Simply, yes, it is a crutch for your mental math skills.
Should you do any of those follow ups? Seems like a judgement call. In my experience strengthening those fundamentals is important, but there are many occaisons where the point of the exercise (such as learning to write legible long form algebra) overshadows other possible benefits - making a crutch such as a pencil and paper, or a computer typing system, the appropriate call to make.
Please, when you pose 'absurd' hypotheticals, follow them to likely or reasonable conclusions. If you shit your brain off when the conclusion seems obvious but before evaluating you will frequently end up just asking reasonable (if somewhat obvious) questions.
There's clearly some limit to this line of thought though. Maybe it's valuable to know how to write your own make file. But have you built your own microprocessor by soldering together transistors? You have?! That's awesome! Have you built your own soldering iron?
Yes, thank you! That is what the latter half of the first paragraph is about - we make judgement calls about the tradeoffs involved with a crutch all the time.
The point isnt to accept a heuristic that points one way or another, but to be conscious about it being a choice that we can make that can have various trade offs along a spectrum. As usual figuring out what trade offs to make is highly dependent on what your goals are.
The point I was aiming for was that learning with a crutch is still learning. I interpreted Avicebron's comment as "real programmers code in binary" and you are "unworthy" if you can build a CMake system without having written a Makefile manually in your life.
But after your comment, a lot of what I see around me are crutches. The keyboard I type on, the heated building I'm in. They really help me perform "normal" functions, and living without them would be a handicap, so they are crutches.
But I see no point in purposely living without them. Live your life, and don't force yourself to do something you don't like unnecessarily.
Should you do any of those follow ups? Seems like a judgement call. In my experience strengthening those fundamentals is important, but there are many occaisons where the point of the exercise (such as learning to write legible long form algebra) overshadows other possible benefits - making a crutch such as a pencil and paper, or a computer typing system, the appropriate call to make.
Please, when you pose 'absurd' hypotheticals, follow them to likely or reasonable conclusions. If you shit your brain off when the conclusion seems obvious but before evaluating you will frequently end up just asking reasonable (if somewhat obvious) questions.