A place to post Singularity links.
/index.php?p=singularity
http://www.singularityactiongroup.com
http://www.aleph.se/Trans/Global/Singularity/
Full Version: Singularity Links
Re: singinst.org
nice site. I like the handshake at the top (one hand is filled with binary values)!
nice site. I like the handshake at the top (one hand is filled with binary values)!
does it interest/amuse anyone else that there is more than one definition of a singularity? 
does it interest/amuse anyone else that there is more than one definition of a singularity?
yes. What defs have you encountered?
yes. What defs have you encountered?
Well the three most prominent i have seen are:
The singularity of Science and economics were our technological achivements will become infinite
The singularity of consciousness where we are all to merge into an infinite god consciousness
And there's always the singularity at the middle of black holes
The singularity of Science and economics were our technological achivements will become infinite
The singularity of consciousness where we are all to merge into an infinite god consciousness
And there's always the singularity at the middle of black holes
as far as I know, the term 'singularity' derives from complex analysis and is defined as a point on the complex plane where the equation in question becomes undefined (a zero in the denominator). As one approaches such a point on the complex plane, the value of the equation tends toward positive or negative infinity in any number of ways, but the same fact remains; at the 'singularity' point the equation is undefined. Computing a line integral across a singluarity is impossible, so an infinitesimal loop integral is drawn around the point in order to 'avoid' it, and a 'residue' caused by the singularity is factored into the computation. This way, a mathematically consistent value for the line integral in question can be obtained for the line that includes the singularity.
In general relativity, the mathematical description of spacetime is complex and the so-called 'singularities' are simply the selfsame mathematical entity. The morphism between the mathematical description of general relativity and reality need not be isomorphic, thus the mathematical 'singularity' is in no way necessarily a physical reality. This is why physicists will say that the inside of a black hole (the physical manifestation corresponding to the mathematical singularity) is simply not understood rather than saying that it is 'infinitely dense'
In general relativity, the mathematical description of spacetime is complex and the so-called 'singularities' are simply the selfsame mathematical entity. The morphism between the mathematical description of general relativity and reality need not be isomorphic, thus the mathematical 'singularity' is in no way necessarily a physical reality. This is why physicists will say that the inside of a black hole (the physical manifestation corresponding to the mathematical singularity) is simply not understood rather than saying that it is 'infinitely dense'
Wow, RtheB has really got you on the defensive!
To add to what Dan was saying..
In Complex Analysis there are different types of singularities as well and they are treated in different ways mathematically because they have different properties.
There are Poles, removable and essential singularites..so in mathematics there are different types of singularities
We cannot even agree whether space-time is continuous or not as yet..
At any rate i would expect different definitions be used for the singularity because we are all viewing the coming of something from different persepectives.
Cheers, Erika
In Complex Analysis there are different types of singularities as well and they are treated in different ways mathematically because they have different properties.
There are Poles, removable and essential singularites..so in mathematics there are different types of singularities
We cannot even agree whether space-time is continuous or not as yet..
At any rate i would expect different definitions be used for the singularity because we are all viewing the coming of something from different persepectives.
Cheers, Erika
| QUOTE (Dan @ Apr 21, 02:51 PM) |
| as far as I know, the term 'singularity' derives from complex analysis and is defined as a point on the complex plane where the equation in question becomes undefined (a zero in the denominator). As one approaches such a point on the complex plane, the value of the equation tends toward positive or negative infinity in any number of ways, but the same fact remains; at the 'singularity' point the equation is undefined. Computing a line integral across a singluarity is impossible, so an infinitesimal loop integral is drawn around the point in order to 'avoid' it, and a 'residue' caused by the singularity is factored into the computation. This way, a mathematically consistent value for the line integral in question can be obtained for the line that includes the singularity. In general relativity, the mathematical description of spacetime is complex and the so-called 'singularities' are simply the selfsame mathematical entity. The morphism between the mathematical description of general relativity and reality need not be isomorphic, thus the mathematical 'singularity' is in no way necessarily a physical reality. |
This is why physicists will say that the inside of a black hole (the physical manifestation corresponding to the mathematical singularity) is simply not understood rather than saying that it is 'infinitely dense'.
How do they know if they can't see inside?
What are physicists now, modernday Freudians and Jungians of Event Horizons?
Hyperspatial cognition = (intuit)ion = singularity.
in to it
in to it
QUOTE(Laz @ Apr 21, 2004, 10:52 AM) 
The singularity of consciousness where we are all to merge into an infinite god consciousness
I would certainly agree with this poster!
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