Fracture

Fracture (pronounced frak-cher)

(1) The breaking of a bone, cartilage, or the like, or the resulting condition.

(2) The act of breaking; state of being broken.

(3) A division, break, breach, or split.

(4) The characteristic manner or appearance of breaking.

(5) In mineralogy, the characteristic appearance of the surface of a freshly broken mineral or rock; the way in which a mineral or rock naturally breaks

(6) To cause or to suffer a fracture in (a bone, etc).

(7) As Fraktur, a typeface of German origin.

Early 1400s: From the Middle English fracture (a breaking of a bone), from the fourteenth century Old French fracture, from the Latin fractūra (a breach, fracture, cleft), from fractus, past participle of frangere (to break), from the primitive Indo-European bhreg (to break) and a doublet of fraktur.  The sense of "a broken surface" dates from 1794.  As a transitive verb meaning “cause a fracture in”, use appears to have begun in the 1610s (implied in fractured) and the intransitive meaning "become fractured" is from 1830.  Fracture & fracturer are nouns, fractured & fracturing (used with an object) are verbs, fracturable, fractured & fractural are adjectives.

The Dürers Fraktur typeface.

The noun fraktur (German black-lettering) dates from 1886 from the German Fraktur (black-letter, Gothic type), also "a fracture, a break", again from the Latin fractūra and so- called because of the styles angular (ie “broken") letters.  Fraktur became a common style in German printing from circa 1540 and was later exported to the Pennsylvania German arts that incorporate the lettering.  Scholars consider Fraktur a fusion of the Textur and Schwabacher letter-forms, the characteristics of Textur evident in the Fraktyr minuscules.  Schwabacher, another black-letter form, was widely used in early German print typefaces and was still in use until the mid twentieth century by which time use was entirely supplanted by Fraktur, an extensive variety of these fonts carved.  The first Fraktur typeface was designed when Maximilian I (1459–1519; King of the Romans 1486-1519 & Holy Roman Emperor 1508-1519) commissioned a series of books and ordered a new typeface created specifically for this publication; this first iteration of Fraktur was designed by Hieronymus Andreae (circa 1490-1556), a craftsman noted also for his woodcuts.  

Fonts in transition: Nazi Party poster advertising a “Freedoms Rally” (the irony not apparent at the time), Schneidemuhl, Germany, (now Pila, Poland) in 1931 (left), Edict issued by Martin Bormann (1900–1945) banning the future use of Judenlettern (Jewish fonts) like Fraktur (the irony of the letterhead being in the now banned typeface presumably didn’t disturb the author) (centre) and (in modern Roman script), an announcement in occupied that 100 Polish hostages had been executed as a reprisal for death of two Germans in Warsaw, 1944 (right).

Sometimes, the message was the typeface itself; it imparted values that were separate from the specific meaning in the text.  The Nazi regime (1933-1945) in Germany was always conscious of spectacle and although in matters of such as architecture customs there was a surprising tolerance of regional difference, in some things it demanded uniformity and one of those was the appearance of official documents.  Early in his rule their rule, Adolf Hitler (1889-1945; Führer (leader), German head of government 1933-1945 & head of state 1934-1945) decreed that “German Black Letter” should be used for all official purposes (and it was used in the cover art of most early editions of Mein Kampf); Hitler, who to the end thought himself an “artist”, liked the heavy, angular form for its encapsulation of the Germanic.  Fraktur is probably the best known of these although it’s but one of a number of variations of the typeface and such was the extend of the state support for the font that the party was critical of newspapers, publishers & magazines which used more modern (and easier to read) forms (and they were used by the German military and civil service when legibility was important), a frequent criticism being the “Roman characters” somehow represented a “Jewish influence”.  In one of the ironies of history however, when it became apparent that when used in letters and notices distributed to enforce rule in the occupied territories the use of the font was counter-productive because it was so hard to read, the Nazis suddenly declared that Fraktur had become contaminated wand was thus proscribed as Judenlettern (Jewish letters), official documents thereafter rendered in modern Roman type.  Martin Bormann's edict was issued thus:

I announce the following, by order of the Führer:

It is false to regard the so-called Gothic typeface as a German typeface. In reality, the so-called Gothic typeface consists of Schwabacher-Jewish letters. Just as they later came to own the newspapers, the Jews living in Germany also owned the printing presses… and thus came about the common use in Germany of Schwabacher-Jewish letters.

