*random access file would be fine too in 2D - I was just thinking about 1D at first and wondering if a sequential access file counted as one dimensional, forgot to edit it..
On the other hand, a circle in 2d is a sphere in 3d, so trying to link 2 circles in 2d is equivalent to trying to link 2 spheres in 3d, which isn't what the video shows.
Yep, that was the part that was getting me too. On the other hand, the circle doesn't have to be a sphere when converted to a 3D object, it could also be a cylinder. I was wondering if mathematically it always had to be a sphere in 3D, but it turns out that just thinking of it as a cross-section of any object that has a circular shape somewhere is valid from a mathematical viewpoint. It is just common sense after all, no magic happening that I'm not going to have to strain to comprehend:P For some reason I had it in my head that objects must always have equivalents in different dimensional spaces.. and of course you could encode a 3D or 4D object in 2 dimensions (I suppose any sequential access file on a computer could be considered 2 dimensional), but it would just be very messy and rather pointless to "visualise" such a thing..
It would be fun to let an AI loose on religious texts after it's done a bit of basic learning, then ask it what it thinks about god.
The internet is obviously a good resource for information too, but I hope we never see an AI that has learned all it knows of the world from Youtube comments *shudder*
Yep I was just trying to take dimensions away to help visualise things moving from 2D to 3D. I was thinking too much of simple objects and thinking of ways to compress a 3D object into 2D, but as a lot of shapes are completely arbitrary, you can't just define them with a simple algorithm, the only way to define complex shapes is probably just to define the 3D object from several angles as with a CAD program.
Thanks, have ordered a copy of his book on the 4th dimension, and I've finally started to get how things could be working here now that I'm not trying to imagine the 3D objects with a 4D component:)
No I can understand that part, I just would also have been translating the safe into 4D space in my mind too which would mean that all versions of the box were encompassed by their own safe so to speak. But if you don't have a 4D safe nor box, but still use 4D space, there is no problem..
Yeah I suppose I've been thinking of actually turning the objects themselves into 4D objects when they move into 4D space, the same as how I think the 3D version of a circle is a sphere.. since a depth-less circle can't really exist in 3D.. but you can kind of imagine it existing in 3D space all the same. That's helpful, thanks:)
I did consider that, but in that case I think you'd still end up with 2 spheres.. I don't think there is an analogy between the two spaces for most objects. Circles have a very similar formula to spheres, and they are both quite simple objects from one perspective, but then imagine irregular shapes - for example imagine a pyramid.. it could be seen as a square if you took a projection from above, or a triangle from the side - there is no 2D representation that can do it justice without drawing several shapes.. I'm thinking to define a donut shape in 2D you'd probably need at least 4 circles.
Still having trouble visualising moving a torus into 2D, let alone 4D.. you might think that getting an orthographic perspective of a 3D object can give you a 2D representation - it works for a circle.. but it doesn't really work for any asymmetric objects, including toruses.. I suppose if you don't actually add an extra dimension to a 3D object when transferring it into 4D space then from a 4D perspective it might be possible to make it look like the two objects have become joined without breaking any boundaries, but that's simply a matter of perspective.. for example someone else pointed out how 2 2D circles can be moved past each other in 3D space without interfering with each other, and from an orthographic perspective they could look like they have passed through each other when they are 3D space.. so yes assuming the equivalent of an orthographic view in 4D space I can accept this game, but in reality I don't think the 2 objects ever actually exist at the same location in 3D space.
Have been thinking about it, and I guess this analogy just isn't working because the 2D representation of a 3D object with a hole in it probably isn't even possible.. so I can't quite imagine with the 4D representation would be, apart from to think that it still would not be possible to intersect them any more than you can cause two circles to merge by changing one of them into a sphere (which would be the real 3D form of a circle, rather than a ring or a cylinder which again are both toruses..). In 2D I'd say that 2 circles can't overlap without breaking each other any more than 2 spheres can overlap each other in 3D space.
I think his comedy work is great too (though actually his character in Hancock had quite a serious personality despite the overall plot concept being a parody), I was just trying to point out roles where certain types of people might be more inclined to take him seriously as an actor. Haven't seen Bagger Vance yet myself, no idea how good he was in that.
