Gravitational singularity (3038 bytes)
1: ...ccurs when the equations produce a [[mathematical singularity]].
3: ...ctions are valid only shortly after the projected singularity.
5: ...ngularity occurs on a ring, and is called a "ring singularity". Rotating black holes are sometimes referred to ...
7: ...arity behind an [[event horizon]], making [[naked singularity|naked singularities]] impossible. This is referre...
9: ...tually occurs where general relativity predicts a singularity. However, no theory of quantum gravity has been e...

The Singularity is Near (505 bytes)
1: ...cerning his belief about a coming [[technological singularity]]. It is due to be released on August 18, 2005.

Singularity (794 bytes)
1: '''Singularity''' has several different meanings:
3: *[[mathematical singularity]] - a point where a [[mathematics|mathematical]] ...
4: ...l, involving infinite curvature (a [[mathematical singularity]]) in the [[Space-time|space/time]] continuum
5: *[[technological singularity]] - a predicted point in the development of a civ...

Technological singularity (19093 bytes)
1: ...chnological progress assumed to follow. Whether a singularity will actually occur is a matter of debate.
3: ==Overview of the Singularity==
7: ... last two decades, the concept of a technological singularity actually dates back to the 1950s:
9: ...ives the appearance of approaching some essential singularity in the history of the race beyond which human aff...
13: ...concept even more similar to today's meaning of ''singularity'', in that it included in it the advent of superh...

Singularity Sky (3249 bytes)
1: '''''Singularity Sky''''' (ISBN 0441010725) is a [[hard science fi...
3: ...ce some time after the immediate aftermath of the singularity.
9: ...ke of singularity, by the time of the events in ''Singularity Sky'', Earth has recovered and become one of the ...

Isolated singularity (1169 bytes)
1: ...ed singularity''' is a [[mathematical singularity|singularity]] of a function ''f'' at a point ''z'' such that ...
3: Every singularity of a [[meromorphic function]] is isolated, but is...
7: ...n <math>\frac {1} {z}</math> contains an isolated singularity at 0.
9: ...ion <math>csc (\pi z)</math> contains an isolated singularity at every [[integer]].
11: ...nction <math>csc (\frac {1} {\pi z})</math> has a singularity at 0 which is ''not'' isolated, since there are a...

Essential singularity (1393 bytes)
1: ...unction is a "severe" [[singularity (mathematics)|singularity]] near which the function exhibits extreme behavi...
3: ...[pole (complex analysis)|pole]] nor a [[removable singularity]].
5: ...onential function|exp]](1/''z'') has an essential singularity at ''a'' = 0.
7: The point ''a'' is an essential singularity if and only if the [[limit (mathematics)|limit]]
11: ...r says that in every neighborhood of an essential singularity ''a'', the function ''f'' takes on ''every'' comp...

Removable singularity (1512 bytes)
1: ...tion is not defined (a [[mathematical singularity|singularity]]) but at which the function can be defined witho...
3: ...sin(''z'')/''z'' for ''z'' &ne; 0 has a removable singularity at ''z'' = 0: we can define ''f''(0) = 1 and the ...
5: ...ic function]], then ''z'' is called a ''removable singularity'' for ''f'' if there exists a holomorphic functio...
7: ...heorem on removable singularities states that the singularity ''a'' is removable if and only if there exists a ...

Singularity (climate) (405 bytes)
1: ...torm that occurs around [[February 1]] would be a singularity. Seasonal trends and their consequences (such as ...

Mathematical singularity (2671 bytes)
1: ..., such as [[derivative|differentiability]]. See [[singularity theory]] for general discussion of the geometric ...
7: ...h defined by ''y''² = ''x'' also has a singularity at (0,0), this time because it has a "corner" (ve...
9: ...up> in the (''x'', ''y'') coordinate system has a singularity ([[singular point]]) at (0, 0) because it does no...
13: In [[complex analysis]], there are four kinds of singularity. Suppose ''U'' is an [[open set|open subset]] of ...
15: * The point ''a'' is a [[removable singularity]] of ''f'' if there exists a holomorphic function...

Naked singularity (1772 bytes)
1: ...d therefore cannot be directly observed. A naked singularity, by contrast, is a point in space where the [[den...
13: ...overlap, and thus cease to exist, forming a naked singularity. (This amount of current would entail something i...

Singularity theory (7728 bytes)
1: ...'For non-mathematical singularity theories, see [[singularity]].''
3: ..., like an underlined 'U'. This is another kind of singularity. Unlike the double point, it is not ''stable'', i...
7: In '''singularity theory''' the general phenomenon of points and se...
9: ...e a [[gravitational singularity]], at which the [[gravitational field]] is strong enough to change the very struc...
31: ...reat deal of attention. This is another branch of singularity theory, based on earlier work of [[Hassler Whitne...

Prandtl-Glauert singularity (2147 bytes)
1: ...ight|250px|[[F/A-18 Hornet|F/A-18]] demonstrating singularity effect]]
3: ...some debate. It is an example of a [[mathematical singularity]] in [[aerodynamics]].
23: [[ja:Prandtl-Glauert Singularity]]

Penrose-Hawking singularity theorems (345 bytes)
1: ...re are several versions of the '''Penrose-Hawking singularity theorem'''. Most versions state, roughly, that if...

Singularity Institute for Artificial Intelligence (744 bytes)
1: The '''Singularity Institute for Artificial Intelligence''' is a 501...
8: * [[technological singularity]]
13: * [http://www.singinst.org/ Singularity Institute for Artificial Intelligence]

Gravitational potential (610 bytes)
1: ...to its position in a [[gravitational field]]. The gravitational potential of an object of mass ''m'' relative to ...
5: where ''G'' is the [[universal gravitational constant]] and ''r'' is the distance between the ...

Gravitational collapse (6739 bytes)
1: ... planets. For example, a star is born through the gravitational collapse of a cloud of interstellar matter. The c...
3: ...age the density of matter is so high that current gravitational theories do not apply. Before the singular state ...
5: ...rough a stellar wind for example), a catastrophic gravitational collapse can be seen as a [[Gamma ray burster|gam...
8: ==Catastrophic gravitational collapse toward a black hole==
9: ...ional_collapse.png|thumb|right|250px|Catastrophic gravitational collapse]]

Gravitational anomaly (1053 bytes)
1: In [[theoretical physics]], a '''gravitational anomaly''' is an example of an [[anomaly (physics...
3: ..."gravitational" is derived from the symmetry of a gravitational theory, namely from general covariance.
9: ...onsistency of the whole theory, and therefore all gravitational anomalies must cancel out.

Gravitational redshift (6901 bytes)
4: [[Albert Einstein]], the '''gravitational redshift''' or '''Einstein shift'''
5: ...spectrum]]) when observed from a point in a lower gravitational field. In the latter case the 'clock' is the freq...
7: The gravitational redshift is a simple consequence of the
12: Observing the gravitational redshift in the solar system, is one of the [[cla...
16: Experimental verification of the gravitational redshift

Gravitational radiation (11448 bytes)
1: In [[physics]], '''gravitational radiation''' is [[energy]] that is transmitted th...
5: ...se on oceans, lakes, etc. as ''Gravity waves.'' ''Gravitational radiation'' is the overall result of gravity wave...
7: ...(but not size) in a pulsating fashion. Similarly, gravitational waves will be emitted by physical objects with a ...
11: ...hat any accelerated mass radiates energy, but the gravitational [[interaction]]'s [[coupling strength]] is small ...
13: ...ith electromagnetic radiation and the [[photon]], gravitational radiation is expected to be [[quantize]]d with th...

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