2 dimensions into 3 dimensions

Discussion in 'Physics & Math' started by Quantum Quack, May 27, 2017.

  1. karenmansker HSIRI Banned

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    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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  3. danshawen Valued Senior Member

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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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  5. Q-reeus Valued Senior Member

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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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  7. Q-reeus Valued Senior Member

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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!
     
  8. karenmansker HSIRI Banned

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

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    " Rolling a two dimensional object " is not even possible .
     
  10. Quantum Quack Life's a tease... Valued Senior Member

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    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.
     
    Last edited: May 28, 2017
  11. The God Valued Senior Member

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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.
     
  12. river Valued Senior Member

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    Extend
     
  13. Quantum Quack Life's a tease... Valued Senior Member

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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..
     
  14. The God Valued Senior Member

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    No, a cylinder is not just the curved surface area.
     
  15. Q-reeus Valued Senior Member

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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.
    A cylinder is, as per #2, a 2D object mathematically. Maybe read that intro part to the Wiki article 'Manifold'.
     
  16. river Valued Senior Member

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    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 .
     
  17. The God Valued Senior Member

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    In physical world there is nothing like 1-D or 2-D, everything in existence is geometrically 3-D.
     
  18. Quantum Quack Life's a tease... Valued Senior Member

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    which makes the OP a mathematics abstraction and not physics.
     
  19. The God Valued Senior Member

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    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.
     
  20. river Valued Senior Member

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    Meaning ?
     
  21. Quantum Quack Life's a tease... Valued Senior Member

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    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?
     
    Last edited: May 28, 2017
  22. The God Valued Senior Member

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    I have expressed similar in #34.
     
  23. Q-reeus Valued Senior Member

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    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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