I was disappointed that it's a different actor, but he is a decent actor nevertheless. I admit I've only seen him in Ocean's Whatever and Hotel Rwanda but again he works well in both comedy and drama roles. You'd think they'd try to stick to the same actors - there must be some reason Terrence didn't get the part.
Hmm... well that would similarly work for a sphere containing another sphere.. but a torus or any other object with a hole is surely a different class of object.. I'm not sure what the 2D representation of a torus would be..?
Yeah I was wondering about moving something into an extra dimension and combining with something from the other dimension.. I suppose the fact is that here they were combining toruses which can actually be linked in 3D.. but I'm still dubious as to whether adding a dimension makes that any easier.. seems moving them into 2D and then back to 3D would be the simple way to do it, and that moving the objects into 4D would just make it even more difficult to manipulate the two objects in such a way that they will be linked when moving back to 3D, even if you were allowed to create breaks in the surface(s?) of the 4D torus.
This doesn't seem so much like a "fourth dimension" as a form of "subspace" or an alternate 3D reality (then again I haven't played the game and maybe am picking things up wrong from the video).
I don't see how adding another dimension can magically allow two objects to become linked when they were unable to be linked in a lower dimension. Two circles on a piece of paper cannot physically merge with each other if you assume their boundaries are solid and cannot pass through each other. Neither can 2 rings lain on a table, or two cylinders or two spheres be overlapped without breaking them somewhere. So how would adding another dimension allow you to join two 3D objects with a hole in the middle, even if you only moved one of them into this higher dimension?
To be fair, there have actually been some decent sequels out in the last few years though - definitely as far as superhero movies go. Probably not so much when it comes to other types of movie (though I have to say I did enjoy AvP2, it's much better than the first at least). Can't wait for Iron Man 2, it is going to kick some serious ass:)
Actually, for the last few years Will Smith has been one of my favourite actors. Have you seen Seven Pounds, The Pursuit of Happyness or Ali for example? All serious movies in which he does a good job, and of course he still does a good job in lighter movies too. The fact that I can take him seriously in the serious movies after watching so much Fresh Prince of Bel-Air as a kid says to me that he's a good actor..
Somehow I don't think voting for one of two or three parties really gets down to the nitty gritty of your exact views on stupid laws and stupid systems. No matter who you vote for there are always going to be things you disagree with that are not changed, and even things that you agree with that will be changed.
Voting is next to worthless as far as getting your opinion across is concerned - there are hundreds of reasons to vote for one guy over another, and it's not very likely that you'd be able to tell everyone's reasons for voting one way or another. I would have voted for Obama simply because Palin was obviously a moron, and there was a risk of her becoming President for a time. I live in the UK though so that's a moot point, but I've never voted here either because it seems so pointless. I've never actually seen any real change in the way this country works in my lifetime so far, and politics is just lie upon lie, mud slinging and generally just something I don't want to have to deal with. I would vote if we could vote on actual issues rather than just for individuals - people who may agree with me on some things, but who likely disagree with me on others. Now that the internet is almost ubiquitous, and if the government ever get their fucking act together, then maybe we will actually be able to vote on individual issues and have a real form of democracy.. but governments and technology just don't seem to go together without an awwwwful lot of money and time wasted in between, so I doubt that's going to happen within the next 10 or 20 years, unless we do something like force everyone in the country to join Facebook and do polls that way.
So when someone simply asks to be put in jail, they should be allowed even if they have done nothing wrong?
Having said that - when so-called punishment becomes more attractive than normal life, there must be something seriously wrong going on. Surely this guy could have found somewhere else to stay for a while, and would be perfectly within his rights to protect himself against vengeful morons (though perhaps now that he's actually killed someone he never wants to have to do anything like it again)
I wasn't talking about deaths, was talking about overall accident rates in built up areas. Cars are generally more powerful and solidly built (less crumple zones etc) in the US though so that probably does have an effect on deaths as a result of accidents..
Slashdot Mirror
*bows in reverence*
*random access file would be fine too in 2D - I was just thinking about 1D at first and wondering if a sequential access file counted as one dimensional, forgot to edit it..
