<article>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#article10_03_19_0540249</id>
	<title>Millennium Prize Awarded For Perelman's Poincar&#233; Proof</title>
	<author>timothy</author>
	<datestamp>1269000720000</datestamp>
	<htmltext>epee1221 writes <i>"The Clay Mathematics Institute has <a href="http://www.claymath.org/poincare/">announced its acceptance of Dr. Grigori Perelman's proof of the Poincar&#233; conjecture</a> and awarded the first Millennium Prize. Poincar&#233; questioned whether there exists a method for determining whether a three-dimensional manifold is a spherical: is there a 3-manifold not homologous to the 3-sphere in which any loop can be gradually shrunk to a single point? The Poincar&#233; conjecture is that there is no such 3-manifold, i.e. any boundless 3-manifold in which the condition holds is homeomorphic to the 3-sphere. A <a href="http://en.wikipedia.org/wiki/Solution\_of\_the\_Poincar\%C3\%A9\_conjecture">sketch of the proof</a> using language intended for the lay reader is available at Wikipedia."</i></htmltext>
<tokenext>epee1221 writes " The Clay Mathematics Institute has announced its acceptance of Dr. Grigori Perelman 's proof of the Poincar   conjecture and awarded the first Millennium Prize .
Poincar   questioned whether there exists a method for determining whether a three-dimensional manifold is a spherical : is there a 3-manifold not homologous to the 3-sphere in which any loop can be gradually shrunk to a single point ?
The Poincar   conjecture is that there is no such 3-manifold , i.e .
any boundless 3-manifold in which the condition holds is homeomorphic to the 3-sphere .
A sketch of the proof using language intended for the lay reader is available at Wikipedia .
"</tokentext>
<sentencetext>epee1221 writes "The Clay Mathematics Institute has announced its acceptance of Dr. Grigori Perelman's proof of the Poincaré conjecture and awarded the first Millennium Prize.
Poincaré questioned whether there exists a method for determining whether a three-dimensional manifold is a spherical: is there a 3-manifold not homologous to the 3-sphere in which any loop can be gradually shrunk to a single point?
The Poincaré conjecture is that there is no such 3-manifold, i.e.
any boundless 3-manifold in which the condition holds is homeomorphic to the 3-sphere.
A sketch of the proof using language intended for the lay reader is available at Wikipedia.
"</sentencetext>
</article>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31538578</id>
	<title>Re:Great news</title>
	<author>Arthur Grumbine</author>
	<datestamp>1269016320000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>I am very happy that they have awarded the price only to him, although he did meet the requirement that the proof should be published in a peer-reviewed journal. I am very happy that they did not included those two Chinese guys who did write down the proof (about 260 pages) and claimed that they had proven the conjecture. Perelman was very upset by this especially that other mathematics did not raise their voice. I hope that Perelman will accept the price. He said (some years ago) that he would only decide when the offer was made, if he would except the price or not.</p></div><p>So, you're saying that for Perelman, The Prize is Right?</p></div>
	</htmltext>
<tokenext>I am very happy that they have awarded the price only to him , although he did meet the requirement that the proof should be published in a peer-reviewed journal .
I am very happy that they did not included those two Chinese guys who did write down the proof ( about 260 pages ) and claimed that they had proven the conjecture .
Perelman was very upset by this especially that other mathematics did not raise their voice .
I hope that Perelman will accept the price .
He said ( some years ago ) that he would only decide when the offer was made , if he would except the price or not.So , you 're saying that for Perelman , The Prize is Right ?</tokentext>
<sentencetext>I am very happy that they have awarded the price only to him, although he did meet the requirement that the proof should be published in a peer-reviewed journal.
I am very happy that they did not included those two Chinese guys who did write down the proof (about 260 pages) and claimed that they had proven the conjecture.
Perelman was very upset by this especially that other mathematics did not raise their voice.
I hope that Perelman will accept the price.
He said (some years ago) that he would only decide when the offer was made, if he would except the price or not.So, you're saying that for Perelman, The Prize is Right?
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534962</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31537612</id>
	<title>Re:English Please</title>
	<author>Coryoth</author>
	<datestamp>1269013980000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>3</modscore>
	<htmltext><p>It's really all about classifying shapes. For two dimensional things this is pretty easy, at least as far as the topology goes: you need to know the curvature and "how many holes does it have" and that's it -- this is the whole topologist not knowing a coffee cup from a donut since they both have one hole and hence can be deformed one into the other (note that this is two dimensional because we are considering the 2-dimensional surface on the donut and coffee cup). In dimensions higher than two things start getting trickier because more bizarre configurations become possible. Perelman's work, which actually goes toward proving the rather more far reaching Geometrization Conjecture (due to Thurston), essentially lays out how you can classify all the different (from a topological point of view) shapes of things in  three dimensions and higher.</p><p>What are the implications? Well, one reasonable question is: what is the topology of the universe like; what shape is the universe? Since the universe is a three dimensional manifold that turns out to be tricky. Perelman's work lays out the groundwork to be able to answer such a question.</p></htmltext>
<tokenext>It 's really all about classifying shapes .
For two dimensional things this is pretty easy , at least as far as the topology goes : you need to know the curvature and " how many holes does it have " and that 's it -- this is the whole topologist not knowing a coffee cup from a donut since they both have one hole and hence can be deformed one into the other ( note that this is two dimensional because we are considering the 2-dimensional surface on the donut and coffee cup ) .
In dimensions higher than two things start getting trickier because more bizarre configurations become possible .
Perelman 's work , which actually goes toward proving the rather more far reaching Geometrization Conjecture ( due to Thurston ) , essentially lays out how you can classify all the different ( from a topological point of view ) shapes of things in three dimensions and higher.What are the implications ?
Well , one reasonable question is : what is the topology of the universe like ; what shape is the universe ?
Since the universe is a three dimensional manifold that turns out to be tricky .
Perelman 's work lays out the groundwork to be able to answer such a question .</tokentext>
<sentencetext>It's really all about classifying shapes.
For two dimensional things this is pretty easy, at least as far as the topology goes: you need to know the curvature and "how many holes does it have" and that's it -- this is the whole topologist not knowing a coffee cup from a donut since they both have one hole and hence can be deformed one into the other (note that this is two dimensional because we are considering the 2-dimensional surface on the donut and coffee cup).
In dimensions higher than two things start getting trickier because more bizarre configurations become possible.
Perelman's work, which actually goes toward proving the rather more far reaching Geometrization Conjecture (due to Thurston), essentially lays out how you can classify all the different (from a topological point of view) shapes of things in  three dimensions and higher.What are the implications?
Well, one reasonable question is: what is the topology of the universe like; what shape is the universe?
Since the universe is a three dimensional manifold that turns out to be tricky.
Perelman's work lays out the groundwork to be able to answer such a question.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535100</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31539192</id>
	<title>Re:Bread and Cheese</title>
	<author>Anonymous</author>
	<datestamp>1269018120000</datestamp>
	<modclass>Funny</modclass>
	<modscore>2</modscore>
	<htmltext><p>Given his personality, I think he'll rather appreciate the fact that he can afford <em>more</em> bread and cheese now.</p></htmltext>
<tokenext>Given his personality , I think he 'll rather appreciate the fact that he can afford more bread and cheese now .</tokentext>
<sentencetext>Given his personality, I think he'll rather appreciate the fact that he can afford more bread and cheese now.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534944</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31555392</id>
	<title>Take away my Slashdot card</title>
	<author>blake182</author>
	<datestamp>1269110640000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Can someone please hyperlink every word of this article to Wikipedia for me?

</p><p>I'll show myself the door. Pout.</p></htmltext>
<tokenext>Can someone please hyperlink every word of this article to Wikipedia for me ?
I 'll show myself the door .
Pout .</tokentext>
<sentencetext>Can someone please hyperlink every word of this article to Wikipedia for me?
I'll show myself the door.
Pout.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534948</id>
	<title>Millennium Prize?</title>
	<author>Anonymous</author>
	<datestamp>1269005940000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>What Millennium are we talking about here? Its now 2010, 9 years after the start of the new Millennium.</p></htmltext>
<tokenext>What Millennium are we talking about here ?
Its now 2010 , 9 years after the start of the new Millennium .</tokentext>
<sentencetext>What Millennium are we talking about here?
