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![Instead, the radical definition of complex systems comes from, what is known as, critical complexity. Work by Paul Cilliers and Alicia Juarrero warned against aggrandising models (even supposedly complex systems models) [3], [4]. They emphasise the need to embrace the ambiguous, messy, fluid, non-determinable, contextual, and historical nature of complex systems. They describe complex phenomena as unfinalizible and inexhaustible, which means that we can never capture any given biological system entirety with models [5]. Fig. 1, adapted from Di Paolo et al. (2018), captures the interdependence, fluidly and interactivity of agents and environments in a complex system [2]. Complex systems are open-ended, which means there is no uncontested way of telling whether what we have included in a model is crucial or what we have omitted as irrelevant is indeed so. Models can, according to the critical complexity approach, be contradictory: we can accept two incompatible predictions as both describing the same system.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:26hkfmtr7jrchexamh7hk6rz/bafkreidbtcuxfz7vv53zk3c37lti4el26hankzdt72dlwwiuphmcjjw6ai)
![This approach views a model as a snapshot of a system and no single snapshot tells the whole story. For modelling the human body, for example, โa portrait of a person, a store mannequin, and a pig can all be modelsโ [6]. None is a perfect representation, but each can be the best model for a human, depending on whether one wants to remember an old friend, to buy clothes, or to study anatomy. The critical complexity view suggests that theoreticians should avoid specialising in any one modelling approach and try to find the right set of models to understand a particular system in a given context.
There can, of course, be more than one definition of complex systems. Indeed, Cilliers and Juarreroโs approach to complexity encourages a plurality of definitions (after all, there is no single view of a system). We would, though, emphasise that it is the radical definition of complexity โ in which systems always resist a complete description, are open and unfinalizable โ which is least well understood by mathematical biologists today. It is therefore important to investigate how complexity should be approached in the study of biological systems.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:26hkfmtr7jrchexamh7hk6rz/bafkreicszmjxfslncbz4br2p7rrkcpyqkq6ayjtveaxcbgswc4hneicscu)
