World Science Scholars

2.6 Symmetry and Unification Discussion

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    • We’ve seen that one object can be “more” symmetrical than another, based on the number of rotational symmetries it has. A circle has infinitely many of these symmetrical transformations, but we also learned that a sphere does as well. Can we say that one of these objects is more symmetrical than the other?

    • Sure. Sphere is the most symmetrical object. One can rotate it how one likes and it always remains the same.

    • As far as I can tell this is a massively complex topic but I would guess it is provable much like (or through the use of) Cantor’s proof of cardinality in number sets (i.e. different sizes of infinity). The sphere definitely has more degrees of freedom to play around with while generating multiple infinite symmetrical transformations so it seems intuitive that it would be a higher cardinality… not sure though, need to learn the proof.

    • I believe the sphere in any dimension is the most symmetrical object in such a dimension.
      Due to all spheres are isomorphic all of them has the same infinite number of symmetries.

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