Its now 2010, 9 years after the start of the new Millennium.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31539196</id>
	<title>from a mathematician</title>
	<author>l2718</author>
	<datestamp>1269018120000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>3</modscore>
	<htmltext><p>It's easier to explain the two-dimensional version, that is the version about surfaces.  A mathematical <b>surface</b> is a kind of quilt: it's what you get from stitching together patches, each of which looks like a small piece of the plane.  Just like with the quilt, if you bend or deform the surface it still is the same surface.  Surfaces are completely "floppy".</p><p>Now, most real-life quilts are rectangular and have a boundary where they end, but you can also "close" the quilt by stitching the boundary back onto itself -- what you get is a "closed" surface.  For example, you can stitch all the boundary together and get a sphere.  Or you can stitch opposite sides together and get a "torus" -- the surface of a doughnut.  You can also make more complicated quilts, which look like the joining of several doughnuts, i.e. a doughnut with several holes.</p><p>Next, one way that the sphere and doughnut-surface differ is that the latter has a hole.  The way we express this is by looping a closed piece of string along the surface.  With the sphere you can always slide the piece of string off the surface (we say that the sphere is "simply connected"), but with the torus you can run a loop of string along it in such a way that no deformation will allow you to take it off (we say the doughnut is "multiply connected").</p><p>Finally, the "2d Poincare conjecture" is the statement that the only simply connected closed 2d surface is the sphere.  In other words, if you can't link a loop with your closed quilt then your quilt can be deformed to be a round sphere.  A strong version of this was proved by Poincare, among others.</p><p>Now for the real "Poincare Conjecture" that was proved by Perelman, replace "2d" by "3d", so the quilt comes from stitching little cubes instead of little squares.  The "closed and simply connected" assumptions are the same, and the conclusion is that the quilt is, up to deformation, the 3d sphere.  It's much harder to visualize since now the quilt may not fit into regular 3d space.   For example, the 3d sphere is what you get by stitching the whole boundary of the 3d cube together into one point (recall how we got a 2d sphere!) -- which is not something that fits into ordinary 3d space.</p></htmltext>
<tokenext>It 's easier to explain the two-dimensional version , that is the version about surfaces .
A mathematical surface is a kind of quilt : it 's what you get from stitching together patches , each of which looks like a small piece of the plane .
Just like with the quilt , if you bend or deform the surface it still is the same surface .
Surfaces are completely " floppy " .Now , most real-life quilts are rectangular and have a boundary where they end , but you can also " close " the quilt by stitching the boundary back onto itself -- what you get is a " closed " surface .
For example , you can stitch all the boundary together and get a sphere .
Or you can stitch opposite sides together and get a " torus " -- the surface of a doughnut .
You can also make more complicated quilts , which look like the joining of several doughnuts , i.e .
a doughnut with several holes.Next , one way that the sphere and doughnut-surface differ is that the latter has a hole .
The way we express this is by looping a closed piece of string along the surface .
With the sphere you can always slide the piece of string off the surface ( we say that the sphere is " simply connected " ) , but with the torus you can run a loop of string along it in such a way that no deformation will allow you to take it off ( we say the doughnut is " multiply connected " ) .Finally , the " 2d Poincare conjecture " is the statement that the only simply connected closed 2d surface is the sphere .
In other words , if you ca n't link a loop with your closed quilt then your quilt can be deformed to be a round sphere .
A strong version of this was proved by Poincare , among others.Now for the real " Poincare Conjecture " that was proved by Perelman , replace " 2d " by " 3d " , so the quilt comes from stitching little cubes instead of little squares .
The " closed and simply connected " assumptions are the same , and the conclusion is that the quilt is , up to deformation , the 3d sphere .
It 's much harder to visualize since now the quilt may not fit into regular 3d space .
For example , the 3d sphere is what you get by stitching the whole boundary of the 3d cube together into one point ( recall how we got a 2d sphere !
) -- which is not something that fits into ordinary 3d space .</tokentext>
<sentencetext>It's easier to explain the two-dimensional version, that is the version about surfaces.
A mathematical surface is a kind of quilt: it's what you get from stitching together patches, each of which looks like a small piece of the plane.
Just like with the quilt, if you bend or deform the surface it still is the same surface.
Surfaces are completely "floppy".Now, most real-life quilts are rectangular and have a boundary where they end, but you can also "close" the quilt by stitching the boundary back onto itself -- what you get is a "closed" surface.
For example, you can stitch all the boundary together and get a sphere.
Or you can stitch opposite sides together and get a "torus" -- the surface of a doughnut.
You can also make more complicated quilts, which look like the joining of several doughnuts, i.e.
a doughnut with several holes.Next, one way that the sphere and doughnut-surface differ is that the latter has a hole.
The way we express this is by looping a closed piece of string along the surface.
With the sphere you can always slide the piece of string off the surface (we say that the sphere is "simply connected"), but with the torus you can run a loop of string along it in such a way that no deformation will allow you to take it off (we say the doughnut is "multiply connected").Finally, the "2d Poincare conjecture" is the statement that the only simply connected closed 2d surface is the sphere.
In other words, if you can't link a loop with your closed quilt then your quilt can be deformed to be a round sphere.
A strong version of this was proved by Poincare, among others.Now for the real "Poincare Conjecture" that was proved by Perelman, replace "2d" by "3d", so the quilt comes from stitching little cubes instead of little squares.
The "closed and simply connected" assumptions are the same, and the conclusion is that the quilt is, up to deformation, the 3d sphere.
It's much harder to visualize since now the quilt may not fit into regular 3d space.
For example, the 3d sphere is what you get by stitching the whole boundary of the 3d cube together into one point (recall how we got a 2d sphere!
) -- which is not something that fits into ordinary 3d space.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535100</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31541378</id>
	<title>Re:So will he accept?</title>
	<author>sans17</author>
	<datestamp>1269025920000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>From what I have read around here he did not reject Fields Medal. Since they never formally offered it to him. Or did they?<br>"We will give it to you if you take it" is just BS.<br>One more point to Perelman.</p></htmltext>
<tokenext>From what I have read around here he did not reject Fields Medal .
Since they never formally offered it to him .
Or did they ?
" We will give it to you if you take it " is just BS.One more point to Perelman .</tokentext>
<sentencetext>From what I have read around here he did not reject Fields Medal.
Since they never formally offered it to him.
Or did they?
"We will give it to you if you take it" is just BS.One more point to Perelman.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535082</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31536558</id>
	<title>controversial "proof"</title>
	<author>Anonymous</author>
	<datestamp>1269011460000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Good to see the Perelman fanboys up so early in the morning.</p><p>But there seems to be just as many credible sources that felt Perelman did not satisfy the test of rigor.<br>I guess Clay math is free to do what they wish with their own money.</p></htmltext>
<tokenext>Good to see the Perelman fanboys up so early in the morning.But there seems to be just as many credible sources that felt Perelman did not satisfy the test of rigor.I guess Clay math is free to do what they wish with their own money .</tokentext>
<sentencetext>Good to see the Perelman fanboys up so early in the morning.But there seems to be just as many credible sources that felt Perelman did not satisfy the test of rigor.I guess Clay math is free to do what they wish with their own money.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31537346</id>
	<title>Re:Who the fuck cares?</title>
	<author>not-my-real-name</author>
	<datestamp>1269013260000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>3</modscore>
	<htmltext><p>Nerds care.</p></htmltext>
<tokenext>Nerds care .</tokentext>
<sentencetext>Nerds care.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31536104</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31537540</id>
	<title>Re:Well, sure</title>
	<author>JoshuaZ</author>
	<datestamp>1269013800000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>2</modscore>
	<htmltext>Ricci flow is an incredibly clever and sophisticated set of techniques. It is a very difficult technique to use and is by no means a "cheat code" for manifold questions. Most obviously, Ricci flow has been used with success to answer some aspects of the geometrization conjecture <a href="http://en.wikipedia.org/wiki/Geometrization\_conjecture" title="wikipedia.org">http://en.wikipedia.org/wiki/Geometrization\_conjecture</a> [wikipedia.org] but still leaves a lot. In order to have a truly good understanding of low-dimensional manifolds we are likely going to need some additional technique that has not yet been discovered.</htmltext>
<tokenext>Ricci flow is an incredibly clever and sophisticated set of techniques .
It is a very difficult technique to use and is by no means a " cheat code " for manifold questions .
Most obviously , Ricci flow has been used with success to answer some aspects of the geometrization conjecture http : //en.wikipedia.org/wiki/Geometrization \ _conjecture [ wikipedia.org ] but still leaves a lot .
In order to have a truly good understanding of low-dimensional manifolds we are likely going to need some additional technique that has not yet been discovered .</tokentext>
<sentencetext>Ricci flow is an incredibly clever and sophisticated set of techniques.
It is a very difficult technique to use and is by no means a "cheat code" for manifold questions.
Most obviously, Ricci flow has been used with success to answer some aspects of the geometrization conjecture http://en.wikipedia.org/wiki/Geometrization\_conjecture [wikipedia.org] but still leaves a lot.
In order to have a truly good understanding of low-dimensional manifolds we are likely going to need some additional technique that has not yet been discovered.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534832</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535082</id>
	<title>So will he accept?</title>
	<author>Puff\_Of\_Hot\_Air</author>
	<datestamp>1269006840000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>5</modscore>
	<htmltext>Perelman has famously turned down the fields medal and shunned the world since the whole Yau political saga. Will he take this prize? I hope that he will. I think that the whole Yau trying to take the credit for the proof issue, sullied the entire world for Perelman. Perhaps now that the honour is being fairly directed at him in response to his work, Perelman will be able to re-enter society and enjoy some of the fruits of his labour.</htmltext>
<tokenext>Perelman has famously turned down the fields medal and shunned the world since the whole Yau political saga .
