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February 2003    Feature
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No. 70
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Knowledge Arithmetic

David J. Skyrme

We talk of the 3Rs of basic literacy - Reading, wRiting, and aRithmetic. Some of the core elements of knowledge sharing (at least knowledge expressed in explicit form) require the first two. But what about arithmetic? Knowledge is so diffuse and varied that it does not lend itself easily to manipulation by numbers - or does it? In this article I consider some fundamentals of knowledge arithmetic. I don't promise any mathematical breakthroughs, merely another way of looking at some aspects of knowledge management.

1. Knowledge Addition: 1 + 1 does not equal 2.

This is probably one of the best appreciated rules. If you combine two items of knowledge, you often finish up with a result that is worth much more than the individual components. People from different disciplines who enter into dialogue can often create innovative breakthroughs that individually they could not. On the other hand 1 + 1 could result in less than 2. How many company mergers end up reducing value for their shareholders, often because key knowledge workers leave or a clash of cultures or incompatible systems (a key part of structural capital)? Knowledge combines in complex mathematical ways that go beyond simple addition.

2. Knowledge Equivalence: 1 does not necessarily equal 1.

Developing a common language is an important enabler of knowledge sharing. However, language evolves and there are local (context sensitive) dialects. One organization's structural capital is anothers organizational capital. One person's pavement is another's sidewalk. And if you're in a specialist field, you soon create and use jargon that is impenetrable to outsiders. If people want a proper knowledge sharing dialogue, then they must take time to adjust to language differences, and listeners must not feel that are disruptive if they keep asking for clarity. This may, after all, encourage speakers to articulate their thoughts more clearly. When computers talk together they need agreed standards (such as XML schemas) to communicate accurately. In an organizational context, you will communicate better if you to keep glossaries for projects that connect with the outside world.

3. Knowledge Multiplication

In KM literature you will come across the notion of the IC multiplier (attributed to Leif Edvinsson). This is the ratio of structural capital to human capital. People are not easily cloned, so can't easily be in several places at the same time, yet documents and databases can be. People are also relatively mobile, so if a person leaves your organization, that's a diminution in human capital. If some of their knowledge is captured into structural capital, then any such loss is mitigated. A higher IC multiplier means that the impact of human capital is multiplied through structural capital. That's why turning some of your most valuable tacit knowledge in to the explicit form of knowledge assets is an important element of any KM programme.

4. Knowledge Division

It is quite common to subdivide a body of knowledge into smaller more manageable chunks. We often use taxonomies to categorize these elements of knowledge and put them into the appropriate boxes. Specialists can then develop that knowledge further. There is also a growing trend in subdividing large problems into smaller chunks for parallel information processing and taking advantage of people's unused PC resources. Drug companies, cancer researchers and aerospace manufacturers now do this as routine, while one of the early pioneers of this approach - SETI@home - is still searching for intelligent life in space with the help of the processing power of home PCs. The problem with division is two-fold. First, there is danger of losing the holistic view, loosing sight of the wood from the trees, as it were. Then there is the problem of interfaces between the different nodes of knowledge. What type of bridges (language translators and knowledge flows) do you need between them? Knowledge division is a sure way of fragmenting knowledge and losing its value. But humans have limited processing capacity, so to some extent it is inevitable. To overcome this it is important to maintain an overview. Just as a project manager oversees what's happening in the many strands of a project, so you need a meta-knowledge manager to keep tabs on the whole body of knowledge. And to help with the overview, the individual elements of knowledge must have descriptive wrappers (metadata) that tell others clearly what gems are held within.

5. Exponential Knowledge

This works in two directions - up and down. In the upward direction knowledge appears to be increasing exponentially. There has been more new knowledge created in the world in the last few decades that in all of previous human history. This can be beneficial - our knowledge of the human genome is one example. But it also creates problems, some practical, some ethical. On the practical side, how do you tell valuable knowledge from mere volumes of data? Should you keep pace with the growing demand for storage capacity? What are appropriate retention and archiving strategies? On the ethical side, what if you have gained some potentially harmful knowledge. With whom should you share it?

