Life, learning and emergence

Many of nature's most striking phenomena are emergent: their behaviour belongs to a system's organisation rather than its substance. Statistical physics makes this precise, and its reach extends from electrons in a solid to the origin of living order and to the nature of learning.

Perhaps the most intriguing emergent phenomenon is life itself. Darwin explained how life evolves, but not how it began. We investigate the thermodynamic basis of self-replication and adaptation, and how flows of energy and matter keep organisms in non-equilibrium states. Which of these principles extend beyond biology, can they guide the creation of artificial life, and can evolution be made predictive?

Living systems also process information. The genome is less a blueprint than a program, run on gene regulatory networks. We study how these networks compute and what their architecture rules out, seeking a theory of cell programming precise enough to steer a cell to a chosen state.

Nature found its computers; we have to design ours. How do we make intelligent machines? We seek mathematical principles for how learning, memory and generalisation arise in biological and artificial networks, and for the part played by causal reasoning, modularity and representations of the environment. AI-assisted discovery treats machine intelligence as an instrument; here it is an object of theory.

Emergence is not confined to things that are alive or that learn. In condensed matter, interactions lead to emergence of new (quasi)particles that are responsible for the remarkable properties of materials. Among the best-known examples are superconductivity, underpinned by Cooper pairing of electrons, and the fractional quantum Hall effect, in which magnetic fields combine to produce excitations carrying a fraction of the electron's charge. But even spacetime — the stage on which these collective phenomena unfold — may itself be an emergent feature of quantum dynamics, rather than a fundamental ingredient of nature. We study phase transitions and the emergence of order in classical and quantum systems, at equilibrium and far from it. Quantum field theory is the common language here, as it is for the fundamental forces, and ideas have long travelled both ways.

We are drawn, too, to questions still taking shape — quantitative measures of selection and assembly, open-ended evolution, collective intelligence and the emergence of autonomy and agency. Our aim is a mathematics of emergence: laws that turn on organisation rather than substance, that hold for matter, organisms and machines alike, and that do not dissolve when a system is taken apart.