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A (Correct) Poincare Proof!?
aphyscher writes "About a year ago, there was an
announcement that M.J. Dunwoody had proved the (in)famous
Poincare conjecture.
His paper turned out to have a slight problem, and so it remained unsolved...
until perhaps now!
Sergey Nikitin has posted a preprint of what may perhaps be an actual proof."
can any one just go ahead and explain it in layman's terms? I mean, I haven't read it yet but I can just tell i'm not going to get it ;) hehe j/k
Mmmm...hypothetical donut...
If your bitterest enemies are people who hack the heads off civilians, then I would say you're doing something right.
I'm not that much into maths, but what will this proof achieve?
have you been defaced today?
But alas, the space alloted in a regular comments window is insufficient to explain further...
Some explain to me what this is. Is it different than a circle? Doesn't a sphere in its basic definition mean 3 dimensions?
"You can now flame me, I am full of love,"
Ok so rad the pre-writeup on this and I can say this: WAY OVER MY HEAD! I understood about
1.05E-60% of that. Holy cow. There is proof that higher education still turns out some bright people. I wish I knew what the hell all that was about, it "looks" cool. You could use that as a prop in a movie for some secret formula or something.
-=[ Who Is John Galt? ]=-
Here is step 2! You win 1 million dollars for the correct proof from claymath!
h tm
http://www.claymath.org/prizeproblems/poincare.
...the most intelligent thing I can think of is: "Mmmmm...donuts."
A.) There's now a correct proof of the Poincare problem!
B.) Jon Katz no longer posts to Slashdot!
C.) Chris D. starts his own gaming company; plans to fill-in Part 2 of the traditional Steps 1, 2, & 3 to Profit!
D.) Microsoft is now the largest paid advertiser on Slashdot.org, the be-all-end-all for all Open-Source/Free-Software news
My brain needs a reboot.
If you celebrate Xmas, befriend me (538
Is it just because it was a thorny problem, a bit of knowledge for the sake of knowledge?
Or is it just that the guy is now eligible for the Clay maths prize?
--
Must go buy a lottery ticket, front page on /. here I come!
For super-geeks, here is is a more thorough discussion of the Poincaré Conjecture.
t ml
http://mathworld.wolfram.com/PoincareConjecture.h
I think. Maybe it is a 3-d doughnut. It's been ten years since I studied that stuff at college.
Best Slashdot Co
This is just mathematical proof that you can wrap a rubberband around an apple. I think the rest of us would be satisfied by a videotape instead.
The name is Poincaré (with the litte thingy on the e)
Poin (POINt) - Ca (CAtastrophic)- Ray
bah, screw it, just call me Henri
Mmmmmmmmm... million dollar donut.... gaaaawwwwww...
Sig:
Barbeque is a noun. Not a verb.
This problem is priced at $1 million if solved.
3.243F6A8885A308D313
Is the proper name for a doughnut shape.
Just thought you might find it amusing.
Unfortunately the money may take a while in coming. The rules state, "a proposed solution must be published in a refereed mathematics journal of world wide repute, and it must also have have general acceptance in the mathematics community two years after." After this a committe is formed to determine whether the money should be awarded.
glad to see that Poincare did other extremely cool stuff as well... even if it did take us a hundered years to prove it to ourselves...
hrm, I've really got to get off of this chaos=order kick... its affecting my life in very unpredictable ways... er, so that was sort of randomly normal... er...
By far one of the few intelligent things being posted for this article.
Simpy put, the poincare conjecture implies that every compact n-manifold is homotopy-equivalent to the n-sphere iff it is homeomorphic to the n-sphere. (From Wolfram's MathWorld) Actually I don't know what that means, but having read and studied a bit about math, I can offer some explanation on the importance of such a proof. When a proof attempts to show that two algebraic structures are equal, as does this conjecture, it allows mathematicians the freedom to look at a problem in two ways instead of one. At last, a compact n-manifold problem can be safely regarded as an n-sphere problem and all the rules regarding n-spheres can be applied to certian n-manifolds. On another topic, these long-standing, but near-universally-believed-to-be-true conjectures are often assumed to be true in order to prove other theorems. i.e. a ground-breaking new primality testing algorithm ASSUMES the truth of the unproven Reimann Hypothesis. So, future encryption keys may rely on unstable hypotheses for their unbreakability.
