Reduction

Reduction (pronounced ri-duhk-shuhn)

(1) The act of reducing or the state of being reduced.

(2) The amount by which something is reduced or diminished.

(3) The form (result) produced by reducing a copy on a smaller scale (including smaller scale copies).

(4) In cell biology, as meiosis, especially the first meiotic cell division in which the chromosome number is reduced by half.

(5) In chemistry, the process or result of reducing (a reaction in which electrons are gained and valence is reduced; often by the removal of oxygen or the addition of hydrogen).

(6) In film production when using physical film stock (celluloid and such), the process of making a print of a narrower gauge from a print of a wider gauge (historically from 35 to 16 mm).

(7) In music, a simplified form, typically an arrangement for a smaller number of parties  such as an orchestral score arranged for a solo instrument.

(8) In computability theory, a transformation of one problem into another problem, such as mapping reduction or polynomial reduction.

(9) In philosophy (notably in phenomenology), a process intended to reveal the objects of consciousness as pure phenomena.

(10) In metalworking, the ratio of a material's change in thickness compared to its thickness prior to forging and/or rolling.

(11) In engineering, (usually as “reduction gear”), a means of energy transmission in which the original speed is reduced to whatever is suitable for the intended application.

(12) In surgery, a procedure to restore a fracture or dislocation to the correct alignment, usually with a closed approach but sometimes with an open approach.

(13) In mathematics, the process of converting a fraction into its decimal form or the rewriting of an expression into a simpler form.

(14) In cooking, the process of rapidly boiling a sauce to concentrate it.

(15) During the colonial period, a village or settlement of Indians in South America established and governed by Spanish Jesuit missionaries.

1475–1485: From the Middle English reduccion, from the earlier reduccion, from the Middle French reduction, from the Latin reductiōnem & reductiōn- (stem of reductiō (a “bringing back”)) the construct being reduct(us) (past participle of redūcere (to lead back) + -iōn- (the noun suffix).  The construct in English was thus reduc(e), -ion.  Reduce was from the Middle English reducen, from the Old French reduire, from the Latin redūcō (reduce), the construct being re- (back) + dūcō (lead).  The –ion suffix was from the Middle English -ioun, from the Old French -ion, from the Latin -iō (genitive -iōnis).  It was appended to a perfect passive participle to form a noun of action or process, or the result of an action or process.  Reduction, reductivism, reductionistic & reductionism are nouns, reductionist is a noun & adjective, reductional & reductive are adjectives; the noun plural is reductions.  Forms like anti-reduction, non-reduction, over-reduction, pre-reduction, post-reduction, pro-reduction, self-reduction have been created as required.

Actor Ariel Winter (b 1998), before (left) and after (right) breast reduction.  Never has satisfactorily it been explained why this procedure is lawful in most jurisdictions.

In philosophy & science, reductionism is an approach used to explain complex phenomena by reducing them to their simpler, more fundamental components.  It posits that understanding the parts of a system and their interactions can provide a complete explanation of the system as a whole an approach which is functional and valuable is some cases and to varying degrees inadequate in others.  The three generally recognized classes of reductionism are (1) Ontological Reductionism, the idea that reality is composed of a small number of basic entities or substances, best illustrated in biology where life processes are explained by reducing things to the molecular level.  (2) Methodological Reductionism, an approach which advocates studying systems by breaking into their constituent parts, much used in psychology where it might involve studying human behavior by examining neurological processes.  (3) Theory Reductionism which involves explaining a theory or phenomenon in one field by the principles of another, more fundamental field as when chemistry is reduced to the physics or chemical properties explained by the operation of quantum mechanics.  Reduction has been an invaluable component in many of the advances in achieved in science in the last two-hundred-odd years and some of the process and mechanics of reductionism have actually been made possible by some of those advances.  The criticism of an over-reliance on reductionism in certain fields in that its very utility can lead to the importance of higher-level structures and interactions being overlooked; there is much which can’t fully be explained by the individual parts or even their interaction.  The diametric opposite of reductionism is holism which emphasizes the importance of whole systems and their properties that emerge from the interactions between parts.  In philosophy, reductionism is the position which holds a system of any level of complexity is nothing but the sum of its parts and an account of it can thus be reduced to accounts of individual constituents.  It’s very much a theoretical model to be used as appropriate rather than an absolutist doctrine but it does hold that phenomena can be explained completely in terms of relations between other more fundamental phenomena: epiphenomena.  A reductionist is either (1) an advocate of reductionism or (2) one who practices reductionism.

