I recently made the argument (successfully?) that computers automate by nature; that anyone who uses a computer is by definition an automation engineer. Couple that with the observation that humans are always "testing something", and one could suggest that anyone who uses a computer is a test automation engineer.
For example, the Internet is automation of data retrieval, one that is engineered based on how we use it. My parents would not immediately identify weather widgets on Google as test automation. They just want to know if they need an umbrella when they go out. I, however, see a dashboard that allows them to interpret important data relevant to their needs and allows them to make decisions based upon their interpretation of that data.
Did they program it? Well, yes and no. While they did not sit down and write the statements that brought this convenience into their lives, they did set its preferences, position where they deemed fit, and ensured that it welcomes them with each new visit. Without these interfaces, the tool is of less use to them.
Another example: spreadsheets help automate data manipulation and presentation. My wife would not immediately identify a budget workbook as test automation. She would see it more of a way to track income and expenses, and how to identify if we're on target this month, can we go on vacation, etc. I, however, see it as a tool that allows us to repeatedly take all our disparate financial activity and produce a cohesive picture that allows us to manage our money better - to make better decisions (or to know the precise value of regret).
Did we program it? Well, yes and no. While we did not sit down and write Excel, we did set set up its inputs and its formulas using the interfaces exposed to us.
The differences between my definition and what is typically identified as test automation engineering have to do with complexity and intention - the scope of our solutions and how aware we are that testing/automating is going on in the first place. Like regular users, we manipulate the interfaces available to us in order to obtain data, arrange it into meaningful statements, test those statements for validity, and make decisions based upon those tests. Where we differ is how aware we are of the interfaces available to us, and how extensively we use them in our tasks.
One side note: neither of the tools used in the my examples actually automate information. That is the sole purview of people - to identify patterns and meanings. These tools may re-organize the underlying data, but we are the ones who are burdened with determining if this stuff makes sense or not; if it is valuable or not.
Hopefully you get my gist: we all use computers to automate tasks that are important to us. We all use more automation tools than we realize. We know more than we think we do, and do ourselves a disservice if we believe that the high-priests of automation are the only people worthy enough to discuss its doctrine.