This has a lot of implications for anything in 4d space.
Basicly before the proof you couldn't be sure what limits existed, now an extra limit has been placed on 4d environments.
The proof may also point the way to other proofs
thank God the internet isn't a human right.
I don't know which is worse; a problem like the Poincare problem, which has been definitively solved for 1-manifolds, 2-manifolds, and n-manifolds where n > 3, leaving only one little hole; or something like Femat's Last Theorem, which was solved for everything up to n equals a million billion and most numbers beyond that, before someone finally come up with a definitive proof.
... but my head just exploded.
I was just telling my buddy on EverQuest that these math guys have too much time on their hands.
wow.. finally.. i can sleep at night!!
Well, duh.
Trying is the first step towards failure.
Finally I can complete the warp engine. We shall fly through space like a rubber band flung from the surface of a sphere. Evil donuts beware. Why do Brits say maths instead of just math?
All the answers can be found at http://quiz.ravenblack.net/blood.pl?3634734612
The Poincaré Conjecture is widely considered the most important unsolved problem in topology. It was first formulated by Henri Poincaré in 1904. In 2000 the Clay Mathematics Institute selected the Poincaré conjecture as one of seven Millennium Prize Problems and offered a $1,000,000 prize for its solution.
The conjecture is that every simply connected compact 3-manifold without boundary is homeomorphic to a 3-sphere. (Loosely speaking, that every 3-dimensional object that has a set of sphere-like properties can be stretched or squeezed until it is a 3-sphere without breaking it).
Analogues of the Poincaré Conjecture in dimensions other than 3 can also be formulated. The difficulty of low-dimensional topology is highlighted by the fact these analogues have now all been proven, while the original 3-dimensional version of Poincaré's conjecture remains unsolved. Its solution is central to the problem of classifying 3-manifolds.
On April 7, 2002 there were reports that the Poincaré conjecture might have been solved by Martin Dunwoody; on April 12 Dunwoody acknowledged a gap in the proof and was attempting to fix it. In October of that year, Sergei Nikitin of Arizona State University announced that he had proved the result.
Sure, it can be pictured:
1) Look at it.
2) Go away for a while.
3) Come back, look at it again.
4) Go away for a while.
5) Come back, look at it again.
Congrats, you have successfully viewed a sphere in four dimensions. Length, width, height, time.
If James Harris (JSH) gives his blessing then maybe I'll believe it.
NOT!
Of course I know this is offtopic, but I kinda doubt the subject will come up...
.NET Developer Studio and I had to do a double take to make sure of what website I was on.
What's with the Micro$oft ads on Slashdot? Just saw one for
Is this just the first step?
Phase 2: Collect Clay Math Prize
Phase 3: Profit
Now *there's* a business model!
Who stands a better chance at proving/refuting the hypothesis: mathematicians pushing chalk or an NSA supercomputer using brute force? After all We're already being searched at airports, now mathematicians can't carry a protractor or a compass without being looked as being suspicious. When will terrorists learn that attacking math problems never solves anything. Wait, maybe it does... Can someone explain exactly what this is and what it means in very small words? And what is n cm? the length of the piece of string is that: I'm not sure it's a good idea to be publicizing this. know that the Poincare conjecture problem is really hard, and that there's no shame at all in all of these Clergy being completely at a loss. But if the public catches wind of such a perceived failure, they may lose faith. A) You can't predict prime numbers. D)If we know how he predicted prime numbers. B) That guy predicted prime numbers. C) Alot of money goes to whoever proves how the hell he predicted prime numbers.
And now your Slashdot front page summary.
Postmodern Computer Science: My cat's breath smells like cat food.
Financial Institutions Balk at MS Licensing: I'm going to eat chocolate till I barf!
Canada to Launch Countrywide Virtual Supercomputer: What's a diorama?
Satellite Radio in Fiscal Trouble: Was President Lincoln okay?
Portable CD-RW/DVD Player: I dress myself!
