Comments on “Sleeping with Sukhi”
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Reading this again, what came to my mind was the history of mathematics question of who first used recursive definitions and who first gave a name to that style of definition.
Used in the nineteenth century for sure, especially in German language texts. This is way later than the period the story is set in, of course.
Before that … it’s a good question of what counts as a recursive, as opposed to iterative, definition. Fibonnaci’s famous problem about reproducing rabbits is a recurrence relation.
I haven’t checked, but presumably Panini’s Sanskrit grammar doesn’t have explicitly recursive grammar rules.
Undone by recursion
A couple of days ago, I had an “undone by recursion” moment, thinking about this story. It went roughly like this:
So, you have some (formal) grammar that includes recursive definitions, and you use proof by induction to prove some theorem about all gramatically correct expressions.
But wait, thinks I. If you’re really trying to prove this sort of theorem rigorously, surely you’ld need something like Peano’s 9th axiom, only for grammars rather than integers. Some axiom that says it’s ok to do induction on grammars, because the recursion always terminates in a finite number of steps. That guarantees you no sentence in the grammar is - for example - a circularly linked list that causes the parser to run forever. You could probably write that sentence in a finite number of symbols, around the circumference of a bracelet, for example…
Love the recursion joke!
I’m (re-?)reading the whole story now and loving it!
The recursion joke(s) are particularly funny!
The “infinity unrolled” ‘being undone by recursion’ bit reminds me of something I remember experiencing as a kid – a feeling of flying or ‘zooming’, but “infinity unrolled before him” is an even better description. Thinking back on it now, I think it would happen when I was in a ‘trance’ or similar kind of ‘meditative’ state. I only remember it happening at night, after I was supposed to be asleep, and I remember it most vividly as happening when I was looking out the window of my bedroom and rubbing a part of a soft blanket folder over onto itself. Something about the sensation felt ‘infinite’. Weird!
“It is no shame to be undone by recursion” – truly! I tell my own ‘pupils’ that, and don’t qualify it with “the first time”. Indeed, even with the most careful spells (unit tests), a failure to properly tame recursion can be fatal (require killing the test job)!