This is a great explanation and I hope it will help your parent commenter realize that, while different and not trivial, this stuff really isn't dark magic and really doesn't require a master's degree level of study to grok.
I can't do the mental gymnastics to think about the code that way.
When I think about the purpose of the code, the result of the code, before the code has been written, I do this by "compiling and running" in my head. Of course, there's no actual compiling. There's just thinking.
When I reason about the code, either code I'm going to write, code I wrote, or code other people wrote, I execute the code in my head.
I'm currently building a web-scraping system, to look information on partner web site. I'm using python 3, selenium, pyodbc to sql server. I'm also developing the same in C# (3.5) using the webbrowser component in systems.forms. It's got a lot of moving parts, lots of languages involved. I read the documentation for the tools, then I assemble in my head, essentially "running the code" in my head, and then, once all the edge cases are dealt with (are there iframes, popups, ajax async calls, flash and pdfs) then I design on paper, with boxes, and then, later, later, if it all works in my head, then I code it.
Can't do that if I can't reason in my head about what the program is going to do, exactly.
Functional Programming, for me, does not fit in my mental model, so I can't use it, regardless of actual implementation.
http://qt-project.org/doc/qt-4.8/widgets-analogclock.html
When you could instead say just what you mean in functional programming:
http://elm-lang.org/edit/examples/Intermediate/Clock.elm
The most important skill for a programmer is to be able to learn new things. Especially when they're there to help you.