Introduction and Idea Sinks

Welcome to my blog. This post will serve as an introduction to why I am starting it, share a little about what it will be about, and do so with some basic principles from graph theory. Let’s get started.

A mathematical graph is made up of two components, nodes (points) and edges (connecting points). A graph is simply a group of nodes, connected by edges. These edges can be either undirected (go both ways) or directed (one-way). For our purposes, we will be focusing on directed graphs (points connected by one-way arrows) as shown in the diagram below. A graph is just an abstraction used to show the flow of some resource between points. For example, trade patterns can be represented as a directed graph where each port is a node and the goods being transferred are the edges. Now that we have a good idea of what graphs, nodes, and edges are, we’ll define a special type of node called a sink.

Fig. 1. A directed graph with a sink

A sink is a node in a directed graph that has edges coming into it, but no edges coming out the other end (the red node in Fig. 1). It has input, but no output. In the maritime trade graph, a port that receives goods from at least one other port but does not send any goods out would be a sink. With these requisite terms defined, we can begin to look at why graphs and sinks are important to an introductory blog post.

Let’s extend this analogy from ports and boats to people and ideas. If our graph represents the transfer of ideas between people, the ideas will be the edges and the nodes will be the humans (another perspective uses ideas as nodes and humans as edges, but that’s for another day). We all consume ideas every day, ranging from in-person dialogue to various forms of media. Likewise, we also share ideas every day, often through the same channels. So although there is both input and output for our nodes, lately I have been feeling like my inputs vastly outweigh my outputs (see Fig. 2). I have been feeling pretty sink-y.

Fig. 2. A node where input outweighs output

Much of the media I consume is from social media like Twitter and Reddit. Not only am I reading posts on the platforms themselves, but also coming across interesting articles, books, videos, podcasts, and other mediums for spreading ideas. Combine this with all the things I have learned in school and work over the years and there are an awful lot of edges coming into my node. Until now, my primary output vectors have been assignments for school and work. These outputs are mostly a product of a narrow group of inputs (again, school and work related) and do not overlap much with all the other ideas I’m consuming in my free time. Despite occasionally coming up in conversations with friends, most of the media I consume is rarely passed on. Since there is a small amount of output the analogy isn’t perfect, but my node on the information exchange graph would be dangerously close to a sink.

Fig. 3. A rough self-portrait of me, as a node, excluding edges from school and work

My motivation for writing these posts is simple - to avoid becoming a sink. While writing has all kinds of great benefits, like organizing the many inputs to develop original ideas, its primary purpose is to share ideas. If they aren’t shared, ideas get lost in the sea of time. I am bound to forget most of the ideas I consume. By writing to others the ideas can live on and perhaps I will have some unique combination of inputs that allow me to produce some novel output in a way that clicks for somebody else.

Fig. 4. A node with well-balanced input and output

The concept of sharing ideas is fairly simple and this sentiment can be expressed in plenty of other ways i.e. switching from a consumer to a producer. In fact, using a mathematical model is probably overkill in this case, but there is some beauty in seeing how applicable these models are to everyday life. There are a certain clarity and rigor that the model provides. That being said, I do not have a set plan for the type of output I will produce. There may be more posts like this, applying models from math, but I also plan to share thoughts on the media I’m consuming and things I’m thinking about. I’ll even try my hand at writing some satire. The main goal is just to take some of the input and turn it into output.

Thank you for reading. I hope you learned something about graphs and sinks or at least discovered a new input arrow.

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