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This paper presents the results of an experiment in using a big and granular dataset from Facebook to invent a new way of measuring political diversity in Copenhagen. The experiment was a collaboration between TANTLab and GEHL architects, and it was sparked by a shared concern that our cities are becoming political filter bubbles. Its outcome was the publication of an interactive datascape that enables the user to explore which urban spaces in Copenhagen break such bubbles. The paper discusses how this datascape reconfigured existing problematizations of urban diversity by problematizing existing assumptions about what urban diversity is and how to design for it. It unfolds how we produced the datascape, how the reception of this alternative cartography sparked a new debate about this issue, and how our findings relate to other literatures on urban diversity. The production of the datascape is an example of how scholars involved in data-driven urbanism can productively engage themselves in the production of critical metrics and imaginative cartographies rather than just using new data sources and algorithms in a framework of prediction and control. This is an important task because urban metrics and cartographic techniques ultimately shape the way we envision our cities.Keywords: Soft City Sensing, urban cartography, political diversity, digital methods, critical metrics