Say a sentence: "Either it rains tomorrow and we stay, or it clears up and we go." Now drop the whole thing inside another one: "If (either it rains and we stay, or it clears and we go), then there is nothing left to settle about the weekend." You can wrap it again. While you wrap it you are doing something quite specific: holding the thought that a "then" is still owed.
Unpaid debts have a shape, and they can only be settled in one order — the debt incurred last is discharged first. That shape decides what kind of device can handle such sentences. It has nothing to do with what the sentence says, or with whether the language is "expressive".
Here is the counterintuitive part: line all languages up by what device they require and there are only four rungs, with human language wedged into a narrow gap between the second and the third. What pinned that gap down was not theoretical argument. It was one Swiss German sentence about painting a house, and the word for "whatever dog" in a West African language.
The cheapest device is a single dial. Its formal name is a finite-state machine: it reads a symbol, the dial jumps to another position, and once it has jumped it retains no record of the path — only where it now sits. The number of positions is fixed in advance, and finite.
Do not be too quick to call that weak. Where it suffices it genuinely suffices, and provably so. Sound and word-form largely fall inside its reach: Johnson in 1972, and Kaplan and Kay in 1994, showed that a whole ordered battery of phonological rules can be compiled into exactly such a dial device, and Koskenniemi in 1983 built Finnish inflection as one — a language in which a single noun has more than a dozen cases. "Sufficient" here is a theorem, not an impression.
Sentences are another matter. The argument in Chomsky's 1956 paper turns on nesting: "if" incurs a debt of a later "then", "either" a debt of a later "or", and these can be stacked to any depth. A dial has finitely many positions, so once the depth runs past that number the device must squeeze two distinct debt states into the same position — and from then on it cannot tell which sentences to accept from which to reject. The next rung therefore needs a last-in-first-out notepad: the entry written last is crossed off first. Its standard name is a stack, and the rung equipped with one is called context-free, meaning that what a piece of structure looks like does not depend on what surrounds it.
Take this English sentence: "The rat the cat the dog chased killed ate the malt." Three nouns pile up at the front, three verbs pile up behind, the grammar is impeccable, and it reads like a knot. In 1964 Miller and Isard asked people to recall such sentences after hearing them: two levels is already hard, three essentially cannot be reproduced. Wedging a clause into the middle of another is called center embedding.
In 2007 Karlsson moved the question into real text: across 119 genuine multiple center-embeddings in seven European languages, written usage reaches a depth of three at most, with not one authentic case of four, while in speech even depth two is close to non-existent. That is a ceiling the corpora grew on their own.
Then comes the reversal. Gibson and Thomas found in 1999 that deleting the middle verb of such a three-level sentence — which makes it ungrammatical — leaves English native speakers reading faster and rating it higher. In 2010 Vasishth and colleagues ran seven self-paced-reading and eyetracking experiments carrying the same contrast into German: German speakers go the other way, reading the complete sentence faster than the one missing a verb.
The first explanation was that memory overload evicts the prediction of the still-owed verb, and that the eviction is a relief. The German result kills the general form of it: German subordinate clauses always park the verb at the end, so German readers settle such debts clause-finally every day and hold the prediction more firmly. But in 2016 Frank, Trompenaars and Vasishth added Dutch — also verb-final, yet patterning with English in showing the illusion. The centre of gravity of the explanation shifted from "how many levels memory holds" to "how often this structure occurs in this particular language".
An unavoidable controversy sits here: should a grammar license what nobody ever utters? The generative side separates knowing from executing and assigns the three-level ceiling to the latter; the usage-based side holds that a structure which never occurs should not be written into the grammar. The disagreement is still live, and neither set of results above takes a side. The evidence is reasonably strong: self-paced reading plus eyetracking, three languages, independent follow-up groups.
A stack does exactly one shape: nesting, innermost settled first. But dependencies come in another shape, crossing — first noun with first verb, second with second, the two links passing through each other in midair.
Shieber did this with Swiss German in 1985. The example is "Jan säit das mer em Hans es huus hälfed aastriiche" (literally "Jan says that we Hans-dative the-house-accusative help paint", meaning "Jan says that we helped Hans paint the house"). "em Hans" carries dative marking, because "hälfe" (help) demands a dative object; "es huus" carries accusative marking, because "aastriiche" (paint) demands an accusative one. The nouns come in the order help-then-paint and so do the verbs — the links cross, they do not nest.
The argument's strength lies in the case marking: however many verbs demand a dative, exactly that many dative nouns must appear, and likewise for the accusative — so there is no reanalysis that turns the crossing into nesting.
A second brick comes from word formation. In 1985 Culy examined Bambara, a Mande language of West Africa: wulu is "dog", wulu-o-wulu is "whatever dog", where the linking o copies the entire preceding word verbatim; and compound nouns can be extended indefinitely, wulu-filela being "dog-watcher", with further elements available. Put the two together and you get an arbitrarily long string repeated as a whole. To judge whether such a word is well formed, a device must align two arbitrarily long segments in the same order.
Hence the narrow gap: human language sits above the rung with a single stack, but only just above it. Joshi's 1985 name for it is mildly context-sensitive, and "mildly" is not politeness — one rung higher and parsing costs stop being realistic. On evidence strength, both arguments have been pressed: native judgements themselves start to blur once three or four verbs are piled up, "arbitrarily long" is an idealisation, and they rest on a few constructions in a few languages. No replacement conclusion has appeared in thirty years, but calling them verified across a large cross-linguistic sample would be dishonest.
Measuring machines with the same yardstick gives a clean picture. In 2023 Delétang and colleagues trained 2200 models on 16 tasks: recurrent networks and Transformers (the architecture behind today's large models) fail to extrapolate on tasks that require backtracking — fine within the lengths seen in training, dropping off beyond them; only networks fitted with an external stack, or with a tape they can read and write back and forth, hold up on tasks needing nesting or same-order alignment.
The difference that falls out is checkable rather than analogical: what the models lack is a debt list of unbounded depth, and bolting one on supplies it; what people lack is not the list but the capacity to maintain it — give a person pen and paper and the manageable depth jumps at once, and a person who cannot parse a sentence can still judge it "legal but too hard". That double response is exactly the kind of judgement the classification needs, while a model offers only a low score on a single scale.
At least three things: judging whether a sentence is accepted, delivering its structure, and stating its meaning. The classification covers only the first, and only in the infinite-set sense. So "natural language is not context-free" is a mathematical fact about a set of legal strings; it does not directly tell you what is inside a human head.
One answer is that writing the ceiling in is more trouble than leaving it out: you would have to say whether it is three or four, and the number shifts with pen and paper, with time, with content. The opposite answer is that what never occurs should not be in the rules, and that the number three is itself the thing to be explained.
What gets discussed is the numeral system and reduplicative word formation, such as 看一看 (kàn-yi-kàn, "take a quick look"), where a component is copied — and copying is precisely the mechanism in the Bambara argument. But prying the rungs apart with Chinese is far less clean than with Swiss German, exactly because Chinese has no case marking, and the reason that argument cannot be dodged is that case marking forces the counts of nouns and verbs to match. Which also explains why arguments of this kind keep resting on a handful of languages: not because those languages are special, but because they happen to carry the marking that nails the argument down.