Are Dimensions Truly Relative to the Observer in the Coastline Paradox?

[Flying_Dutchman]

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 ?

 

[phinds]

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. The OBSERVED or APPARENT size will depend on distance but the actual will not.

 

[Ibix]

If a point is viewed say at 1000x enlarged the point appears as a plane

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.

"I personally cannot see it therefore it does not exist" is not the way to do science.

 

[russ_watters]

No - a point is always a point.

Follow-up question: How do we know?
Answer: Because we define it that way.

 

[PeroK]

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 ?

If you want to study something interesting about dimensions try this:

 

[Herman Trivilino]

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.

 

[diogenesNY]

PeoK beat me to the punch! :)

The following classic paper provide some diversion:

https://users.math.yale.edu/~bbm3/web_pdfs/howLongIsTheCoastOfBritain.pdf
further: 'coastline paradox' and 'fractal dimensions' might prove fun and edifying as search terms.

diogenesNY