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Internet mapping and the widespread availability of mapping software are revolutionizing the world of cartography: anyone can now produce maps of many areas of the world. However, these tools typically only allow one to produce pictures, and the process undertaken to achieve these pictures is lost. We present a new approach to cartography in which maps are understood to be the visual representation of a multidimensional context, and the space being mapped is one such context. This approach to mapping -- called intensional -- allows the developers of maps to keep track of all the choices that are being made, whether visual, structural or socio-historical, and to share these choices with others, in real-time. As a result, electronic maps become much more flexible and versatile, and much more supportive of speculative research.