  Current techniques for predicting climate change are mainly based on
"massive" deterministic numerical modeling. However, the ocean-atmosphere
system is a so-called "complex system", made up of a large number of
interacting elements. We show that, in such systems, owing to the particularly
large sensitivity to initial conditions, the approach of a possible tipping
over a critical point cannot be evidenced "by construction" using numerical
modeling, due to the divergence of computation time in the vicinity of the
tipping point. On the other hand, the increasing amplitudes of observed
climatic instabilities seem to be an obvious sign of the approach of such a
tipping point, easily interpreted as a "critical softening", well known in the
theory of dynamical systems, that would bring us irreversibly into a new and
totally unexplored equilibrium state, except for a significantly higher
temperature and in a much closer time than expected from numerical modeling
extrapolations. Thus, maintaining climate warming around 1.5$^o$C or 2$^o$C by
2030 or 2050 appears fairly unrealistic unless worldwide drastic green house
gases reduction measures are immediately taken and applied.
