Power = Knowledge^Shared

According to the old adage, with synergy, one plus one equals three. The whole exceeds the sum of its parts.

The adage led us to wonder if there might be an equation that captures the effect of knowledge management, combining the power of knowledge with the power of a knowledge-sharing network.

We start with two familiar ideas.

The first is Metcalfe's Law (described in C. Shapiro and H.R. Varian, Information Rules: A Strategic Guide to the Network Economy. Harvard Business School Press, Boston, 1998).

If there are n people in a network, and the value of the network to each of them is proportional to the number of other users, then the total value of the network (to all users) is proportional to n • (n - 1) =  n²- n  n², for large n.

The second is knowledge is power.

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Let's first see what happens if we assume knowledge accumulates additively in a knowledge-sharing network. In this case, if each person in a network knows k facts that are disjoint from those known by all others, and if this knowledge (sets of facts) is shared among s members of the network, then each member knows k + (s - 1) • k = s • k total facts.

If knowledge is shared among all members, then s = n and each member knows n • k total facts. Therefore, the "power" of the network p = n² • k. This is roughly Metcalfe's law with a knowledge multiplier.

However, the above equation does not account for the capacity of the network to generate new knowledge.

To address this, let's see what happens if we assume knowledge accumulates multiplicatively. Then, in the case where each member shares knowledge with s other members, each member knows k^s. As a result, the power of the network p = n • k^s.

However, this is an overestimate because it does not account for overlap in the knowledge of each individual member. If we assume that the overlap is proportional to the number of members, we get p = n • k^s / n or p = k^s ...

Power = Knowledge^Shared

While the above equation is certainly not a mathematical derivation in any strict sense, it does capture our intuitive understanding of the effect of knowledge sharing. The power of a network is related to the amount of knowledge held by the individual members, how much they share with others (and re-use from others), the number of others with whom they share and the capability of the network to generate new knowledge.

For an organization, the equation suggests a few practical steps.

1. Hire and retain people who have a high level of expertise (and therefore a large amount of knowledge).
2. Hire and retain people who are natural sharers.
3. Hire a diverse population of people so that the knowledge they have is varied; i.e., there is enough similarity so that they can understand each other, but not so much that they all know the same things.
4. Put in place a work environment that encourages and enables knowledge sharing.

The bottom line is power is knowledge shared. Through knowledge management you can increase the power of your organization exponentially to solve problems, to invent new methods, and to overcome physical distance.

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