Where does redundancy collide?

The fraction of a message that is predictable, the part that carries no new information because the rest of the message already fixes it. In A Mathematical Theory of Communication (1948), Claude Shannon defined a source's redundancy as one minus the ratio of its entropy to the maximum entropy its symbols could carry, so a source that used every symbol with equal surprise would have zero redundancy and ordinary English, which is roughly half predictable, a good deal of it. The referent is a signal or source, and the unit is a proportion of bits above the entropy minimum. It is the surplus that compression removes and, read the other way, the surplus that lets a receiver detect and correct errors. It differs from the other meanings because nothing is duplicated on purpose and no one loses anything; the redundancy is simply a statistical property of the message.[1]

Unit

Fraction of a message above its entropy minimum

Recovery means

Relevant: the predictable surplus is what lets a receiver detect and correct corrupted symbols

Measured by

One minus the ratio of a source's entropy to its maximum entropy, as a proportion or in bits

Extra components added to a system so it keeps working when one of them fails, the duplication that buys fault tolerance. In their taxonomy of dependable and secure computing, Avizienis, Laprie, Randell, and Landwehr (2004) treat redundancy as a principal means to reliability: spare units, replicated modules, or an N+1 arrangement in which one more component is provided than the load strictly requires, so a single failure is masked rather than felt. The referent is a physical or logical system, and the unit is components held beyond the working minimum. Here the surplus is deliberate and costs money, the reverse of Shannon's surplus, which one tries to strip away; an engineer builds redundancy in precisely so that a failure has somewhere to go.[2]

Unit

Components provided beyond the minimum needed to function

Recovery means

The point of the construct: a spare component takes over so the system survives a failure

Measured by

Configuration counts such as N+1 or 2-out-of-3, and the reliability gain they provide

A dismissal that happens because the employer no longer needs the job done, not because of anything the worker did wrong. Under section 139 of the United Kingdom's Employment Rights Act 1996, a dismissal is by reason of redundancy when the employer has ceased or intends to cease the business, or the workplace has closed, or the requirement for employees to carry out work of a particular kind has ceased or diminished. The referent is an event that ends one person's employment, and the unit is a legal test applied to that dismissal. This meaning shares only the bare idea of surplus with the others: it is the job, not a signal or a component, that has become surplus to requirements, and the consequence falls on a person rather than on a message or a machine.[5][3]

Unit

A dismissal attributable to a diminished need for the work

Recovery means

Not applicable

Measured by

A statutory test: whether the need for employees to do work of a particular kind has ceased or diminished

Grammatical or semantic information that a language marks more than once, so the same relation is signalled by several overlapping cues at the same time. Pijpops and Zehentner (2022) studied redundant marking of grammatical relations in English and Dutch, showing how case, agreement, and word order can pile up to distinguish who did what to whom. The referent is an utterance or a grammatical system, and the unit is the count of cues that mark one relation. Like Shannon's redundancy it makes a message partly predictable and lets a hearer recover a relation when one cue is lost or noisy; unlike the engineering meaning it is not designed by anyone but emerges from the grammar, and unlike the employment meaning nothing and no one is dismissed.[4]

Unit

Grammatical information marked more than once in an utterance

Recovery means

Relevant: redundant marking lets a hearer recover a grammatical relation when one cue is missing

Measured by

Counts of overlapping cues, such as case, agreement, and word order, that mark the same relation