Hardware Manufacturing in China's 'Hot Zone': Lisa's bad dancing makes my feet sad.
Congress Members Oppose GPL for Government Research: Then the doctor told me that BOTH my eyes were lazy.
Music and the Internet Reprise: Everybody's hugging!
and finally,
A (Complete) Poincare Proof!?: When I grow up, I'm going to Bovine University.
discretely.
Best Slashdot Co
Comment removed based on user account deletion
I have zee MICROFILM!
Exqueeze moi? That one made me do a double-take. Or maybe those two made me do a triple-take, I'm not sure... Maybe if you look at a coloured circle using red-green glasses?
Money for nothing, pix for free
It's simple
N=N+1
Therefore God must exist.
-=[ Who Is John Galt? ]=-
no text
See, he's got it all wrong already. It's the Circle K, and strange things are afoot there.
Seriously, there was more greek in that thing than the local sammitch shop. Mmm. Gyro...
"Don't do what Donny Dont does" is a Simpsons reference from when Bart tries to get his knife after joining the Boy Scouts. I thought it was funny.
Dear God, moderator, don't you understand a joke when you see one?
It's more like a proof that the rubber band will pop off the apple if you nudge it a bit. Oh, yeah, and the apple has to be 4-dimensional (and no, you can't count time as one of them). Good luck making that video....
How do we use this to take down the RIAA/MPAA?
Is it trying to prove that there can exist a 4-dimensional object that has all points equidistant from a single point in space-time or something?
Assume that you have a sculpture made of Play-Doh® modeling compound, without any holes in it. If the Poincaré conjecture is true, then you can reshape the sculpture into a ball without breaking or joining anything.
Will I retire or break 10K?
"If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface."
How is the band being shrunk? How can it be shrunk to a single point yet still be wrapped around the apple? Why can't science types properly describe something in english? Science is about descriptions!
Though that story seems to be apocryphal, especially given that much earlier metallurgists than Archimedes already knew ways to test the purity of metal.
All's true that is mistrusted
You could take a magical rubber band and stretch it around a sphere and then slide the rubber band along the surface. As you work your way around, you'd find that the length of the rubber band varied along the surface. The important thing is that you can slide the rubber band so its length is essentially zero--a.k.a. a single point.
Poincare (Poincaré really but thanks a lot Slashdot for not letting me ...) speculated that if you had any simply connected closed 3-manifold is homeomorphic to the 3-sphere (which I'm just parroting back from the Mathworld site at Wolfram.) The theory was later expanded to include the equivalent in N dimensions. In other words, if you take something that only has an "outside" and no holes, you could mash it into the shape of a sphere, or slide the rubber band right off it no matter what.
The other side of the story is things like a torus, or for a tastier example, donut. It's not "simply connected closed 3-manifold" because if you put a rubber band around the "meat" of the donut through the hollow middle and never be able to get the rubber band off without breaking the donut or the rubber band. Yum.
The thing that hasn't yet been proven is whether this is true for 3-dimensions as originally speculated. The Mathworld site at Wolfram says that it's been proven for N=1, 2, 4, 5, 6, and >=7, but not for 3. I don't know why ... I mean, can't you just define a point that is in the center of a given manifold then make a sphere that is the average distance from all points on the surface and define a new surface that is half-way between the two surfaces, and repeat forever to show that you really get a sphere ... for a torus, for instance, you'd get a point, but for a cube you'd get a finite sized sphere ... same for a Dixie cup, except it'd be really small.
--- Jason Olshefsky
Karma: Poser (mostly affected by adding this line long after everyone else did)
Do you realize you are bordering on 1000 posts!? Your a maniac! :)
-=[ Who Is John Galt? ]=-
Hadn't you heard? They recently discovered that "eureka" actually means "oh my, this bathwater is too hot".
Gallagher could reduce both an apple and a donut to a point...with just one swing!
People in cars cause accidents....accidents in cars cause people
For example. You can draw a smooth shape (no sharp corners, no intersections) on a piece of paper. Assume you can come up with some equation that defines that shape. Then there exists not more than 2 equations that will transform (map) your original equation into a circle. Now the problem is prooving this in 3 dimensions. You start with a blob (actually just the surface of the blob), the blob has no holes and no sharp angles and doesn't intersect with itself (just your standard blob). There exists not more than 3 equations that will map your original blob defining equation into a sphere.
