From: PointedEars@web.de   
      
   Ross Finlayson wrote:   
   > On 12/07/2025 02:03 AM, Thomas 'PointedEars' Lahn wrote:   
   >> Ross Finlayson wrote:   
   >>> Of course, you will agree that 1) the solar system is in a geodesy   
   >>> that's always instantaneously evaluated everywhere its orbifold,   
   >>> and the apparent force vectors of gravity are by the bodies in   
   >>> their orbifold as modeled by the geodesy not their image's locations,   
   >>> and 2) dark-matter/dark-energy or rather the observations that imply   
   >>> their existence have long ago falsified standard cosmology   
   >>> (Einsteinian/Newtonian/Galilean), then also there's that 3) readily   
   >>> apparent gyroscopic effects are not explained by Magnus effect and   
   >>> have falsified Galilean theories of trajectory.   
   >>   
   >> How can I possibly agree to this?  It is pseudo-scientific word salad,   
   >> bereft of meaning.   
   >>   
   >> For example, an orbifold (orbit-manifold) does NOT have to do with orbits in   
   >> celestial mechanics, but with orbits as understood in *group theory*: "The   
   >> orbit of an element x in X is the set of elements in X to which x can be   
   >> moved by the elements of G [which is acting on X]:   
   >>   
   >>    G ⋅ x = {g ⋅ x : g ∈ G}."   
   >>   
   >>    
   >>   
   >> You keep using words because they sound scientific, not because you know and   
   >> have understood their meaning.  The result is utter nonsense, not even   
   wrong.   
   >   
   > Now that you mention it I do intend "orbifold" for "geodesy".   
      
   It does not matter what you intend; there are only orbifolds in mathematics,   
   and you are not using the term as it is defined.  You can not invent your   
   own terminology in the same field (if you want to be understood).   
      
   > The geodesy is the usual notion that anything anywhere (or, material points   
   > in Einstein's parlance) is going on a straight line   
      
   No, geodesy (or geodetics) "is the science of measuring and representing the   
   geometry, gravity, and spatial orientation of the Earth in temporally   
   varying 3D":   
      
      
      
   The word that you meant is _geodesic_, but that *also* does NOT mean what   
   you think.  Instead, a geodesic is the shortest local path between two   
   points of a space that is entirely *in* the space, a solution curve x(λ) of   
   the *geodesic equation*   
      
     [x''(λ)]^a + Γ^a_bc [x'(λ)]^b [x'(λ)]^c = 0,   
      
   where λ is an affine parameter, "'" means to take the derivative with   
   respect to that, and here and in the following Einstein summation is used   
   (superscripts are contravariant indices, not exponents).   
      
   It is NOT always a straight line because the Christoffel symbols of   
   the first kind, Γ^a_bc, are not zero for all spaces and coordinates:   
      
     Γ^a_bc = 1/2 g^ad (g_db,c + g_dc,b - g_bc,d),   
      
   where [g]_ab is the metric tensor and ",c" means the partial derivative with   
   respect to the coordinate with index c, x^c [x is a vector].   
      
   Particularly relevant in this newsgroup: in general relativity (where λ = τ,   
   the proper time), spacetime geodesics are not straight lines because   
   spacetime is curved.   
      
      
      
   > (as from its own perspective) its world-line in the geodesy,   
   > which is basically a vector field.   
      
   No.   
      
   > So, "orbits" for "trajectories", is the ideas that since the   
   > geodesy always is instantaneously evaluated everywhere, it's   
   > no different than "orbits" the trajectories, [...]   
      
   Word salad, not even wrong.   
      
   --   
   PointedEars   
      
   Twitter: @PointedEars2   
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