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The Copernican Hypothesis

The two extremes of evidence based decision making are:

Paralysis-by-Analysis

This expression describes the situation where there is more information than can be assimilated by the decision maker, thus no decision is made.  In practice, this situation arises because the analysis process has not identified the variables which will have the greatest effect on the outcome.  It is worth considering the 80/20 rule which can be loosely interpreted as meaning that 80% of the variance comes from 20% of the variables.  In other words, find the ones which matter.  In the realms of commerce, analysis-by-paralysis often occurs in mature, data-rich businesses that need to change.

Next-to-Nothing is Known

The other extreme is where very little is known, but a decision still has to be made.  Attempting to move forward in this environment has attendant risks and success is largely the result of good entrepreneurial skills.

It is in this latter case, that the Copernican Hypothesis can prove to be useful.  It can be roughly stated as "If you don't know where you are, there is nothing special about it, so assume you're in the middle".  The concept is used to speculate about the lifetime of species and the geometry of the universe.  The example is based on rail travel.

Copernicus and Network Rail

Part of my job involves travelling around the South East using the bus and rail networks, I have no time constraints other than to visit a set number of places within the space of a day.  With the exception of of some cross country bus routes, the service frequency is usually better than one bus or train per hour.  Time spent messing with timetables is time which could be better spent with a book, writing notes or a bottle of wine.  For practical purposes, it is only necessary to know that a service exists.  On a couple of days, when I arrived at a station I took a note the time of the time I got there, the time of the train I had missed and the time of the next train I could catch.  Other than moving as swiftly as possible, I make no effort catch a specific train, the time of my arrival at a station is a random variable (as is sometimes the station at which I arrive).

The Copernican Hypothesis suggests, that on average, I will arrive at in the middle of of the interval between the departure of the train I missed and the next one available.  Here are my notes:

Journey Departure of missed train Departure of next train My arrival time My arrival as fraction of service interval
1 11:58 12:11 12:03 0.38
2 12:33 12:52 12:44 0.58
3 12:55 13:04 12:56 0.11
4 08:02 09:04 08:55 0.85
5 09:37 10:07 10:07 1.00
6 10:15 10:58 10:45 0.70
7 11:26 12:00 11:44 0.53
8 12:28 13:01 12:52 0.73
9 13:53 14:15 13:57 0.18
10 15:36 16:36 16:07 0.53
      Mean 0.56

Over ten journeys, I arrived at a time which was on average 0.56 of the service interval.  It is a measure of my dedication to the study of maths and stats that in several hundred journeys, I have managed to document only ten, thus I don't have a value for the population standard deviation.  The data gives an unbiased estimate for standard deviation of 0.28.

The Copernican Hypothesis suggests that for all journeys, on average, I will arrive at a time which is 0.50 of the service interval.  Is my sample of ten journeys consistent with this?  The difference between 0.50 and 0.56 is within the range consistent with random variation.

Page updated: 06-Jan-2010

 

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