> Note that you can be a programmer without ever having touched a computer, people have been coming up with algorithms and integrating them into systems for ages.

Slightly different, but the first episode of SICP videos helped me to reach the same conclusion:

https://www.youtube.com/watch?v=2Op3QLzMgSY

We can even say Newton, or Euclid wrote programs. Maybe not by sitting in front of a computer, but they described a process to calculate something.