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The Standard Model of the elementary particles is controlled by more than 20 parameters, of which it is not known today how they can be linked to deeper principles. Any attempt to clean up this theory, in general results in producing more such parameters rather than less. Yet it is clear that, at distance scales of the order of the Planck length, the gravitational force presents itself in such a way that the need for new physical principles is evident. A stand-in-the-way is then quantum mechanics, a theory that demands the occurrence of superpositions of physical states in such a way that, when combined with general relativity, space and time themselves may require new formalisms for being used as primary frames for the descriptions of events. In previous papers the author proposed that quantum mechanics as a theory for the elementary particles should be rephrased as originating from a combination of deterministic evolution laws and discreteness at the Planck scale. This may well have a drastic effect on the symmetry structures and algebras. Local, discrete and continuous symmetries do not emerge without a cause, and we suggest that the symmetries can tell us more about fundamental constants, among which the Higgs mass is the most peculiar and the most challenging one.