On ambiguity

We perceive something as ambiguous when it can be interpreted in two or more ways.

Draft

This is a draft and is subject to revision.

Ambiguity in language

The causes of ambiguity are not restricted to language, but types of ambiguity are well-defined in the domain of linguistics.

Lexical ambiguity occurs when a word has multiple meanings. In the case of homonyms, a word can have multiple, unrelated meanings (river bank, money bank). In polysemy, a word can have multiple related meanings (tree branch, git branch).

Syntactic ambiguity arises from an arrangement of words that generates multiple possible meanings: the program loads files from the server during startup (startup of the program, the server, or both?).

Semantic ambiguity comes from a sentence with multiple meanings, which can be due to many factors: update the app after the window closes (does the user close the window or does it happen automatically?).

Endophoric ambiguity is due to a reference that could refer to multiple independent parts: from the example above... (which of the preceding examples?).

Some of these cases are related; for example, lexical and syntactic ambiguity can contribute to semantic ambiguity.

Ambiguity beyond language

Anything that we perceive, and are capable of interpreting, can be ambiguous.

What does this button do? How did the audience respond to my talk? What did the ending of the movie mean? Why did they wear that particular outfit? What is causing that smoke in the distance?

In general, an ambiguity involves a one-to-many relationship between what is perceived and the set of its possible interpretations.

Ambiguity can arise in different phases of learning and discovery:

• Identifying a new ambiguity to investigate (increased ambiguity)
• Mapping a perception to a finite set of valid interpretations (reduced ambiguity)
• Accepting one valid interpretation (resolved ambiguity)
• Introducing alternatives to the accepted interpretation (restored ambiguity)

Ambiguity as harmful

Ambiguity can be dangerous. When operating industrial machinery, an ambiguous instruction can be fatal.

Yet, not all ambiguous instructions are so consequential. When a recipe prompts us to add seasoning "to taste", the instruction is ambiguous with respect to the quantity, but it is unlikely to harm us. Moreover, it grants us the agency to experiment and determine our preferred quantity.

Similarly, critics talk of artistic works that "respect their audience", often meaning that an artist acknowledges that their audience has degree of tolerance for ambiguity.

Ambiguity and discovery

Ambiguity can be understood as a necessary stage in the activity of discovery.

Scientific discovery is often initiated by the recognition of an ambiguity — a phenomenon that admits of multiple possible interpretations. This prompts the scientist to seek the interpretation that has the highest probability of being correct.

Great scientists seek an ambiguity with just as much vigor as they do the resolution of that ambiguity.

Ambiguity in technology

Technology can be ambiguous in different ways. There can be ambiguity of:

• Function: multiple interpretations of what it does
• Procedure: multiple interpretations of how to use it
• Mechanism: multiple interpretations of how it works

A technology may have multiple valid functions and different valid procedures for its use. This can result in that technology being experienced as ambiguous by the user, even if the design is intentional and useful. As one becomes skilled, the sense of ambiguity may be replaced with a sense of possibility.

A technology is discoverable when it enables the resolution of its own ambiguity. This typically coincides with the user recognising the intention of the designer.

Ambiguity in reality

Things that exist in reality have been referred to as "ambiguous".

Enzymes were classically considered to be specific to one substrate, a kind of lock-and-key relationship. In other words: an enzyme had a one-to-one binding relationship with its substrate. It is now known that some enzymes exhibit what scientists call "substrate ambiguity", in which an enzyme can potentially interact with multiple different substrates.

It should be noted that this is a kind of real ambiguity. When an enzyme has been demonstrated to bind with multiple enzymes then that is its actual behaviour. If a new enzyme exhibits substrate ambiguity then it is ambiguous for the observer, who may have expected more narrow binding behaviour. Forcing the enzyme's behaviour into the classical lock-and-key model to reduce ambiguity could well result in a flawed account of reality.

Ambiguity and generalisation

Both ambiguity and generalisation involve one-to-many relationships:

• Ambiguity: one perception with many possible interpretations
• Generalisation: one class with many possible instances

The distinction is that the interpretations in a case of ambiguity ($A$) are mutually independent, whereas the instances in a generalisation ($G$) are members of some class (note to author: there may be some analogy here to the distinction between homonymy and polysemy).

$$A: a \rightarrow \{x, y,..., z\}$$ $$G: g \rightarrow C, \ C = \{g_1, g_2,..., g_n\}$$

A generalisation assumes some model that explains the class and its membership. Without an understanding of the model, a generalisation may have the appearance of an ambiguity.

Ambiguity in documentation

The general view is that ambiguity in documentation should be eliminated, so that the user can reliably and safely follow a given document. This is almost certainly good advice in most cases.

Another way of thinking of a technical document, is that its reading should result in a progressive reduction in ambiguity; thus, for example, a document may introduce a possible failure state that creates ambiguity for the user, before guiding the user towards a level of understanding that resolves that ambiguity.

There may not always be a linear reduction in ambiguity as a reader navigates a document. For example, a tutorial may introduce an ambiguous learning situation, which is resolved as the user develops competence. Then, the tutorial may prompt the user to apply their new skills in unfamiliar scenarios, reintroducing ambiguity, and thereby empowering the user to explore new possibilities.

Tell all the truth but tell it slant

— Emily Dickinson