Artículos con la etiqueta ‘sistemas de simetrias continuas’

Mathematics via Symmetry

Por • 1 jul, 2013 • Category: Opinion

We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement’s truth value remains the same. This view of mathematics as satisfying such symmetry places mathematics as comparable with modern views of physics and science where, over the past century, symmetry also plays a defining role. We explore the very nature of mathematics and its relationship with natural science from this perspective. This point of view helps clarify some standard problems in the philosophy of mathematics.



First Conservation Laws Derived For A Virtual Universe

Por • 30 mar, 2011 • Category: Leyes

One of the most important, powerful and beautiful ideas in modern physics is Noether’s theorem. This essentially says that the fundamental laws of physics are a manifestations of symmetry in the universe. And yet, peer more closely at Noether’s theorem and you soon find its severe limitations. It turns out that this approach can only be applied to certain types of systems that have continuous symmetries. That specifically excludes discrete systems, which proceed step-by-step. These include systems such as Turing machines, which one or two readers may be familiar with.Clearly Noether’s theorem cannot apply. So what happens to the conservation laws? In the game of life do we have to abandon conservation of energy, angular momentum and the like?