CidTheKid said
Oh boy, that sounds something I'd like. If one were to try to understand it, what would you recommend to avoid losing your head?

I have no idea. I don't understand it! :P I assumed you did, as I know you have a mathematical background, and the rules discussed in the video are essentially those that are in place in the study of mathematical topology. The idea is that any two objects that can be morphed into one another without puncturing or ripping the "material" are the same - as long as they're transformed into eachother through continuous deformation. A donut and a coffee mug? They're the same, 'cause they both only have one hole (donut in the centre, mug in the handle) and can be morphed into one another without puncturing or ripping. It's a huge area of study and I'm woefully clueless on it, honestly - but I need to be clued up on it in order to study theoretical physics, particularly string theory. I mean, spacetime itself is a 4-dimensional manifold, and string theory does some crazy shit with multidimensional space... bosonic string theory requires there to be 26 dimensions and superstring theory requires there to be 10.
Sorry if I've missed a joke you were making or something, or am repeating stuff you're already aware of. I decided to take the post at face value xD

This thread stayed remarkably on-topic.

Doivid said
This thread stayed remarkably on-topic.

Halo said
I have no idea. I don't understand it! :P I assumed you did, as I know you have a mathematical background, and the rules discussed in the video are essentially those that are in place in the study of mathematical topology. The idea is that any two objects that can be morphed into one another without puncturing or ripping the "material" are the same - as long as they're transformed into eachother through continuous deformation. A donut and a coffee mug? They're the same, 'cause they both only have one hole (donut in the centre, mug in the handle) and can be morphed into one another without puncturing or ripping. It's a huge area of study and I'm woefully clueless on it, honestly - but I need to be clued up on it in order to study theoretical physics, particularly string theory. I mean, spacetime itself is a 4-dimensional manifold, and string theory does some crazy shit with multidimensional space... bosonic string theory requires there to be 26 dimensions and superstring theory requires there to be 10.Sorry if I've missed a joke you were making or something, or am repeating stuff you're already aware of. I decided to take the post at face value xD

Do you mind explaining Manifolds to me? I remember reading about them at one point (can't remember why?) but I didn't get them 100%.

natsumehack said
That is one possible outcome, another is you don't exist in what is considered existence, yet at the same time you are in existence, so in other words, you become what you have made, a paradox in of it's self.

Oh right I see what you mean now, you're saying they would exist within the universe despite the factors which brought about their existence no longer exist. Okay I understand but still, what prevents their death?

K-97 said
Do you mind explaining Manifolds to me? I remember reading about them at one point (can't remember why?) but I didn't get them 100%. Oh right I see what you mean now, you're saying they would exist within the universe despite the factors which brought about their existence no longer exist. Okay I understand but still, what prevents their death?

By pure fact that you don't exist, how do you kill which does not exist?

Doivid said
This thread stayed remarkably on-topic.

Funny how I am the creator of it.

natsumehack said
By pure fact that you don't exist, how do you kill which does not exist?

The problem with this is that from this notion, you could extend its implications until you return to my previous proposition in which you would be unable to interact with existence as ''How does non-existence interact with existence?'' or perhaps a simpler way of saying it ''How does nothing interact with something,''.

In the situation you described about becoming a paradox (in a universe where paradoxes aren't dealt with by fate), you would still exist albeit as a being without a traceable history. You did come into existence and then grew up and decided to kill yourself however in your situation your actions do not erase you from existence rather they erase your history, actions and their consequences after your past self's death from the timeline. Therefore while you would be a paradox, a being with no traceable history, since your actions do not cause you to be removed from existence you must still be able to die.

K-97 said
The problem with this is that from this notion, you could extend its implications until you return to my previous proposition in which you would be unable to interact with existence as ''How does non-existence interact with existence?'' or perhaps a simpler way of saying it ''How does nothing interact with something,''. In the situation you described about becoming a paradox (in a universe where paradoxes aren't dealt with by fate), you would still exist albeit as a being without a traceable history. You did come into existence and then grew up and decided to kill yourself however in your situation your actions do not erase you from existence rather they erase your history, actions and their consequences after your past self's death from the timeline. Therefore while you would be a paradox, a being with no traceable history, since your actions do not cause you to be removed from existence you must still be able to die.

Which brings up another question, if you are a paradox, and killed your self, wouldn't you already be dead? Can you kill what is already dead?

natsumehack said
Which brings up another question, if you are a paradox, and killed your self, wouldn't you already be dead? Can you kill what is already dead?

No as from the moment your past self is dead, you destroy any connection between you and the past self. As I said you are a being with no traceable history who while you have no cause is still alive and still exists. Your actions don't erase your existence only your history. So it is still possible to kill yourself or have someone kill you, you still exist and are still alive.

K-97 said
Do you mind explaining Manifolds to me? I remember reading about them at one point (can't remember why?) but I didn't get them 100%.

