Sexy Math For Lawyers : Gott’s Principle To Estimate How Long Something Will Endure

Thinking about new ways to approach difficult problems is something we enjoy, and something we have in common with our lawyers.

Whether it’s a different way of measuring key metrics, a cool use of game theory, or just a novel way of challenging a long-standing established practice, thinking through problems from different angles is a big part of finding innovative solutions.

One particularly interesting technique is the “Gott Principle”, a simple method for estimating the remaining life of something knowing only how long it has already survived at the time it is observed. It’s about making estimates with virtually no information at hand.

Developed by physicist J. Richard Gott, his method accurately predicted the expected run of Broadway shows, the survival of the Berlin Wall, and many other things.

To use a specific example, we could ask a question such as:  Whose music is more likely to be listened to 100 years from now – Bach or Britney Spears?

Expressed mathematically, Gott says that there is:

  • A 50% chance that your particular observation, when made, is occurring somewhere in the middle 50% of the true full lifetime of the what you’re observing (i.e. Britney Spears’ music popularity);
  • A 60% chance that it’s in the middle 60% of the true full lifetime; and
  • A 95% chance that it’s in the middle 95% of the true full lifetime.

If we assume we know only one fact about both – specifically, how long their music has been around at the time we’re asking this question – we can answer the question with Gott’s principle.

Again, we’re assuming that we know nothing about the underlying facts surrounding this question i.e. we’re not a music teacher, a music afficiando – we may not have heard of either Bach or Spears at all). The analysis works like this:

Bach’s music has been popular for about 310 years; Britney’s music for about 12.

Using Gott’s Principle and a 60% confidence interval, we could estimate Bach’s music to be popular for another 77.5 – 1240 years.  Britney’s music between 3 – 48 years (arithmetic is calculated below for the hardcore math attorney).

So, whose music is more likely to be around 100 years from now? Bach, by far. And we don’t need to know anything about music to make that conclusion. (If we were music experts, we may better use other methods to come to these estimates. The point is that we’re assuming we’re not experts, and we have no better information available to us.)

Now, of course, as the confidence interval increases, Gott’s method can result in very wide ranges. However, it’s important to reiterate that this is a method best used in situations where no specific facts or knowledge is available.

Gott says we can approach such a situation, and instead of simply throwing our hands up and saying an estimate is impossible because we don’t know enough about the other operative facts, come up with a reasonable, defensible framework for analysis.

The method itself is useful, but the concept is much bigger.

That is, skills that great lawyers work with everyday – creative thinking, analogy, and logic – can go a long way in developing workable solutions for problems that initially appear to be completely inestimable, too complicated, or having too many moving or unknown parts to solve.

That’s a skill that many lawyers are terrific at, and the type of skill that clients will value long after document assembly, and other “commodity” type services have lost most of their value.

FOR THE HARDCORE MATH ATTORNEY:

Using Gott’s rules, we’ll construct some simple parameters.  We’ll use the letter ‘t’ to stand in for the age of the observation at the time observed (i.e. how long Britney Spears has been popular).

50% confidence level: Minimum duration = t /3;  Maximum duration = 3 * t
60% confidence level: Minimum duration = t /4;  Maximum duration = 4 * t
95% confidence level: Minimum duration = t /39;  Maximum duration = 39 * t

Using Gott’s Principle and a 60% confidence interval, we could estimate the continued popularity of Bach’s music.
t=310
Minimum = (310/4) or 77.5 years.
Maximum = (4 * 310) or 1,240 years.

The same math gives us Britney’s paltry popularity ranging from 3 to (please let it be the minimum! please please please!) 48 years.