Fractals are alright, extra dimensions hurt my brain
RE multiple dimensions, what confused me most is that i thought I understood 3D, as the world we experience is 3D. But it isn't that trivial.
From a 2D plane a 3rd dimension can be obtained either by simply extending the 2D plane (as in (x,y) -> (x,y,z)), but it can also exist as a space through which the 2D plane can be deformed, i.e. the 2D sheet can be warped through the 3rd dimension. This addition of dimensions opens up a whole host of conceivable dimensions.
I'm just saying that the concept of multiple dimensions isn't conceptually difficult, rather it just isn't demonstrated or explained that often. I imagine many make the same mistake I did of trying to imagine how 3D can go to 4D in the same way (x,y) -> (x,y,z)
RE multiple dimensions, what confused me most is that i thought I understood 3D, as the world we experience is 3D. But it isn't that trivial.
From a 2D plane a 3rd dimension can be obtained either by simply extending the 2D plane (as in (x,y) -> (x,y,z)), but it can also exist as a space through which the 2D plane can be deformed, i.e. the 2D sheet can be warped through the 3rd dimension. This addition of dimensions opens up a whole host of conceivable dimensions.
I'm just saying that the concept of multiple dimensions isn't conceptually difficult, rather it just isn't demonstrated or explained that often. I imagine many make the same mistake I did of trying to imagine how 3D can go to 4D in the same way (x,y) -> (x,y,z)