Today the Führer… decided that Antiqua type is to be regarded as the standard typeface. Over time, all printed matter should be converted to this standard typeface. This will occur as soon as possible in regard to school textbooks, only the standard script will be taught in village and primary schools. The use of Schwabacher-Jewish letters by authorities will in future cease. Certificates of appointment for officials, street signs and the like will in future only be produced in standard lettering…

Broken bones, fractured bones

There’s a widespread perception among lay-people that when it comes to broken bones, there’s a difference between a fracture and a break, a fracture being a kind of crack which doesn’t result in a clear separation whereas in a break, there’s a visible gap between the two broken pieces.  However, to physicians, the two mean the same thing, the only difference being that “fracture” is the preferred medical jargon, whereas a “break” is just a term sometimes used casually with customers (whom they prefer to call patients).  Anatomists list fourteen distinguishing characteristics of fractures, adding that injuries may result in some overlap in the categorization and (at least) a duplication of terminology in any description.

(1) Avulsion fracture: A muscle or ligament pulls on the bone, fracturing it.

(2) Comminuted fracture: An impact shatters the bone into many pieces.

(3) Compression, or crush, fracture: This generally occurs in the spongy bone in the spine. For example, the front portion of a vertebra in the spine may collapse due to osteoporosis.

(4) Fracture dislocation: This occurs when a joint dislocates, and one of the bones of the joint fractures.

(5) Greenstick fracture: The bone partly fractures on one side but does not break completely, because the rest of the bone can bend.

(6) Hairline fracture: This is a thin, partial fracture of the bone.

(7) Impacted fracture: When a bone fractures, a piece of the bone may impact another bone.

(8) Intra-articular fracture: This occurs when a fracture extends into the surface of a joint.

(9) Longitudinal fracture: This is when the fracture extends along the length of the bone.

(10) Oblique fracture: An oblique fracture is one that occurs opposite to a bone’s long axis.

(11) Pathological fracture: This occurs when an underlying condition weakens the bone and causes a fracture.

(12) Spiral fracture: Here, at least one part of the bone twists during a break.

(13) Stress fracture: Repeated stress and strain can fracture a bone. This is common among athletes.

(14) Transverse fracture: This is a straight break across the bone.

Bones are (substantially) rigid organs that support and protect many organs as well as producing red and white blood cells and storing minerals.  While there are variations, a typical adult human has 206 separate bones which, although tough and sometimes slightly flexible to absorb stress, if the pressure sustained is beyond a certain point, the bone will fracture.  In casual use, this is called a “broken bone” but to physicians it’s always a fracture which means simply there’s a break in the continuity of the bone. Symptoms vary, including pain, bones protruding through the skin, swelling, distortion in the appearance of body parts (especially limbs & digits) and loss of function.  Generally, bone fractures are either traumatic or pathological.  A traumatic fracture is where blunt force trauma has been applied such as the impact injuries sustained by falling or hitting something hard.  Pathological fractures are those which are the result of diseases such as Osteoporosis, chronic kidney or liver conditions, rickettes and hypovitaminosis D.

Fractures are sub-classified by anatomical location (skull fracture, rib fracture etc (an in casual use broken arm, broken leg etc)).  Physicians further refine their descriptions by mapping on an orthopaedic schematic in which fractures are defined by their state such as open fracture (bone is visible and the skin ripped), closed fracture (skin is intact), compression fractures, incomplete fracture, linear fracture etc.  Bone fractures are now most often diagnosed through imaging, most commonly with X-rays and treatment consists of pain management, keeping bones intact with splints or screws (or surgery depending on severity).  In extreme cases, amputation may be required if an infection can’t be controlled.

