On creating new informational primitives in minds and machines Peter Cariani 1 Abstract Emergence is the creative process by which new structures and functions come into being. There are two fundamental, complementary conceptions of emergence: combinatoric emergence, wherein novelty arises by new combinations of pre-existing primitives 2 , and creative emergence, wherein novelty arises by de novo creation of new kinds of primitives. Combinatoric emergence in the syntactic realm is exemplified by new strings constructed from existing alphabetic letters, whereas creative emergence is exemplified by the addition of new kinds of letters to an alphabet. The two conceptions provide two modes for describing and understanding change and creativity: as the unfolding consequences of fixed combinatorial rules on bounded sets of pre-defined primitives or as new processes and interactions that come into play over time to define new primitives. We discuss the capabilities and limitations of various types of adaptive systems vis- à-vis these two creative modalities and the functionalities created (new syntactic states, new semantic observables & actions, new pragmatic goals). Finally, we point towards the possibility of new kinds of neural networks that operate on temporal patterns of pulses to create new signals. Within these networks, interacting sets of neural assemblies might ramify existing, circulating signals to construct new kinds of signal primitives in an apparently open-ended manner. Emergence and creativity Emergence concerns the means by which novelty arises in the world. Intuitively, emergence is the process by which new, more complex order arises from that which is, in some sense, simpler or more predictable. As such, images of birth, development, and evolution infuse our notions of emergence. These images provide explanations for how novelty, spontaneity, and creativity are possible and how complex organizations arise and become further elaborated. All around us we see the complex organizations that are the emergent products of biological, psychological and social processes. Our current discourses on emergence consequently encompass a wide range of phenomena: the appearance of new material structures (thermodynamic emergence), formal structures (computational emergence), biological structures and functions (emergent evolution), scientific theories (emergence vs. reduction), modeling relations in observers, percepts, ideas, notational systems, and economic and social relations. Two fundamental conceptions of emergence can be distinguished: combinatoric emergence and creative emergence. These two accounts of the origin of novelty parallel notions of the origin Symposium on "Creativity: The Mind, Machines, and Mathematics", MIT Stata Center, November 30-December 2, 2006, sponsored by the John Templeton Foundation. 1 629 Watertown St., Newton, MA 02460; cariani@mac.com, www.cariani.com. For deeper discussion see, Emergence of new signal-primitives in neural networks, Intellectica 2:95-143: 1997 (available on my website). 2 By primitive, we mean an indivisible, unitary entity, atom, or element in a system that has no internal parts of structure from the perspective of that system. Individual symbols are the primitives of string rewrite systems, binary distinctions are primitives in flip-flop-based digital computers , total machine states are primitives in finite state automata.