Wonderful.
I am a writer and Orwell is my hero. I love to see him discussed, and I find there is never a time at which I couldn’t use a refresher. “Politics and the English Language” is an all-time gem.
When you say “If you analyze words deliberatively, rephrasing propositions, trying out different meanings, searching for nuggets of truthiness, then you’re losing track of the first impression”, it’s a bit confusing. It sounds like you are saying “Don’t use stock phrases as interchangeable tokens in an attempt to construct something truthy-sounding,” which I gather is your meaning, which Orwell would endorse, and which would be of a piece with the rest of this blog.
But it also sounds very close to saying, “A writer should write from the gut and not worry about rephrasing and editing because editing is phony,” which is of course the opposite of what Orwell teaches. What the most romantic-minded writers call “from the gut” is very often nothing more than received wisdom that “feels” true because they have never really questioned it. A good writer, like you say, is always reevaluating his words and the ways they might be construed. He rephrases his prepostions not his propositons, if I may be so cheeky.
It seems like one of the key factors in your story, Eliezer, is that you had read that book on math cranks. You were able to make the leap from your project of disproving Cantor and see its implications for the rest of your life thanks in part to having the example of the math crank in your mind.
Seeking evidence outside the immediate domain of inquiry can be tricky because it might lead one to include evidence that has no bearing on the actual problem, but because human endeavors don’t happen in a vacuum, it’s a great way of checking yourself for more general errors (like tilting at windmills).