The discussion revolves around the nature of dimensions and whether they are relative to the observer, particularly in the context of the coastline paradox. Participants explore the implications of viewing geometric objects at different scales and distances, touching on theoretical and conceptual aspects of dimensions.
Participants express disagreement regarding the relativity of dimensions, with some asserting that dimensions are fixed while others suggest they may vary based on observation. The discussion remains unresolved with multiple competing views present.
Participants rely on definitions and perspectives that may not be universally accepted, and the discussion includes assumptions about the nature of observation and measurement that are not fully explored.
No. The OBSERVED or APPARENT size will depend on distance but the actual will not.Flying_Dutchman said:A point is taken as an example of a 1D, a plane 2D and a sphere is 3D. If a point is viewed say at 1000x enlarged the point appears as a plane similarly if we a view a large sphere from very far it does appear as a dot. So can we say that dimension are relative to the observer ? Had our sights been different would dimension be different ?
No - a point is always a point. If it looks different at any distance then it's an extended object. Similarly an extended object is an extended object always, even if you can't resolve it.Flying_Dutchman said:If a point is viewed say at 1000x enlarged the point appears as a plane
Follow-up question: How do we know?Ibix said:No - a point is always a point.
Flying_Dutchman said:A point is taken as an example of a 1D, a plane 2D and a sphere is 3D. If a point is viewed say at 1000x enlarged the point appears as a plane similarly if we a view a large sphere from very far it does appear as a dot. So can we say that dimension are relative to the observer ? Had our sights been different would dimension be different ?
The point, the plane, and the sphere are all mathematical objects. In physics we create models that make use of these objects. For example, we can model Earth as a point and get a really good understanding of how it behaves relative to other members of our solar system. However, for other purposes we may model a patch of Earth's surface as a plane, like when we are building a house. For other purposes, we model it as a sphere.Flying_Dutchman said:A point is taken as an example of a 1D, a plane 2D and a sphere is 3D. If a point is viewed say at 1000x enlarged the point appears as a plane similarly if we a view a large sphere from very far it does appear as a dot. So can we say that dimension are relative to the observer ? Had our sights been different would dimension be different ?