Will he take this prize ?
I hope that he will .
I think that the whole Yau trying to take the credit for the proof issue , sullied the entire world for Perelman .
Perhaps now that the honour is being fairly directed at him in response to his work , Perelman will be able to re-enter society and enjoy some of the fruits of his labour .</tokentext>
<sentencetext>Perelman has famously turned down the fields medal and shunned the world since the whole Yau political saga.
Will he take this prize?
I hope that he will.
I think that the whole Yau trying to take the credit for the proof issue, sullied the entire world for Perelman.
Perhaps now that the honour is being fairly directed at him in response to his work, Perelman will be able to re-enter society and enjoy some of the fruits of his labour.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31538562</id>
	<title>Summary of the Poincare conjecture is inaccurate</title>
	<author>TheEmptySet</author>
	<datestamp>1269016260000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>2</modscore>
	<htmltext>As someone who's job involves research into geometry and topology, I would like to point out that the summary is wrong in a couple of places. The Poincare conjecture states (in simple terms) that:
<p>
Any closed smooth three dimensional space ('manifold') without boundary where all loops can be contracted to a point is 'homeomorphic' (essentially the same as) the three dimensional sphere (that is, the unit sphere in 4 dimensions).
</p><p>
The words "homologous" and "boundless" have little/nothing to do with it.</p></htmltext>
<tokenext>As someone who 's job involves research into geometry and topology , I would like to point out that the summary is wrong in a couple of places .
The Poincare conjecture states ( in simple terms ) that : Any closed smooth three dimensional space ( 'manifold ' ) without boundary where all loops can be contracted to a point is 'homeomorphic ' ( essentially the same as ) the three dimensional sphere ( that is , the unit sphere in 4 dimensions ) .
The words " homologous " and " boundless " have little/nothing to do with it .</tokentext>
<sentencetext>As someone who's job involves research into geometry and topology, I would like to point out that the summary is wrong in a couple of places.
The Poincare conjecture states (in simple terms) that:

Any closed smooth three dimensional space ('manifold') without boundary where all loops can be contracted to a point is 'homeomorphic' (essentially the same as) the three dimensional sphere (that is, the unit sphere in 4 dimensions).
The words "homologous" and "boundless" have little/nothing to do with it.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535394</id>
	<title>Re:Well, sure</title>
	<author>Obyron</author>
	<datestamp>1269008040000</datestamp>
	<modclass>Funny</modclass>
	<modscore>2</modscore>
	<htmltext>Look, if you're going to use the Quadratic Formula to complete the proof, we all might as well pack up and go home. It's like the cheat code for all these binomial questions</htmltext>
<tokenext>Look , if you 're going to use the Quadratic Formula to complete the proof , we all might as well pack up and go home .
It 's like the cheat code for all these binomial questions</tokentext>
<sentencetext>Look, if you're going to use the Quadratic Formula to complete the proof, we all might as well pack up and go home.
It's like the cheat code for all these binomial questions</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534832</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31548486</id>
	<title>Re:English Please</title>
	<author>Anonymous</author>
	<datestamp>1269086520000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I'm sorry to be petty, but your explanations of those mathematical terms is slightly misleading.<br>Manifold (technically a 2 dimensional manifold) - A shape that when you look at it really closely resembles a plane.  For example a sphere, a doughnut, 2 spheres, a plane.</p><p>Homeomorphisms must be continuous and have a continuous inverse (this is much stronger than just requiring continuity).</p><p>Simply Connected spaces must be connected as well as allowing loops to contract.  Connected meaning that you can't 'pull the space apart'.  For example two disjoint spheres are not connected.</p><p>Homology is a theory which makes it easier to tell if two spaces are not homeomorphic (I'm not going to attempt a explanation of homologous, try http://en.wikipedia.org/wiki/Homology\_theory )</p><p>Roughly speaking in topology, people like to classify 'up to homeomorphism', ie. to regard two spaces that are homeomorphic as being 'the same', so the conjecture tells us that if a space satisfies the right properties then it is 'the same as' a sphere.</p></htmltext>
<tokenext>I 'm sorry to be petty , but your explanations of those mathematical terms is slightly misleading.Manifold ( technically a 2 dimensional manifold ) - A shape that when you look at it really closely resembles a plane .
For example a sphere , a doughnut , 2 spheres , a plane.Homeomorphisms must be continuous and have a continuous inverse ( this is much stronger than just requiring continuity ) .Simply Connected spaces must be connected as well as allowing loops to contract .
Connected meaning that you ca n't 'pull the space apart' .
For example two disjoint spheres are not connected.Homology is a theory which makes it easier to tell if two spaces are not homeomorphic ( I 'm not going to attempt a explanation of homologous , try http : //en.wikipedia.org/wiki/Homology \ _theory ) Roughly speaking in topology , people like to classify 'up to homeomorphism ' , ie .
to regard two spaces that are homeomorphic as being 'the same ' , so the conjecture tells us that if a space satisfies the right properties then it is 'the same as ' a sphere .</tokentext>
<sentencetext>I'm sorry to be petty, but your explanations of those mathematical terms is slightly misleading.Manifold (technically a 2 dimensional manifold) - A shape that when you look at it really closely resembles a plane.
For example a sphere, a doughnut, 2 spheres, a plane.Homeomorphisms must be continuous and have a continuous inverse (this is much stronger than just requiring continuity).Simply Connected spaces must be connected as well as allowing loops to contract.
Connected meaning that you can't 'pull the space apart'.
For example two disjoint spheres are not connected.Homology is a theory which makes it easier to tell if two spaces are not homeomorphic (I'm not going to attempt a explanation of homologous, try http://en.wikipedia.org/wiki/Homology\_theory )Roughly speaking in topology, people like to classify 'up to homeomorphism', ie.
to regard two spaces that are homeomorphic as being 'the same', so the conjecture tells us that if a space satisfies the right properties then it is 'the same as' a sphere.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535562</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535826</id>
	<title>c08</title>
	<author>Anonymous</author>
	<datestamp>1269009300000</datestamp>
	<modclass>Troll</modclass>
	<modscore>-1</modscore>
	<htmltext><A HREF="http://goat.cx/" title="goat.cx" rel="nofollow">of business and 4ropaganda Fand</a> [goat.cx]</htmltext>
<tokenext>of business and 4ropaganda Fand [ goat.cx ]</tokentext>
<sentencetext>of business and 4ropaganda Fand [goat.cx]</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535562</id>
	<title>Re:English Please</title>
	<author>selven</author>
	<datestamp>1269008520000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>3</modscore>
	<htmltext><p>Manifold = a surface created by taking pieces of paper and warping them. For example, cylinder is a manifold since it can be formed by attaching the two opposite sides of the paper to each other. If you then attach the two circles at the ends of the cylinder, you get a torus (ie. donut).</p><p>Homeomorphic = there's a continuous function mapping points from one object to the other. This means that if two points are close to each other in the first object, they will be close together when the homeomorphism (the function) is used to map the points onto the second object. A square and the surface of a sphere, for example, are not homeomorphic since the square has edges and the sphere doesn't, so the mapping function has to jump somewhere, making it not continuous. Generally, two shapes are homeomorphic if you can deform one into the other (see animation <a href="http://en.wikipedia.org/wiki/Homeomorphism" title="wikipedia.org">here</a> [wikipedia.org])</p><p>Homologous = I don't know how that word got in there. It's not in the Wikipedia article.<br>Simply connected = Any line drawn on the manifold that starts and ends at the same point can be slowly shrunk down to one point without taking any part of it off the manifold. A torus is not simply connected, since you can draw a line going around the cylinder and there's no way to take it off.</p><p>As for implications, as far as I can see, it just tells us that lots of things can be deformed into spheres and gives us a simple test for determining if something can.</p></htmltext>
<tokenext>Manifold = a surface created by taking pieces of paper and warping them .
For example , cylinder is a manifold since it can be formed by attaching the two opposite sides of the paper to each other .
If you then attach the two circles at the ends of the cylinder , you get a torus ( ie .
donut ) .Homeomorphic = there 's a continuous function mapping points from one object to the other .
This means that if two points are close to each other in the first object , they will be close together when the homeomorphism ( the function ) is used to map the points onto the second object .
A square and the surface of a sphere , for example , are not homeomorphic since the square has edges and the sphere does n't , so the mapping function has to jump somewhere , making it not continuous .
Generally , two shapes are homeomorphic if you can deform one into the other ( see animation here [ wikipedia.org ] ) Homologous = I do n't know how that word got in there .
It 's not in the Wikipedia article.Simply connected = Any line drawn on the manifold that starts and ends at the same point can be slowly shrunk down to one point without taking any part of it off the manifold .
