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This paper explores some of the potential connections between natural and artificial intelligence and natural and artificial consciousness. In humans we use batteries of tests to indirectly measure intelligence. This approach breaks down when we try to apply it to radically different animals and to the many varieties of artificial intelligence. To address this issue people are starting to develop algorithms that can measure intelligence in any type of system. Progress is also being made in the scientific study of consciousness: we can neutralize the philosophical problems, we have data about the neural correlates and we have some idea about how we can develop mathematical theories that can map between physical and conscious states. While intelligence is a purely functional property of a system, there are good reasons for thinking that consciousness is linked to particular spatiotemporal patterns in specific physical materials. This paper outlines some of the weak inferences that can be made about the relationships between intelligence and consciousness in natural and artificial systems. To make real scientific progress we need to develop practical universal measures of intelligence and mathematical theories of consciousness that can reliably map between physical and conscious states.