We propose a mathematically robust measure for food web intervality. Intervality of a food web---the complex network of trophic interactions between species in an ecosystem---is related to the number of trophic dimensions characterizing the possible niches found within a community. We aim to determine the minimum number of variables required to describe the factors that influence the trophic organization of the species in a community. We find that empirical food webs are not interval by the strictest sense of the definition. However, upon comparison to suitable null hypotheses, we conclude that empirical food webs exhibit a strong bias toward contiguity of prey. Though a very computationally difficult problem, we demonstrate that much ecological information can be captured within a small number of dimensions. Our conclusion that species and their diets can be so closely mapped to a single dimension represents a tremendous insight that can, for example, guide us on how best to go about developing dynamic ecosystem models.