Beyond crystals: the dialectic of materials and information

We argue for a convergence of crystallography, materials science and biology, that will come about through asking materials questions about biology and biological questions about materials, illuminated by considerations of information. The complex structures now being studied in biology and produced in nanotechnology have outstripped the framework of classical crystallography, and a variety of organizing concepts are now taking shape into a more modern and dynamic science of structure, form and function. Absolute stability and equilibrium are replaced by metastable structures existing in a flux of energy-carrying information and moving within an energy landscape of complex topology. Structures give place to processes and processes to systems. The fundamental level is that of atoms. As smaller and smaller groups of atoms are used for their physical properties, quantum effects become important; already we see quantum computation taking shape. Concepts move towards those in life with the emergence of specifically informational structures. We now see the possibility of the artificial construction of a synthetic living system, different from biological life, but having many or all of the same properties. Interactions are essentially nonlinear and collective. Structures begin to have an evolutionary history with episodes of symbiosis. Underlying all the structures are constraints of time and space. Through hierarchization, a more general principle than the periodicity of crystals, structures may be found within structures on different scales. We must integrate unifying concepts from dynamical systems and information theory to form a coherent language and science of shape and structure beyond crystals. To this end, we discuss the idea of categorizing structures based on information according to the algorithmic complexity of their assembly.