There is a binary test for a programmer: someone with basic proficiency in a Turing-complete language. I like this answer on SO about what that is:

https://programmers.stackexchange.com/questions/132385/what-...

> In general, for an imperative language to be Turing-complete, it needs:

1. A form of conditional repetition or conditional jump (e.g., while, if+goto)

2. A way to read and write some form of storage (e.g., variables, tape)

For a lambda-calculus–based functional language to be TC, it needs:

1. The ability to abstract functions over arguments (e.g., lambda abstraction, quotation)

2. The ability to apply functions to arguments (e.g., reduction)

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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.