On the downside, the usefulness of knowledge decays. It has a 'half-life'. Nuclear physics provides an analogy. The rate of decay of radioactivity depends on the amount that remains. It therefore decays exponentially so the time to decay to zero is theoretically infinite. Therefore we talk in terms of 'half-life', the time period by which their potency is reduced to half. The half life of Uranium-235, for example, is 713 million years, while that of Cobalt-58 is 71 days. Other man-made radioactive isotopes have half-lives of hours or even milliseconds. What is the half-live of your knowledge? Different knowledge has different half-lives, so different replenishment strategies are needed.

Numbers and Knowledge Processes

Now consider the nature of knowledge work. Simply stated we take knowledge inputs, we process them and generate knowledge outputs. If things were that simple, we could develop some straightforward mathematics that defines conversion efficiency rates. But knowledge transformation is not a highly structured process. There are many interactions. However, a cursory consideration of knowledge mathematics help give us think about how different arithmetic operators influence different stages of the knowledge life cycle. Some examples:

  • Knowledge creation - addition and combination creates new knowledge. The number of knowledge sharing connections in a team or network is a function of multiplication. Division appears as part of the conversion ratio - how many good ideas are followed through to implementation?

  • Knowledge organization - categorization is an aspect of division. But other branches of mathematics features - group theory and statistics. How distinctive are different categories? Are there patterns and clusters of words that identify distinctive concepts?

  • Knowledge diffusion and dissemination - the multiplication factor is dominant here. Because of the lost cost of information reproduction, one item of explicit knowledge can be multiplied many times. But, exponential arithmetic also features. The rate of diffusion of knowledge is largely proportional to the numbers of people who already have that knowledge.

  • Knowledge absorption - it's all right to diffuse knowledge, but has it properly been absorbed and understood by the recipient? The level of absorption depends on division. What is the capacity of the recipient divided by the number of items of knowledge to absorb? The lower this ratio, the less chance there is of accurate comprehension?

Of all the operators, multiplication is perhaps the most powerful. From a small number of knowledge elements, the number of combinations or knowledge recipes multiplies rapidly. For example, it is estimated that from choice in twelve parameters of an automobile - body trim, paint colour, engine etc. - over 20 million variants of a Ford Fiesta can be created.

But there's another arithmetic operator, that we haven't yet discussed, and this is perhaps the most important one of all.

6. Knowledge subtraction.

Once you have learnt something, it's difficult to unlearn it. Sometimes we wish we could take away old knowledge, not just to make room for some new, but to stop us repeating mistakes, or to remove knowledge (such as that to create nuclear weapons) where it might be abused. But the real value of subtraction comes in what we subtract from our total knowledge when we express something. We all know a lot more than we can write, but sometimes when we write, we write too much. Delivering a thoughtful 3 minute presentation can be more challenging that a one hour lecture. Putting a business proposal on one page of paper is harder than spreading it over many more pages. Applying the concept of knowledge subtraction forces you to figure out what is valuable and what is trivia (or supplementary knowledge for later) in a given situation.

Narrative As Well As Numbers

In the examples above, we have only just scratched the surface of knowledge mathematics. Some academics have developed complicated mathematical formulas on the way that knowledge behaves and is transformed. We have just taken some of the most common arithmetic operators and suggested how they add a perspective to some typical knowledge problems.

But what we must remember is that it is not easy to express knowledge in numbers. Even in the field of knowledge metrics, those who have practical experience of developing and using knowledge metric stress the importance of narrative to accompany the numbers. Examine any intellectual capital report and you will find that the numbers are only a small part of it - see for example the IC Report of Carl Bro that also uses pictures. All knowledge value-adding processes depend on dialogue - knowledge creation, knowledge sharing, knowledge dissemination.

Therefore, while mathematics may provide a useful notation for certain types of knowledge, its the narrative that makes the numbers meaningful.

And if you have anything to add, remember the power of subtraction!


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