We build on the interpretation of the Economic Complexity method as Correspondence Analysis (CA), and propose that the Canonical form of CA (CCA), which originated in the ecology literature, can be used to calculate multi-dimensional economic complexity. The traditional (CA) way of calculating economic complexity includes no "external" information such as countries' development characteristics to facilitate interpretation of "complexity". This has led to a wide range of fairly ad hoc interpretations of economic complexity on the basis of ex-post correlation to a long list of other variables. By the ex-ante inclusion of a number of country variables in the construction of the complexity indicators, CCA enables better interpretation, also in the case of multi-dimensional indicators. The analysis is further facilitated by another element of the ecologists' toolbox, the so-called biplots, which are CCA-based graph embeddings that represent a lower-dimensional product-space in which products and countries are positioned together, in mutual correspondence to each other. We show that in this way, CCA provides a richer account of development in many of its aspects, especially economic growth.