Break was from the Middle English breken, from the Old English brecan (to divide solid matter violently into parts or fragments; to injure, violate (a promise, etc), destroy, curtail; to break into, rush into; to burst forth, spring out; to subdue or tame), from the Proto-West Germanic brekan, from the Proto-Germanic brekaną & brekanan (to break), from the primitive Indo-European bhreg- (to break) and a doublet of bray.  Etymologists list the brecan as a (class IV) strong verb; past tense bræc, past participle brocen), the Proto-Germanic brekanan source also of the Old Frisian breka, the Dutch breken, the Old High German brehhan, the German brechen and the Gothic brikan), all ultimately from the primitive Indo-European root bhreg- (to break).

It was related closely to the nouns breach, brake & brick. The old past tense brake is obsolete or archaic and while still sometimes erroneously used, it’s long been an irregular form.  The past participle is broken but the shortened form broke is attested from the fourteenth century and the Oxford English Dictionary reported it was "exceedingly common" in the seventeenth & eighteenth century.  The meaning in the Old English applied to bones but formerly had been used also of also of cloth, paper and other fabrics, the meaning "escape by breaking an enclosure" dating from the late fourteenth century whereas the intransitive sense "be or become separated into fragments or parts under action of some force" was known by the late twelfth and the sense of "lessen, impair" was noted in the late fifteenth.  

Forks in the meaning emerged continuously: "make a first and partial disclosure" is from early 1200s and "destroy continuity or completeness" in any way is from 1741.  As applied to physical legal tender (coins or bills), break was being used to describe “converting a larger unit into smaller units of currency" by 1882 although the oral tradition may have long predated this.  That favorite of authors and poets, the “break her heart” is an intransitive verb from the fourteenth century.  To break bread (share food with someone) is from the late 1300s while to break ground (to dig or plough) was noted first in 1674 while the now rare figurative sense "begin to execute a plan" is from 1709.  To break the ice in the sense of "overcome the feeling of restraint in a new acquaintanceship" is from circa 1600, the reference an allusion to the "coldness" found sometimes in encounters with strangers.  To break wind was first attested in the 1550s although it may have been long used as one of the many way of describing this ancient practice.  To break (something) out is though probably is an image from dock work, of freeing cargo before unloading it and it is documented from the 1890s.

Lindsay Lohan with broken left wrist (fractured in two places in an unfortunate fall at Milk Studios during New York Fashion Week) and 355 ml (12 fluid oz) can of Rehab energy drink, Los Angeles, September 2006.  The car is a 2005 Mercedes-Benz SL 65 (R230; 2004-2011) which earlier had featured in the tabloids after a low-speed crash.  The R230 range (2001-2011) was unusual because of the quirk of the SL 550 (2006-2011), a designation used exclusively in the North American market, the RoW (rest of the world) cars retaining the SL 500 badge even though both used the 5.5 litre (333 cubic inch) V8 (M273).

While the ironic theatrical good luck formula “break a leg” appears not to have been documented until 1948, it’s thought to have been in use since at least the 1920s and has a parallels in the German Hals- und Beinbruch (break your neck and leg) and the similar Italian in bocca al lupo. (into the wolf's mouth), the standard response to which is crepi il lupo! (may the wolf die), truncate usually as simply crepi! (may it die) although, in a sign of the times, the animal welfare lobby has suggested viva il lupo! (may the wolf live) but this is said not to have caught on with the thespians.  According to one dictionary of etymology, the expression “break a leg” was in the seventeenth century used euphemistically, of a woman, "to have a bastard" although whether this had any relationship to the traditions of theatre isn’t noted.

The noun break (act of breaking, forcible disruption or separation) was derived from the verb circa 1300 and the break of day "first appearance of light in the morning" dates from the 1580s, that senses extended by 1725 to mean any "sudden, marked transition from one course, place, or state to another".  The sense of a "short interval between spells of work" applied originally between lessons at school and was from 1861, enduring to this day in concepts such as the notorious “spring breaks”.  The “lucky break” meaning "stroke of good luck" is attested by 1911, thought to be drawn from the game of billiards (where the break that scatters the ordered balls and starts the game is attested from 1865). The now archaic meaning "stroke of mercy" is from 1914 and the use in Jazz music to describe an "improvised passage, solo" is from 1920s.  Broadcasting adopted the term in 1941 and applied it variously to handle the intervals between programmes although it was later augmented by the “sting”, a short piece of music to cover any break.  The "mini-break" is a (UK) colloquial term for a short "holiday" of 2-3 days; it was popularized in Helen Fielding's (b 1958) 1996 novel Bridget Jones's Diary and is used sometimes as a euphemism for a dirty weekend.

