For work, I tend to have to explain quantitative ideas to people with only some informal computer science training.
Yesterday, my friend wanted to draw a map on his computer and was concerned we could locate specific latitude and longitude on his computer screen. This image is 256 pixels across and 256 pixels wide.
Here a really close-up view of San Juan, Puerto Rico. According to Openstreetmap the scale is
Level Degree Area m / pixel ~Scale 13 0.044 village or town 19.093 1:70,000 14 0.022 9.547 1:35,000* 15 0.011 street 4.773 1:15,000
Since all maps are stored as squares tiles of various sizes, he has to identify the tiles he will need and place them together himself.
Then if he wants to identify specific landmarks - he needs to compute the proportion between the pixels and the lat-long using information he can find in this page on the various zoom levels or other resource.
Even though it is easy to point things out on a map, this is because computers do the quantitative reasoning for us. This is about as simple as I can make the work-flow for my friend -- and I didn't do nearly as good a job yesterday.
These concepts are not obvious and it took me a while to learn about map projections and re-learn them when using them on a computer.
The "math" involved was hardly traditional... I think we do one or two multiplcation problems in the entire process. Instead we deal with issues like scale and proportion maybe angle.
Worst of all, I didn't get to explain to him that in Mercator Projection, column 4 - meters per pixel - actually changes with the latitude on the map
What level would this be considered? More importantly, this computation is a sequence of steps I will have to explain over and over - how could I explain this better?