Using mathematics and category theory to gain understanding
Let's work with something we can relate to soccer!
How can we know the position of a ball in the air as it moves from Messi's foot into the goal?
Note that due to spin on the ball and the imbalance of air pressure, when in the air, the ball may curve left to right and up and sharply down.
Note
Check out Messi's curving goals here:
Suppose we have a small soccer field with the dimensions of 50 yards X 100 yards and a net that is 8 feet tall. The height of the goal is the z dimension:
If the sun is directly overhead and makes a shadow on the field, then we can know the x, y coordinates. If we can also measure the height of the ball as it moves, then we know the z coordinate. Combining both of those pieces of information, we can know the ball's position in the three-dimensional space.
The following diagram says that if we know A and B...
