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We could want connect 2 dots , 2 strings , 2 planes or 2 volumes in a 4d space. They must be parallel ; one object is the seat and the other the ground ; gravity or any other force exerts a perpendicular attraction between them. The container space may have an arbitrarily high dimension. Only accounts the dimension of the objects to connect, obviously lower ...


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In the following I will attempt a slightly ridiculous way of stating that you need as many legs as dimensions in your space. I.e. for 4D: four legs. I will ignore any peculiarities of n-dimensional Gravity for simplicity. Instead I will assume that there is a uniform directional Newtonian force field acting in the n-dimensional space. I.e. "down" is along ...


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I would suggest we need 4 legs to stabilize in 4D space. Consider this: we need at least 3 legs in 3D spacetime to project onto the ground a polygon with non-zero area. If the area of the polygon was zero, the center of mass would be in an unstable equilibrium and would likely tip. So, we draw the analogy to 4D: we project onto a 3D hypersurface which is the ...


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I have no idea, but here's a guess. If you think about how many legs a chair would need in 2 spatial dimensions, the answer seems to be 2. If there were only one leg, then a slight push to either the left or right would cause the "chair" to tip over. See the image below for an unstable (left) and stable (right) 2d "chair" In 3 spatial dimensions (i.e. the ...


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Such a spacetime is called an ultrahyperbolic spacetime, so called because it produces ultrahyperbolic equations (equations with more than one negative eigenvalue). Those spacetimes are not overly nice to work with. They pretty trivially include closed timelike curves, since a closed curve in any plane of two time directions will be timelike. They permit ...



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