal then μP(S) = P(S)μ for each point mass measure μ.
1 citations
TL;DR: For example, the authors argues that the belief in a "scientific revolution" brought about by the appl icat ion of "the scientific method" is the greatest source of confusion in the history of science.
Abstract: I believe tha t I do not s tand alone in the conviction tha t the greatest m y t h about the seventeenth century, announced with varying degrees of r e fmemen t and historical unders tanding (or misunder s t and ing) , is the belief in a "Scientific Revolution" brought about by the appl icat ion of "the scientific method." Elsewhere and at o ther t imes I have said e n o u g h p e r h a p s too m u c h a b o u t m y general reasons for regarding this half t ruth as an unfor tuna te introduct ion into the terminology of historiography. There are indications that the shibboleth "scientific method" is losing some of its cha rm; but the "Scientific Revolution" we shall a lways have with us, like the "Renaissance"-a fa r worse source of confusion. I have been careful in m y title to employ the adjectival f o rm "biological"; since to talk about seventeenth-century "biology" would not only be a linguistic a n a c h r o n i s m n o very serious ma t t e r pe rhaps -bu t also and m u c h more seriously to force the fluid thought of tha t revolut ionary period into a r igorous f r a m e w o r k and thus pre judge a very impor tan t aspect of the very question I a m to examine . This quest ion involves a correlative prejudice of mine tha t the over-simplification of the historical process implied by the expression "The Scientific Revolution" was the consequence of the very c o m m o n assumpt ion tha t "science" is coterminous with wha t w e t h o u g h not the seventeenth-century p ionee r s ca l l "physics." Of course some of the work of m e n like Niels Stensen and Wil l iam Harvey could be made to look like physics, just as some of the ingenious work of the arch-physicist Mersenne can be made to look like p s y c h i a t r y o r worse. But the ques-