Frango

Frango (pronounced fran-goh)

(1) A young chicken (rare in English and in Portuguese, literally “chicken”).

(2) Various chicken dishes (an un-adapted borrowing from the Portuguese).

(3) In football (soccer) (1) a goal resulting from a goalkeeper’s error and (2) the unfortunate goalkeeper.

(4) The trade name of a chocolate truffle, now sold in Macy's department stores. 

In English, “frango” is most used in the Portuguese sense of “chicken” (variously “a young chicken”, “chicken meat”, “chicken disk” etc) and was from the earlier Portuguese frângão of unknown origin.  In colloquial figurative use, a frango can be “a young boy” and presumably that’s an allusion to the use referring to “a young chicken”.  In football (soccer), it’s used (sometimes trans-nationally) of a goal resulting from an especially egregious mistake by the goalkeeper (often described in English by the more generalized “howler”.  In Brazil, where football teams are quasi-religious institutions, such a frango (also as frangueiro) is personalized to describe the goalkeeper who made the error and on-field blunders are not without lethal consequence in South America, the Colombian centre-back Andrés Escobar (1967–1994) murdered in the days after the 1994 FIFA World Cup, an event reported as a retribution for him having scored the own goal which contributed to Colombia's elimination from the tournament. Frango is a noun; the noun plural is frangos.

The Classical Latin verb frangō (to break, to shatter) (present infinitive frangere, perfect active frēgī, supine frāctum) which may have been from the primitive Indo-European bhreg- (to break) by not all etymologists agree because descendants have never been detected in Celtic or Germanic forks, thus the possibility it might be an organic Latin creation.  The synonyms were īnfringō, irrumpō, rumpō & violō.  As well as memorable art, architecture and learning, Ancient Rome was a world also of violence and conflict and there was much breaking of stuff, the us the figurative use of various forms of frangō to convey the idea of (1) to break, shatter (a promise, a treaty, someone's ideas (dreams, projects), someone's spirit), (2) to break up into pieces (a war from too many battles, a nation) and (3) to reduce, weaken (one's desires, a nation).

A frangō in the sense of the Classical Latin: Lindsay Lohan with broken left wrist (fractured in two places in an unfortunate fall at Milk Studios during New York Fashion Week) and 355 ml (12 fluid oz) can of Rehab energy drink, Los Angeles, September 2006.  The car is a 2005 Mercedes-Benz SL 65 AMG (R230; 2004-2011) which earlier had featured in the tabloids after a low-speed crash.  The R230 range (2001-2011) was unusual because of the quirk of the SL 550 (2006-2011), a designation used exclusively in the North American market, the RoW (rest of the world) cars retaining the SL 500 badge even though both used the 5.5 litre (333 cubic inch) V8 (M273).

The descendents from the Classical Latin frangō (to break, to shatter) included the Aromanian frãngu (to break, to destroy; to defeat), the Asturian frañer (to break; to smash) & francer (to smash), the English fract (to break; to violate (long obsolete)) & fracture ((1) an instance of breaking, a place where something has broken, (2) in medicine a break in a bone or cartilage and (3) in geology a fault or crack in a rock), the Friulian franzi (to break), the German Fraktur ((1) in medicine, a break in a bone & (2) a typeface) & Fraktion (2) in politics, a faction, a parliamentary grouping, (3) in chemistry, a fraction (in the sense of a component of a mixture), (4) a fraction (part of a whole) and (5) in the German-speaking populations of Switzerland, South Tyrol & Liechtenstein, a hamlet (adapted from the Italian frazione)), the Italian: frangere (1) to break (into pieces), (2) to press or crush (olives), (3) in figurative use and as a literary device, to transgress (a commandment, a convention of behavior etc), (4) in figurative use to weaken (someone's resistance, etc.) and (5) to break (of the sea) (archaic)), the Ladin franjer (to break into pieces), the Old Franco provençal fraindre (to break; significantly to damage), the Old & Middle French fraindre (significantly to damage), the Portuguese franzir (to frown (to form wrinkles in forehead)), the Romanian frânge (1) to break, smash, fracture & (2) in figurative use, to defeat) and frângere (breaking), the Old Spanish to break), and the Spanish frangir (to split; to divide).

