“To define distance in their non-Euclidean geometries, Cayley and Klein proceeded by analogy with a discovery of Laguerre... who had shown that the distances and angles of ordinary Euclidean geometry can be expressed as cross ratios, in other words, that the Euclidean metric geometry is clearly a specialization of projective geometry. The concept of the "absolute" and the definition of distance unified Euclidean and non-Euclidean geometries into a single all-embracing theory.”
“It appears... that the elastic theories of light, if Kelvin's gyrostatic adynamic ether be admitted, have not been wholly routed. Nevertheless the great electromagnetic theory of light propounded by M...”
Unification in science and mathematics
“Whatever its source, mathematics has come down to the present by the two main streams of number and form. The first carried along arithmetic and algebra, the second, geometry. In the seventeenth centu...”
Unification in science and mathematics
“Science is an attempt to represent the known world as a closed system with a perfect formalism. Scientific discovery is a constant maverick process of breaking out at the ends of the system... and the...”
Unification in science and mathematics
“[T]he attempt to embrace the whole course of things in time and to relate the successive epochs to one another—the transition to the view that time is actually aiming at something, that temporal succe...”
Unification in science and mathematics
“Let us assert, as our original postulate, that, the multiple (that is, non-being, if taken in the pure state) being the only rational form of a creatable (creabile) nothingness, the creative act is co...”
Unification in science and mathematics