A torus is not simply connected , since you can draw a line going around the cylinder and there 's no way to take it off.As for implications , as far as I can see , it just tells us that lots of things can be deformed into spheres and gives us a simple test for determining if something can .</tokentext>
<sentencetext>Manifold = a surface created by taking pieces of paper and warping them.
For example, cylinder is a manifold since it can be formed by attaching the two opposite sides of the paper to each other.
If you then attach the two circles at the ends of the cylinder, you get a torus (ie.
donut).Homeomorphic = there's a continuous function mapping points from one object to the other.
This means that if two points are close to each other in the first object, they will be close together when the homeomorphism (the function) is used to map the points onto the second object.
A square and the surface of a sphere, for example, are not homeomorphic since the square has edges and the sphere doesn't, so the mapping function has to jump somewhere, making it not continuous.
Generally, two shapes are homeomorphic if you can deform one into the other (see animation here [wikipedia.org])Homologous = I don't know how that word got in there.
It's not in the Wikipedia article.Simply connected = Any line drawn on the manifold that starts and ends at the same point can be slowly shrunk down to one point without taking any part of it off the manifold.
A torus is not simply connected, since you can draw a line going around the cylinder and there's no way to take it off.As for implications, as far as I can see, it just tells us that lots of things can be deformed into spheres and gives us a simple test for determining if something can.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535100</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31541228</id>
	<title>Re:Summary of the Poincare conjecture is inaccurat</title>
	<author>Anonymous</author>
	<datestamp>1269025200000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>For your next trick, maybe you can learn to use the apostrophe correctly? Who's means WHO IS.</p></htmltext>
<tokenext>For your next trick , maybe you can learn to use the apostrophe correctly ?
Who 's means WHO IS .</tokentext>
<sentencetext>For your next trick, maybe you can learn to use the apostrophe correctly?
Who's means WHO IS.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31538562</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535898</id>
	<title>Re:English Please</title>
	<author>Anonymous</author>
	<datestamp>1269009540000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>4</modscore>
	<htmltext>I think the question is easier to understand if you knock everything down a dimension, because then it can actually be visualized.  Take the surface of any three-dimensional object that doesn't contain any holes (e.g., a cup, but NOT a coffee mug with a handle).  Can the surface be stretched/distorted to be shaped into a sphere?  The answer is fairly obviously yes.  But is this also true for four-dimensional objects?  Stop trying to visualize it; you can't.  You have to rely on the math instead.  But that, I believe, is the question.</htmltext>
<tokenext>I think the question is easier to understand if you knock everything down a dimension , because then it can actually be visualized .
Take the surface of any three-dimensional object that does n't contain any holes ( e.g. , a cup , but NOT a coffee mug with a handle ) .
Can the surface be stretched/distorted to be shaped into a sphere ?
The answer is fairly obviously yes .
But is this also true for four-dimensional objects ?
Stop trying to visualize it ; you ca n't .
You have to rely on the math instead .
But that , I believe , is the question .</tokentext>
<sentencetext>I think the question is easier to understand if you knock everything down a dimension, because then it can actually be visualized.
Take the surface of any three-dimensional object that doesn't contain any holes (e.g., a cup, but NOT a coffee mug with a handle).
Can the surface be stretched/distorted to be shaped into a sphere?
The answer is fairly obviously yes.
But is this also true for four-dimensional objects?
Stop trying to visualize it; you can't.
You have to rely on the math instead.
But that, I believe, is the question.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535100</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31538144</id>
	<title>Re:So will he accept?</title>
	<author>mapkinase</author>
	<datestamp>1269015240000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Obviously, the question will he or will not cannot be answered this minute.</p><p>What could be answered is the question of what will be more surprising: if he will accept or if he will not.</p><p>I personally think that him accepting it would be more surprising for me.</p></htmltext>
<tokenext>Obviously , the question will he or will not can not be answered this minute.What could be answered is the question of what will be more surprising : if he will accept or if he will not.I personally think that him accepting it would be more surprising for me .</tokentext>
<sentencetext>Obviously, the question will he or will not cannot be answered this minute.What could be answered is the question of what will be more surprising: if he will accept or if he will not.I personally think that him accepting it would be more surprising for me.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535082</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534864</id>
	<title>Some background</title>
	<author>ThoughtMonster</author>
	<datestamp>1269005040000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>5</modscore>
	<htmltext>For those just in, here's an <a href="http://www.newyorker.com/archive/2006/08/28/060828fa\_fact2?printable=true" title="newyorker.com" rel="nofollow">article</a> [newyorker.com] covering Perelman and his theorem.<br> <br> This <a href="http://en.wikipedia.org/wiki/Manifold\_Destiny" title="wikipedia.org" rel="nofollow">wikipedia entry</a> [wikipedia.org] covers some controversies following the article.</htmltext>
<tokenext>For those just in , here 's an article [ newyorker.com ] covering Perelman and his theorem .
This wikipedia entry [ wikipedia.org ] covers some controversies following the article .</tokentext>
<sentencetext>For those just in, here's an article [newyorker.com] covering Perelman and his theorem.
This wikipedia entry [wikipedia.org] covers some controversies following the article.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535558</id>
	<title>Re:English Please</title>
	<author>gbutler69</author>
	<datestamp>1269008460000</datestamp>
	<modclass>Troll</modclass>
	<modscore>-1</modscore>
	<htmltext>They wanted to prove if a Man Homo can be made equivalent to a She-Male! In other words, are all Man Homos the same as a She-Male? This proves, beyond a shadow of a doubt then Man Homos cannot be reduces to Altar Boys and so are in fact She-Males.</htmltext>
<tokenext>They wanted to prove if a Man Homo can be made equivalent to a She-Male !
In other words , are all Man Homos the same as a She-Male ?
This proves , beyond a shadow of a doubt then Man Homos can not be reduces to Altar Boys and so are in fact She-Males .</tokentext>
<sentencetext>They wanted to prove if a Man Homo can be made equivalent to a She-Male!
In other words, are all Man Homos the same as a She-Male?
This proves, beyond a shadow of a doubt then Man Homos cannot be reduces to Altar Boys and so are in fact She-Males.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535100</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534980</id>
	<title>What I would like to know is</title>
	<author>Anonymous</author>
	<datestamp>1269006120000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>what was PRISM's contribution on the discovery.</p><p>(obscure?)</p></htmltext>
<tokenext>what was PRISM 's contribution on the discovery. ( obscure ?
)</tokentext>
<sentencetext>what was PRISM's contribution on the discovery.(obscure?
)</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31623954</id>
	<title>Re:Bread and Cheese</title>
	<author>Anonymous</author>
	<datestamp>1269605520000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><div class="quote"><p>I hope Perelman will be able to afford better food than bread and cheese now.</p></div><p>I think he is more into mushrooms, actually.</p></div>
	</htmltext>
<tokenext>I hope Perelman will be able to afford better food than bread and cheese now.I think he is more into mushrooms , actually .</tokentext>
<sentencetext>I hope Perelman will be able to afford better food than bread and cheese now.I think he is more into mushrooms, actually.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534944</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535066</id>
	<title>Whatever...</title>
	<author>Bentov</author>
	<datestamp>1269006780000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>2</modscore>
	<htmltext><p>It's not like wants the money or anything.  He should at least take it and form a scholarship in his name.  Jeez, the man is like a<nobr> <wbr></nobr>./er, he lives with his mother.</p></htmltext>
<tokenext>It 's not like wants the money or anything .
He should at least take it and form a scholarship in his name .
Jeez , the man is like a ./er , he lives with his mother .</tokentext>
<sentencetext>It's not like wants the money or anything.
He should at least take it and form a scholarship in his name.
Jeez, the man is like a ./er, he lives with his mother.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31538304</id>
	<title>Re:English Please</title>
	<author>darkmeridian</author>
	<datestamp>1269015660000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>That is the problem that was solved. The crazy thing is that it was proven for all dimensions other than ours in 1982. It took that long to prove the conjecture for the three-dimensional world that we live in. That's wild, no?</p></htmltext>
<tokenext>That is the problem that was solved .
The crazy thing is that it was proven for all dimensions other than ours in 1982 .
It took that long to prove the conjecture for the three-dimensional world that we live in .
That 's wild , no ?</tokentext>
<sentencetext>That is the problem that was solved.
The crazy thing is that it was proven for all dimensions other than ours in 1982.
It took that long to prove the conjecture for the three-dimensional world that we live in.
That's wild, no?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535898</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31540428</id>
	<title>Come again!</title>
	<author>Kreeben</author>
	<datestamp>1269022200000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext>"...is there a 3-manifold not homologous to the 3-sphere in which any loop can be gradually shrunk to a single point?"
<br>
There's that whoosing sound again. I hear it once in a while.</htmltext>
<tokenext>" ...is there a 3-manifold not homologous to the 3-sphere in which any loop can be gradually shrunk to a single point ?
" There 's that whoosing sound again .