Portuguese lasanha de frango (chicken lasagna).

In Portuguese restaurants, often heard is the phrase de vaca ou de frango? (beef or chicken?) and that’s because so many dishes offer the choice, much the same as in most of the world (though obviously not India).  In fast-food outlets, the standard verbal shorthand for “fried chicken” is “FF” which turns out to be one of the world’s most common two letter abbreviations, the reason being one “F” representing the once infamous "F-word", one of English language’s most un-adapted exports.  One mystery for foreigners sampling Portuguese cuisine is: Why is chicken “frango” but chicken soup is “sopa de galinha?”  That’s because frango is used to mean “a young male chicken” while a galinha is an adult female.  Because galinha meat doesn’t possess the same tender quality as that of a frango, (the females bred and retained mostly for egg production), slaughtered galinhas traditionally were minced or shredded and used for dishes such as soups, thus: sopa de galinha (also as canja de galinha or the clipped caldo and in modern use, although rare, sopa de frango is not unknown).  That has changed as modern techniques of industrial farming have resulted in a vastly expanded supply of frango meat so, by volume, most sopa de galinha is now made using frangos (the birds killed young, typically between 3-4 months).  Frangos have white, drier, softer meat while that of the galinha is darker, less tender and juicer and the difference does attract chefs in who do sometimes offer a true sopa de galinha as a kind of “authentic peasant cuisine”.

There are also pintos (pintinhos in the diminutive) which are chicks only a few days old but these are no longer a part of mainstream Portuguese cuisine although galetos (chicks killed between at 3-4 weeks) are something of a delicacy, usually roasted.  The reproductive males (cocks or roosters in English use) are galos.  There is no tradition, anywhere in Europe, of eating the boiled, late-developing fertilized eggs (ie a bird in the early stages of development), a popular dish in the Philippines and one which seems to attract virulent disapprobation from many which culturally is interesting because often, the same critics happily will consume both the eggs and the birds yet express revulsion at even the sight of the intermediate stage.  Such attitudes are cultural constructs and may be anthropomorphic because there’s some resemblance to a human foetus.

Lindsay Lohan at Macy's and Teen People's Freaky Friday Mother/Daughter Fashion Show, Macy's Herald Square, New York City, August 2003.  It's hoped she had time for a Frango.

Now sold in Macy’s, Frangos are a chocolate truffle created in 1918 for sale in Frederick & Nelson department stores.  Although originally infused with mint, many variations ensued and they became popular when made available in the Marshall Field department stores which in 1929 acquired Frederick & Nelson although it’s probably their distribution by Macy's which remains best known.  Marshall Field's marketing sense was sound and they turned the Frango into something of a cult, producing them in large melting pots on the 13th floor of the flagship Marshall Field's store on State Street until 1999 when production was out-sourced to a third party manufacturer in Pennsylvania.  In the way of modern corporate life, the Frango has had many owners, a few changes in production method and packaging and some appearances in court cases over rights to the thing but it remains a fixture on Macy’s price lists, the troubled history reflected in the “Pacific Northwest version” being sold in Macy's Northwest locations in Washington, Idaho, Montana and Oregon while the “Seattle version” is available in Macy's Northwest establishments.  There are differences between the two and each has its champions but doubtless there are those who relish both.

A patent application (with a supporting trademark document) for the Frango was filed in 1918, the name a re-purposing of a frozen dessert sold in the up-market tea-room at Frederick & Nelson's department store in Seattle, Washington.  The surviving records suggest the “Seattle Frangos” were flavoured not with mint but with maple and orange but what remains uncertain is the origin of the name.  One theory is the construct was Fr(ederick’s) + (t)ango which is romantic but there are also reports employees were told, if asked, to respond it was from Fr(ederick) –an(d) Nelson Co(mpany) with the “c” switched to a “g” because the word “Franco” had a long established meaning.  Franco was a word-forming element meaning “French” or “the Franks”, from the Medieval Latin combining form Franci (the Franks), thus, by extension, “the French”.  Since the early eighteenth century it had been used when forming English phrases & compound words including “Franco-Spanish border” (national boundary between France & Spain), Francophile (characterized by excessive fondness of France and all things French (and thus its antonym Francophobe)) and Francophone (French speaking).

