Philosophy Of The Cosmos - Curved Space
I was thinking about the dimensions of space today and something occured to me. If space (or is it spacetime?) is curved, does this not imply a 4th dimension? If the 3 straight axis of space are not really able to describe the universe properly due to its curvature don't we then need more dimensions than that to describe the space of the universe?
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No we don't need an extra dimension, but you have a point: adding dimensions might help us to visualise what's going on. Think about the pictures Dayal's been using in lectures, where the surface of a sphere makes a 2D space which is similar to (analogous to) our 3D space. It's most obvious what's going on when we look at Dayal's 2D spaces embedded in a 3D space. This sort of embedding is something mathematicians often do when they have to manipulate these spaces. You can learn all about how to do this if you do geometry and topology courses. Does that make sense?
So, my interpritation of what you are saying is that it helps to visualise things with the extra dimension, but it is not actually necissary in reality? If so, this does make sense, because I have goten somewhat used to the idea of accepting things without them making perfect logical sense through this course.