[deeThrow94]

100% agree, I've been saying this for years. I'm terrible with arithmetic but great with symbols and relations. Recursion is also fundamentally linguistic, and although our internal "stacks" for processing it naturally are quite small, language remains the easiest demonstration of recursion in our daily lives.

Oddly, I also use spatial intuition when thinking about stuff like stacks and the shape of data structures.

[karmakaze]

> Recursion is also fundamentally linguistic

You sure about that? How about inductive proofs?

I would just say that language is more familiar to most. Mathematics are also languages, but more formal and foreign to most.

[trealira]

This is just a guess on my part, but I'd also bet that writing inductive proofs (or proofs in general) require more of the language brain than just doing math problems.

[retrac]

Language has an inherently recursive structure: I saw the man who saw the man who saw the man who saw the man who saw the man who... While our brains have practical limits to how deeply such things can actually be nested, language has a recursive tree-like aspect to it.

[umanwizard]

Yes, but “language is fundamentally recursive” doesn’t mean the same thing as “recursion is fundamentally linguistic”. Language is just one example of a recursive structure.

[a4isms]

I am also unsure whether recursion is fundamentally linguistic, but I thought that “language remains the easiest demonstration of recursion in our daily lives” to be useful. If I ever write another essay about recursion, I'll now consider starting with a linguistic example before diving into recursive functions or data structures.

[Jensson]

Language has nothing that corresponds to a recursive function, so that is a bad example. You can write a sentence that could correspond to a call to a recursive function, but its not the same thing as a recursive function.

If recursion was just writing the function 10 times like you did in language then people wouldn't struggle with it.

[deeThrow94]

Recursive functions are just a subset of all possibly recursive concepts. In the case of human spoken language, the recursion exists in our characterization of the grammar. You could just as easily frame this in "iterative" terms just like you can make any recursive function iterative, but that's less convenient for analysis.

So in this case, "recursive function" would be "clause" or something like that; I'm no linguist. But clauses can embed clauses which can embed further clauses, etc.

I think your usage of recursive functions is just high-level logic—you're describing an inductive proof. We also frame a lot of our social games as recursive processes. But these are conscious processes that we can evaluate consciously; the recursion in spoken language is largely unconscious and very shallow.

[deeThrow94]

Can you come up with some conception of recursion that doesn't involve symbols referring to themselves, directly or indirectly? Ie what is left of recursion when you remove the linguistic component?

[karmakaze]

Yes. But it's in my mind, I can't write it down for you.

[deeThrow94]

How do you communicate an inductive proof without language? Even formal symbolic logic is fundamentally linguistic.

[Jensson]

> How do you communicate an inductive proof without language?

With that argument everything is fundamentally linguistic since everything is communicated using a language.

Can you come up with a more reasonable argument?

[DiscourseFan]

Recursion itself is simply a conjecture. Nothing fundamental about it unless you believe Chomsky, but his is a speculative claim, not empirical per se.

[deeThrow94]

I don't really know what you mean by "conjecture", but I thought apriori was implied by positing it as a linguistic construct. "Fundamental" doesn't imply empiricism at all. All of apriori knowledge for a language is a set of all sets of coherent statements: the outer set represents a set of implied axioms required to make the statements cohere. Recursion just broadens the complexity of the statements you can express, but it's fundamentally a concept that arises from language and can be evaluated for coherency (like all other apriori concepts).

Edit: added a definition of apriori knowledge.

Edit2: to put this another way, nobody is arguing that recursion doesn't exist. Or that it is empirically-derived. No, it's a useful construct to show certain relations.

Edit3: added a sentence

Edit4: The extent to which our own grammars are inherently recursive vs this being culture or technology is irrelevant to identifying the concept of recursion as an apriori, linguistic concept.

Edit5: i suppose you might also be referring to the idea that we naturally process recursion. I mean, we clearly, evidently do; whether or not that's inherent to being human is a separate question entirely. Hell in the free software world there's a whole recursive acronym meme that taps into some part of our brain and tickles it.

[umanwizard]

It kinda is empirically true that human language is recursive. Every human language ever discovered is recursive, except, supposedly, for one: Pirahã. And Pirahã has mainly been described by one researcher whose results are controversial.

[umanwizard]

> Recursion is also fundamentally linguistic

What does this mean exactly?

[hbn]

>> Recursion is also fundamentally linguistic

> What does this mean exactly?

What does this mean exactly?

[umanwizard]

Cute, but do you have a serious answer?

[deeThrow94]

If you define recursion as a symbol referencing itself, either directly or indirectly, and if you define language as a system of relating symbols to each other, recursion is a linguistic concept, it is a concept that describes a relationship between symbols. There are good reasons to define each concept differently, but if you identify recursion empirically, recursion won't "actually" exist outside of the description of the process. It's our characterization of the process that reveals the recursive structure, even if that characterization doesn't actually exist outside of language.

[Jensson]

> If you define recursion as a symbol referencing itself, either directly or indirectly, and if you define language as a system of relating symbols to each other, recursion is a linguistic concept

But that isn't what we mean with recursive function. We don't call this recursive:

    x = x + 1

Its just incrementing x.

[deeThrow94]

> We don't call this recursive... it's just incrementing x

That's not a recursive function as it's written, but you could certainly consider it a form of symbolic recursion. This just isn't a very useful characterization in an iterative/imperative context. You could frame incrementing as recursive, though—this is just peano axioms/church encoding.

[RHSeeger]

I would argue that

- Defining recursion is linguistic

- Defining a function recursively is mathmatic

[deeThrow94]

I agree that there's enormous value in carving out mathematics from other linguistic reasoning, but I don't see defining as something as mathematic rather than linguistic is generally useful. You use the same skills to look for incoherency in both situations, but human language is generally expected to be incoherent on some level.

Besides, a lot of what people mean when they say they're bad at math is that they're bad at arithmetic, which is honestly understandable.