From: tkoenig@netcologne.de   
      
   Stefan Ram  schrieb:   
   > ram@zedat.fu-berlin.de (Stefan Ram) writes:   
   >>To better understand symmetries, I have a few questions, but for   
   >>simplicity's sake I'll start with one:   
   >   
   >   And here's my other question:   
   >   
   >   It's about something I often encounter in texts about   
   >   symmetries, the point where I find it hard to follow.   
   >   
   >   Here's an example:   
   >   
   >|Given a perfect circle, you can rotate it by a tiny amount   
   >|and find that you still have the same circle.   
   > "Why String Theory?" (2016) - Joseph Conlon (1981/)   
   >   
   >   . A kinematic "rotation", to me, is a change in the angular   
   >   position of an object. I think of a "circle" as a physical object,   
      
   A circle is a mathematical construct, which can be described in   
   a variety of ways.  Perfect circles do not exist in the physical   
   reallity, where there is no such thing as an infinitely thin line   
   (or a fully Euclidean space, for that matter).   
      
   Likewise, rotation in this context is a mathematical transformation,   
   and you can, of course, show that rotating a circle by a tiny (or   
   huge) amount around its center does not change the set of points   
   that the circle is composed of.   
      
   So, whatever argument the author goes on to make, I do not think   
   it can be understood to be grounded in physical reality.   
      
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