X-Nico

2 unusual facts about Nonzero: The Logic of Human Destiny


Nonzero: The Logic of Human Destiny

The main thrust of his argument is that we may be on the threshold of a new phase of development involving the creation of a unified global consciousness, along the lines suggested in the writings of Jesuit Pierre Teilhard de Chardin.

Through this lens, and an overview of human and global history, Wright typifies the argument against the views of noted paleontologist Stephen Jay Gould.


Ehrenfest paradox

1937: Jan Weyssenhoff (now perhaps best known for his work on Cartan connections with zero curvature and nonzero torsion) notices that the Langevin observers are not hypersurface orthogonal.

Infinite-dimensional vector function

Moreover, for any set A, there exist infinite-dimensional vector spaces having the (Hamel) dimension of the cardinality of A (e.g., the space of functions A\rightarrow K with finitely-many nonzero elements, where K is the desired field of scalars).

Lehmer–Schur algorithm

Given that the function is analytic within each of these quarters, a nonzero winding number N (always an integer) identifies N zeros of the function inside the quarter in question by Rouché's theorem, each zero counted as many times as its multiplicity.

Precision tests of QED

One type of these tests, for example, work by checking Coulomb's law at high accuracy, as Coulomb's law would be modified if the photon mass were nonzero.

Q-ball

It should be pointed out that while this kind of Q-ball is stable against decay into scalars, it is not stable against decay into fermions if the scalar field \phi has nonzero Yukawa couplings to some fermions.

Raychaudhuri equation

unstable: for example, the world lines of the dust particles in the Gödel solution have vanishing shear, expansion, and acceleration, but constant vorticity just balancing a constant Raychuadhuri scalar due to nonzero vacuum energy ("cosmological constant").

Zorn's lemma

It occurs in the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space has a basis, Tychonoff's theorem in topology stating that every product of compact spaces is compact, and the theorems in abstract algebra that every nonzero ring has a maximal ideal and that every field has an algebraic closure.


see also