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The monodromy theory of differential equations, in the complex domain, around singularities, does however come into relation with the geometric theory. Roughly speaking, monodromy studies the way a covering map can degenerate, while singularity theory studies the way a manifold can degenerate; and these fields are linked.
The concept and the term "singularity" were popularized by Vernor Vinge – first in 1983 (in an article that claimed that once humans create intelligences greater than their own, there will be a technological and social transition similar in some sense to "the knotted space-time at the center of a black hole", [10]) and later in his 1993 essay ...
The currently dominant theory of the origin of our universe postulates a physical singularity (specifically the Big Bang). It is suggested to have dispersed plasma uniformly throughout space, and to have cooled by increasing expansion, till atoms formed; subsequently, very small (singular) fluctuations in the uniform density created self ...
Singularity (system theory), in dynamical and social systems, a context in which a small change can cause a large effect Gravitational singularity, in general relativity, a point in which gravity is so intense that spacetime itself becomes ill-defined
The Penrose–Hawking singularity theorems define a singularity to have geodesics that cannot be extended in a smooth manner. [6] The termination of such a geodesic is considered to be the singularity. Modern theory asserts that the initial state of the universe, at the beginning of the Big Bang, was a singularity.
When will the singularity occur? According to new research, humanity may achieve singularity within just 7 years—much sooner than we originally thought.
The singularity at the center of a Schwarzschild black hole is an example of a strong singularity. Space-like singularities are a feature of non-rotating uncharged black holes as described by the Schwarzschild metric , while time-like singularities are those that occur in charged or rotating black hole exact solutions.
Ray Kurzweil predicts humans and AI will merge by 2045, boosting intelligence a millionfold with nanobots, bringing both hope and challenges for the future.