The high cost of low ambiguity

Natural language is often frustratingly ambiguous.

Homonyms are ambiguous at the individual word level

There are scenarios where ambiguity is useful. For example, in diplomacy, the ambiguity of a statement can provide wiggle room so that the parties can both claim that they agree on a statement, while simultaneously disagreeing on what the statement actually means. (Mind you, this difference in interpretation might lead to problems later on).

Surprisingly, ambiguity can also be useful in engineering work, specifically around design artifacts. The sociologist Kathryn Henderson has done some really interesting research on how these ambiguous boundary objects are able to bridge participants from different engineering domains to work together, where each participant has a different, domain-specific interpretation of the artifact. For more on this, check out her paper Flexible Sketches and Inflexible Data Bases: Visual Communication, Conscription Devices, and Boundary Objects in Design Engineering and her book On Line and On Paper.

Humorists and poets have also made good use of the ambiguity of natural language. Here’s a classic example from Grouch Marx:

Groucho Marx was a virtuoso in using ambiguous wordplay to humorous effect

Despite these advantages, ambiguity in communication hurts more often than it helps. Anyone who has coordinated over Slack during the incident has felt the pain of the ambiguity of Slack messages. There’s the famous $5 million missing comma. As John Gall, the author of Systemantics, reminds us, ambiguity is often the enemy of effective communication.

This type of ambiguity is rarely helpful

Given the harmful nature of ambiguity in communication, the question arises: why is human communication ambiguous?

One theory, which I find convincing, is that communication is ambiguous because it reduces overall communication costs. In particular, it’s much cheaper for the speaker to make utterances that are ambiguous than to speak in a fully unambiguous way. For more details on this theory, check out the paper The communicative function of ambiguity in language by Piantodosi, Tily, and Gibson.

Note that there’s a tradeoff: easier for the speaker is more difficult for the listener, because the listener has to do the work of resolving the ambiguity based on the context. I think people pine for fully unambiguous forms of communication because they have experienced firsthand the costs of ambiguity as listeners but haven’t experienced what the cost to the speaker would be of fully unambiguous communication.

Even in mathematics, a field which we think of us being the most formal and hence unambiguous, mathematical proofs themselves are, in some sense, not completely formal. This has led to amusing responses from mathematical-inclined computer scientists who think that mathematicians are doing proofs in an insufficiently formal way, like Leslie Lamport’s How to Write a Proof and Guy Steele’s It’s Time for a New Old Language.

My claim is that the reason you don’t see mathematical proofs written in a formal-in-the-machine-checkable sense is that mathematicians have collectively come to the conclusion that it isn’t worth the effort.

The role of cost-to-the-speaker vs cost-to-the-listener in language ambiguity is a great example of the nature of negotiated boundaries. We are constantly negotiating boundaries with other people, and those negotiations are generally of the form “we both agree that this joint activity would benefit both of us, but we need to resolve how we are going to distribute the costs amongst us.” Human evolution has worked out how to distribute the costs of verbal communication between speaker and listener, and the solution that evolution hit upon involves ambiguity in natural language.

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