Non-Tree Grammars

Every human language ever studied, from Mandarin to Pirahã, can be represented using tree structures — hierarchical arrangements where words group into phrases, phrases into clauses, clauses into sentences. Computer scientists call these "rooted trees"; linguists call them constituency or dependency trees. The universality of this structure is one of the strongest claims in linguistics, often cited alongside recursion as evidence for some deep constraint on human cognition. But is it actually a necessary property of language, or just a reflection of what brains like ours happen to produce?

A brilliantly detailed thought experiment by Justin B. Rye explores what a language would look like if it broke this constraint. "Europan" is a fictional alien language from the moons of Jupiter, designed to have a grammar whose sentence structures are genuinely incompatible with tree representation.¹

What Trees Buy You

First, it helps to understand why trees are so ubiquitous. In a tree structure, every word (or phrase) has exactly one parent — one higher-level node it belongs to. The word "big" in "the big red ball" modifies "ball" and only "ball." This single-parent constraint makes parsing tractable: when you hear a sentence, you can incrementally build up the structure, attaching each new word to exactly one place in the tree. Ambiguity exists (garden-path sentences exploit it), but the underlying representation is always a tree.

Europan keeps the basic constraint that each word has at most one parent, but relaxes two assumptions that human languages maintain. First, it allows disconnected sentences — multiple independent subgraphs spoken simultaneously, like saying two clauses at once. Their physiology supported this: communication was electrical, with multiple organs transmitting words in parallel, and tags indicating which words were syntactically related. Second, and more radically, it allows cyclic graphs — loops where word A depends on word B which depends on word C which depends on A.

Loops as Grammar

The cyclic sentences are the genuinely alien part. In human languages, if A modifies B and B modifies C, then C never modifies A. Europan permits this, and the most natural use case turns out to be reciprocal actions. A sentence meaning "I sell you food" is literally structured as a loop: "I give food to you who give money to me" — two mirrored transactions, each one's subject being the other's object, forming a cycle. The syntax mirrors the symmetry of the exchange.

This is not mere cleverness. Rye works out the consequences carefully. Loop sentences naturally express relationships that tree-structured languages can only approximate through paired clauses or specialized vocabulary. "I am south of you, and you are upstream of me" becomes a single cyclic structure that encodes the spatial relationship without privileging either perspective. Even tighter loops are possible — a three-verb cycle appears in the corpus, still undeciphered, and the tightest possible loop (two verbs each depending on the other) is used for philosophical epigrams: "The less reliable the data, the less reliable the worldview; the less reliable the worldview, the less reliable the data."

What This Tells Us About Human Language

The whole exercise is fictional, but it makes a serious point about constructed languages and linguistic universals. Computer scientists sometimes dismiss non-tree grammars by noting that any stack-based grammar can be reanalyzed as a tree. Rye's response is sharp: just because you can map something to a tree doesn't mean the native processing works that way. The distinction matters for the same reason that saying "a quantum wavefunction can be represented as a vector in Hilbert space" doesn't mean electrons think in linear algebra.

The deeper question is whether tree structure is a property of language itself or a property of human cognitive architecture. If our brains process language by building trees — and there's good neurolinguistic evidence for this — then alien minds with different neural architectures might genuinely parse cyclic structures as naturally as we parse subordinate clauses. The constraint would be biological, not logical. Europan's non-tree syntax is perfectly coherent as a formal system; it just requires a mind comfortable with parallel transmission and loop resolution.

This connects to the long-running debate about whether Chomsky's universal grammar reflects something about language or something about brains. If tree structure is universal because all human brains share an architecture that builds trees, then encountering a non-human intelligence that doesn't share that architecture would be the ultimate test. We'd discover whether our linguistic universals are truly about communication or merely about us.