Something From Nothing - Predicting the Future

How often have you wondered how long a supplier, relationship or employee will last?  How often have you been surprised when something that you expected to be constant suddenly changes?  All too often, we would like greater insight into the future, but lack tools for estimation.  One very useful estimation tool has been put forward by J. Richard Gott, a Princeton astrophysicist based on the notion of the “Copernican Principle”.  The Copernican Principle is named after the astronomer who rejected the notion of Ptolemy and proposed that we (on the earth) are not at the center of the solar system.  Gott’s application of this astrophysical theory to time based estimation is to indicate it is unlikely we are making an observation at a special, but much more likely to be predicting the future from an unremarkable time.

The time analog to the center of the solar system, is we are not observing a phenomenon at a special time, so it is just as likely that we are sampling a process at a random point in time.  In fact the longer something has been around; the longer it is likely to last.  For example, if one were sample a process and desire to make a prediction at the 95% confidence limits, it is unlikely that this point in the process is be in the first 1/40 whole duration (2.5%) so it is just as likely to last 39 time longer, and conversely, it is probably still in the first 39/40 of its total lifespan, and not in the final 1/40 – so you can predict the remaining lifetime is likely to be at least 1/39th of the time.  These two estimates, defined by the upper and lower 95% confidence limits define a range (rather large) of the possible duration.  And if we look at 50% confidence limits, it is just as likely that we are in the first half as the second half of the process, so we would estimate the total duration as twice the time of existence.

This range of estimates corresponds approximately to the 2 sigma limits, and the mean, in the Gaussian curve below.

Similarly, we can predict to the 50% confidence that we are in the middle of the lifespan, so if a process (such as the lifetime of a Broadway play, something Gott analyzed) has lasted 52 weeks, our best estimate for the total lifetime is another 52 weeks (again, without any other information or better estimates).

The range of T/39 < t < 39*T for 95% confidence is often too wide to be of use in technical & management consulting, but using the point estimate of the average can be a very good gauge.  Here are some examples where this estimation technique can provide useful guidelines.

-          Lifetime of partner relationship

-          Lifetime of a consulting business

-          Length of an engagement with a client

-          Lifetime of  a startup

-          Lifetime of a vendor

-          Lifetime of a business

-          Duration of employment

-          Time to fill an open requisition

-          Longevity of a process

-          Time in position

So in the future, you are trying to estimate the likelihood a partnership will be around in another 2 years, the first thing to ask is when did we get started.  Although it is a very coarse estimate, a coarse estimate is much better than no estimate.