I'm no mathematition, but thats how I read the description. I think where this would be useful is in manipulating very complex shapes. You start with a shape, find the transformation equations. Manipulate a shpere (easy), then apply the inverse maping back to the original, and you get the result.
Like I said, I may be way off on this, but I did pass high school.
This guy doesn't have any background in algebraic topology. All his papers are on control theory.
Sounds fishy to me.
Han-Wen Nienhuys -- LilyPond
Here is the importance of this conjecture. It's really about a 3-dimensional subset of 4-dimensional space, but think of the usual 2- in 3- situation if it helps.
Basically, if somebody gives you a twisted and knotted object, you would like to be able to say whether its really just a twisted and knotted sack (the sphere). It could in principle have any weird basic shape, you can't identify it when it's all twisted up. Showing the object is just a sphere, would require you to try to unknot it and smooth it out and say: look, I told you it was really just an ordinary sack.
In pathological cases it can be really hard to figure out how to undo all the knotting and twisting possible, and the case of dimension 3- in 4- was the only one still unkown.
So what you would like to do is not have to provide instructions for untangling the object, but rather just put it into a CAT scan, map its shape and perform some kind of calculation to verify it must be a sphere.
This is the homotopic equivalence of the conjecture. You can calculate the homotopy groups of the sphere. You can also calculate the homotopy groups of the weird twisted object. If they are equivalent, you don't have to go to the effort of unknotting the shape. Before you didn't know for sure it must just be a sack, but now you do!
Actually, that's assuming the proof holds up. Don't rush to judge these things so fast.
Aye, as most objects of uniform density do :)
Doesn't "uniform density" mean "as opposed to something like swiss cheese"? I was talking about holes as in donut, not holes as in swiss cheese or holes as in IIS. Can a torus have a uniform density?
Will I retire or break 10K?
What I mean is a maximum limitation to be eligble for the voucher (perhaps I need to revise my sig), i.e., you cannot qualify for a voucher unless you can demonstrate need.
The purpose of the argument is to demonstrate that the real objection is not about quality of education, it's about the powerful in this country staying powerful by limiting the choices of the less powerful.
If your bitterest enemies are people who hack the heads off civilians, then I would say you're doing something right.
I've read your stupid god damned sig about 50 times over the last several months... remove it from public display
Remove it yourself. Slashdot has an option to turn SIGs off. Preferences/Comments/Disable Sigs.
A glance at Nikitin's publication list will show that he works in Control Theory, and never published in Topology or Geometry journals before... It's a bit as if a statistician announced a proof of Fermat, with a (by math standards) surprisingly short and elementary proof. Hats off if it's right, anyway I guess any mistake would be found pretty soon.
Timeo idiotikOS et dona ferentes
Step 1) Prove that it is possible that a fundamental group of 3-dimensional manifolds (V) could be trivial, even though V is not homeomorphic to the 3-dimensional sphere.
Step 2) ??????
Step 3) ????????
[PowerPoint] is a tool for capitalist presentation
There are proofs for all dimensions but the 4th. There were 16 wrong demonstrations of the poincare conjucture for the 4th dimension. So for me, it is just too hard to belive. I won't be happy until I see the Clay Mathematics Institute give him the prize. http://www.claymath.org
The explanation of the problem linked in the posting said you can compress an apple down to a point by moving a rubber band around it? I know for a fact there is no way to compress an apple that small without breaking it. Trust me, I've tried.
Donuts, on the other hand...
"I don't care about the Constitution!" --Bill O'Reilly, November 17, 2009
"The conjecture that every simply connected closed 3-manifold is homeomorphic to the 3-sphere"
A manifold is simply a surface, like the surface of a peice of paper. There are different types of manifolds ( topological, smooth,...), but for the near term that's not important.
A 3-manifold is simply a manifold that has a surface of three dimensions.
A simply connected manifold is a surface on which any loop you place one the surface can be continuously deformed to a point. What that means is that when you place a rubber band on the surface you can squench the rubber band down to a point without having to make it lose contact with the surface. For example you can do this for a soccer ball. But you can't for a dount. So a soccer ball is simply connected while a donut is not.
