The veil

I am very familiar with this type of Z2 topological insulator. The relevant symmetry is time-reversal symmetry. Most discovered topological insulators require this symmetry, so what I am proposing with C4v symmetry is unique in that it doesn't require it. Reading the article impressed upon me how ubiquitous topology is in crystals, independent of the actual constituents of the crystal. The space of crystal momentum is a torus, and a torus is such a ripe playgroud for winding numbers and other topological invariants. Such topological invariants are not well-defined for a parameter space that is unbounded, such as that of ordinary momentum, which characterizes states with continuous translational symmetry. In this sense does topology emerge from the symmetry-breaking formation of a crystal.

I read with pleasure the article 'The descent of electrons'. It all begins with the natural production of hydrogen and carbon dioxide in deep sea vents? Then energetic electrons begin their descent, aided by molecules that carry out the reductive citric cycle. A diverse chemical soap is created, on which natural selection may act. I like it! If not correct in detail, it must be correct in spirit. This must be what is missing in Darwin's theory, as Kauffman claims. I am surprised Kauffman isn't cited in this paper. My attitude toward life thus far has been sickly, a dismal reflection of my ignorance, it borders on disbelief. Now I feel healthier, I am grounded by a idea, simple in concept though difficult in application, it pushes back the veil.