Astrophysics Term
A singularity is a point in space within a black hole that has is predicted by general relativity to have infinite density and infinite gravitational force. Predicting what actually occurs at a singularity will have to await the development of a theory of quantum gravity.
One question that has been asked are naked singularities possible. The answer has been determined to be yes.
German astrophysicist [Kurt Schwarzschild]? used Albert Einstein's Field Equations to determine the critical radius for any given mass at which matter would collapse into a singularity.
See also Event horizon
Information Theory Term
If, as seems true, technological progress has been following an exponential curve for a very long time, then there will come a point at which technological progress accelerates essentially to infinity. This is known as "the singularity."
There are many different specific definitions of the term, but all seem to have a common theme, perhaps summed up best by Vernor Vinge in his famous essay Singularity, published in 1993:
"Within thirty years, we will have the technological means to create superhuman intelligence. Shortly thereafter, the human era will be ended."
(full article is at: http://www.ugcs.caltech.edu/~phoenix/vinge/vinge-sing.html)
The basic idea of "the singularity" can be thought of as a natural extrapolation of Moore's Law. If the computing power per dollar cost continues to double every 18 to 24 months, then it is only a matter of time (some estimates range from 2020-2050) until we have inexpensive computer hardware ($1000, say) that is as powerful as the human brain. When that happens, it seems inevitable that realistic artificial intelligence that equals ours can be created.
But due to such factors as "the [AI advantage]?" (i.e., downloadable consciousness, replicable consciousness), it seems likely that such AIs would quickly be able to create even more intelligent machines. If we can create a single $1000 Einstein, you might say, we can easily create a billion Einsteins. Working together, they can surely generate enough technological progress to build machines so smart that they boggle the human mind.
It's a really interesting idea, no?
Prominent theorists/speculators on the subject include:
Some key concepts are:
Mathematics term Refers to a point where a function goes to infinity. For a function defined on the complex plane, an essential singularity exists at a point if and only if, for any real number R and complex number Z you take, there will be a point no farther than R from the point of essential singularity for which the function has the value Z. In other words, no matter how small a region around the point of essential singularity you take, you will still find all of the complex numbers inside it as values of the function.
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