On the other hand, a circle in 2d is a sphere in 3d, so trying to link 2 circles in 2d is equivalent to trying to link 2 spheres in 3d, which isn't what the video shows.
Yep, that was the part that was getting me too. On the other hand, the circle doesn't have to be a sphere when converted to a 3D object, it could also be a cylinder. I was wondering if mathematically it always had to be a sphere in 3D, but it turns out that just thinking of it as a cross-section of any object that has a circular shape somewhere is valid from a mathematical viewpoint. It is just common sense after all, no magic happening that I'm not going to have to strain to comprehend :P For some reason I had it in my head that objects must always have equivalents in different dimensional spaces.. and of course you could encode a 3D or 4D object in 2 dimensions (I suppose any sequential access file on a computer could be considered 2 dimensional), but it would just be very messy and rather pointless to "visualise" such a thing..
It would be fun to let an AI loose on religious texts after it's done a bit of basic learning, then ask it what it thinks about god.
The internet is obviously a good resource for information too, but I hope we never see an AI that has learned all it knows of the world from Youtube comments *shudder*
Yep I was just trying to take dimensions away to help visualise things moving from 2D to 3D. I was thinking too much of simple objects and thinking of ways to compress a 3D object into 2D, but as a lot of shapes are completely arbitrary, you can't just define them with a simple algorithm, the only way to define complex shapes is probably just to define the 3D object from several angles as with a CAD program.
Thanks, have ordered a copy of his book on the 4th dimension, and I've finally started to get how things could be working here now that I'm not trying to imagine the 3D objects with a 4D component :)
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(This is to get around the lameness filter)
No I can understand that part, I just would also have been translating the safe into 4D space in my mind too which would mean that all versions of the box were encompassed by their own safe so to speak. But if you don't have a 4D safe nor box, but still use 4D space, there is no problem..
Yeah I suppose I've been thinking of actually turning the objects themselves into 4D objects when they move into 4D space, the same as how I think the 3D version of a circle is a sphere.. since a depth-less circle can't really exist in 3D.. but you can kind of imagine it existing in 3D space all the same. That's helpful, thanks :)
I did consider that, but in that case I think you'd still end up with 2 spheres.. I don't think there is an analogy between the two spaces for most objects. Circles have a very similar formula to spheres, and they are both quite simple objects from one perspective, but then imagine irregular shapes - for example imagine a pyramid.. it could be seen as a square if you took a projection from above, or a triangle from the side - there is no 2D representation that can do it justice without drawing several shapes.. I'm thinking to define a donut shape in 2D you'd probably need at least 4 circles.
Still having trouble visualising moving a torus into 2D, let alone 4D.. you might think that getting an orthographic perspective of a 3D object can give you a 2D representation - it works for a circle.. but it doesn't really work for any asymmetric objects, including toruses.. I suppose if you don't actually add an extra dimension to a 3D object when transferring it into 4D space then from a 4D perspective it might be possible to make it look like the two objects have become joined without breaking any boundaries, but that's simply a matter of perspective.. for example someone else pointed out how 2 2D circles can be moved past each other in 3D space without interfering with each other, and from an orthographic perspective they could look like they have passed through each other when they are 3D space.. so yes assuming the equivalent of an orthographic view in 4D space I can accept this game, but in reality I don't think the 2 objects ever actually exist at the same location in 3D space.
Wow, this is fun :p
I actually don't think I was consciously considering the context when I wrote my post, but I did enjoy the vague analogy when I noticed it.
Have been thinking about it, and I guess this analogy just isn't working because the 2D representation of a 3D object with a hole in it probably isn't even possible.. so I can't quite imagine with the 4D representation would be, apart from to think that it still would not be possible to intersect them any more than you can cause two circles to merge by changing one of them into a sphere (which would be the real 3D form of a circle, rather than a ring or a cylinder which again are both toruses..). In 2D I'd say that 2 circles can't overlap without breaking each other any more than 2 spheres can overlap each other in 3D space.
