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The attributes of singularities include the following in various degrees, according to context: Instability: because singularities tend to produce effects out of proportion to the size of initial causes. System relatedness: the effects of a singularity are characteristic of the system.
Penrose–Hawking singularity theorems, in general relativity theory, theorems about how gravitation produces singularities such as in black holes; Prandtl–Glauert singularity, the point at which a sudden drop in air pressure occurs; Singularity (climate), a weather phenomenon associated with a specific calendar date
Such singularities in algebraic geometry are the easiest in principle to study, since they are defined by polynomial equations and therefore in terms of a coordinate system. One can say that the extrinsic meaning of a singular point isn't in question; it is just that in intrinsic terms the coordinates in the ambient space don't ...
In 1986, Vernor Vinge published Marooned in Realtime, a science-fiction novel where a few remaining humans traveling forward in the future have survived an unknown extinction event that might well be a singularity. In a short afterword, the author states that an actual technological singularity would not be the end of the human species: "of ...
In general relativity, a naked singularity is a hypothetical gravitational singularity without an event horizon.. When there exists at least one causal geodesic that, in the future, extends to an observer either at infinity or to an observer comoving with the collapsing cloud, and in the past terminates at the gravitational singularity, then that singularity is referred to as a naked ...
Gravitational singularities exist at a junction between general relativity and quantum mechanics; therefore, the properties of the singularity cannot be described without an established theory of quantum gravity. Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of ...
Historians and sociologists have remarked the occurrence, in science, of "multiple independent discovery". Robert K. Merton defined such "multiples" as instances in which similar discoveries are made by scientists working independently of each other. [1] "
One could define the x-axis as a tangent at this point, but this definition can not be the same as the definition at other points. In fact, in this case, the x-axis is a "double tangent." For affine and projective varieties, the singularities are the points where the Jacobian matrix has a rank which is lower than at other points of the variety.