I will propose a causal model of the sensorimotor loop, which allows us to apply various formal tools to the field of embodied intelligence, in particular from information theory, information geometry, and measure theory. I will demonstrate its generality by addressing important subjects of the field and thereby outline corresponding research directions. In particular, I will present recent results on the design of embodied systems with concise control architectures, formalising the notion of "cheap design" within the field of embodied intelligence. This notion highlights the fact that high behavioural complexity, seen from the external observer perspective, does not necessarily imply high control complexity. This complexity gap is a result of two different frames of reference, which is closely related to Uexküll's Umwelt concept. If time allows, I will present a measure-theoretic formalisation of this concept and discuss its implications.