Hitler and Franco, photographed at their day-long meeting at Hendaye, on the Franco-Spanish border, 23 October 1940.  Within half a decade, Hitler would kill himself; still ruling Spain, Franco died peacefully in his bed, 35 years later.

Remarkably, the Frango truffles have been a part of two political controversies.  The first was a bit of a conspiracy theory, claiming the sweet treats were originally called “Franco Mints”, the name changed only after the outbreak of the Spanish Civil War (1936-1939) in which the (notionally right-wing and ultimately victorious) Nationalist forces were led by Generalissimo Francisco Franco (1892-1975; Caudillo of Spain 1939-1975) and the explanation was that Marshall Field wanted to avoid adverse publicity.  Some tellings of the tale claim the change was made only after the Generalissimo’s meeting with Adolf Hitler (1889-1945; Führer (leader) and German head of government 1933-1945 & head of state 1934-1945) at Hendaye on 23 October 1940.  Their discussions concerned Spain's participation in the War against the British but it proved most unsatisfactory for the Germans, the Führer declaring as he left that he'd rather have "three of four teeth pulled out" than have to again spend a day with the Caudillo.  Unlike Hitler, Franco was a professional soldier, thought war a hateful business best avoided and, more significantly, had a shrewd understanding of the military potential of the British Empire and the implications for the war of the wealth and industrial might of the United States.  The British were fortunate Franco took the view he did because had he agreed to afford the Wehrmacht (the German armed forces) the requested cooperation to enable them to seize control of Gibraltar, the Royal Navy might have lost control of the Mediterranean, endangering the vital supplies of oil from the Middle East, complicating passage to the Indian Ocean and beyond; it would have transformed the strategic position in the whole hemisphere.  However, in the archives is the patent application form for “Frangos” dated 1 June 1918 and there has never been any evidence to support the notion “Franco” was ever used for the chocolate truffles.

Macy's Dark Mint Frangos.

The other political stoush (late nineteenth century Antipodean slang meaning a "fight or small-scale brawl") came in 1999 when, after seventy years, production of Frangos was shifted from the famous melting pots on the thirteenth floor of Marshall Field's flagship State Street store to Gertrude Hawk Chocolates in Dunmore, Pennsylvania, the decision taken by the accountants at the Dayton-Hudson Corporation which had assumed control in 1990.  The rationale for this shift was logical, demand for Frangos having grown far beyond the capacity of the relatively small space in State Street to meet demand but it upset many locals, the populist response led Richard Daley (b 1942; mayor (Democratic Party) of Chicago Illinois 1989-2011), the son of his namesake father (1902–1976; mayor (Democratic Party) of Chicago, Illinois 1955-1976) who in 1968 simultaneously achieved national infamy and national celebrity (one’s politics dictating how one felt) in his handling of the police response to the violence which beset the 1968 Democratic National Convention held that year in the city.  The campaign to have the Frangos made instead by a Chicago-based chocolate house was briefly a thing but was ignored by Dayton-Hudson and predictably, whatever the lingering nostalgia for the melting pots, the pragmatic Mid-Westerners adjusted to the new reality and, with much the same enthusiasm, soon were buying the Pennsylvanian imports.

Macy's Frango Mint Trios.