I hear it once in a while .</tokentext>
<sentencetext>"...is there a 3-manifold not homologous to the 3-sphere in which any loop can be gradually shrunk to a single point?
"

There's that whoosing sound again.
I hear it once in a while.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31578566</id>
	<title>He turned it down</title>
	<author>Frans Faase</author>
	<datestamp>1269269820000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>According to <a href="http://news.ninemsn.com.au/world/1030927/worlds-smartest-man-turns-down-1-1m" title="ninemsn.com.au">this news announcement</a> [ninemsn.com.au] Perelman turned down the price offer saying "he had all he wanted." and that "he is not interested in money or fame."</p></htmltext>
<tokenext>According to this news announcement [ ninemsn.com.au ] Perelman turned down the price offer saying " he had all he wanted .
" and that " he is not interested in money or fame .
"</tokentext>
<sentencetext>According to this news announcement [ninemsn.com.au] Perelman turned down the price offer saying "he had all he wanted.
" and that "he is not interested in money or fame.
"</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534798</id>
	<title>what about...</title>
	<author>Adolf Hitroll</author>
	<datestamp>1269004440000</datestamp>
	<modclass>Funny</modclass>
	<modscore>-1</modscore>
	<htmltext><p>...deter-mining the internal squared volume of a <a href="http://goatse.fr/" title="goatse.fr" rel="nofollow">spherical cavity</a> [goatse.fr]?</p></htmltext>
<tokenext>...deter-mining the internal squared volume of a spherical cavity [ goatse.fr ] ?</tokentext>
<sentencetext>...deter-mining the internal squared volume of a spherical cavity [goatse.fr]?</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31540062</id>
	<title>Re:English Please</title>
	<author>TeknoHog</author>
	<datestamp>1269020940000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p><div class="quote"><p>Stop trying to visualize it; you can't.</p></div><p>
But some people can visualize such things, you insensitive 3-clod!
</p><p>
Seriously though, mathematical proofs cannot rely on a human's ability to visualize. Even the version in our dimensionality must be proved by doing the math.
</p></div>
	</htmltext>
<tokenext>Stop trying to visualize it ; you ca n't .
But some people can visualize such things , you insensitive 3-clod !
Seriously though , mathematical proofs can not rely on a human 's ability to visualize .
Even the version in our dimensionality must be proved by doing the math .</tokentext>
<sentencetext>Stop trying to visualize it; you can't.
But some people can visualize such things, you insensitive 3-clod!
Seriously though, mathematical proofs cannot rely on a human's ability to visualize.
Even the version in our dimensionality must be proved by doing the math.

	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535898</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31547336</id>
	<title>Re:English Please</title>
	<author>daver00</author>
	<datestamp>1269019980000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Unfortunately, there is absolutely no way to describe this stuff in "human" terms, you really just have to get your head around the concepts and even then you are likely to have no idea what this stuff is on about. Mathematicians could spend their whole career not understanding this stuff, easily.</p><p>I'll try as best I can, but I can barely get my head around the most basic concepts here, so here I go: In topology we don't care so much about what you normally think of as mathematics, topology I guess you could say is a study of bulk mathematical structure in some sense, highly abstracted notions of geometric structure in this case, but topology goes beyond geometry and it is wrong to think of it as simply the study of manifolds and such. A manifold, the kind they are talking about, is a 'locally smooth surface', that means if you have the surface of a 3d object and zoom into a point anywhere, the region around the point will eventually begin to look 'flat', this means if you move around on the 3d surface, you can move in 2 dimensions only and encounter nothing discontinuous about the surface. Of course this extends to higher dimensions too. If you think of a map of the earth as a flat 2d grid, then the sphere that is the earth is a 2-manifold. Here we have embedded a 2-dimensional plane into a 3-dimensional space. If you then think about the general plane and how it stretches out infinitely, we can actually 'compactify' that infinite plane into a finite manifold by 'mapping' each point on the plane onto a point on the surface of a sphere, we and add one single point we can call 'infinity' and the once infinite plane is now 'compact'. The infinite plane has now become finite (sort of) by embedding it into higher dimensions.</p><p>In topology a homeomorphism between topological spaces (a manifold is a topological space) just means we can find a perfectly reversible function which maps every point from one to every point in the other exactly one way, it means the two spaces will have the same structure and all theorems proven for one are true for the other. This is where the famous saying "the coffee cup is no different to the donut" comes from. If two topological spaces are homeomorphic, we can find some function which morphs one into the other, and hence they are simply the same thing. In terms of manifolds this is like saying we can warp, bend, twist and pass the manifold through itself, but never fold or cut, until one matches the shape of the other. So a donut can be made into a coffee cup, but never a sphere.</p><p>The Poincarre conjecture is a way of characterizing a 3-manifold as homeomorphic to the 3-sphere. So we have stepped up a dimension from the flat earth/spherical earth example above. Now our basic manifold is locally flat in 3 dimensions, so locally it might look like 3-dimensional space while it globally exists in 4-dimensional space. If you walked around on the surface of a 3-sphere, you could move in 3 directions. In the case of the 2-sphere, we can characterize homeomorphic manifolds by the fact that if you take any circle on the surface of a sphere, you can contract it down to a point on the surface. This is not true for donuts, as some circles cannot contract down to a point, hence the sphere is not homeomorphic to the donut. So we then have a simple way of describing which manifolds are homeomorphic to the 2-sphere. Poincarre conjectured that this was possible for the 3-sphere.</p><p>The proof, I can give no insight on, and I imagine most of the worlds best mathematicians would struggle to follow it. It took years to verify this proof, years of work and teams of mathematicians.</p><p>As for usefulness, you need to step out of the structured world of classical applied mathematics and think in abstract ways. At face value there is very little of anything useful about this proof, other than gaining deeper insight into the geometry of 4 dimensional space. Topology is used in spatial databasing, image processing, protein folding/knot theory, lots and lots of physics (string theory especially) and ma</p></htmltext>
<tokenext>Unfortunately , there is absolutely no way to describe this stuff in " human " terms , you really just have to get your head around the concepts and even then you are likely to have no idea what this stuff is on about .
Mathematicians could spend their whole career not understanding this stuff , easily.I 'll try as best I can , but I can barely get my head around the most basic concepts here , so here I go : In topology we do n't care so much about what you normally think of as mathematics , topology I guess you could say is a study of bulk mathematical structure in some sense , highly abstracted notions of geometric structure in this case , but topology goes beyond geometry and it is wrong to think of it as simply the study of manifolds and such .
A manifold , the kind they are talking about , is a 'locally smooth surface ' , that means if you have the surface of a 3d object and zoom into a point anywhere , the region around the point will eventually begin to look 'flat ' , this means if you move around on the 3d surface , you can move in 2 dimensions only and encounter nothing discontinuous about the surface .
Of course this extends to higher dimensions too .
If you think of a map of the earth as a flat 2d grid , then the sphere that is the earth is a 2-manifold .
Here we have embedded a 2-dimensional plane into a 3-dimensional space .
If you then think about the general plane and how it stretches out infinitely , we can actually 'compactify ' that infinite plane into a finite manifold by 'mapping ' each point on the plane onto a point on the surface of a sphere , we and add one single point we can call 'infinity ' and the once infinite plane is now 'compact' .
The infinite plane has now become finite ( sort of ) by embedding it into higher dimensions.In topology a homeomorphism between topological spaces ( a manifold is a topological space ) just means we can find a perfectly reversible function which maps every point from one to every point in the other exactly one way , it means the two spaces will have the same structure and all theorems proven for one are true for the other .
This is where the famous saying " the coffee cup is no different to the donut " comes from .
If two topological spaces are homeomorphic , we can find some function which morphs one into the other , and hence they are simply the same thing .
In terms of manifolds this is like saying we can warp , bend , twist and pass the manifold through itself , but never fold or cut , until one matches the shape of the other .
So a donut can be made into a coffee cup , but never a sphere.The Poincarre conjecture is a way of characterizing a 3-manifold as homeomorphic to the 3-sphere .
So we have stepped up a dimension from the flat earth/spherical earth example above .
Now our basic manifold is locally flat in 3 dimensions , so locally it might look like 3-dimensional space while it globally exists in 4-dimensional space .
If you walked around on the surface of a 3-sphere , you could move in 3 directions .
In the case of the 2-sphere , we can characterize homeomorphic manifolds by the fact that if you take any circle on the surface of a sphere , you can contract it down to a point on the surface .
This is not true for donuts , as some circles can not contract down to a point , hence the sphere is not homeomorphic to the donut .
So we then have a simple way of describing which manifolds are homeomorphic to the 2-sphere .
Poincarre conjectured that this was possible for the 3-sphere.The proof , I can give no insight on , and I imagine most of the worlds best mathematicians would struggle to follow it .
It took years to verify this proof , years of work and teams of mathematicians.As for usefulness , you need to step out of the structured world of classical applied mathematics and think in abstract ways .
At face value there is very little of anything useful about this proof , other than gaining deeper insight into the geometry of 4 dimensional space .
