Tuesday, October 16, 2012

A thought on taxonomy of knowledge

In Daniel Engber's review of  The Half-Life of Facts: Why Everything We Know Has an Expiration Date by Samuel Arbesman, it is pointed out that we can categorize facts into:

  • those that never change, such as the atomic weight of Hydrogen,
  • those that change all the time, such as the price of a stock of the Dow Jones Industrial Average.
  • those that change at an rate somewhere between these two.
The population of the United States changes, growing by a small percentage per year. The rate of change of the population changes even more slowly. We might consider that there is a continuum on which the rates of change of facts may be located.

If we think of a fact such as how many genes are known, the rate of change was relatively low when few genes were known, increased rapidly with the development of gene sequencing technology, and for humans must trail off as all the genes eventually become known.

We can assume that the total number of known facts increases over time. Of course, some of the things we find out mean that some of the things we once knew are now seen to be untrue. Thus, as Arbesman points out, there is a decay of knowledge as well as growth of knowledge.

Knowledge has value. Not all knowledge has the same value, and the value of a piece of knowledge may change over time. Consider technological knowledge, such as how to grow a crop. The income of farmers growing the crop who have the knowledge can be compared with that of farmers growing the crop without the knowledge in order to determine the value of the knowledge itself. But farming technology changes as new crop varieties are developed, as new diseases and pests are encountered, as new chemical inputs are made available, etc. We can assume that little of the knowledge about farming that was valuable in the 19th century is valuable today.

Again, we can consider the value of technological knowledge as distributed over a continuum, and the rate of depreciation of that knowledge also distributed over a continuum, leading to a distribution over a two dimensional space. Alternatively, we can think of different pieces of knowledge describing trajectories on a graph of current value versus time.

Our access to knowledge is changing rapidly. For example, as the Internet grows and as we get better in searching the Internet, the amount of knowledge that is reasonable available to us grows. We find however, that as we go down the list of pages returned in a Google search, the expected value of each added piece of information goes down (assuming that the page ranking algorithms work well),

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