Experiments featuring fast heat propagation, or so called non-local transport, were a puzzle for almost two decades. However recently it was shown, and it is recalled here, that a collective ideal MHD response of the plasma provides a quantitative ag
reement with these experiments, whereas transport plays just a secondary role. Then this work reviews the algebraic approach to transport data inversion that provides a formally exact solution, as well as a quantitative assessment of error bars, limited to periodic signals. Conversely, standard transport reconstructions are shown to sometimes fail to match the exact solution. The adoption of automated global search algorithms based upon Genetic Algorithms is bound to greatly increase the probability of finding optimal solutions. Finally, the standard methods of reconstruction infer the diffusivity D and pinch V by matching experimental data against those simulated by transport codes. These methods do not warrant the validity neither of the underlying models of transport, nor of the reconstructed D(r) and V(r), even when the results look reasonable.