Topology is used in spatial databasing , image processing , protein folding/knot theory , lots and lots of physics ( string theory especially ) and ma</tokentext>
<sentencetext>Unfortunately, there is absolutely no way to describe this stuff in "human" terms, you really just have to get your head around the concepts and even then you are likely to have no idea what this stuff is on about.
Mathematicians could spend their whole career not understanding this stuff, easily.I'll try as best I can, but I can barely get my head around the most basic concepts here, so here I go: In topology we don't care so much about what you normally think of as mathematics, topology I guess you could say is a study of bulk mathematical structure in some sense, highly abstracted notions of geometric structure in this case, but topology goes beyond geometry and it is wrong to think of it as simply the study of manifolds and such.
A manifold, the kind they are talking about, is a 'locally smooth surface', that means if you have the surface of a 3d object and zoom into a point anywhere, the region around the point will eventually begin to look 'flat', this means if you move around on the 3d surface, you can move in 2 dimensions only and encounter nothing discontinuous about the surface.
Of course this extends to higher dimensions too.
If you think of a map of the earth as a flat 2d grid, then the sphere that is the earth is a 2-manifold.
Here we have embedded a 2-dimensional plane into a 3-dimensional space.
If you then think about the general plane and how it stretches out infinitely, we can actually 'compactify' that infinite plane into a finite manifold by 'mapping' each point on the plane onto a point on the surface of a sphere, we and add one single point we can call 'infinity' and the once infinite plane is now 'compact'.
The infinite plane has now become finite (sort of) by embedding it into higher dimensions.In topology a homeomorphism between topological spaces (a manifold is a topological space) just means we can find a perfectly reversible function which maps every point from one to every point in the other exactly one way, it means the two spaces will have the same structure and all theorems proven for one are true for the other.
This is where the famous saying "the coffee cup is no different to the donut" comes from.
If two topological spaces are homeomorphic, we can find some function which morphs one into the other, and hence they are simply the same thing.
In terms of manifolds this is like saying we can warp, bend, twist and pass the manifold through itself, but never fold or cut, until one matches the shape of the other.
So a donut can be made into a coffee cup, but never a sphere.The Poincarre conjecture is a way of characterizing a 3-manifold as homeomorphic to the 3-sphere.
So we have stepped up a dimension from the flat earth/spherical earth example above.
Now our basic manifold is locally flat in 3 dimensions, so locally it might look like 3-dimensional space while it globally exists in 4-dimensional space.
If you walked around on the surface of a 3-sphere, you could move in 3 directions.
In the case of the 2-sphere, we can characterize homeomorphic manifolds by the fact that if you take any circle on the surface of a sphere, you can contract it down to a point on the surface.
This is not true for donuts, as some circles cannot contract down to a point, hence the sphere is not homeomorphic to the donut.
So we then have a simple way of describing which manifolds are homeomorphic to the 2-sphere.
Poincarre conjectured that this was possible for the 3-sphere.The proof, I can give no insight on, and I imagine most of the worlds best mathematicians would struggle to follow it.
It took years to verify this proof, years of work and teams of mathematicians.As for usefulness, you need to step out of the structured world of classical applied mathematics and think in abstract ways.
At face value there is very little of anything useful about this proof, other than gaining deeper insight into the geometry of 4 dimensional space.
Topology is used in spatial databasing, image processing, protein folding/knot theory, lots and lots of physics (string theory especially) and ma</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535100</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534944</id>
	<title>Bread and Cheese</title>
	<author>Anonymous</author>
	<datestamp>1269005880000</datestamp>
	<modclass>Funny</modclass>
	<modscore>2</modscore>
	<htmltext>I hope Perelman will be able to afford better food than bread and cheese now.</htmltext>
<tokenext>I hope Perelman will be able to afford better food than bread and cheese now .</tokentext>
<sentencetext>I hope Perelman will be able to afford better food than bread and cheese now.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535092</id>
	<title>Re:what about...</title>
	<author>Anonymous</author>
	<datestamp>1269006900000</datestamp>
	<modclass>Troll</modclass>
	<modscore>-1</modscore>
	<htmltext><p><div class="quote"><p>...deter-mining the internal squared volume of a <a href="http://goatse.fr/" title="goatse.fr" rel="nofollow">spherical cavity</a> [goatse.fr]?</p></div><p>The correct illustration you are trying to present is <a href="http://lm.loldongs.eu/" title="loldongs.eu" rel="nofollow">this</a> [loldongs.eu]</p></div>
	</htmltext>
<tokenext>...deter-mining the internal squared volume of a spherical cavity [ goatse.fr ] ? The correct illustration you are trying to present is this [ loldongs.eu ]</tokentext>
<sentencetext>...deter-mining the internal squared volume of a spherical cavity [goatse.fr]?The correct illustration you are trying to present is this [loldongs.eu]
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534798</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31538184</id>
	<title>you inseNsitive clod!</title>
	<author>Anonymous</author>
	<datestamp>1269015300000</datestamp>
	<modclass>Offtopic</modclass>
	<modscore>-1</modscore>
	<htmltext><A HREF="http://goat.cx/" title="goat.cx" rel="nofollow">The 4roject iS in subscribers. Please</a> [goat.cx]</htmltext>
<tokenext>The 4roject iS in subscribers .
Please [ goat.cx ]</tokentext>
<sentencetext>The 4roject iS in subscribers.
Please [goat.cx]</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535526</id>
	<title>Re:English Please</title>
	<author>Obyron</author>
	<datestamp>1269008340000</datestamp>
	<modclass>Offtopic</modclass>
	<modscore>0</modscore>
	<htmltext>Maybe Read the last sentence of TFS?</htmltext>
<tokenext>Maybe Read the last sentence of TFS ?</tokentext>
<sentencetext>Maybe Read the last sentence of TFS?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535100</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535502</id>
	<title>Re:So will he accept?</title>
	<author>Obyron</author>
	<datestamp>1269008280000</datestamp>
	<modclass>Interestin</modclass>
	<modscore>5</modscore>
	<htmltext>I can't take credit for finding this. Another Slashdotter was kind enough to link it the last time Perelman came up, but I found this to be very enlightening and illustrative of Perelman's personality as well as the whole Yau controversy. It's an article from the New Yorker co-written by Sylvia Nasar, who wrote the biography of John Nash, A Beautiful Mind. It contains what was at the time the only interview with Grigori Perelman, but I'm not sure if that's still true.<br> <br>

<a href="http://www.newyorker.com/archive/2006/08/28/060828fa\_fact2" title="newyorker.com">Annals of Mathematic: Manifold Destiny</a> [newyorker.com]</htmltext>
<tokenext>I ca n't take credit for finding this .
Another Slashdotter was kind enough to link it the last time Perelman came up , but I found this to be very enlightening and illustrative of Perelman 's personality as well as the whole Yau controversy .
It 's an article from the New Yorker co-written by Sylvia Nasar , who wrote the biography of John Nash , A Beautiful Mind .
It contains what was at the time the only interview with Grigori Perelman , but I 'm not sure if that 's still true .
Annals of Mathematic : Manifold Destiny [ newyorker.com ]</tokentext>
<sentencetext>I can't take credit for finding this.
Another Slashdotter was kind enough to link it the last time Perelman came up, but I found this to be very enlightening and illustrative of Perelman's personality as well as the whole Yau controversy.
It's an article from the New Yorker co-written by Sylvia Nasar, who wrote the biography of John Nash, A Beautiful Mind.
It contains what was at the time the only interview with Grigori Perelman, but I'm not sure if that's still true.
Annals of Mathematic: Manifold Destiny [newyorker.com]</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535082</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31545408</id>
	<title>Re:So will he accept?</title>
	<author>Anonymous</author>
	<datestamp>1269000840000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p><div class="quote"><p> <i>
It contains what was at the time the only interview with Grigori Perelman, but I'm not sure if that's still true.
</i></p> </div><p>No, he was also quoted giving a favourable review to <a href="http://www.datingforengineers.com/About\_Us.html" title="datingforengineers.com" rel="nofollow">"Dating for Engineers"</a> [datingforengineers.com].</p></div>
	</htmltext>
<tokenext>It contains what was at the time the only interview with Grigori Perelman , but I 'm not sure if that 's still true .
No , he was also quoted giving a favourable review to " Dating for Engineers " [ datingforengineers.com ] .</tokentext>
<sentencetext> 
It contains what was at the time the only interview with Grigori Perelman, but I'm not sure if that's still true.
No, he was also quoted giving a favourable review to "Dating for Engineers" [datingforengineers.com].
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535502</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534832</id>
	<title>Well, sure</title>
	<author>Anonymous</author>
	<datestamp>1269004860000</datestamp>
	<modclass>Funny</modclass>
	<modscore>2</modscore>
	<htmltext><p>Look, if you're going to use Ricci Flow to complete the proof, we all might as well pack up and go home. It's like the cheat code for all these manifold questions.</p></htmltext>
<tokenext>Look , if you 're going to use Ricci Flow to complete the proof , we all might as well pack up and go home .