This is where it gets a little abstract, and I'll admit I'm referencing Wikipedia a bit for guidance on the technical terminology, but essentially a manifold is a space in which every point is like Euclidean space (do you know about Euclidean and non-Euclidean space?). So, essentially, although a manifold as a whole may not exist in Euclidean space, as long as at each point on the object the local area resembles Euclidean space then it's still a manifold.
The best way to describe it is using a sphere, imo - that's how it was explained to me. The surface of a sphere is a 3D non-Euclidean space as a whole, but at each individual point on that surface it looks like a 2D Euclidean space. If you were standing on a sphere (like the Earth), the local area looks like a 2D plane to you, as the curvature is very subtle, and the laws of Euclidean space hold within that local, plane-like area. So, the surface of a sphere is a two-dimensional manifold, because even though the whole thing is non-Euclidean, at each local point it resembles Euclidean space. Note, though, that it only resembles Euclidean space at each point - the curvature is still there, it's just unnoticeable. A way to understand this is by thinking about map projections of the earth. We can take a small geographic area of the Earth (which will have a subtle curvature and so technically be 3D space) and project it onto a 2D plane - a map. However, the way you transpose it to 2D is dependent on where you are on the curvature - if you then map the same space but standing in a different place, your two maps will differ slightly despite describing the same space, because the 2D projection of the 3D space is merely an approximation and therefore changes defending on your relative perspective.
Of course, all of this gives rise to some pretty cool concepts, and ways to define objects in terms of visualisable space even when those objects exist outside of that. An example is the Klein bottle (yay for wikipedia giving me this example xD), which is actually a 4D object that cannot be implanted in 3D space (though we can represent it in 3D or even 2D space as a sculpture or drawing), but is actually a 2D-manifold!

Halo said
This is where it gets a little abstract, and I'll admit I'm referencing Wikipedia a bit for guidance on the technical terminology, but essentially a manifold is a space in which every point is like Euclidean space (do you know about Euclidean and non-Euclidean space?). So, essentially, although a manifold as a whole may not exist in Euclidean space, as long as at each point on the object the local area resembles Euclidean space then it's still a manifold.The best way to describe it is using a sphere, imo - that's how it was explained to me. The surface of a sphere is a 3D non-Euclidean space as a whole, but at each individual point on that surface it looks like a 2D Euclidean space. If you were standing on a sphere (like the Earth), the local area looks like a 2D plane to you, as the curvature is very subtle, and the laws of Euclidean space hold within that local, plane-like area. So, the surface of a sphere is a two-dimensional manifold, because even though the whole thing is non-Euclidean, at each local point it resembles Euclidean space. Note, though, that it only Euclidean space at each point - the curvature is still there, it's just unnoticeable. A way to understand this is by thinking about map projections of the earth. We can take a small geographic area of the Earth (which will have a subtle curvature and so technically be 3D space) and project it onto a 2D plane - a map. However, the way you transpose it to 2D is dependent on where you are on the curvature - if you then map the same space but standing in a different place, your two maps will differ slightly despite describing the same space, because the 2D projection of the 3D space is merely an approximation and therefore changes defending on your relative perspective.Of course, all of this gives rise to some pretty cool concepts, and ways to define objects in terms of visualisable space even when those objects exist outside of that. An example is the Klein bottle (yay for wikipedia giving me this example xD), which is actually a 4D object that cannot be implanted in 3D space (though we can it in 3D or even 2D space as a sculpture or drawing), but is actually a 2D-manifold!

*nods*

Okay I think I get manifolds now, thanks for the explanation!

jesus server. behave man. I dun wan no double posts.

Halo said
I have no idea. I don't understand it! :P I assumed you did, as I know you have a mathematical background, and the rules discussed in the video are essentially those that are in place in the study of mathematical topology. The idea is that any two objects that can be morphed into one another without puncturing or ripping the "material" are the same - as long as they're transformed into eachother through continuous deformation. A donut and a coffee mug? They're the same, 'cause they both only have one hole (donut in the centre, mug in the handle) and can be morphed into one another without puncturing or ripping. It's a huge area of study and I'm woefully clueless on it, honestly - but I need to be clued up on it in order to study theoretical physics, particularly string theory. I mean, spacetime itself is a 4-dimensional manifold, and string theory does some crazy shit with multidimensional space... bosonic string theory requires there to be 26 dimensions and superstring theory requires there to be 10.Sorry if I've missed a joke you were making or something, or am repeating stuff you're already aware of. I decided to take the post at face value xD

I wasn't actually joking. I don't really know any more than the cliffnotes version of it, so I figured I might as well ask you for more background on it. I think I'm still pretty far from calling myself good at maths, even if it seems like I've studied up a bit. I suppose I should've rephrased that as "What do I need to learn to learn topology?"

A lot of my maths knowledge is hacked from bits and pieces of a lot of different fields rather than any one in specific, and it all feels rather inadecuate, when it comes down to it, mostly because it's all very superficial knowledge.

I'm still learning, mind you.