To explain the term closed requires a bit of work. When one studies this kind of thing one covers manifolds with smaller sets of points that look just like the normal Euclidian balls, ie all points with a radius less than R say. These are open sets. [Experts only: Yeah I can define another topology but I am trying to explain things here! ] The complement of a set A which is a subset of a set B is the set of all points in B that are not in A. A closed set is a set that has a complement that is open.
Two manifolds are homeomorphic if they can be [continuously] deformed in to one another.
Finally a 3-sphere is simply the set of points in, a 4 dimensional space (x,y,z,t) that are equidistant from the origin, (0,0,0,0).
So that should be it...now you know what this drek...
"The conjecture that every simply connected closed 3-manifold is homeomorphic to the 3-sphere"
That said I have not read the paper, don't have the time right now.
The preprint is posted on the arXiv.org web site, which is exactly that, a place to put preprints. Preprints that appear there have not been subject to peer review, so at this point, this is an annoucement of a result, which is very different than a number of mathematicians with the appropriate background agreeing that this is a proof.
The abstract from the arXiv is:
This paper proves that any simply connected closed three dimensional stellar manifold is stellar equivalent to the three dimensional sphere.
and the intro of the paper says that "Since every 3-dimensional manifold can be triangulated and any two stellar equivalent manifolds are PL homeomorphic, our result does imply the famous Poincare conjecture."
There is a nice front end to the math part of the arXiv from UC-Davis at this link
It's psychosomatic. You need a lobotomy. I'll get a saw.
A mathematician was once asked about how he could visualize a 3-D Sphere. His response was, "Simple! First visualize an n-D Sphere and then set n to 3".
Read this a while ago somewhere. Couldn't resist posting it.
S
Danica McKellar, who played Winnie Cooper on The Wonder Years, has a degree in mathematics from UCLA.
If I recall correctly, assuming that the Reimann Hypothesis is true results in an algorithm that runs *faster* (has a lower polynomial running time), but they also provided an algorithm that is polynomial time *without* assuming Reimann hypothesis is true.
In other words, primality testing is in P -- unconditionally.
A.
In his paper he claims to prove that a simply connected closed 3 dimensional manifold is stellar equivalent to the 3-sphere. However, his definition of page 11 of simply connected is incorrect. Using his "definition" it is trivial to prove the Poincare conjecture in every dimension. (Even though it is known to be false in higher dimensions.)
Nice try. But I guess we'll have to wait for the next incorrect proof.
I don't remember if it is in polynomial time, but the one that assumes the Riemann Hypothesis is the first algorithm to give a 100% probability of primality. Previously they fell around a measly 99%.
Everyone knows engineering chicks have significant figures. Plus, no couple enjoy a better moment.
Actually, it seems even a line may cast an (N-1)_dim shadow onto an N_dim surface.
oh yeah? My Edelbrock high-rise manifold on my '68 Camaro can beat the shit out of your "3-dimensional manifold V", plus it comes with a bumper sticker!
Actually, all the article says is that they have finally realized that Douglas Adams is right.... the last line of the proof is:
= 42
Full-Featured GPL Web Hosting Control Panel
Piece by piece:
By which he means: there is one equivalence set of loops through the manifold. Every possible loop (A path that returns to its beginning point. Duh.) in the manifold belongs to one set of loops that are pretty much the same - you could push any one of them around and get any other one. A sphere has this quality - any loop you draw on the surface of a 2-sphere (the one that exists in three dimensions), but a torus doesn't - there are the loops that are equivalent to the loop around the outside of the torus, and the ones that run through the hole.
What he's asking is, is it possible there could be an object in 4-dimensions, that has some kind of tangle in it such that you can't make it into a hypersphere, but isn't so mangled that there are fundamentally different ways to "draw lines" on it. The suggestion is fairly reasonable, I think.
