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Curiosity555User ID: 13177291 Belgium 11/28/2012 03:54 PM Report Abusive Post Report Copyright Violation | In mathematics, the Poincaré conjecture ( /pwɛn.kɑːˈreɪ/ pwen-kar-AY; French: [pwɛ̃kaʁe])[1] is a theorem about the characterization of the three-dimensional sphere (3-sphere), which is the hypersphere that bounds the unit ball in four-dimensional space. The conjecture states: Quoting: Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. [link to en.wikipedia.org] Main article: Poincaré conjecture In November 2002, Perelman posted the first of a series of eprints to the arXiv, in which he claimed to have outlined a proof of the geometrization conjecture, of which the Poincaré conjecture is a particular case.[11][12][13] Perelman modified Richard Hamilton's program for a proof of the conjecture, in which the central idea is the notion of the Ricci flow. Hamilton's basic idea is to formulate a "dynamical process" in which a given three-manifold is geometrically distorted, such that this distortion process is governed by a differential equation analogous to the heat equation. The heat equation describes the behavior of scalar quantities such as temperature; it ensures that concentrations of elevated temperature will spread out until a uniform temperature is achieved throughout an object. Similarly, the Ricci flow describes the behavior of a tensorial quantity, the Ricci curvature tensor. Hamilton's hope was that under the Ricci flow, concentrations of large curvature will spread out until a uniform curvature is achieved over the entire three-manifold. If so, if one starts with any three-manifold and lets the Ricci flow occur, eventually one should in principle obtain a kind of "normal form". According to William Thurston, this normal form must take one of a small number of possibilities, each having a different kind of geometry, called Thurston model geometries. This is similar to formulating a dynamical process that gradually "perturbs" a given square matrix, and that is guaranteed to result after a finite time in its rational canonical form. Hamilton's idea attracted a great deal of attention, but no one could prove that the process would not be impeded by developing "singularities", until Perelman's eprints sketched a program for overcoming these obstacles. According to Perelman, a modification of the standard Ricci flow, called Ricci flow with surgery, can systematically excise singular regions as they develop, in a controlled way. We know that singularities (including those that, roughly speaking, occur after the flow has continued for an infinite amount of time) must occur in many cases. However, any singularity that develops in a finite time is essentially a "pinching" along certain spheres corresponding to the prime decomposition of the 3-manifold. Furthermore, any "infinite time" singularities result from certain collapsing pieces of the JSJ decomposition. Perelman's work proves this claim and thus proves the geometrization conjecture. [link to en.wikipedia.org] Villi VonderVeener I NEVER IMPLEMENTED THIS FEATURE For I am beyond time. I am beyond space. I am with you always. |

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Anonymous Coward User ID: 28603382 Canada 11/28/2012 04:03 PM Report Abusive Post Report Copyright Violation | In mathematics, the Poincaré conjecture ( /pwɛn.kɑːˈreɪ/ pwen-kar-AY; French: [pwɛ̃kaʁe])[1] is a theorem about the characterization of the three-dimensional sphere (3-sphere), which is the hypersphere that bounds the unit ball in four-dimensional space. The conjecture states: Quoting: Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. [link to en.wikipedia.org] Main article: Poincaré conjecture In November 2002, Perelman posted the first of a series of eprints to the arXiv, in which he claimed to have outlined a proof of the geometrization conjecture, of which the Poincaré conjecture is a particular case.[11][12][13] Perelman modified Richard Hamilton's program for a proof of the conjecture, in which the central idea is the notion of the Ricci flow. Hamilton's basic idea is to formulate a "dynamical process" in which a given three-manifold is geometrically distorted, such that this distortion process is governed by a differential equation analogous to the heat equation. The heat equation describes the behavior of scalar quantities such as temperature; it ensures that concentrations of elevated temperature will spread out until a uniform temperature is achieved throughout an object. Similarly, the Ricci flow describes the behavior of a tensorial quantity, the Ricci curvature tensor. Hamilton's hope was that under the Ricci flow, concentrations of large curvature will spread out until a uniform curvature is achieved over the entire three-manifold. If so, if one starts with any three-manifold and lets the Ricci flow occur, eventually one should in principle obtain a kind of "normal form". According to William Thurston, this normal form must take one of a small number of possibilities, each having a different kind of geometry, called Thurston model geometries. This is similar to formulating a dynamical process that gradually "perturbs" a given square matrix, and that is guaranteed to result after a finite time in its rational canonical form. Hamilton's idea attracted a great deal of attention, but no one could prove that the process would not be impeded by developing "singularities", until Perelman's eprints sketched a program for overcoming these obstacles. According to Perelman, a modification of the standard Ricci flow, called Ricci flow with surgery, can systematically excise singular regions as they develop, in a controlled way. We know that singularities (including those that, roughly speaking, occur after the flow has continued for an infinite amount of time) must occur in many cases. However, any singularity that develops in a finite time is essentially a "pinching" along certain spheres corresponding to the prime decomposition of the 3-manifold. Furthermore, any "infinite time" singularities result from certain collapsing pieces of the JSJ decomposition. Perelman's work proves this claim and thus proves the geometrization conjecture. [link to en.wikipedia.org] Villi VonderVeener I NEVER IMPLEMENTED THIS FEATURE Curiosity555 LOL, It is a function of form and it's flow; There is no conciousness before it. The manifold self, apparently, there's Nothing to it. |