It 's like the cheat code for all these manifold questions .</tokentext>
<sentencetext>Look, if you're going to use Ricci Flow to complete the proof, we all might as well pack up and go home.
It's like the cheat code for all these manifold questions.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534956</id>
	<title>What does he win?</title>
	<author>name\_already\_taken</author>
	<datestamp>1269006000000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>2</modscore>
	<htmltext><p>Since neither the summary nor either article tell you what the guy wins, (almost like it's a secret), here's a <a href="http://en.wikipedia.org/wiki/Millennium\_Prize\_Problems" title="wikipedia.org">wikipedia entry</a> [wikipedia.org] that does.</p><p>It's a million dollars.</p></htmltext>
<tokenext>Since neither the summary nor either article tell you what the guy wins , ( almost like it 's a secret ) , here 's a wikipedia entry [ wikipedia.org ] that does.It 's a million dollars .</tokentext>
<sentencetext>Since neither the summary nor either article tell you what the guy wins, (almost like it's a secret), here's a wikipedia entry [wikipedia.org] that does.It's a million dollars.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31536104</id>
	<title>Who the fuck cares?</title>
	<author>malp</author>
	<datestamp>1269010080000</datestamp>
	<modclass>Funny</modclass>
	<modscore>2</modscore>
	<htmltext><p>The<nobr> <wbr></nobr>/. eds could make this article 10x more relevant to most people by titling it 'Man wins million dollar mental masturbation prize' or by explaining the practical applications of this discovery. Instead the summary is a list of techno jargon that'd put Star Trek to shame with no mention of the $$ prize nor details of the winner. Who is this guy? Why did someone give him so much money for solving for x? Can I too win cash money for balls? If not, can I out source next year's winner to india and take a cut of the prize?</p><p>Anyway, this article's a lot better:<a href="http://www.newscientist.com/blogs/culturelab/2009/11/grigori-perelman-the-genius-in-hiding.php" title="newscientist.com" rel="nofollow">http://www.newscientist.com/blogs/culturelab/2009/11/grigori-perelman-the-genius-in-hiding.php</a> [newscientist.com]</p></htmltext>
<tokenext>The / .
eds could make this article 10x more relevant to most people by titling it 'Man wins million dollar mental masturbation prize ' or by explaining the practical applications of this discovery .
Instead the summary is a list of techno jargon that 'd put Star Trek to shame with no mention of the $ $ prize nor details of the winner .
Who is this guy ?
Why did someone give him so much money for solving for x ?
Can I too win cash money for balls ?
If not , can I out source next year 's winner to india and take a cut of the prize ? Anyway , this article 's a lot better : http : //www.newscientist.com/blogs/culturelab/2009/11/grigori-perelman-the-genius-in-hiding.php [ newscientist.com ]</tokentext>
<sentencetext>The /.
eds could make this article 10x more relevant to most people by titling it 'Man wins million dollar mental masturbation prize' or by explaining the practical applications of this discovery.
Instead the summary is a list of techno jargon that'd put Star Trek to shame with no mention of the $$ prize nor details of the winner.
Who is this guy?
Why did someone give him so much money for solving for x?
Can I too win cash money for balls?
If not, can I out source next year's winner to india and take a cut of the prize?Anyway, this article's a lot better:http://www.newscientist.com/blogs/culturelab/2009/11/grigori-perelman-the-genius-in-hiding.php [newscientist.com]</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31546674</id>
	<title>A triumph for Perelman</title>
	<author>amightywind</author>
	<datestamp>1269011760000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>A triumph for Perelman. I hope he accepts the prize and rejoins the mathematical world. It is a little surprising that Hamilton did did share it as the Ricci flow was a crucial idea. But there is no doubting that Perelman did the heavy lifting.</p><p>For those of you who dismiss this result is of little worth, you will not likely see a comparable achievement of the human mind for 50 years.</p></htmltext>
<tokenext>A triumph for Perelman .
I hope he accepts the prize and rejoins the mathematical world .
It is a little surprising that Hamilton did did share it as the Ricci flow was a crucial idea .
But there is no doubting that Perelman did the heavy lifting.For those of you who dismiss this result is of little worth , you will not likely see a comparable achievement of the human mind for 50 years .</tokentext>
<sentencetext>A triumph for Perelman.
I hope he accepts the prize and rejoins the mathematical world.
It is a little surprising that Hamilton did did share it as the Ricci flow was a crucial idea.
But there is no doubting that Perelman did the heavy lifting.For those of you who dismiss this result is of little worth, you will not likely see a comparable achievement of the human mind for 50 years.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31539442</id>
	<title>Re:Who the fuck cares?</title>
	<author>mariuszbi</author>
	<datestamp>1269018900000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>2</modscore>
	<htmltext>The prize is 1 million USD and Perelman is this guy in the picture

<a href="http://englishrussia.com/index.php/2007/06/15/perelman-in-a-subway/" title="englishrussia.com" rel="nofollow">http://englishrussia.com/index.php/2007/06/15/perelman-in-a-subway/</a> [englishrussia.com]</htmltext>
<tokenext>The prize is 1 million USD and Perelman is this guy in the picture http : //englishrussia.com/index.php/2007/06/15/perelman-in-a-subway/ [ englishrussia.com ]</tokentext>
<sentencetext>The prize is 1 million USD and Perelman is this guy in the picture

http://englishrussia.com/index.php/2007/06/15/perelman-in-a-subway/ [englishrussia.com]</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31538250</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535114</id>
	<title>Layman's terms?</title>
	<author>Wizard Drongo</author>
	<datestamp>1269006960000</datestamp>
	<modclass>Flamebait</modclass>
	<modscore>-1</modscore>
	<htmltext><p>Fuck layman's terms, do you speak English??!</p></htmltext>
<tokenext>Fuck layman 's terms , do you speak English ? ?
!</tokentext>
<sentencetext>Fuck layman's terms, do you speak English??
!</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534962</id>
	<title>Great news</title>
	<author>Anonymous</author>
	<datestamp>1269006000000</datestamp>
	<modclass>Informativ</modclass>
	<modscore>5</modscore>
	<htmltext>I am very happy that they have awarded the price only to him, although he did meet the requirement that the proof should be published in a peer-reviewed journal. I am very happy that they did not included those two Chinese guys who did write down the proof (about 260 pages) and claimed that they had proven the conjecture. Perelman was very upset by this especially that other mathematics did not raise their voice. I hope that Perelman will accept the price. He said (some years ago) that he would only decide when the offer was made, if he would except the price or not.</htmltext>
<tokenext>I am very happy that they have awarded the price only to him , although he did meet the requirement that the proof should be published in a peer-reviewed journal .
I am very happy that they did not included those two Chinese guys who did write down the proof ( about 260 pages ) and claimed that they had proven the conjecture .
Perelman was very upset by this especially that other mathematics did not raise their voice .
I hope that Perelman will accept the price .
He said ( some years ago ) that he would only decide when the offer was made , if he would except the price or not .</tokentext>
<sentencetext>I am very happy that they have awarded the price only to him, although he did meet the requirement that the proof should be published in a peer-reviewed journal.
I am very happy that they did not included those two Chinese guys who did write down the proof (about 260 pages) and claimed that they had proven the conjecture.
Perelman was very upset by this especially that other mathematics did not raise their voice.
I hope that Perelman will accept the price.
He said (some years ago) that he would only decide when the offer was made, if he would except the price or not.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31548444</id>
	<title>Re:Layman's terms?</title>
	<author>Wizard Drongo</author>
	<datestamp>1269085680000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>Apparently people didn't watch "Event Horizon".<br>And they call themselves nerds!</p></htmltext>
<tokenext>Apparently people did n't watch " Event Horizon " .And they call themselves nerds !</tokentext>
<sentencetext>Apparently people didn't watch "Event Horizon".And they call themselves nerds!</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535114</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31546820</id>
	<title>Re:Great news</title>
	<author>Anonymous</author>
	<datestamp>1269013080000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Accept.  Just saying.</p></htmltext>
<tokenext>Accept .
Just saying .</tokentext>
<sentencetext>Accept.
Just saying.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534962</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535548</id>
	<title>Linux  Windows</title>
	<author>Anonymous</author>
	<datestamp>1269008460000</datestamp>
	<modclass>Troll</modclass>
	<modscore>-1</modscore>
	<htmltext><p>I bet this was calculated using Linux. If he tried to use Windows to work out the answer, all of the DRM code would have gotten in the way, and the sums would have been in propriatery Excel format and no good scientists (who use GIMP) would have been able to read them.</p></htmltext>
<tokenext>I bet this was calculated using Linux .
If he tried to use Windows to work out the answer , all of the DRM code would have gotten in the way , and the sums would have been in propriatery Excel format and no good scientists ( who use GIMP ) would have been able to read them .</tokentext>
<sentencetext>I bet this was calculated using Linux.