For instance, any loop drawn on a plane is homeomorphic to a circle. You're options in connected finite 1-d manifolds amount to line segments, or cirles. But when you upgrade to 2-d, suddenly you've got holes. You can't have holes in 1-d and still be connected, but in 2-d you get donuts and dresses and honeycombs and whatnot. But the thing about a hole is that it means that your fundamental group have more than one set in it, and without a hole, you wind up being a sphere.
So why shouldn't there be another characteristic of 3-d objects, one which allows for more than one kind of simply connected, non-contractable manifold?
IP is just rude.
Is there any torture so subl
Did Katz really stop posting to slashdot? Permanently? Did he say why? I haven't seen him for awhile, but I'm not sure if this is because he's on sabbatical or what have you. Please do tell! I rather detest his drivel.
You can calculate the homotopy groups of the sphere.
If you could produce an algorithm for determining the homotopy groups of spheres, you'd be in possession of a Fields medal.
Once someone mentioned Nitikin's specialty is Control Theory, it all snaps into place. Yep, there are realworld applications here. I can almost grasp the networking and communications implications, the ability to deal with n-dimensional spaces as simpler topological states. Ah, if only I'd done that two more years of calculus class. But those applications have little to do with the proof itself, more the implications of the topological network system he uses.
Now let us know when he wins the Clay Mathematics Prize, wow a megabuck, that's better than a Nobel.
It takes a long time to turn around a failing school. Having a solid educational foundation is critical for elementary school children in setting the tone for their future in education. Those kids don't have 5 years to wait on the district. They need a solution now.
That said, vouchers are only one part in a total school system solution. Here are some things I thought of off the top of my head. (FWIW, I'm a single parent of a 6 year old who attends a National Blue Ribbon public elementary school.)
As we all know, good schools are only 50% of education. The other 50% is a good home. Districts can't solve those problems, but they can help by encouraging parents who do care to participate in ways that help more children than just their own.
Cheers,
-l
Help cure AIDS, cancer, and more. Donate your unused computer time to worldcommunitygrid.org. Join Team Slashdot!
"The purpose of the argument is to demonstrate that the real objection is not about quality of education, it's about the powerful in this country staying powerful by limiting the choices of the less powerful."
Do you know who gives a person power? Himself.
If you are equating money==power here, you've just become logic-poisoned by the anti-capitalists.
There is no vast right-wing conspiracy. Trust me. >:D
I was waiting to argue with you, on thing such as "Those kids don't have 5 years to wait on the district."
But then you said: "As we all know, good schools are only 50% of education. The other 50% is a good home."
And then you got the point, so there was no reason for me to argue.
Morons beget morons. Bad public schools are bad because in agregate, the the administrators, the students, the parents, and the administrators are all mentally and/or physically lazy. The only ones who can make a difference in raising and educating better kids are smart, patient teachers, reasonably unbureaucratic administrators, and parents who aren't busy sending their kids down the street to buy them crack.
Remember Twain: I never let schooling get in the way of my education.
this is the property of a non-euclidean riemann geometry. suppose that you had a front yard, and you wanted to put a fence around it, to show it was yours. the yard is 2D, so the bigger the yard, the bigger the fence. however, since the flat surface of the earth curves and folds on itself as a sphere, you can own a yard the size of the earth and NOT need a fence, since there are no edges. the same thing applies here.
BSD is for people who love UNIX. Linux is for those who hate Microsoft.
what i find really interesting is that the solutions of these topology problems have a characteristic very similar to the mathematics of random walks, both self-avoiding and regular:
there exists some phenomena that is dimensionally dependent. there exists some critical dimension for which the case is simple and hence reduces, and much easier to prove. the 2d case is classical, and often yields elegant results and rational numbers.
however, the MOST interesting thing, is that in all 3 problems (random walks, self-avoiding walks, and the pointcare conjecture) the d=3 case is the most mind-boggling. it yields VERY ugly mathematics, and ends up being much harder to prove for. just a thought...
BSD is for people who love UNIX. Linux is for those who hate Microsoft.
If memory serves correctly, Nikitin was also one of the founding members of the blackdown port of Java to linux.
I also had a calculus class (95 or 96) with professor Nikitin at ASU, we had many conversations about programming and linux in particular. So not only is he a genius mathmetitian, but also a complete linux geek like the rest of us.
