2 dimensions into 3 dimensions

I agree with QQ:

Also . . . . . semantics? . . . . . to more technically approach the subject of this discussion while minimizing argumentation, we would likely need to agree on definitions and technical usage - for example, what is a object? What is an entity? Are 3-D ONLY solids?, What are 'surfaces', 'solids', etc., etc.
 
Instead of rolling the 2D surface longways (aligned with one of its long dimensions), what if you take two diagonally opposed corners and curl the 2D surface until the diagonal vertices just touch each other. Is it '3D' now?

Not if you are neither mathematically or geometrically interested in any of the points outside of the original 2D surface, until or unless someone mathematically asks the question: "How far apart are two of the diagonal corners?"
 
karenmansker said:
Q-reeus: You are probably techically/mathematically correct. The point I was making (mainly) is that when you rotate a surface INTO an additional dimension that is NOT the original 2-D depiction, you increase the dimensional attributes. 2-D surfaces thus rotated assume attributes of 3-D structures. Since I am not a technical mathematician, I won't argue this point further, except to reiterate (IMO) that 2-D surfaces rotated (or transformed) as described assumes 3-D attributes. Projection accomplishes the opposite effect - for example, one can reduce the dimensional attributes by 'projecting' (from a preferred POV) a 3-D entity to a lower dimensional (2-D) aspect - not unlike 'shadows cast on a cave wall'.
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Karenmasker I agree with the general thrust of what you write here, if not the technical niceties that an academic would insist on. Particularly agree with the last part re projection.
 
Quantum Quack said:
is there something of interest in this subject you wished to discuss ? Something that would extend the conversation in a way that ultimately benefits you?
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Well QQ, the OP piece was easily dealt with and formally should have ended by #3. I will admit to being guilty myself by at times forking off in a tangent. Mostly though as a corrective to someone else's introducing nonsense or rarely, a particularly interesting side issue.
Regarding extending the OP query, well it could become hugely complex requiring specialized maths and concepts way over my head. For instance:
https://en.wikipedia.org/wiki/Manifold
Do you really want to start wandering through such an enchanted forest here? Please, please say NO!
 
Q-reeus said:
Well QQ, the OP piece was easily dealt with and formally should have ended by #3. I will admit to being guilty myself by at times forking off in a tangent. Mostly though as a corrective to someone else's introducing nonsense or rarely, a particularly interesting side issue.
Regarding extending the OP query, well it could become hugely complex requiring specialized maths and concepts way over my head. For instance:
https://en.wikipedia.org/wiki/Manifold
Do you really want to start wandering through such an enchanted forest here? Please, please say NO!
Click to expand...

I prefer maintaining a K.I.S.S. (Keep It Simple, Stupid!) approach to the discussion . . . . . math/equations/proofs make me sleepy! (HAHA!)
 
Q-reeus said:
Well QQ, the OP piece was easily dealt with and formally should have ended by #3. I will admit to being guilty myself by at times forking off in a tangent. Mostly though as a corrective to someone else's introducing nonsense or rarely, a particularly interesting side issue.
Regarding extending the OP query, well it could become hugely complex requiring specialized maths and concepts way over my head. For instance:
https://en.wikipedia.org/wiki/Manifold
Do you really want to start wandering through such an enchanted forest here? Please, please say NO!
Click to expand...
I was going to suggest something like that...but have no particular interest manifold topology except to suggest that perhaps it may provide a bridge between our theoretical 2d surface and a 3 d object. (Math and Physics) But this would be more a philosophical discussion that I am far from being qualified to entertain, so I wont. ( but don't mind me)

There are a couple of extensions that I am considering but that depends on the level of trolling this thread experiences.
 
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This thread needs a push, as this is a very interesting point.

K.I.S.S
In general in any coordinate system if one can define all the points of an object with just one variable then it is 1D, if two variables then 2D and if three variables then 3D..