Doubtlessly to the delight of economists (sweet-toothed or not), there appears to be a “Frango spot market”.  Although the increasing capacity of AI (artificial intelligence) has improved the mechanics of “dynamic pricing” (responding in real-time to movements in demand), as long ago as the Christmas season in 2014, CBS News ran what they called the “Macy's State Street Store Frango Mint Price Tracker”, finding the truffle’s price was subject to fluctuations as varied over the holiday period as movements in the cost of gas (petrol).  On the evening of Thanksgiving, “early bird” shoppers could buy a 1 lb one-pound box of Frango mint “Meltaways” for US$11.99, the price jumping by the second week in December to US$14.99 although that still represented quite a nominal discount from the RRP (recommended retail price) of US$24.00.  Within days, the same box was again listed at US$11.99 and a survey of advertising from the previous season confirmed that in the weeks immediately after Christmas, the price had fallen to US$9.99.  It may be time for the Chicago Mercantile Exchange (CME) to open a market for Frango Futures (the latest “FF”!).

Callosity

Callosity (pronounced kuh-los-i-tee)

(1) In pathology, an alternative name for a callus.

(2) In botany, a hardened or thickened part of a plant.

(3) In zoology, as ischial callosity, a large callus on the butts of certain animals.

(4) In the human condition, being of a callous demeanor; insensitivity or hard-heartedness

1375–1425: From the late Middle English calosite, from the Late Latin callōsitās, the construct being callōs(us) (callous) (from callum (hardened skin) +‎ -ōsus (the suffix added to a noun to form an adjective indicating an abundance of that noun)) + -itās which in English was rendered as callus + -ity, the substitute “o” a familiar device.  The –ity suffix was from the French -ité, from the Middle French -ité, from the Old French –ete & -eteit (-ity), from the Latin -itātem, from -itās, from the primitive Indo-European suffix –it.  It was cognate with the Gothic –iþa (-th), the Old High German -ida (-th) and the Old English -þo, -þu & -þ (-th).  It was used to form nouns from adjectives (especially abstract nouns), thus most often associated with nouns referring to the state, property, or quality of conforming to the adjective's description.  Callosity is a noun; the noun plural is callosities.

Essentially a thickening of the skin which forms in response to damage, a callus is one of the body’s protective mechanisms and example of how human skin have evolved to respond to a “fragile” area by replacing it with something “anti-fragile”.  The skin is a good barrier to much which would be dangerous if able to penetrate the surface but easily it can be cut and it’s prone to delimitation if exposed to repeated friction, something well known to gardeners digging holes, the skin on the palms of the hands soon “wearing off” at the points where the handle of the shovel repeatedly rubs.  That will be painful but the body will respond, replacing the dead skin with new skin which is thicker and harder, thus enabling the gardener to soon again pick up their shovel and return to their excavations.  This is an example of the general principle of healthy human physiology which responds to damage not by replacing things with something just as strong but something stronger, able to resist whatever force it was which caused the injury and it is the same with a bone fracture; when the bone knits back together, it will not be merely as strong as it was but a little stronger.  The new skin on the gardener’s hands will also be stronger and as the holes continue to be dug, the skin will become more robust still but the difference should not be thought of as fragile vs robust but as fragile vs anti-fragile, the point being that as pressure is applied, the material responds by becoming less-fragile.

Fragile and robust, although often used as antonyms (and in general use usefully so because the meanings are so well conveyed and understood) are really not opposites but simply degrees of the same thing.  In the narrow technical sense an expression of robustness or fragility is a measure of the same thing; a degree of strength.  The traditions of language obscure this but it becomes clear if measures of fragility or robustness are reduced to mathematics and expressed as comparative values in numbers.  It's true that on such a continuum a point could be set at which point something is regarded as no longer robust and becomes defined as fragile (indeed this is the essence of stress-testing) but this doesn't mean one is the antonym of the other.  The opposite of fragile is actually anti-fragile (the anti prefix was from the Ancient Greek ἀντι- (anti-) (against, hostile to, contrasting with the norm, opposite of, reverse (also "like, reminiscent of"))).  The concept is well known in physiology and part of the object in some forms of strength training is to exploit the propensity of muscles to tear at stress points, relying on the body to repair these tears in a way that doesn’t restore them to their original form but makes them stronger so that if subjected again to the same stress, a tear won’t happen.  It’s thus an act of anti-fragility, the process illustrated also by the calluses which form on the hands after the skin blisters in response to work.  Fragile and robust merely express points on a spectrum and are used according to emphasize the extent of strength; anti-fragile is the true opposite.