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Anonymous Coward User ID: 865798 United States 12/04/2012 11:12 AM Report Abusive Post Report Copyright Violation | In mathematics, the Poincaré conjecture ( /pwɛn.kɑːˈreɪ/ pwen-kar-AY; French: [pwɛ̃kaʁe])[1] is a theorem about the characterization of the three-dimensional sphere (3-sphere), which is the hypersphere that bounds the unit ball in four-dimensional space. The conjecture states: Quoting: Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. [link to en.wikipedia.org] Main article: Poincaré conjecture In November 2002, Perelman posted the first of a series of eprints to the arXiv, in which he claimed to have outlined a proof of the geometrization conjecture, of which the Poincaré conjecture is a particular case.[11][12][13] Perelman modified Richard Hamilton's program for a proof of the conjecture, in which the central idea is the notion of the Ricci flow. Hamilton's basic idea is to formulate a "dynamical process" in which a given three-manifold is geometrically distorted, such that this distortion process is governed by a differential equation analogous to the heat equation. The heat equation describes the behavior of scalar quantities such as temperature; it ensures that concentrations of elevated temperature will spread out until a uniform temperature is achieved throughout an object. Similarly, the Ricci flow describes the behavior of a tensorial quantity, the Ricci curvature tensor. Hamilton's hope was that under the Ricci flow, concentrations of large curvature will spread out until a uniform curvature is achieved over the entire three-manifold. If so, if one starts with any three-manifold and lets the Ricci flow occur, eventually one should in principle obtain a kind of "normal form". According to William Thurston, this normal form must take one of a small number of possibilities, each having a different kind of geometry, called Thurston model geometries. This is similar to formulating a dynamical process that gradually "perturbs" a given square matrix, and that is guaranteed to result after a finite time in its rational canonical form. Hamilton's idea attracted a great deal of attention, but no one could prove that the process would not be impeded by developing "singularities", until Perelman's eprints sketched a program for overcoming these obstacles. According to Perelman, a modification of the standard Ricci flow, called Ricci flow with surgery, can systematically excise singular regions as they develop, in a controlled way. We know that singularities (including those that, roughly speaking, occur after the flow has continued for an infinite amount of time) must occur in many cases. However, any singularity that develops in a finite time is essentially a "pinching" along certain spheres corresponding to the prime decomposition of the 3-manifold. Furthermore, any "infinite time" singularities result from certain collapsing pieces of the JSJ decomposition. Perelman's work proves this claim and thus proves the geometrization conjecture. [link to en.wikipedia.org] Villi VonderVeener Ok, I just started this thread. Is this the theory as to why things smooth out naturally? Accretion within dust disks, aftermath of celestial events, etc. Basically it is an organizational quality embedded in the aether...I'm thinking. |

Anonymous Coward User ID: 865798 United States 12/04/2012 11:18 AM Report Abusive Post Report Copyright Violation | The sphere and toroid as symbol of the head and halo or to some the crown of thorns. Quoting: The sphere as echoing dreamer with buoyant rings (toroids) radiating forth with electromagnetic interplay. The distillation of the dream circulating, concressing and returning to echoing sphere. [link to www.laetusinpraesens.org] Villi VonderVeener HAH! This is exactly what I was thinking...well, so far after only reading a few paragraphs. Basically it was an idea I had about forming governance using the blueprint as to how non-material manifests into material, or how toroids are the stability of aether. |