For example all the points on a line can be defined with one variable so it is 1D, all the points on a flat surface by 2 variables so 2D, for a cylinder it will be 3 points, so it will be 3-D. It is hardly an argument that a cylinder surface can be cut into a flat surface, so it would be 2-D. A cylinder is 3D, cut it and spread it, it is no longer a cylinder.
 
Quantum Quack said:
I was going to suggest something like that...but have no particular interest manifold topology except to suggest that perhaps it may provide a bridge between our theoretical 2d surface and a 3 d object. (Math and Physics) But this would be more a philosophical discussion that I am far from being qualified to entertain, so I wont. ( but don't mind me).

The are a couple of extensions that I am considering but that depends on the level of trolling this thread experiences.
Click to expand...

Extend
 
The God said:
This thread needs a push, as this is a very interesting point.

In general in any coordinate system if one can define all the points of an object with just one variable then it is 1D, if two variables then 2D and if three variables then 3D..

For example all the points on a line can be defined with one variable so it is 1D, all the points on a flat surface by 2 variables so 2D, for a cylinder it will be 3 points, so it will be 3-D. It is hardly an argument that a cylinder surface can be cut into a flat surface, so it would be 2-D. A cylinder is 3D, cut it and spread it, it is no longer a cylinder.
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you would base your answer purely on a co-ordinate system and the number of variables..? Even if the "thickness of the surface variable remained zero? interesting..
 
The God said:
In general in any coordinate system if one can define all the points of an object with just one variable then it is 1D, if two variables then 2D and if three variables then 3D..

For example all the points on a line can be defined with one variable so it is 1D, all the points on a flat surface by 2 variables so 2D, for a cylinder it will be 3 points, so it will be 3-D.
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Wrong. An obvious counterexample is a curved line, which needs more than one variable to specify it, but it remains 1D nevertheless. And so on for ND objects embedded in (N+1)D spaces.
It is hardly an argument that a cylinder surface can be cut into a flat surface, so it would be 2-D. A cylinder is 3D, cut it and spread it, it is no longer a cylinder.
Click to expand...
A cylinder is, as per #2, a 2D object mathematically. Maybe read that intro part to the Wiki article 'Manifold'.
 
The God said:
This thread needs a push, as this is a very interesting point.

K.I.S.S
In general in any coordinate system if one can define all the points of an object with just one variable then it is 1D, if two variables then 2D and if three variables then 3D..

For example all the points on a line can be defined with one variable so it is 1D, all the points on a flat surface by 2 variables so 2D, for a cylinder it will be 3 points, so it will be 3-D. It is hardly an argument that a cylinder surface can be cut into a flat surface, so it would be 2-D. A cylinder is 3D, cut it and spread it, it is no longer a cylinder.
Click to expand...

Disagree

To form a three D object is not possible from 1or2 dimensional concept . Since neither 1 or 2 dimensions can exist , in the first place .
 
In physical world there is nothing like 1-D or 2-D, everything in existence is geometrically 3-D.
 
Q-reeus said:
Wrong. An obvious counterexample is a curved line, which needs more than one variable to specify it, but it remains 1D nevertheless. And so on for ND objects embedded in (N+1)D spaces.

A cylinder is, as per #2, a 2D object mathematically. Maybe read that intro part to the Wiki article 'Manifold'.
Click to expand...

Q-reeus,

I know what you are talking about. Are we living in an universe where curved path of a planet around its star is a straight line? Euclidian cannot be erased by Einsteinian.
 
The God said:
In physical world there is nothing like 1-D or 2-D, everything in existence is geometrically 3-D.
Click to expand...
ok here comes one of the extensions I had in mind:

A sphere with a diameter of 1/infinity (infinitesimal)
Describe the spheres volume



worth discussing?
 
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The God said:
Q-reeus,

I know what you are talking about. Are we living in an universe where curved path of a planet around its star is a straight line? Euclidian cannot be erased by Einsteinian.
Click to expand...
Locally the planet follows a 'straight line' i.e. geodesic path through spacetime, but the global geometry cannot be encapsulated in anything corresponding to 'straight lines' Euclidean.
 
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