  For Connes' spectral triples, the group of automorphisms lifted to the
Hilbert space is defined and used to fluctuate the metric. A few commutative
examples are presented including Chamseddine and Connes' spectral unification
of gravity and electromagnetism. One almost commutative example is treated: the
full standard model. Here the lifted automorphisms explain O'Raifeartaigh's
reduction $SU(2)\times U(3)/\zz_2.$
