Abstract
The origin of asymptotic freedom is clarified by a simple probabilistic argument: It is much more difficult for balls to point out the same direction than sticks and disks. This fact is used to show that the effective potentials of the two-dimensional O(N)-invariant σ models (with hierarchical kinematical energy terms) are driven into the high-temperature region by the Kadanoff-Wilson block-spin transformations, if N is larger than or equal to 3.