This is the sixth bimonthly 'What are you working On?' thread. Previous threads are here. So here's the question:
What are you working on?
Here are some guidelines:
- Focus on projects that you have recently made progress on, not projects that you're thinking about doing but haven't started.
- Why this project and not others? Mention reasons why you're doing the project and/or why others should contribute to your project (if applicable).
- Talk about your goals for the project.
- Any kind of project is fair game: personal improvement, research project, art project, whatever.
- Link to your work if it's linkable.
Off the top of my head, it sounds like you're going to run into computability problems.
I've annoyingly forgotten the terminology and don't have time to look it up, and some details may be incorrect, but: some algorithms can be written in a programming language which imposes bounds on their running time before the algorithm is actually run. (The runtime is allowed to depend on the arguments to a function.) Others can only be written in a language which allows you to write infinite loops. (This is true even of some algorithms which are guaranteed to terminate on all inputs.)
The algorithms you iterate over will have to be of the first kind, or you'll quickly run into an infinite loop. But the algorithm to do the iteration and diagonalise will be of the second kind. Thus, no paradox.
(IIRC, exactly this problem was discussed in GEB.)
I am not doing it very seriously. Only before I sleep, for example. But it might be a paradox there, after all.