I don’t think the radiation should be too big of a problem, they are in a very low earth orbit, well inside of the Earth’s magnetosphere. Not to say there are no health risks, they lose a lot of bone and muscle mass, but radiation shouldn’t be a big concern
Noo, Joker! Don’t implicitly assume the continuum hypothesis!
I had to look up what poutine was, and I can assure you that we don’t have anything like that in Italy
It’s not so weird, and if someone wants to take the extra risk with their own payload (and get a discount on the launch, i imagine) i see no problems with it.
While what you write is not too far from the conclusion of Gödel’s proof (he proves you can construct a statement which is equivalent to “this statement is not provable”), the point of Gödel’s theorem is that you require a minuscule amount of language (just enough to work with numbers) to do this.
English is very complicated and not a very formal language, so it’s less surprising that you can come up with unprovable statements like yours. Building such a statement in a language that can barely talk about arithmetic is not obvious at all in my opinion. People had already spent a good amount of time choosing a system of axioms that made certain paradoxes impossible to write (for example Russel’s paradox, “does the set of all sets that don’t contain themselves contain itself”, can be written in english, but not in ZFC, the most commonly used axiomatic system in math), and they thought they reached a point where they had fixed all of these paradoxical statements, but Gödel proved not only that they were wrong, but that their goal of a perfect set of axioms where everything could be proven or disproven was impossible to reach.
Also, there are unprovable statements that don’t look anything like yours, like the continuum hypothesis: “there is no infinity that is larger that the number of natural numbers, but smaller that the number of real numbers”. This a perfectly reasonable statement, not only in english but also in ZFC, which looks like something we should be able to either prove or disprove, but in fact we can’t do either. If you want you can add it (or it’s opposite) to the axioms of ZFC, getting a new set of axioms, and you shouldn’t find any inconsistencies. After Gödel’s proof people started asking themselves “is this thing that I’m trying to prove even provable?”, which I don’t think happend very often before.
By the way, this ability to talk about arithmetic is fundamental to the proof: euclidean geometry can’t do that, so Gödel’ theorem doesn’t apply, and it turns out that it’s both consistent and complete.