From: ram@zedat.fu-berlin.de   
      
   john larkin  wrote or quoted:   
   >On Mon, 2 Feb 2026 05:40:10 +0100, Thomas 'PointedEars' Lahn   
   > wrote:   
   >>Ian wrote:   
   >>>Stefan Ram wrote:   
   >>>>Jan Panteltje  wrote or quoted:   
   >>>>>What are the effects of magnetic field lines on star formation in   
   >>>>>galaxies?   
   >>>>These natural magnetic fields in galaxies and their gradients,   
   >>>>I think, are relatively weak. Over long timescales and over larger   
   >>>>spatial regions, their effects can accumulate and become noticeable.   
   >>>>But to drive a spacecraft, you'd need fields that are fairly strong   
   >>>>at the location of the ship and at the moment the ship is there.   
   >>>You also need a large _gradient_ of magnetic field.   
   >>What is that even supposed to mean?   
   >It means that there is no perpetual motion, no free energy.   
      
     In rectangular coordinates, the gradient of a vector field   
     f =( f_1, f_2, f_3 ) is defined by:   
      
   "nabla" f   
   = g^jk ("partial"f^i/"partial"x^j) e_i "tensor product" e_k,   
      
     according to the section "Gradient of a vector field"   
     of the Wikipedia page "Gradient".   
      
     So, when these derivatices ("partial"f^i/"partial"x^j) are   
     large, the gradient is large, meaning the field changes a lot,   
     which is need for a significant force on a magnetic dipole.   
      
     Unicode:   
      
   𝙛=(𝑓¹,𝑓²,𝑓³)   
      
   ∇𝙛=gⁱᵏ(∂fⁱ/∂xʲ) eᵢ⊗eₖ   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)