Anonymous Coward User ID: 865798 United States 12/04/2012 11:22 AM Report Abusive Post Report Copyright Violation | The sphere and toroid as symbol of the head and halo or to some the crown of thorns. Quoting: The sphere as echoing dreamer with buoyant rings (toroids) radiating forth with electromagnetic interplay. The distillation of the dream circulating, concressing and returning to echoing sphere. [link to www.laetusinpraesens.org] Villi VonderVeener HAH! This is exactly what I was thinking...well, so far after only reading a few paragraphs. Basically it was an idea I had about forming governance using the blueprint as to how non-material manifests into material, or how toroids are the stability of aether. Septenary Man And, using other models like in the original post, governance would eventually and wholly naturally 'smooth out', instead of becoming chaotic and thorn-like as it is now. The thorns being the areas that are unable to cross pollinate to other areas of the systems. In effect the "thorns" are the various pieces of a global system which lack appropriate connectivity, resulting in unsustainability and instability -- and potentially chaos and collapse. [link to www.laetusinpraesens.org] |

aetherUser ID: 28218601 United Kingdom 12/04/2012 11:22 AM Report Abusive Post Report Copyright Violation | The sphere and toroid as symbol of the head and halo or to some the crown of thorns. Quoting: The sphere as echoing dreamer with buoyant rings (toroids) radiating forth with electromagnetic interplay. The distillation of the dream circulating, concressing and returning to echoing sphere. [link to www.laetusinpraesens.org] Villi VonderVeener HAH! This is exactly what I was thinking...well, so far after only reading a few paragraphs. Basically it was an idea I had about forming governance using the blueprint as to how non-material manifests into material, or how toroids are the stability of aether. Septenary Man |

Anonymous Coward User ID: 865798 United States 12/04/2012 11:24 AM Report Abusive Post Report Copyright Violation | The sphere as echoing dreamer with buoyant rings (toroids) radiating forth with electromagnetic interplay. The distillation of the dream circulating, concressing and returning to echoing sphere. [link to www.laetusinpraesens.org] Villi VonderVeener HAH! This is exactly what I was thinking...well, so far after only reading a few paragraphs. Basically it was an idea I had about forming governance using the blueprint as to how non-material manifests into material, or how toroids are the stability of aether. Septenary Man aether What an incredible website! |

Anonymous Coward User ID: 24542515 United States 12/04/2012 12:11 PM Report Abusive Post Report Copyright Violation | The sphere as echoing dreamer with buoyant rings (toroids) radiating forth with electromagnetic interplay. The distillation of the dream circulating, concressing and returning to echoing sphere. [link to www.laetusinpraesens.org] Villi VonderVeener HAH! This is exactly what I was thinking...well, so far after only reading a few paragraphs. Basically it was an idea I had about forming governance using the blueprint as to how non-material manifests into material, or how toroids are the stability of aether. Septenary Man aether What an incredible website! Septenary Man hmmm: "The subtle combination of creativity, irrationality, surprise and "cognitive catastrophe" are associated with the non-linearity of the Knight's move. Change is to be understood and achieved by the possibility of "getting off a train" of linear thought -- otherwise expressed as "out-of-the-box"." he 'knight's move' is perpendicular. and: think entropy. being able to describe it's 'shape' still doesn't come close to what or why. just sayin' |

aetherUser ID: 28218601 United Kingdom 12/04/2012 12:22 PM Report Abusive Post Report Copyright Violation | hmmm: "The subtle combination of creativity, irrationality, surprise and "cognitive catastrophe" are associated with the non-linearity of the Knight's move. Change is to be understood and achieved by the possibility of "getting off a train" of linear thought -- otherwise expressed as "out-of-the-box"." he 'knight's move' is perpendicular. and: think entropy. being able to describe it's 'shape' still doesn't come close to what or why. just sayin' Anonymous Coward 24542515 how do you explain a machine who`s parts transform into other parts that transform into other parts that........... Quoting: ...........for ever a transient machine feels like eternal whoa! aether in the end, we are all transients. This topic (the study of electrical transients) can have very broad reaching implications to philosophy on religion, history, music / tonal structure, myth, nature, and the human-modern science dogmas that plague thought processes of our institutions. There is a deep fear of the transient, ironically that which nature chooses to use, to power things. Quoting: observationour new philosophy feels tangible aether Time-invariant systemA time-invariant (TIV) system is one whose output does not depend explicitly on time Quoting: observation[link to en.wikipedia.org] then we discovered our environment (universe) utilizes time invariant system (timeless) that manifest transient dynamical systems a layer of a layer aether |