In case this is relevant, in Doom 3 there will be 8 light sources at any given point. Thus, er, wait. No.
Oh, yes, and the parent, too. Okay, 5, Interesting will suffice.
my
The Poincare Conjecture and the issues surrounding it can be described using nothing but anagrams of the famous mathematicians name.
IE NO CRAP
Poincare was A NICE PRO by the standards of the time. I wish I had A COIN PER attempt to prove his theorem! Believe me, its NO PI RACE
I'd ususally begin with a topological approach.
Take a tennis ball and try to ARC ONE PI around the circumference, then PAIR ONCE.
Getting too hard, need to go home to use super-computer.
I OPEN CAR and drive home. ARE I PC ON? Click on PEAR ICON to load fruity maths app.
Finally prove the theorem!
I RAP ONCE and then REAP COIN.
Thats all, I NO RECAP
Sorry, someone had to do it!
I. PORN ACE
I've been studying EE stuff for a long time now.
Very frequently we use K-maps, which can take any number of dimensions. 1-d Kmaps exist in things we call LINES. 2-D K-maps exist in things we call SQUARES. 3-D K-maps exist in things we call CUBES, and higher than that, we call the things the K-maps are in HYPERCUBES.
Extending this terminology...shouldn't a 4-d object with all surface points equidistant from a single point be called a hypersphere to distinguish it from normal usage?
Mod me down and I will become more powerful than you can possibly imagine!
So, theoretically, the shape and structure and position if you neglect the uncertainty principle could be mathematically defined.. and we could all be "shadows" of a 4th dimensional world? Makes me wonder what that does to free will.
Ummmmm..... If you think that a manifold is simply a surface then I can see why you haven't read the paper yet. You should probably be able to understand basic point-set topology before attempting to read proofs of the Poincare conjecture.
Don't waste your time increasing his web page hits.
What AD&D module is this die used in?
Fuck you, E r i c.
I notice that rpresser got a score of 2 for his reply where he put in the subject line that I'm a "crank", and I'm now motivated to see how this discussion area works, so I've noticed a few things.
1) People who are familiar with it all can pull in an outsider with an anonymous post by making that post and putting up a link, as was done with the original post that drew me here as it was posted on the sci.math newsgroup, which is how I knew about it.
2) The person they're drawing in, if they rush in and make a post as I did, is unlikely to have an understanding of the system, so they're unlikely to make an effective reply (like my problems with html formatting).
3) Then someone else can come in and clean up, like rpresser and score some points at the sucker's expense, as he got 2 points even though he was off-topic.
But isn't that the point of these pages anyway? Get as much action as possible, no matter how it's done?
Moderation points are entirely the decision of other people. It's true that potentially everyone can moderate, but in fact not everyone does. (I never have; I'm a relative newcomer, and I've not yet been offered the chance.) I didn't post what I posted hoping to be moderated up; I posted it because it came to mind when I read your ... um ... post.
The point of these pages varies from person to person, but personally I don't give a damn about whether what I post is modded or not. I read slashdot to be informed; I'm not well known either on Slashdot or elsewhere, and I don't care if I ever am.
You, on the other hand, are well known. Celebrity always attracts attention; if the attention is uniformly negative, perhaps that says something about you or your contributions.
And it's people like you who end up helping to break a system. You called me a "crank" which is derogatory, but you were rewarded by the SlashDot system. And here you get another point which makes this look like loser-ville. As for those who might be deluded about the how big SlashDot is, just consider that when I first saw that link on sci.math and clicked on it, soon after it was posted, I couldn't even reach the post as SlashDot itself was unavailable. My Internet activity has created reactions from organizations as diverse as MSN and Google, as I pull and push the Internet, so you might want to consider that when you consider celebrity. And also consider that as far as I'm concerned SlashDot replies more often than not attract people who try to win at someone else's expense, so I *quit* reading them.
I said that about SlashDot, MSN and Google, then I went to check Google statistics and saw no mention of me! Mein Gott!!! I'm cuckoo! Macht's nicht. Ich will nicht geschwunden. And no, ich nicht spreche deutsch. I just know a little bit that I like to throw out when I'm dealing with a certain type of people.