There is a phrase that I sometimes hear from string theorists saying that any other option is “mathematically impossible”… really? is it? And I go back to the discussion about “interactions” in mathematics… no kidding? Really impossible? Let me give you an example: in spectroscopy, a field that I find rather boring unless someone discovers the electron is an ellipsoid, there is something called “selection rule”. In principle it says that if the symmetry groups to which the various parts of a matrix element do not fit together (have no common irreducible representation) the matrix element is zero and there is no transition allowed… Well, this never happens in reality. There is NEVER in reality a situation in which the symmetry is exact or the selection rule is perfectly applied! Every student after he/she (or it) finishes the 1st year of physics knows that selection rules should be taken with a pitch of salt and pepper and that in principle corrections to perfect symmetries are always there: the operator in the middle has corrections, the wavefunctions are not perfect etc. Why am I giving now such a trivial example? I mean: spectroscopy??? Well, because the same thing happens in string theory: you cannot simply say you have a specific structure, say a monoid and whatever goes beyond that structure and is induced by who knows what “does not exist”… because that is NONSENSE!