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.
