Where does representation collide?

Making present, in some sense, something that is nonetheless not literally present. Pitkin's analysis separated four views that the word runs together: formalistic (authorisation and accountability), descriptive (the representative resembles the represented), symbolic (the representative stands for them), and substantive (the representative acts for them, in their interest, responsively). Mansbridge added that the electoral, sanction-based model covers only one of several ways representatives and constituents are actually linked: anticipatory, gyroscopic, and surrogate representation work without a mandate from the person represented. What sets this meaning apart is that the representative is an agent who can be judged, and who can be judged to have failed.[1][2]

Unit

A representative–constituency relation

Recovery means

Not applicable, the criterion is responsiveness and accountability, tested at elections

Measured by

Policy congruence between constituents and legislators; roll-call and opinion data; descriptive shares of a body by group

A picture represents an object when it denotes it (refers to it) within a symbol system, not when it resembles it. Goodman's Languages of Art argued that resemblance is neither necessary nor sufficient: a painting resembles another painting more than it resembles its sitter, and a portrait of a fictional character represents no one yet is still a picture of a certain kind. Pictorial systems differ from linguistic ones by being dense and replete rather than by copying. The distinctive move is that representation is a relation of reference, governed by convention, which makes "realistic" a fact about habit rather than about accuracy.[3]

Unit

A symbol within a symbol system

Recovery means

Not applicable, a semantic relation

Measured by

Not measured, analysed by the syntactic and semantic properties of the symbol system

A structure inside a mind or machine that stands for something outside it and that computations operate over. Marr defined a representation as a formal scheme for making certain information explicit, together with the rules for how it is used, and made the choice of representation a level of explanation in its own right, between the computational theory and the hardware. Fodor argued that thought requires a language-like representational medium (a language of thought) with combinatorial syntax and semantics, so that mental states are relations to sentences in it. The contested question is whether the stand-in must be symbolic; the shared commitment is that it exists and is causally efficacious.[4][5]

Unit

A mental or computational state

Recovery means

Not applicable, a component of an explanation

Measured by

Inferred from behaviour: reaction times, errors, priming, and neural decoding; tested by whether the posited format predicts them

A transformation of raw data into a form (usually a vector) that makes the useful structure easy for a downstream learner to pick out. Bengio, Courville, and Vincent defined representation learning as learning that transformation instead of hand-engineering it, and set out what a good representation should do: disentangle the underlying explanatory factors, be reusable across tasks, and be hierarchical so that abstractions build on lower-level ones. Nothing in it need stand for anything a person can name; the representation is judged by transfer and by what a linear probe can read out of it.[6]

Unit

A layer's activation vector, an embedding

Recovery means

Not applicable, a learned function

Measured by

Downstream task performance, linear-probe accuracy, disentanglement metrics, transfer across tasks

A homomorphism from a group (or algebra, or Lie algebra) into the group of invertible linear transformations of a vector space, so that abstract elements act as concrete matrices. Fulton and Harris fix the standard first-course meaning: a representation is the vector space together with the action, irreducible representations are the building blocks, and characters classify them. The word is exact here: a representation is not about the group, it is a realisation of it, and two representations are the same if they differ only by a change of basis.[7]

Unit

A vector space with a group action

Recovery means

Not applicable, a defined object

Measured by

Not measured, classified by dimension, character, and decomposition into irreducibles

A sample is representative when inferences from it to the population are warranted. Kruskal and Mosteller surveyed how the phrase is used and found at least nine distinct meanings, from a vague seal of approval, through a miniature of the population, to the strict meaning: a sample drawn by a probability mechanism whose properties permit an estimate with a known error. They recommended abandoning the word where a precise term exists. The distinctive feature is that representativeness attaches to the procedure, not to the sample in hand: a random sample is representative even when, by chance, it looks nothing like the population.[8]

Unit

A sample relative to a target population

Recovery means

Not applicable, weighting and post-stratification are corrections, not recovery

Measured by

Sampling design and coverage; comparison of sample and population margins; design effect; bias estimates

In cultural studies, representation refers to the production of meaning through language and other signs, so that representation helps make rather than simply mirror what it depicts. This meaning comes from Hall (1997) in Representation.[9]

Unit

Recovery means

Measured by