What happens below or above d u depends on whether one is interested in long distances (statistical field theory) or short distances (quantum field theory). Quantum field theories are trivial (convergent) below d u and not renormalizable above d u . Statistical field theories are trivial (convergent) above d u and renormalizable below d u . In the latter case there arise "anomalous" contributions to the naive scaling exponents N . These anomalous contributions to the effective critical exponents vanish at the upper critical dimension.