Prof Eric Hehner's April 2025 article on interpreting the Halting Problem: https://www.cs.utoronto.ca/~hehner/Boxes.pdf

This feel like an appropriate time to bring in Douglas Hofstadter and Metamagical Themas. I immediately though of his question: How would you translate the following sentence to Chinese: "This sentence is in English"

Having done some translating long ago, I can answer that question: it depends on context. You need to figure out what the role of "English" is in this context, and then pick one out of mainly three options: 1. Keep "English" 2. Replace by "Chinese" 3. Reformulate the surrounding paragraph to convey the intended message in a different way.

For sure - the point about the sentence is recognizing that its self-referential, and how that creates a new meaning not purely conveyed by a direct translation of the words. I thought that was interesting relating to:

Here is the crux of the argument: Translating programs from one language to another, changes their correctness when self-references is involved.

The crux of a universal computer is that you can write an interpreter for any programming language in any Turing Complete programming language. The halting problem is just a mathematical truth, and it is equivalent to Gödel’s Incompleteness Theorem.

1. if you need to run program and wait for it to finish to know whether it halts or not (sync) – language of test implementation and running it in different process/machine - is irrelevant. 2. if you think you can tell just by analyzing source code (async): if program involves any outside data – there is always a chance an irreducible computation is required, which can be done only by running program, goto 1.