The principle of biological autonomy, introduced by Francisco J. Varela, addresses the dilemma of Cartesian mind-body dualism by re-casting mind and body, or subject and object, observer and observed, not as irreconcilable categories, but as complementary perspectives on the same biological phenomena. Indeed, this distinction between self and non-self may be seen as a necessary precondition for autonomy. An autonomous system is self-governing in that it is concerned with preserving its unique character, or unity. Furthermore, an autonomous system is operationally closed in that it forms a self-referential network without reference to an external world. This paper develops these ideas in relation to thinking about embodied, enactive robotics. As well as being constructed artefacts, what is it to look at robots as truly autonomous agents? In this context we begin to explore the concept of operational closure analytically. We utilise natural connectivity as a quantitative measure of the cyclicity of these operationally closed internal processes. In doing so we discover that increased natural connectivity of an autonomous system confers a greater behavioural robustness when it is coupled with the external world.