I think his comedy work is great too (though actually his character in Hancock had quite a serious personality despite the overall plot concept being a parody), I was just trying to point out roles where certain types of people might be more inclined to take him seriously as an actor. Haven't seen Bagger Vance yet myself, no idea how good he was in that.
I was disappointed that it's a different actor, but he is a decent actor nevertheless. I admit I've only seen him in Ocean's Whatever and Hotel Rwanda but again he works well in both comedy and drama roles. You'd think they'd try to stick to the same actors - there must be some reason Terrence didn't get the part.
Hmm... well that would similarly work for a sphere containing another sphere.. but a torus or any other object with a hole is surely a different class of object.. I'm not sure what the 2D representation of a torus would be..?
Yeah I was wondering about moving something into an extra dimension and combining with something from the other dimension.. I suppose the fact is that here they were combining toruses which can actually be linked in 3D.. but I'm still dubious as to whether adding a dimension makes that any easier.. seems moving them into 2D and then back to 3D would be the simple way to do it, and that moving the objects into 4D would just make it even more difficult to manipulate the two objects in such a way that they will be linked when moving back to 3D, even if you were allowed to create breaks in the surface(s?) of the 4D torus.
This doesn't seem so much like a "fourth dimension" as a form of "subspace" or an alternate 3D reality (then again I haven't played the game and maybe am picking things up wrong from the video).
I don't see how adding another dimension can magically allow two objects to become linked when they were unable to be linked in a lower dimension. Two circles on a piece of paper cannot physically merge with each other if you assume their boundaries are solid and cannot pass through each other. Neither can 2 rings lain on a table, or two cylinders or two spheres be overlapped without breaking them somewhere. So how would adding another dimension allow you to join two 3D objects with a hole in the middle, even if you only moved one of them into this higher dimension?
Now I know what us 6 digit users must look like to the 5 digit users..
To be fair, there have actually been some decent sequels out in the last few years though - definitely as far as superhero movies go. Probably not so much when it comes to other types of movie (though I have to say I did enjoy AvP2, it's much better than the first at least). Can't wait for Iron Man 2, it is going to kick some serious ass :)
Actually, for the last few years Will Smith has been one of my favourite actors. Have you seen Seven Pounds, The Pursuit of Happyness or Ali for example? All serious movies in which he does a good job, and of course he still does a good job in lighter movies too. The fact that I can take him seriously in the serious movies after watching so much Fresh Prince of Bel-Air as a kid says to me that he's a good actor..
Somehow I don't think voting for one of two or three parties really gets down to the nitty gritty of your exact views on stupid laws and stupid systems. No matter who you vote for there are always going to be things you disagree with that are not changed, and even things that you agree with that will be changed.
Voting is next to worthless as far as getting your opinion across is concerned - there are hundreds of reasons to vote for one guy over another, and it's not very likely that you'd be able to tell everyone's reasons for voting one way or another. I would have voted for Obama simply because Palin was obviously a moron, and there was a risk of her becoming President for a time. I live in the UK though so that's a moot point, but I've never voted here either because it seems so pointless. I've never actually seen any real change in the way this country works in my lifetime so far, and politics is just lie upon lie, mud slinging and generally just something I don't want to have to deal with. I would vote if we could vote on actual issues rather than just for individuals - people who may agree with me on some things, but who likely disagree with me on others. Now that the internet is almost ubiquitous, and if the government ever get their fucking act together, then maybe we will actually be able to vote on individual issues and have a real form of democracy.. but governments and technology just don't seem to go together without an awwwwful lot of money and time wasted in between, so I doubt that's going to happen within the next 10 or 20 years, unless we do something like force everyone in the country to join Facebook and do polls that way.
So when someone simply asks to be put in jail, they should be allowed even if they have done nothing wrong?
Having said that - when so-called punishment becomes more attractive than normal life, there must be something seriously wrong going on. Surely this guy could have found somewhere else to stay for a while, and would be perfectly within his rights to protect himself against vengeful morons (though perhaps now that he's actually killed someone he never wants to have to do anything like it again)
Nope.
I wasn't talking about deaths, was talking about overall accident rates in built up areas. Cars are generally more powerful and solidly built (less crumple zones etc) in the US though so that probably does have an effect on deaths as a result of accidents..