The parable of the three builders

Once upon a time, there were three builders.  Each of the builders purchased a large parcel of land, intending to subdivide that parcel into smaller lots on which to build houses.

As the first builder erected his houses, he managed to find buyers for them.  He named the houses after the buyers.  The house purchased by the Campbell’s was known as “The Campbell Residence”.  All went well for a while, though people did find it a bit tricky to keep track of the names of all of the houses.  But, after a few years, the Campbell’s moved out and sold their house to Mr. and Mrs. Robert Smith.  So now, what had been known as “The Campbell Residence” had to change its name.  And it could not be called “The Smith Residence”, because the Mr and Mrs William Smith also owned a house in this parcel.  So what had been known as “The Campbell Residence” now had to be renamed as the “The Robert Smith” residence.  And, to avoid confusion, what had previously been known as “The Smith Residence” now had to be referred to as “The William Smith Residence.”

The second builder also erected houses and sold them to buyers.  But he decided to be more systematic by assigning names to the streets that were used for access to the house.  So there was an Elm Street, an Oak Street, a Poplar Street, a Pine Street to name just a few.  The builder put house numbers on the houses, so that the houses could be given street addresses, such as 121 Pine Street.  The people in the second builder’s parcel found it easier to keep track of the locations of houses.  And when one family moved out and sold their house to new buyers, they did not have to make any changes to the street addresses being used to identify the houses.

The third builder was even more systematic.  He made sure that the streets were equally spaced.  The names he used for the east-west streets were First Street, Second Street, and so on.  And for the north-south streets he used names First Avenue, Second Avenue, and so on.  He arranged the numbering so that for the houses on an east-west street that were between Fifth Avenue and Sixth avenue, the houses were given numbers between 500 and 599, with similar assignments for the other streets.  It was very easy to keep track of location in this parcel.  The street addresses were like mathematical coordinates in a grid.  You might even be able to find ways of using a differential equation somewhere.