Language captures only a subset of the perceptions, intuitions and intents that form meaning between speakers. What, then, are the limits of language? We take steps towards measuring this in LLMs as follows: for a set of concepts, we measure how well each concept can be transmitted between two LLMs as their capabilities scale. This requires novel measurement tools: (1) optimal messages: we introduce a prompt optimization algorithm that beats existing algorithms by up to 14% on benchmarks and accurately estimates prompt upper bounds. (2) A transmission measure: the sender is asked to label text; the receiver then tries to recover the sender's prompt, and recovery is measured; we find this correlates strongly with human label error. With these measures, we use observational scaling laws to study how transmissibility of a concept, conveyed with optimal messages, increases as transmitter and receiver capacity grows: does it asymptote below or above a threshold? Measuring 1.2k concepts in eight domains, we find concepts that (a) can be fully articulated; these concepts usually depend on local patterns, e.g. "joke ends with surprise"; (b) might be articulated by future, stronger models; these rely on whole-text structural patterns, e.g. "story's worldbuilding coherence"; (c) concepts that face articulability limits; these concepts' meaning, we find, is tied to identity and social-group awareness, e.g. "comic voice". Interesting, these same concepts are not all challenging for humans: humans have moderate-to-high levels of agreement in 76% of concepts that LLMs struggle with; articulation limits, we find, are executor relative. Finally, we characterize the nature of improvement in each case: while recoverable concepts can be articulated through definitions and explanations, irrecoverable concepts cannot be transmitted, even with examples, and might require novel learning mechanisms.

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