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.

 

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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?"

 

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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.

 

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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!

 

I prefer maintaining a K.I.S.S. (Keep It Simple, Stupid!) approach to the discussion . . . . . math/equations/proofs make me sleepy! (HAHA!)

 

" Rolling a two dimensional object " is not even possible .

 

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.

 

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.

 

Extend

 

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..

 

No, a cylinder is not just the curved surface area.

 

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'.

 

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.

 

which makes the OP a mathematics abstraction and not physics.

 

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.

 

Meaning ?

 

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?

 

I have expressed similar in #34.

 

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.