Reductionism: Lindsay Lohan during "thin phase".

The adjective reductive has a special meaning in Scots law pertaining to reduction of a decree or other legal device (ie something rescissory in its effect); dating from the sixteenth century, it’s now rarely invoked.  In the sense of “causing the physical reduction or diminution of something” it’s been in use since the seventeenth century in fields including chemistry, metallurgy, biology & economics, always to convey the idea of reduces a substance, object or some abstract quantum to a lesser, simplified or less elaborated form.  At that time, it came to be used also to mean “that can be derived from, or referred back to; something else” and although archaic by the early 1800s, it existence in historic texts can be misleading.  It wasn’t until after World War II (1939-1945) that reductive emerged as a derogatory term, used to suggest an argument, issue or explanation has been “reduced” to a level of such simplicity that so much has been lost as to rob things of meaning.  The phrase “reductio ad absurdum” (reduction to the absurd) is an un-adapted borrowing from the Latin reductiō ad absurdum, and began in mathematics, logic (where it was a useful tool in deriving proofs in fields like).  In wider use, it has come to be used of a method of disproving a statement by assuming the statement is true and, with that assumption, arriving at a blatant contradiction; the synonyms are apagoge & “proof by contradiction”.

Single-family houses (D-Zug) built in 1922 on the principle of architectural reductionism by Heinrich Tessenow in collaboration with Austrian architect Franz Schuster (1892–1972), Moritzburger Weg 19-39 (the former Pillnitzer Weg), Gartenstadt Hellerau, Dresden, Germany.

As a noun, a reductivist is one who advocates or adheres to the principles of reductionism or reductivism.  In art & architecture (and some aspects of engineering) this can be synonymous with the label “a minimalist” (one who practices minimalism).  As an adjective, reductivist (the comparative “more reductivist”, the superlative “most reductivist”) means (1) tending to reduce to a minimum or to simplify in an extreme way and (2) belonging to the reductivism movement in art or music.  The notion of “extreme simplification” (a reduction to a minimum; the use of the fewest essentials) has always appealed some and appalled others attracted to intricacy and complexity.  The German architect Professor Heinrich Tessenow (1876-1950) summed it up in the phrase for which he’s remembered more than his buildings: “The simplest form is not always the best, but the best is always simple.”, one of those epigrams which may not reveal a universal truth but is probably a useful thing to remind students of this and that lest they be seduced by the process and lose sight of the goal.  Tessenow was expanding on the principle of Occam's Razor (the reductionist philosophic position attributed to English Franciscan friar & theologian William of Ockham (circa 1288–1347) written usually as Entia non sunt multiplicanda praeter necessitatem (literally "Entities must not be multiplied beyond necessity" which translates best as “the simplest solution is usually the best”.

Reductio in extrema

1960 Lotus Elite Series 1 (left) and at the Le Mans 24 Hour endurance classic, June 1959 (left) Lotus Elite #41 leads Ferrari 250TR #14. The Ferrari (DNF) retired after overheating, the Elite finishing eighth overall, winning the 1.5 litre GT class.

Weighing a mere 500-odd kg (1100 lb), the early versions of the exquisite Lotus Elite (1957-1963) enchanted most who drove it but the extent of the reductionism compromised the structural integrity and things sometimes broke when used under everyday conditions which of course includes potholed roads.  Introduced late in 1961 the Series 2 Elite greatly improved this but some residual fragility was inherent to the design.  On the smooth surfaces of racing circuits however, it enjoyed an illustrious career, notable especially for success in long-distance events at the Nürburgring and Le Mans.  The combination of light weight and advanced aerodynamics meant the surprisingly powerful engine (a robust unit which began life power the water pumps of fire engines!) delivered outstanding performance, frugal fuel consumption and low tyre wear.  As well as claiming five class trophies in the Le Mans 24 hour race, the Elite twice won the mysterious Indice de performance (an index of thermal efficiency), a curious piece of mathematics actually designed to ensure, regardless of other results, a French car would always win something.

