We at ManyWorlds have spent the past couple years researching the future of learning, and thinking deep thoughts about the subject. See our recent white paper, “The Future of Learning”, for an overview of some that research. One of the modes of thinking we apply to any subject we are studying seriously is to model it mathematically. Following is a somewhat serious, somewhat fanciful, summary of what I call the “calculus of learning”.

Let’s start with knowledge. Knowledge is a stock – you can measure it in absolute terms (in theory) at any point in time. Learning, on the other hand, is a flow. As a flow, learning is really just the difference between stocks of knowledge at two different points in time. In other words, in the terms of calculus, learning is the derivative with respect to time of the knowledge function. Inversely, integrating the learning function over a period of time yields a stock of knowledge. So in Newtonian terms, knowledge is analogous to distance, and learning is analogous to velocity. Or, if you prefer accounting to calculus, think of knowledge as the balance sheet, and learning as the income statement. (And yes, you can have negative net learning, just like you can have negative net income – I can cite some examples!)

Ok, simple enough. But even the calculus above delivers some insights. For example, it makes really clear just how inseparable knowledge management is from learning processes, even though many organizations seem to try their hardest to keep them separate.

All well and good, but let’s kick it up a notch (apologies to Emril Legasse). Arie de Geus is famous for the idea that the only sustainable competitive advantage is to learn to learn faster than the competition. (Just to set the record straight – that phrase actually originated with a friend of mine at Royal Dutch/Shell Group, Renata Karlin, who is Shell’s current resident scenario planning expert). Leaning to learn faster? Let’s see, that is the change in the rate of learning, meaning the derivative of learning, or the second derivative of knowledge. In Newtonian terms that’s analogous to a change in velocity, which equals acceleration!

So sustainable competitive advantage = the first derivative of learning = the second derivative of knowledge.

It makes sense — think about it – the great human advances have revolved around infrastructure that has enabled learning to learn better. Language, writing, the Internet, all fit in that category of break-through infrastructure. The kinds of infrastructure that serve to not just increase, but to accelerate the increase, in the stock of knowledge and understanding.

Going back to Arie, for businesses, the imperative, then, is to turn the equation of sustainable competitive advantage into reality, not just a quaint slogan. To find the levers that really do accelerate learning. And clearly our math suggests the levers will be at the intersection of the fields of organizational learning, information and knowledge management, and information technology.