It is a funny and quite medieval assumption that reality or nature must be constructed out of some sort of fundamental building blocks… this view is deep rooted in the modern western way of thinking and it is not easy to get rid of. Although nature showed us several times that there is no such thing as “elementary object” or “fundamental symmetry” we keep looking in the same way at reality: some sort of underlying thing that we would call symmetry and some sort of particles that must exist in order to satisfy this “need” of ours. Fortunately in mathematics this aspect is not so strongly emphasized. Actually mathematicians deal with concepts rather differently but only very few of their ideas actually penetrated undistorted into physics. Most of the symmetry requirements are just representing appealable artifacts constructed by us such that they give some results also observed in nature. They are neither fundamental nor absolute. They are not accidents either, nor are they “broken” etc. They are all just in our heads. If you get rid of everything that is just “method of knowledge” you may find reality as it really is… There is much more into relativity than what is thought today… I salute the recent hiring of some mathematicians at the Perimeter Institute. I think that little school there can give quite some interesting ideas after all… 


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