  This paper fails to derive quantum mechanics from a few simple postulates.
But it gets very close --- and it does so without much exertion. More exactly,
I obtain a representation of finite-dimensional probabilistic systems in terms
of euclidean Jordan algebras, in a strikingly easy way, from simple
assumptions. This provides a framework within which real, complex and
quaternionic QM can play happily together, and allows some --- but not too much
--- room for more exotic alternatives. (This is a leisurely summary, based on
recent lectures, of material from the papers arXiv:1206:2897 and
arXiv:1507.06278, the latter joint work with Howard Barnum and Matthew Graydon.
Some further ideas are also explored.)
