I know I promised triangles last time, but to get a triangle, we need to start with a line. If we collapse one of the dimensions into a straight line, we get a representation of that dimension. Now, if we take the lines we get from collapsing both diversion and sport into two straight lines, we can place them perpendicular to each other to form a two-dimensional space. As you see, we've created a chart with two axes:
Using this chart we can express our opinion about the relative quality of the game, first by assigning a value to "sport":
The quality of sport is mapped onto the "Sport" axis
...assigning a value to "diversion":
The quality of diversion is mapped onto the "Diversion" axis
...and then drawing a line on the chart from the "quality of sport" value to the "quality of diversion." The length of the line gives an approximation on the perceived quality of the game:
The quality of the game is represented by the length of the line
Obviously, these are subjective judgments at this point, and they will remain that way to a large extent. But we can use this method to visually demonstrate that a game with lesser values of sport and diversion has less quality:
Game 2 is of lesser quality
...and that a game with the same diversion value of the first game and the sport value of the second will have a lesser quality than the first game, but a greater quality than the second.
Game 3 is amusing, but offers little in the way of sport
This all seems self-evident, but illustrates a key point. We can agree about the quality of games when we are looking at both of these dimensions, but if there were a player who only looking at the sport dimension while another looked exclusively at the diversion dimension, they would inexplicably find that they disagreed about the third game--inexplicably because they were in almost complete agreement about the first two! Notice:
Both players agree Game 1 is good
Both players agree Game 2 is not as good as Game 1
One player thinks Game 3 is as good as Game 1 while the other thinks it's as bad as Game 2
Until the two players understood that they were grading a game using two different dimensions, they would be stuck forever talking past each other. While it's perfectly valid to decide that diversion is the only dimension worth looking at when judging a game, or that in certain contexts the sport dimension requires greater emphasis over the diversion dimension, we must be using a common language in order to communicate.
In the next part we'll identify some complications with this metaphor and ways we can address them.