The prevalence of algorithmic recommendations has raised public concern about undesired societal effects. A central threat is the risk of polarization, which is difficult to conceptualize and to measure, making it difficult to assess the role of Recommender Systems in this phenomenon. These difficulties have yielded two types of analyses: 1) purely topological approaches that study how recommenders isolate or connect types of nodes in a graph, and 2) spatial opinion approaches that study how recommenders change the distribution of users on a given opinion scale. The former analyses prove inadequate in settings where users are not classified into categorical types (e.g., in two-party systems with binary social divides), while the latter rely on synthetic data due to the unobservability of opinions. To overcome both difficulties we present the first analysis of friend recommendations acting on real-world sub-graphs of the Twitter network where users are embedded in multidimensional ideological spaces and in which dimensions are indicators of attitudes towards issues in the public debate. We present a polarization metric adapted to these dual topological and spatial states of social network, and use it to track both the evolution of polarization on Twitter networks where the graph evolves following well-known Recommender Systems, and opinions co-evolve following a De-Groot opinion model. We show that different recommendation principles can sometimes drive or mitigate polarization appearing in real social networks.