Anonymous Coward User ID: 28792938 Canada 12/04/2012 12:22 PM Report Abusive Post Report Copyright Violation | The sphere as echoing dreamer with buoyant rings (toroids) radiating forth with electromagnetic interplay. The distillation of the dream circulating, concressing and returning to echoing sphere. [link to www.laetusinpraesens.org] Villi VonderVeener HAH! This is exactly what I was thinking...well, so far after only reading a few paragraphs. Basically it was an idea I had about forming governance using the blueprint as to how non-material manifests into material, or how toroids are the stability of aether. Septenary Man aether What an incredible website! Septenary Man figure 17b as a form programming function has many of the interpolated concepts we discussed last winter and have fruited over the past several moonths. |

Anonymous Coward User ID: 28792938 Canada 12/04/2012 12:27 PM Report Abusive Post Report Copyright Violation | hmmm: "The subtle combination of creativity, irrationality, surprise and "cognitive catastrophe" are associated with the non-linearity of the Knight's move. Change is to be understood and achieved by the possibility of "getting off a train" of linear thought -- otherwise expressed as "out-of-the-box"." he 'knight's move' is perpendicular. and: think entropy. being able to describe it's 'shape' still doesn't come close to what or why. just sayin' Anonymous Coward 24542515 how do you explain a machine who`s parts transform into other parts that transform into other parts that........... Quoting: ...........for ever a transient machine feels like eternal whoa! aether in the end, we are all transients. This topic (the study of electrical transients) can have very broad reaching implications to philosophy on religion, history, music / tonal structure, myth, nature, and the human-modern science dogmas that plague thought processes of our institutions. There is a deep fear of the transient, ironically that which nature chooses to use, to power things. Quoting: observationour new philosophy feels tangible aether Time-invariant systemA time-invariant (TIV) system is one whose output does not depend explicitly on time Quoting: observation[link to en.wikipedia.org] then we discovered our environment (universe) utilizes time invariant system (timeless) that manifest transient dynamical systems a layer of a layer aether aether I visually see it as what I've previously called the onion blossom. As every external layer is unfolded it is renested at the heart of the torrus and becomes its inner wall. There are two circulations unfolding and as such 2 dimensions; the third being in their interplay and time being a function on the necessity of form or cause of visual spatial interpretation. Form is inherent in effect. Cheers |

Anonymous Coward User ID: 28792938 Canada 12/04/2012 12:31 PM Report Abusive Post Report Copyright Violation | Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. [link to en.wikipedia.org] Main article: Poincaré conjecture In November 2002, Perelman posted the first of a series of eprints to the arXiv, in which he claimed to have outlined a proof of the geometrization conjecture, of which the Poincaré conjecture is a particular case.[11][12][13] Perelman modified Richard Hamilton's program for a proof of the conjecture, in which the central idea is the notion of the Ricci flow. Hamilton's basic idea is to formulate a "dynamical process" in which a given three-manifold is geometrically distorted, such that this distortion process is governed by a differential equation analogous to the heat equation. The heat equation describes the behavior of scalar quantities such as temperature; it ensures that concentrations of elevated temperature will spread out until a uniform temperature is achieved throughout an object. Similarly, the Ricci flow describes the behavior of a tensorial quantity, the Ricci curvature tensor. Hamilton's hope was that under the Ricci flow, concentrations of large curvature will spread out until a uniform curvature is achieved over the entire three-manifold. If so, if one starts with any three-manifold and lets the Ricci flow occur, eventually one should in principle obtain a kind of "normal form". According to William Thurston, this normal form must take one of a small number of possibilities, each having a different kind of geometry, called Thurston model geometries. This is similar to formulating a dynamical process that gradually "perturbs" a given square matrix, and that is guaranteed to result after a finite time in its rational canonical form. Hamilton's idea attracted a great deal of attention, but no one could prove that the process would not be impeded by developing "singularities", until Perelman's eprints sketched a program for overcoming these obstacles. According to Perelman, a modification of the standard Ricci flow, called Ricci flow with surgery, can systematically excise singular regions as they develop, in a controlled way. We know that singularities (including those that, roughly speaking, occur after the flow has continued for an infinite amount of time) must occur in many cases. However, any singularity that develops in a finite time is essentially a "pinching" along certain spheres corresponding to the prime decomposition of the 3-manifold. Furthermore, any "infinite time" singularities result from certain collapsing pieces of the JSJ decomposition. Perelman's work proves this claim and thus proves the geometrization conjecture. [link to en.wikipedia.org] Villi VonderVeener Ok, I just started this thread. Is this the theory as to why things smooth out naturally? Accretion within dust disks, aftermath of celestial events, etc. Basically it is an organizational quality embedded in the aether...I'm thinking. Septenary Man As towards the Ricci flows and thermal dynamics, yes, it is the function of form and vice versa. How organization is inasmuch the form of that construed as nothing as the active components which make it up. Nothing to me dictates that which is not yet seen or repetitively understood. As it becomes something when we can 'see' it. |

