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marcus

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## Main Question or Discussion Point

This post is just concerned with definition of terms, for them as wants it. If you are NOT confused about what is meant by a singularity in math/physics, please ignore this. Sometimes a good online source, if you want the meaning of math and physics terms, is Wolfram Mathworld. Wolfram also has a comparable reference for Physics terms. However the term singularity came into physics from mathematics, over a hundred years ago, so the place to look it up is Mathworld.

http://mathworld.wolfram.com/Singularity.html

The primary meaning is a place (point or region) where a function blows up and fails to give meaningful results. This was taken over into physics: a place where a man-made mathematical

Of course the word has other meanings in ordinary non-technical speech (it can mean oddness or peculiarity) but that is outside of physics and cosmology.

Wikipedia says this

http://en.wikipedia.org/wiki/Mathematical_singularity

and they give the example of the function f(x) = 1/x, which is not defined at x = 0 and which blows up there.

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it is a point where a man-made mathematical model breaks down and fails to compute.

Historically, in the mathematical sciences there has been a process of singularity

Mathematicians and physicists have been dealing with singularities for hundreds of years. Just to take one example, Quantum Mechanics has its roots in several inventions of mathematical ways to resolve singularities-----the Planck radiation curve (1900) replaced earlier models of thermal radiation that blew up----the Bohr model atom (1913) took care of an instability in the classical model atom. This process of singularity resolution, by improving theory, is generally expected to continue as in the past.

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The word singularity, as a technical term in mathematics and the mathematical sciences, has had the same meaning for hundreds of years. If you look at what Wolfram Mathworld says, you will see that singularities do not always occur as ISOLATED POINTS.

The bad points where something doesnt work can sometimes occur connected in a line or surface or hypersurface.

That is, a mathematical model can blow up and fail to apply in a WHOLE REGION.

Sometimes people get the mistaken idea that because the word "singularity" sounds like the word "single", a singularity must somehow refer to a single isolated point. That isn't so.

http://mathworld.wolfram.com/Singularity.html

The primary meaning is a place (point or region) where a function blows up and fails to give meaningful results. This was taken over into physics: a place where a man-made mathematical

**model**blows up and fails to give meaningful results.Of course the word has other meanings in ordinary non-technical speech (it can mean oddness or peculiarity) but that is outside of physics and cosmology.

Wikipedia says this

http://en.wikipedia.org/wiki/Mathematical_singularity

**a singularity is in general a point at which a given mathematical object is not defined**and they give the example of the function f(x) = 1/x, which is not defined at x = 0 and which blows up there.

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**the point to remember is that a singularity is not something which exists in nature.**it is a point where a man-made mathematical model breaks down and fails to compute.

Historically, in the mathematical sciences there has been a process of singularity

**removal or resolution**. In a number of cases people have gotten rid of singularities by improving the model. You replace the model with a better version which does not break down---and so does not have the singularity---and that gets rid of the problem.Mathematicians and physicists have been dealing with singularities for hundreds of years. Just to take one example, Quantum Mechanics has its roots in several inventions of mathematical ways to resolve singularities-----the Planck radiation curve (1900) replaced earlier models of thermal radiation that blew up----the Bohr model atom (1913) took care of an instability in the classical model atom. This process of singularity resolution, by improving theory, is generally expected to continue as in the past.

====================

The word singularity, as a technical term in mathematics and the mathematical sciences, has had the same meaning for hundreds of years. If you look at what Wolfram Mathworld says, you will see that singularities do not always occur as ISOLATED POINTS.

The bad points where something doesnt work can sometimes occur connected in a line or surface or hypersurface.

That is, a mathematical model can blow up and fail to apply in a WHOLE REGION.

Sometimes people get the mistaken idea that because the word "singularity" sounds like the word "single", a singularity must somehow refer to a single isolated point. That isn't so.

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