But also, if the criteria for allowed functions is that they are "reasonable, elemental" (as per the fine article), then I think it would be quite hard to come up with a set of rules to encode that in a way that includes log() and sqrt(), but not S(). It's hard to imagine a function that is less elemental than S() (except maybe the identity function), or why its inclusion would be unreasonable when the other two aren't.
Given how the article is laid out, I think it would be more appropriate to view the game from the lens of when we teach the operations in school, as opposed to what are fundamental or elementary operations / functions in math.
Though I also think square root is cheating, it has an implicit 2 inside of it, where as raising to the power of 2 and log 2 are explicit.
You could also argue for only infix operators.
A good game must be somewhat challenging or else it is not really a game. Anything that makes the game trivial ought be omitted for it to be a game.
Yeah, thinking of the puzzle as a game, rather than a competition, allows for a different perspective.
If I think of a competition, then I'd expect the rules to be determined ahead of time according to some pre-imagined criteria. If someone manages to find a clever hack within the rules that allows for trivial "breaks", then that's good for them and they just get to beat everyone else at it.
But if I think of a game, then it's much more natural for the rules to adapt over time as people realise that some types of "play" make the game less fun, or straight-up boring. They don't have to be self-consistent, or logical. They're essentially arbitrary, and just whatever they need to be to make the game "better".
My criteria are "no letters or digits from any language" (other than 2). So you can't use the log or S() or the gamma function, but you can use sqrt, because there is accepted symbology that does not require any atom of non-mathematical language to represent.
What if it turns out that the radical (square root) symbol is a letter from a language (if a little squished)? And we somehow figure out one day which letter it is, for sure?
While you are right that Succ() is as elemental as it gets (including in both Peano and set-theory construction of natural numbers), it is seldom used outside of theoretical foundations.
So perhaps the implied rule is not about it being "reasonable, elemental", but rather about "common" functions and operands (yes, it's still a can of worms, and you'd need to be explicit about what that is).
> While you are right that Succ() is as elemental as it gets (including in both Peano and set-theory construction of natural numbers), it is seldom used outside of theoretical foundations.
Well, depends on how you define seldom. What if I told you that twitter would break without the use of Succ()? :-)