Anonymous Coward User ID: 865798 United States 12/04/2012 12:32 PM Report Abusive Post Report Copyright Violation | ...HAH! This is exactly what I was thinking...well, so far after only reading a few paragraphs. Basically it was an idea I had about forming governance using the blueprint as to how non-material manifests into material, or how toroids are the stability of aether. Septenary Man aether What an incredible website! Septenary Man hmmm: "The subtle combination of creativity, irrationality, surprise and "cognitive catastrophe" are associated with the non-linearity of the Knight's move. Change is to be understood and achieved by the possibility of "getting off a train" of linear thought -- otherwise expressed as "out-of-the-box"." he 'knight's move' is perpendicular. and: think entropy. being able to describe it's 'shape' still doesn't come close to what or why. just sayin' Anonymous Coward 24542515 A Knight's move is spiral in form as well. |

Anonymous Coward User ID: 24542515 United States 12/04/2012 01:30 PM Report Abusive Post Report Copyright Violation | hmmm: "The subtle combination of creativity, irrationality, surprise and "cognitive catastrophe" are associated with the non-linearity of the Knight's move. Change is to be understood and achieved by the possibility of "getting off a train" of linear thought -- otherwise expressed as "out-of-the-box"." he 'knight's move' is perpendicular. and: think entropy. being able to describe it's 'shape' still doesn't come close to what or why. just sayin' Anonymous Coward 24542515 A Knight's move is spiral in form as well. Septenary Man time for u to 'square' the spiral, SS? |

Anonymous Coward User ID: 865798 United States 12/04/2012 01:31 PM Report Abusive Post Report Copyright Violation | hmmm: "The subtle combination of creativity, irrationality, surprise and "cognitive catastrophe" are associated with the non-linearity of the Knight's move. Change is to be understood and achieved by the possibility of "getting off a train" of linear thought -- otherwise expressed as "out-of-the-box"." he 'knight's move' is perpendicular. and: think entropy. being able to describe it's 'shape' still doesn't come close to what or why. just sayin' Anonymous Coward 24542515 A Knight's move is spiral in form as well. Septenary Man time for u to 'square' the spiral, SS? Anonymous Coward 24542515 I suppose so. |

Anonymous Coward User ID: 865798 United States 12/04/2012 02:06 PM Report Abusive Post Report Copyright Violation | Bubbles within bubbles and inversions. The scientist was working on his dissertation under the direction of academician Aleksandrov. "The subject was not hard: "Saddle surfaces in Euclidean geometry." Can you imagine equal-sized and irregularly spaced surfaces in infinity? We have to measure the cavities between them," the mathematician said. Quoting: [link to english.pravda.ru] |

Anonymous Coward User ID: 28792938 Canada 12/04/2012 02:58 PM Report Abusive Post Report Copyright Violation | ...hmmm: "The subtle combination of creativity, irrationality, surprise and "cognitive catastrophe" are associated with the non-linearity of the Knight's move. Change is to be understood and achieved by the possibility of "getting off a train" of linear thought -- otherwise expressed as "out-of-the-box"." he 'knight's move' is perpendicular. and: think entropy. being able to describe it's 'shape' still doesn't come close to what or why. just sayin' Anonymous Coward 24542515 A Knight's move is spiral in form as well. Septenary Man time for u to 'square' the spiral, SS? Anonymous Coward 24542515 I suppose so. Septenary Man No worries, it's just a thrown peddle which starts the rippling cascade. And then again you don't even have to throw it. Just peck on a keyboard and walk away. Horatio Alger and his bootstrap mechanism just rolled in their graves. Back to the abyss! |

Anonymous Coward User ID: 865798 United States 12/04/2012 03:09 PM Report Abusive Post Report Copyright Violation | Quoting: Septenary Man No worries, it's just a thrown peddle which starts the rippling cascade. And then again you don't even have to throw it. Just peck on a keyboard and walk away. Horatio Alger and his bootstrap mechanism just rolled in their graves. Back to the abyss! Dionysian Fullaflattus There are no worries on that front anymore. Many changes have I wrought through myself in the last few years. As I've said before, I am finally content in a manner of speaking. |