Convention (3) – why we need conventions

In this post, I shall give a couple of examples to illustrate why we use and need conventions.

3D Space

For the first example, consider 3-dimensional space as discussed by mathematicians and scientists.  We usually represent objects in space in terms of coordinate axes.  We typically use an x-axis in the left-right direction, a y-axis in the forward (away from me) direction, and a z-axis which is vertical.

The first thing to notice about this choice of axes,  is that the choice is rather arbitrary.  When I am at home, the x-axis is in a north-south direction, because my desk happens to face east.  And at work, where my desk faces roughly north, the x-axis is close to an east-west orientation.  The direction of the vertical axis also changes with location, due to the curvature (the spheroidal shape) of the earth.