If he tried to use Windows to work out the answer, all of the DRM code would have gotten in the way, and the sums would have been in propriatery Excel format and no good scientists (who use GIMP) would have been able to read them.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534798</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31536092</id>
	<title>Re:English Please</title>
	<author>Kjella</author>
	<datestamp>1269010080000</datestamp>
	<modclass>Flamebait</modclass>
	<modscore>-1</modscore>
	<htmltext><p><div class="quote"><p>i'll read the wiki page too, but i'm hoping someone here will take a crack at explaining in it plain English.</p></div><p>Some math doohickey is similar to some other math doohickey. Seriously, how much more "in plain English" than the linked wiki can you get without losing the point of trying? The only thing you end up with are misunderstandings like the other guy modded up replying to your post saying "As for implications, as far as I can see, it just tells us that lots of things can be deformed into spheres" even though the 3-sphere has about as little to with regular spheres as a sphere has to do with circles.</p></div>
	</htmltext>
<tokenext>i 'll read the wiki page too , but i 'm hoping someone here will take a crack at explaining in it plain English.Some math doohickey is similar to some other math doohickey .
Seriously , how much more " in plain English " than the linked wiki can you get without losing the point of trying ?
The only thing you end up with are misunderstandings like the other guy modded up replying to your post saying " As for implications , as far as I can see , it just tells us that lots of things can be deformed into spheres " even though the 3-sphere has about as little to with regular spheres as a sphere has to do with circles .</tokentext>
<sentencetext>i'll read the wiki page too, but i'm hoping someone here will take a crack at explaining in it plain English.Some math doohickey is similar to some other math doohickey.
Seriously, how much more "in plain English" than the linked wiki can you get without losing the point of trying?
The only thing you end up with are misunderstandings like the other guy modded up replying to your post saying "As for implications, as far as I can see, it just tells us that lots of things can be deformed into spheres" even though the 3-sphere has about as little to with regular spheres as a sphere has to do with circles.
	</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535100</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534818</id>
	<title>I'm amazed.</title>
	<author>Anonymous</author>
	<datestamp>1269004620000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>I was thinking about the same subject during American Idiot, err Idle,  Idol.</p></htmltext>
<tokenext>I was thinking about the same subject during American Idiot , err Idle , Idol .</tokentext>
<sentencetext>I was thinking about the same subject during American Idiot, err Idle,  Idol.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31544226</id>
	<title>Where's Obama's?</title>
	<author>Anonymous</author>
	<datestamp>1268994900000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>Why hasn't Obama got this prize?</p><p>Damn Republicans.</p></htmltext>
<tokenext>Why has n't Obama got this prize ? Damn Republicans .</tokentext>
<sentencetext>Why hasn't Obama got this prize?Damn Republicans.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535100</id>
	<title>English Please</title>
	<author>Anonymous</author>
	<datestamp>1269006900000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>3</modscore>
	<htmltext><p>Could someone give us non-math geeks an explaination of this that does not include the following words: manifold homologous homeomorphic?</p><p>i'll read the wiki page too, but i'm hoping someone here will take a crack at explaining in it plain English.</p><p>Also: What does this mean?  What are the applications?  Not that it has to have any to be interesting.</p></htmltext>
<tokenext>Could someone give us non-math geeks an explaination of this that does not include the following words : manifold homologous homeomorphic ? i 'll read the wiki page too , but i 'm hoping someone here will take a crack at explaining in it plain English.Also : What does this mean ?
What are the applications ?
Not that it has to have any to be interesting .</tokentext>
<sentencetext>Could someone give us non-math geeks an explaination of this that does not include the following words: manifold homologous homeomorphic?i'll read the wiki page too, but i'm hoping someone here will take a crack at explaining in it plain English.Also: What does this mean?
What are the applications?
Not that it has to have any to be interesting.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31536276</id>
	<title>I would now like him to demonstrate...</title>
	<author>Anonymous</author>
	<datestamp>1269010620000</datestamp>
	<modclass>Flamebait</modclass>
	<modscore>-1</modscore>
	<htmltext><p><nobr> <wbr></nobr>... how much wood a woodchuck could chuck if a woodchuck could chuck wood.</p><p>The results would be about equally valuable.</p></htmltext>
<tokenext>... how much wood a woodchuck could chuck if a woodchuck could chuck wood.The results would be about equally valuable .</tokentext>
<sentencetext> ... how much wood a woodchuck could chuck if a woodchuck could chuck wood.The results would be about equally valuable.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31538250</id>
	<title>Re:Who the fuck cares?</title>
	<author>pjt33</author>
	<datestamp>1269015540000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>What are "most people" doing on<nobr> <wbr></nobr>/.? The people who do care already know how much the CMI prizes are and who Perelman is.</p></htmltext>
<tokenext>What are " most people " doing on /. ?
The people who do care already know how much the CMI prizes are and who Perelman is .</tokentext>
<sentencetext>What are "most people" doing on /.?
The people who do care already know how much the CMI prizes are and who Perelman is.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31536104</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31537718</id>
	<title>Re:English Please</title>
	<author>John Hasler</author>
	<datestamp>1269014220000</datestamp>
	<modclass>None</modclass>
	<modscore>1</modscore>
	<htmltext><p>&gt; it just tells us that lots of things can be deformed into spheres and gives<br>&gt; us a simple test for determining if something can.</p><p>3-spheres ("ordinary" spheres are 2-spheres).  Equivalent results have existed for all other spheres for some time.</p></htmltext>
<tokenext>&gt; it just tells us that lots of things can be deformed into spheres and gives &gt; us a simple test for determining if something can.3-spheres ( " ordinary " spheres are 2-spheres ) .
Equivalent results have existed for all other spheres for some time .</tokentext>
<sentencetext>&gt; it just tells us that lots of things can be deformed into spheres and gives&gt; us a simple test for determining if something can.3-spheres ("ordinary" spheres are 2-spheres).
Equivalent results have existed for all other spheres for some time.</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535562</parent>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31562854</id>
	<title>His ethnicity: Jewish.</title>
	<author>Anonymous</author>
	<datestamp>1269185700000</datestamp>
	<modclass>None</modclass>
	<modscore>0</modscore>
	<htmltext><p>It should be noted, that though he is from Russia, he is not Russian, but a Jew. Russia, a country full of anti-semites, yet still and once again, only a Jewish Scientist is able to make a break through of such magnitude. Perelman, I salute you, You join the ranks of Feynman, Einstein, Neuman and many others who have literally created modern Physics, Cybernetics, Mathematics, and everything else that is Science and technology.</p></htmltext>
<tokenext>It should be noted , that though he is from Russia , he is not Russian , but a Jew .
Russia , a country full of anti-semites , yet still and once again , only a Jewish Scientist is able to make a break through of such magnitude .
Perelman , I salute you , You join the ranks of Feynman , Einstein , Neuman and many others who have literally created modern Physics , Cybernetics , Mathematics , and everything else that is Science and technology .</tokentext>
<sentencetext>It should be noted, that though he is from Russia, he is not Russian, but a Jew.
Russia, a country full of anti-semites, yet still and once again, only a Jewish Scientist is able to make a break through of such magnitude.
Perelman, I salute you, You join the ranks of Feynman, Einstein, Neuman and many others who have literally created modern Physics, Cybernetics, Mathematics, and everything else that is Science and technology.</sentencetext>
</comment>
<comment>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535084</id>
	<title>Re:What does he win?</title>
	<author>Anonymous</author>
	<datestamp>1269006840000</datestamp>
	<modclass>Insightful</modclass>
	<modscore>3</modscore>
	<htmltext>It's amazing that TFA doesn't mention a thing about whether Perelman will actually accept the prize. What will happen to the prize money if he does not accept? The million dollars disappears into Lichtenstein numbered bank accounts 2718-282 and 3141-519?</htmltext>
<tokenext>It 's amazing that TFA does n't mention a thing about whether Perelman will actually accept the prize .
What will happen to the prize money if he does not accept ?
The million dollars disappears into Lichtenstein numbered bank accounts 2718-282 and 3141-519 ?</tokentext>
<sentencetext>It's amazing that TFA doesn't mention a thing about whether Perelman will actually accept the prize.
What will happen to the prize money if he does not accept?
The million dollars disappears into Lichtenstein numbered bank accounts 2718-282 and 3141-519?</sentencetext>
	<parent>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534956</parent>
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-http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535502
--http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31545408
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	<commentlist>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534944
-http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31623954
-http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31539192
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	<commentlist>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534818
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	<commentlist>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534832
-http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31535394
-http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31537540
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<conversation>
	<id>http://www.semanticweb.org/ontologies/ConversationInstances.owl#conversation10_03_19_0540249.14</id>
	<commentlist>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31534962
-http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31546820
-http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31538578
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	<commentlist>http://www.semanticweb.org/ontologies/ConversationInstances.owl#comment10_03_19_0540249.31536558
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