  We study the error calculus from a mathematical point of view, in particular
for the infinite dimensional models met in stochastic analysis. Gauss was the
first to propose an error calculus. It can be reinforced by an extension
principle based on Dirichlet forms which gives more strength to the coherence
property. One gets a Lipschitzian complete error calculus which behaves well by
images and by products and allows a quick and easy construction of the basic
mathematical tools of Malliavin calculus. This allows also to revisit the
delicate question of error permanency that Poincar\'{e} emphasized. This error
calculus is connected with statistics by mean of the notion of Fisher
information.
