Ideas in Space (1) - a dimensional approach to innovation

For several years we've been working on what might be called a "dimensional" approach to innovation, in our work with clients.  Although it has many precedents, it is possible we've pursued it more literally and monomaniacally than most.

A previous post on Sternberg's Sternberg's  "propulsion model" of  leadership, suggested by Adam Hansen (@adhansen on Twitter) jogged my interest in exploring the concept more publicly.  I'm going to put together a series of posts over time, under the title of "Ideas in Space".

At its most basic, thinking of ideas (or thoughts or models or strategies) as dimensional simply means that we're placing them in a metaphorical space that can be measured in one or more dimensions.   We do it all the time ... an idea is "close" to another idea, or a possible solution is "a stretch" implying that it too far away from where we are currently located.

Mind-mapping adds at least one other dimension to a linear outline or list, implying a certain flexible kind of dimensionality. There are many forms of visualization and diagramming which use dimensionality to express relationships between concepts ... up, down, left, right, near, far, bigger, smaller.

Sternberg's model required a way of describing business strategies dimensionally, in terms of direction, movement and distance.  So do many other strategic analyses, including the popular "Blue Ocean Strategy" which advises looking "outside" of the red ocean (along some metaphorical dimension of differentiation) to find an area with no competition.

So the idea of ideas being in space is obvious, right?  Okay, but let's drill down a little more and see what are the implications of such an implied dimensionality.  Here are a few:

Distance = Differentiation

What we are mapping into the metaphorical space is some intuitive feeling for "how different" one idea is from another.  If Idea1 is similar to Idea2, it's close.  If it's very different, it's much farther away.  How are we "measuring" quantities of difference?  Is it possible to be objective or rigorous about such a metric?  What would we call a "unit of difference"?

Distance + Directionality

Different in what way?  Idea3 maybe the same distance away from Idea1 as Idea2, but in a different direction.  That is, the difference itself is different, a variation in some other component or characteristic.  How many dimensions of difference are possible?  Are ideas always located in an "n-dimensional" space?  Is it possible to be rigorous and objective about defining the dimensions?

Discovery vs. Creation

Here's a very tricky and perhaps non-obvious (but potentially profound) implication: if the ideas are in space, who put them there?  If I "come up" with an idea (generate it, create it, etc.) and then put it on a map, in between three or four other ideas which are similar but different, defined by those dimensions of differentiation, did I in fact create something, or was it ALREADY THERE?  If I invent a vehicle with three wheels, but on the map before me was a vehicle with four wheels and one with two wheels, wasn't the possibility of a three-wheeled vehicle already there, in between the other variations?  (Along with six, eight, and one-wheeled variations.)  And if all ideas are already implied as variations along a series of differentiated characteristics, are we really "generating" ideas (giving birth to them, with all the implications of genetics, parenting and identity) or are we "discovering" them by exploring an idea space and shining a light on regions previously unknown?