mbt2402 [none/use name]

  • 1 Post
  • 9 Comments
Joined 2 months ago
cake
Cake day: September 13th, 2024

help-circle







  • firstly understand the context which is smooth manifolds, for simplicity imagine a 2d manifold embedded in 3d space - so a sheet of rubber that can pass through itself but can’t kink or do any funny business, just like in that sphere inversion video.

    the definition of a manifold is basically that it can be built out of patches (sheets of rubber in our analogy), for instance to make a sphere, we need two sheets of rubber (ignore the actual logistics of the deformation required).

    Now say that our sheets of rubber come with a textured and a smooth side, there are two ways to attach the sheets of rubber to make a sphere, one of which produces a sphere which is entirely smooth on the outside. This is what we mean by orientable, we can build it out of patches with a consistent “outside”.

    Consider the counterexample of a mobius strip, which we construct from a single strip of rubber by attaching one end to the other “backwards” (rough-smooth). Since we have defined it this way, it cannot be orientable. The klein bottle is another example, but somewhat cooler than the mobius strip since its a surface without edges.

    There are many other definitions of orientable depending on the context, since manifolds are a lot more general than I have shown you here.

    I don’t know what orientable manifolds have to do with being responsible.


  • techno utopianism, the synthesis of defence lab hacker culture and the new left has inherited the flaws of both. the disillusion of the children raised on this heady mix was inevitable. nostalgia beckons, the punch card and mainframe once a symbol of dehumanization is now a quaint museum piece, sublime objects of engineering prowess. i could spend my whole life exploring the intricacies of these old systems. the dream of connecting people through computers is perverted into the goal of connecting to computers. “ah, but it could have been different, if only my preferred programming language or paradigm had won out!” so we tell ourselves, nursing our pet projects. ahhh i’m feeling depressed now