  We propose a new action principle to be associated with a noncommutative
space $(\Ac ,\Hc ,D)$. The universal formula for the spectral action is $(\psi
,D\psi) + \Trace (\chi (D /$ $\Lb))$ where $\psi$ is a spinor on the Hilbert
space, $\Lb$ is a scale and $\chi$ a positive function. When this principle is
applied to the noncommutative space defined by the spectrum of the standard
model one obtains the standard model action coupled to Einstein plus Weyl
gravity. There are relations between the gauge coupling constants identical to
those of $SU(5)$ as well as the Higgs self-coupling, to be taken at a fixed
high energy scale.
