The aim of this paper is to propose a new overarching challenge for AI: the design of imagination machines. Imagination has been defined as the capacity to mentally transcend time, place, and/or circumstance. Much of the success of AI currently comes from a revolution in data science, specifically the use of deep learning neural networks to extract structure from data. This paper argues for the development of a new field called imagination science, which extends data science beyond its current realm of learning probability distributions from samples. Numerous examples are given in the paper to illustrate that human achievements in the arts, literature, poetry, and science may lie beyond the realm of data science, because they require abilities that go beyond finding correlations: for example, generating samples from a novel probability distribution different from the one given during training; causal reasoning to uncover interpretable explanations; or analogical reasoning to generalize to novel situations (e.g., imagination in art, representing alien life in a distant galaxy, understanding a story about talking animals, or inventing representations to model the larg
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