Philosophically, the Halting Problem and the Pigeonhole Principle are very similar. They both talk about what is not possible with arbitrary input, but they have very little to say about practical input. You can't compress a random number generator. You can compress human communication, in any form, some of them famously. The existence of PP or HP are only boundary conditions, as entropy goes to infinity.
Humans also call entropy 'chaos', which has a connotation that's doubly meaningful in information theory. Chaos obfuscates. It's only useful when obfuscation is the point (encryption). We run away from it as fast as we can, and the farther we get from in the more interesting opportunities open up. Languages that disallow certain patterns can solve the halting problem for pieces of the application, maybe even entire 'useful' applications.
For some categories of applications, or even components of applications, the inability to meet a deadline in handling an event is a safety violation in the category of "or else people could die". I mentioned the halting problem instead since it's close enough to those requirements for an HN comment.
Rust has nothing special to say about that definition of safety, except that it thinks it has a better model for avoiding certain kinds of memory bugs that could contribute to those issues. Given that, I can see that "safe language" as a concept can be confusing and even leave engineers a little unprepared for unexpected categories of bugs.
Anyway, I brought up the halting problem to illustrate. I'm sure there are other illustrations you can substitute regardless of your opinion on the halting problem.
Philosophically, the Halting Problem and the Pigeonhole Principle are very similar. They both talk about what is not possible with arbitrary input, but they have very little to say about practical input. You can't compress a random number generator. You can compress human communication, in any form, some of them famously. The existence of PP or HP are only boundary conditions, as entropy goes to infinity.
Humans also call entropy 'chaos', which has a connotation that's doubly meaningful in information theory. Chaos obfuscates. It's only useful when obfuscation is the point (encryption). We run away from it as fast as we can, and the farther we get from in the more interesting opportunities open up. Languages that disallow certain patterns can solve the halting problem for pieces of the application, maybe even entire 'useful' applications.