Where does reduction collide?

In chemistry, reduction is the gain of electrons by an atom, ion, or molecule, seen as a decrease in its oxidation state: it is one half of every oxidation-reduction (redox) reaction, always paired with an oxidation elsewhere, since the electrons a reduced species gains are the electrons an oxidised species loses. Silverstein's 2011 Oxidation and Reduction: Too Many Definitions? reviewed the several definitions in use and argued that the change in oxidation state is the most reliable one to teach. The referent is a change in the electronic state of matter, tracked by oxidation number and electrode potential, and it has nothing to do with reducing a theory, a problem, or a broken bone beyond the shared word.[1]

Unit

A gain of electrons by a species, shown as a fall in its oxidation state

Recovery means

The reverse change is oxidation, the loss of electrons; the two always occur together as a redox pair

Measured by

Tracked by assigning oxidation states, and by measuring electrode potentials and the number of electrons transferred in a half-reaction

In the philosophy of science, reduction is the explanation of one theory or body of phenomena in terms of another, more fundamental one: a higher-level theory is said to reduce to a lower-level theory when its terms can be connected to, and its laws derived from, those of the more basic theory, as thermodynamics is often said to reduce to statistical mechanics. Nagel's 1961 The Structure of Science set out the classic conditions for such a theory reduction, requiring bridge principles that link the two vocabularies and a derivation of the reduced laws. The referent is a logical and explanatory relation between theories or levels of description, argued for with evidence and inference, not a transfer of electrons, a mapping between problems, or the setting of a bone.[2]

Unit

A derivation of one theory's laws from those of a more basic theory

Recovery means

Not applicable

Measured by

Assessed by whether the reduced theory's terms can be linked by bridge principles to the reducing theory, and its laws derived from it

In computer science, a reduction is a transformation that turns one problem into another, so that any solution to the second yields a solution to the first: it is the central tool for comparing the difficulty of problems, and a many-one reduction that runs within a resource bound shows that the target problem is at least as hard as the source. Karp's 1972 Reducibility among combinatorial problems used polynomial-time reductions to show that twenty-one combinatorial problems are NP-complete, each reachable from the others by such a transformation. The referent is a constructed mapping between computational problems, proved to preserve solutions, and it is unrelated to electrons gained, theories derived, or fractures set.[3]

Unit

A mapping that turns instances of one problem into instances of another

Recovery means

Not applicable

Measured by

Shown by constructing the transformation and proving it preserves yes-instances while running within a stated resource bound

In orthopaedic surgery, reduction is the manoeuvre that restores the fragments of a broken or dislocated bone to their normal position and alignment: it may be closed, done by manipulation without opening the skin, or open, done through a surgical incision, and it is the step that precedes holding the bone with a cast or fixation while it heals. Søsborg-Würtz and colleagues' 2018 Closed reduction of distal radius fractures reviewed how closed reduction of one common fracture is carried out and how well it restores position. The referent is a physical act of realigning bone, judged on radiographs, and it shares nothing with a gain of electrons, a relation between theories, or a mapping between problems.[4]

Unit

The realignment of displaced bone fragments to their normal position

Recovery means

The reduced bone is held by cast, splint, or fixation while it heals in the restored position

Measured by

Checked on radiographs by alignment, angulation, and displacement of the fragments before and after the manoeuvre

In religious studies, reduction refers to explaining religion in non-religious terms, such as social or psychological causes, which this essay defends against the view that religion must be explained on its own terms. This meaning comes from Segal (1983) in Journal of the American Academy of Religion.[5]

Unit

Recovery means

Measured by