Brains and machine learning systems are selected or designed to exhibit learning and adaptation. But what kinds of systems can learn and adapt spontaneously, without selection or design? We might like the idea that societies, ecological communities or perhaps the biosphere as a whole can learn and exhibit adaptation, but since these are not evolutionary units, by what mechanism can this happen except by intensional design or as fortuitous happenstance? Our work shows general conditions for a dynamical system to adapt spontaneously. ‘Natural induction’ occurs in dynamical systems described by networks of viscoelastic connections (connections that give-way slightly under stress or over time). This is a natural assumption, described by local energy minimisation acting on connection parameters. It does not require the entities, their connections nor the system as a whole to be reproducing units, subject to natural selection or composed of utility-maximising agents (although they might be). When the state variables of this system are subject to episodic stress or occasionally perturbed, such that the system visits a distribution of attractor states, and the relatively slow plasticity of the connections naturally accommodates to these states, the system as a whole exhibits associative learning that produces adaptive organisation or ‘systemic intelligence’. This is not just self-organisation or memory (attractor) formation – the generalisation capabilities of associative learning produce an optimisation ability that can be quantified by an increase in the quality of solutions it finds to a combinatorial optimisation problem. We give some simulation examples of a spring-damper system, a social network and an ecological community solving MAX-2-SAT problems and Sudoku puzzles by natural induction. To the extent that interactions are rarely perfectly elastic, and stresses are rarely constant, natural induction may be ubiquitous in networks of all kinds from autocatalytic chemical networks, to multi-cellular bioelectric networks, to societies and the biosphere. We note (however) that the design principles to enhance systemic intelligence through natural induction are different from those that enhance performance under selection or utility maximisation. In particular, sustained stress (such as sustained profit maximisation, performance improvement or cost reduction) destroys systemic intelligence, causing the system to forget what it has learned (the analogue of overfitting). We discuss the implications for us as individuals, and our relationships with one another and the natural world.