 Consider this task. Select a letter from this tableau. Then, without identifying the letter by name, describe where the letter is in enough detail that someone else could also select the same letter. Now think about how you describe the position of your chosen letter. What words did you use? Now I will choose a letter. Can you also describe for me the position of the letter I? Let me see if I can find it based on your description. I'm guessing now that you may have made some assumptions in creating your description that may not seem quite so valid at the moment. For example, it's likely that you use the terms like upper right or maybe near the corner that may not be so valid from this new perspective because I don't see a letter I anywhere in the upper right or near a corner. Although it is generally not necessarily a normal conversation, a detailed definition of context known as a basis can be important for accurately describing locations in physical space. And there are three key elements to establishing a basis. First, we must establish a reference location, some unmoving place in space that can easily be identified by any observers who will care about our description of position. Yes, every description of where begins with a known starting point which we will formally name as the origin. Now, next, we must confirm a reference orientation indicating directions in space that will have a prioritized meaning. There are different ways of indicating this depending on the system that we choose to work with but the goal is to communicate how three-dimensional human beings like myself and you are expected to be oriented as we observe the space around the origin. For example, here I might define an arrow there as this being up and this being to the right. Finally, we must indicate a scale which consists of one or more reference units of length or a distance between two locations. For example, perhaps we might say a scale is something from a distance between this point here, right in front of my face and another point a little further to the right of that origin and that there might be a single unit in our scale. The combination of these three elements, the location, the orientation and the scale will then allow for a quantitative description, one that uses numbers for identifying locations in space. Origin, our reference location, orientation and scale. We will use each of these three as we define coordinate systems used to describe locations in two and three-dimensional space.