@fobvius,
Any description of a loop is in some way a rough circle...you don't need geometry to find loops everywhere.
On the topic of dimensional reductionism I am not a fan...our description of dimensions is in my own amateur view obscure to say the least.
When we isolate dimensions we are always idealizing a domain as I have yet to see anything which is not ultimately tridimensional in reality.
That said there is a theoretical case to be made against the 4th dimension time and even against the 3th dimension on holography...if you can do away with the 2 you end up destroying geometry and reduce the world to Maths...
I have yet to see any meaningful proposal to get rid of the 1 dimension Reality.
One Dimensional Reality represents just the order of things described to form a loop as such order cannot shrink nor grow in Being, so it has to meet itself in some way. The reason to believe this specifically, is intimately related with the absolute need to get rid of off the concept of Nothingness as it being a valid concept. Once you do away with Nothingness Maths transforms into Meta-Mathematics...zero represents balance not absence, and infinities represent loops of finite information without boundaries, not true qualitative infinities...
Finally as soon as numbers like 0 or infinities pop up I am usually out of the debate...those concepts are poorly understood Philosophically speaking...and while I have my own idea on what they truly represent and mean it has nothing to do with the current foundations for them in Mathematics.
Since I am not a mathematician because I always asked to many questions in Maths specially at its foundations and never got any answers I rather leave the debate for the experts in their platonic Marvel cacophony of concepts.