Context: Mathematical Model Reveals the Patterns of How Innovations Arise
The reference above is to a fascinating article from MIT Technology Review on the topic of mathematically modelling aspects of the processes underlying the emergence of innovation. Conspicuous by its absence is a measure of the “usefulness” or significance of an innovation, suggesting rich complexity and contextual semantics for further exploration. If innovation is the combination of previously unassociated concepts, entities, patterns, etc. – some combinations are clearly more useful (and more probable) than others. Shoes + wheels = roller skates. Shoes + pickles = a bad sandwich.
The model presented indicates a “walk” in a local possibility space. Each path taken and each node arrived at then reflexively transforms the “dancing landscape” of the overall possibility space. The system is recursively self-gravitating – local paths or solutions redefine the shape of a global possibility-space which then provides the menu of possible (i.e. most probable, causal) local paths for future exploration.
An analysis of innovation as reasoning probabilistically-weighted towards a general or directed solution may suggest ways in which cognition generates novelty. The most significant conceptual innovations or developmental inflection points arise where non-local (or less probable) recombinatory paths are followed – as a matter of insight, intuition or axiomatic reformulation.
What is a significant innovation? What are the most algorithmically concise paths in any recombinatory possibility-space between significant innovations?