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Creative Combinatorics

The math of innovation is combinatorics. We create by building on what comes before, or more precisely, by decomposing, abstracting, recombining, and extending what comes before. The more combinations that we generate, the greater the creative potential. The complementary challenge is to effectively and presciently evaluate the combinations.

At the macro level, these combinatorics-based dynamics of innovation have often been exemplified by what is known as “clustering economics.” New York, for example, has had self-reinforcing advantages in financial markets; Silicon Valley has enjoyed unique, self-sustaining advantages in emerging technologies. But the advantages of the physical clustering of these and similar examples really boil down to advantages in combinatorics. The innumerable additional encounters, discussions, collaborations, and competitions due to physical proximity lead to massively greater idea combinations than would otherwise occur. And where there is superior infrastructure to evaluate and nurture (e.g., wide-spread, accessible venture capital) and implement (e.g., flexible, risk-taking resources) the ideas, the combinatoric advantages inevitably lead to extraordinary value creation.

Learning layers obey the same math. They create value directly through enhancing collective learning, but the ability to amplify the power of combinatorics is at the heart of their value proposition. The learning layer is an engine of serendipity driven not by physical proximities, but by virtual proximities within multi-dimensional “idea spaces.” Its aim is to bring to our attention useful affinities and clusters among ideas and people of which we might not otherwise be aware. A learning layer can be considered an example of what the cognitive scientist and author Steven Pinker calls discrete combinatorial systems, which, as I discuss in The Learning Layer, occupy a very special place in nature:

We know of, however, two discrete combinatorial systems in the natural universe: DNA and human language. Not coincidently, these systems have the unique capability of generating an endless stream of novelties through a combinatorics made infinite by the application of a kind of generative grammar–a grammar comprising a recursive set a rules for combining and extending the constituent elements.

The discrete combinatorial nature of the learning layer is yet another reason it occupies a special place in the realm of systems. In combination with us, and by continually learning from us, it can engender ever greater streams of valuable, recombinant innovations. Of course, we still need the proper environments to nurture and implement the best of these innovations, and that’s a challenge we need to really be focusing on because somewhere in that multi-dimensional innovation space a very important creative combination impatiently awaits . . .

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2 Comments Post a comment
  1. This is heady stuff. One wonders if it actually can be applied to the real world or organizations or if it ultimately will be relegated forever to theory.

    April 4, 2011
  2. @Lynnea–just using Google or Facebook is a basic example of this kind of engineered serendipity since those systems infer preferences from behavioral cues to make recommendations (e.g., search responses, news feeds, etc). That approach can be taken much farther, which is the learning layer concept. In five years or so I suspect most of the systems we deal with in our organizations will have this capacity of built-in learning, capable of evaluating myriad combinations, since it is both technically very feasible and useful. Of course, most of us will just routinely use these systems and not bother to contemplate the mathematical underpinnings. But the theory can help get us there . . .

    April 4, 2011

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