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Abstract: Collective computations take place in nature in two major classes of architecture, which we can roughly classify as "solid" (the standard, synaptic connectivity picture) versus those that are performed by "liquid" networks, such as the Immune system or ant colonies. Additionally, other solutions (or constraints) associated with plant and fungal communication or the potential of unicellular systems such as Physarum emerged as relevant actors. Finally, synthetic systems such as robot swarms and engineered communicating cells offer additional avenues for inquiry. We need to address many questions, notably: What are the computational limits associated with the physical state displayed by the collective? Are there a limited number of possibilities (as those already observed) or many others? What can or cannot be computed? How do we define a proper evolutionary framework to understand the origins of different solutions? What are the trade-offs involved? Can we evolve other solutions using artificial life models? Can a statistical physics approach to computation, including physical phases, help find universality classes? What is the impact of fluid versus solid on the values and meaning of integrated information theory? Answering these questions will help to define a theoretical framework for the emergence and design of cognitive networks and explore the limits of A.I. systems.