Colin Chapman (1928–1982), who in 1952 founded Lotus Cars, applied reductionism even to the Tessenow mantra in his design philosophy: “Simplify, then add lightness.”  Whether at the drawing board, on the factory floor or on the racetrack, Chapman seldom deviated from his rule and while it lent his cars sparking performance and delightful characteristics, more than one of the early models displayed an infamous fragility.  Chapman died of a heart attack which was a good career move, given the likely legal consequences of his involvement with John DeLorean (1925–2005) and the curious financial arrangements made with OPM (other people's money) during the strange episode which was the tale of the DMC DeLorean gullwing coupé.

1929 Mercedes-Benz SSKL blueprint (recreation, left) and the SSKL “streamliner”, AVUS, Berlin, May 1932 (right).

The Mercedes-Benz SSKL was one of the last of the road cars which could win top-line grand prix races.  An evolution of the earlier S, SS and SSK, the SSKL (Super Sports Kurz (short) Leicht (light)) was notable for the extensive drilling of its chassis frame to the point where it was compared to Swiss cheese; reducing weight with no loss of strength.  The SSK had enjoyed success in competition but even in its heyday was in some ways antiquated and although powerful, was very heavy, thus the expedient of the chassis-drilling intended to make it competitive for another season.  Lighter (which didn't solve but at least to a degree ameliorated the high tyre wear) and easier to handle than the SSK (although the higher speed brought its own problems, notably in braking), the SSKL enjoyed a long Indian summer and even on tighter circuits where its bulk meant it could be out-manoeuvred, sometimes it still prevailed by virtue of sheer power.  By 1932 however the engine’s potential had been reached and there was no more metal which could be removed without dangerously compromising safety.  The solution was an early exercise in aerodynamics (“streamlining” the then fashionable term), an aluminium skin prepared for the 1932 race held on Berlin’s AVUS (Automobil-Versuchs und Übungsstraße (automobile traffic and practice road)).  The reduction in air-resistance permitted the thing to touch 255 km/h (158 mph), some 20 km/h (12 mph) more than a standard SSLK, an increase the engineers calculated would otherwise have demanded another 120 horsepower.  The extra speed was most useful at the unique AVUS which comprised two straights (each almost six miles (ten kilometres) in length) linked by two hairpin curves, one a dramatic banked turn.  The SSKL was the last of the breed, the factory’s subsequent Grand Prix machines all specialized racing cars.

Reduction gears: Known casually as "speed reducers", reduction gears are widely used in just about every type of motor and many other mechanical devices.  What they do is allow the energy of a rotating shaft to be transferred to another shaft running at a reduced speed (achieved usually by the use of gears (cogs) of different diameters.

In chemistry, a reduction is the process or result of reducing (a reaction in which electrons are gained and valence is reduced; often by the removal of oxygen or the addition of hydrogen) and as an example, if an iron atom (valence +3) gains an electron, the valence decreases to +2.  Linguistically, it’s obviously counterintuitive to imagine a “reduced atom” is one which gains rather than loses electrons but the term in this context dates from the early days of modern chemistry, where reduction (and its counterpart: “oxidation”) were created to describe reactions in which one substance lost an oxygen atom and the other substance gained it.   In a reaction such as that between two molecules of hydrogen (2H₂)and one of oxygen (O₂) combining to produce two molecules of water (2H₂O), the hydrogen atoms have gained oxygen atoms and were said to have become “oxidized,” while the oxygen atoms have “lost them” by attaching themselves to the hydrogens, and were thus “reduced”.  Chemically however, in the process of gaining an oxygen atom, the hydrogen atoms have had to give up their electrons and share them with the oxygen atoms, while the oxygen atoms have gained electrons, thus the seeming paradox that the “reduced” oxygen has in fact gained something, namely electrons.