In this paper, we propose an interactive magic lens visualization applying hyperdimensional computing to provide users with an intuitive and interactive way, to analyze and explore multidimensional and multivariate data. To this end, we project the data as a scatter plot into a two dimensional coordinate system, select data points with the lens and then compare or classify the selected data via hyperdimensional computing. By allowing the user to interact with the data in real time through the lens, users can exploratively find and focus on distinct subspaces within the data and compare them to other subspaces to observe relationships and different aspects of the data set. To evaluate the performance we apply the magic lens to several data sets and look at the accuracy and the impact of the number of data points as well as the impact of different subspaces. The results show that the magic lens can simplify the exploration and analysis and also that it can show relationships within the data which were not clear beforehand. In conclusion, the interactive magic lens is a visualization tool that can make the analysis of multidimensional and multivariate data accessible to people without the required technical background.