I am writing a line right now. If I was writing in Chinese would I be writing a line? Maybe I would be writing a vertical line. If I was writing Hebrew I would be writing a line in a different direction.
If I look around my space right now I see a lot of lines. I see the lines of the contour of a lamp, I see the lines of the scaffolding of another lamp, I see the outlines of pillows, I see the lines of hair, I see the line where the sleeve of a shirt crosses the arm.
My fingers feel the computer keys, and the lines that delineate each key. If I hold my guitar pick between my thumb and forefinger I can feel the line of the pick that is the edge. Edges can often be represented as lines. Edges can also be represented as boundaries.
There is a mathematical study of edges called graph theory. In graph theory, a Graph is defined as G = (V, E). This looks very mysterious but really it means a Graph G has Vertices V and Edges E. Edges are represented as two vertices, as the line between two vertices.
This is from a website about programming graphs with python, but also discusses the application of graphs in different industries. Since the advent of social networking software a lot of work has gone into thinking about graphs and networks, just think about things like your linked in network, or your friend network.
Graph theory is the mathematical study of the relation between things. Different collections of nodes and edges can have different shapes, just like four lines can form a square or a rectangle or a rhombus in geometry. We can have directed graphs where the lines have a direction (think of an arrow), we can have mixed graphs where some lines have directions and some do not, and we can have lines that have attributes like cost or weight.
The history of graph theory can be traced back to Leonard Euler.
Euler discussed how one could walk through Konigsberg and cross each of the Seven Bridges of Konigsberg only once. It you are new to it, it may seem strange that this would be a mathematical problem. But this expands the idea of lines to maps and routes and connects them with a way to abstract these issues with mathematics.
In the Liddell and Scott Greek Lexicon, online, we can see that the mathematics comes from the greek word μάθημα (mathema): learning, knowledge, that which is learned. It is also related to specific disciplines of geometry and astrology. It is interesting to think of the disciplines of the ancient greek world and something like philosophy (lover of wisdom) vs something like mathematics (knowledge/learning). Today we seem focused on knowledge and there is a convergence in the sense that the most valuable knowledge these days, in the market economy is mathematical knowledge, or perhaps scientific knowledge (physics, chemistry, or computer science). That there is this other path to understanding perhaps different from knowledge, or mathema, is not something that we discuss.
This photo of neolithic cave paintings from thoughtco displays the lines of the hands. There is no connection between the hands unless the hands overlap or the edges of the hands overlap. We can imagine here that there are no edges like modern graph theory but only nodes, and the boundaries of those nodes have different attributes, color, size weight. The boundaries overlap with one another and put objects in relation to one another - there is no additional construct called an edge.
(I also love covers)
xo
Meredith