Saturday, January 10, 2009

The myth of the exponential

Continuing on a theme related to my recent post about so-called accelerating change, I also get annoyed every time I hear somebody claim that some process is "exponential." While it is certainly true that many processes can be "exponential" for periods of time, it is always the case that eventually some limits are reached and the process ceases to be exponential, meaning that the overall process is not exponential at all. Availability of resources is one of the most common limits that is reached. In human social processes, mere desire may be the limiting factor. For example, a group might grow exponentially while relatively small, but the desirability of being part of the group may decline when the benefits of the group are no longer achievable with a large group size. Communication overhead, crowding of voices, and limitations of meeting space may deter the former "exponential" growth. Another example would be a process that depends on a scarce commodity that is available in moderate supply for low or moderate demand, but whose price rises ("exponentially"?!?) as demand rises, once again dampening the effective growth rate so that it is not exponential at all, except for a short stretch of time.

A true exponential rises to infinity, but a typical real-world process that rises rapidly will typically reach a stage where the rate of change declines rapidly and may even reverse.

In my experience, people label a process as "exponential" simply because it is currently fast, without any deep analysis of how the process might evolve far beyond the very near future. And the real problem is that people are using the recent past to project endlessly into the future.

People sometimes talk about the world population growth being exponential, but the fact is that global population growth has been slowing since the 1970's. The simple fact is that processes evolve, which results in changes to their rate.

The core problem to me is that people are using the "exponential" label as a hit-and-run sales tactic, less interested in truly enlightening us about the future and more focused on attracting our attention in the near term to serve some undisclosed agenda. Besides, if a process really is exponential, you are not really losing out by failing to jump in early since later growth will be just as great for latecomers. But the sad truth is that current excitement is a poor indicator of future growth.

The real truth is that time is the enemy of all supposed exponential processes. Not the enemy to the process itself (such as global population), but enemy to the claim that the process rate is "exponential."

-- Jack Krupansky


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