mathematics. Surely because of all that tinkering yesterday, trying
to visualize how the complex plane redraws a simple
cartesian one.
Reading about how Bernard Riemann, who came to believe conventional
planes were restrictive. There could be many spaces with different
metrics, one might move around on. Or that could transform one
into another. Voilà Topology, a new branch of mathematics.
A manifold is a topological space that resembles Euclidean space near each point.
More precisely, each point of an n-dimensional manifold has a neighborhood that
is homeomorphic to the Euclidean space of dimension n.Wikipedia
We are in the world of that beleaguered mathematical hero, the small bug
on the sphere, who is perhaps encountering strange phenomena...
* * *
Below, the well-known Möbius strip, a long-standing object of fascination.
One can travel the lenth of the strip on both sides, without lifting a finger.
Verified this for myself by making one with a black line on one side.
But if one travelled one, how would one know the distance travelled.
One would need markers on the strip (maybe construct one with lined
paper). Even so, there are difficulties.
Let us consider an application, using what in French is referred to
metro-boulot-dodo: the daily grind of the urban worker one might
translate to tube-cube-snooze. A simple work day would involve metro
to and metro back, but repeated forays from the metro to shop, browse,
have a cupa...etc do add up. A bit like twisting the M-strip and yanking.
Because eventually there are two round trips, overground and underground!
* * *
* * *
https://www.quora.com/Is-a-mobius-strip-flat
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