mathematical

Singularity

A singularity is a kind of discontinuity. It might or might not be interesting. A vaguer use of the term is simply "a point where something happens" (although this equally describes an event.) Deleuze and Guattari are fascinated by singularities because they are points of unpredictability, even when deterministic. They are thus the sites of revolutionary potential.

As used by mathematical physicists, a singularity means a place where slopes become infinite, where the rate of change of one variable with another exceeds all bounds, and where a big change in an observable is caused by an arbitrarily small change in something else. (cf sensitivity to initial conditions). It is an actual point of infinite density and energy that's kind of a rupture in the fabric of space-time.


Astrophysics describe the centers of black holes as singularities.The Big Bang is considered to be a singularity.
A phase singularity is a point at which phase is ambiguous and near which phase takes on all values. Time at the poles of the earth is an example.

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phyllotaxis

Phyllotaxis (gr: phyllous means leaf, taxis means order) refers to the arrangement of leaves on a stem or florets in a composite flower such as a sunflower or pinecone along logarithmic spirals, or summation series, in which each term is the sum of the two preceding ones: 1,2,3,5,8,13,21,34,55,89,144 etc.. The scales form in double spirals which radiate from the center, one clockwise, the other counterclockwise. The surprising feature is that the number of spirals in one direction is related to the number in the other direction as two adjacent numbers in the Fibonacci series.

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