The idea of anti-fragile was introduced by Lebanese-born, US-based mathematician and trader Nassim Nicholas Taleb (b 1960) in the book Antifragile: Things That Gain From Disorder (2012), the fourth of five works which explore his ideas relation to uncertainty, randomness & probability, the best-known and most influential was The Black Swan: The Impact of the Highly Improbable (2007).  His work was thoughtful, intriguing and practical and was well received although the more accessible writing he adopted for the later volumes attracted criticism from some who felt an academic style more suited to the complex nature of his material; probably few who read the texts agreed with that.  Apart from the ideas and the use to which they can be put, his deconstruction of many suppositions was also an exploration of the rigidities of thought we allow our use of language to create.

Anti-callus devices (gloves the most common type) are used when the aim is to avoid the growth of a callus, the use of an “artificial callus” sometimes preferable to the natural.  A carpet layer in knee pads (left) and bra strap “cushions” (right).

When the new areas of skin are called calluses (calli the alternative plural), callus from the Latin callum (hard skin).  Most often used to describe the hardened areas of skin (typically on hands & feet) induced as a response to repeated friction, wear or use, in anatomy, the same word is applied to the initially soft or cartilaginous substance exuded at the site of a bone fracture which converts ultimately into bone, knitting the fragments into the one piece.  One the process fully is complete, if again exposed to the same stress, the bone will not break.  In botany, it’s used of the new formation over the end of a cutting. Callus is a noun & verb, the calluses, the present participle callusing and the past, callused.

In some professions, the callus can be close to essential; those whose life involves supporting weights on their shoulders form them on the pressure points, enabling them to ply their trade without undue pain or further damage.  However, not all whose shoulders might suffer welcome calluses, however beneficial they might be:  Women who wish to avoid what manufactures term the “shoulder grooving” caused by the pressure of their bra’s shoulder straps (the physics of this a product of (1) the weight supported and (2) its surface distribution which is dictated essentially by the width of the strap) can buy inserts for the straps which increase the surface area, thereby reducing the specific loading by re-distributing the downward pressure.  A variation on this idea is the “knee pad” worn by those who lay carpets, floor tiles and such.  These folk are compelled to work “on their knees” for hours at a time, often upon hard and sometimes rough surfaces and although, given time, calluses would form were the work to be performed unprotected, it would not be a pleasant experience and the degree of hardening needed would likely adversely affect normal mobility.  In zoology, calluses are a noted environmental adaptation among some species, (Old World) gibbons, monkeys and some chimpanzees having evolved notably large calluses on their butts (described as ischial callosities (the seventeenth century ischium (from the Latin ischium, from the Ancient Greek ἰσχίον (iskhíon) (hip joint)) describing the lowest of the three bones that make up each side of the pelvis).  On the animals so endowed, the advantage is the ability to sleep while sitting upright on thin branches, safe from both predators and the risk of falling.

Lindsay Lohan and her lawyer in court, Los Angeles, December 2011.

In figurative use callosity came to be used to refer to one with a lack of feeling or capacity for emotion but the use when documented comes usually with the caveat that those so described are not “psychopaths” but merely the “hard-hearted”.  So it’s there to be used and if it seems not to suit, English offers has quite an array of choice when speaking of those lacking emotional range.  There is “heartless” & “hard-hearted”, both of which allude to the ancient idea of the special significance of the heart as the source of all that human feeling and character; even now it’s known to be a “just a pump”, the romantic notions persist in many culture and variations of the ❤ symbol are among the most frequently used emojis.  “Cold-blooded” is different in that although it’s blood the heart pumps, the operative word really is “cold”, implying decisions made or actions taken without emotion intruding and in idiomatic use, a “cold-blooded murder” (such as a contract killing done for payment) is viewed with less sympathy than a crime of passion (such murderers of said to have been “seeing the red mist” of “hot” blood at the time of their crime.  “Stolid” and “impassive” differs in that they can often be virtues and anyway suggest not an absence of capacity for feeling but its repression and one who wrote on how essential that was to civilization yet simultaneous damaging to individuals was Sigmund Freud (1856-1939), his ideas later taken up by German-American philosopher Herbert Marcuse (1898–1979).  Mankind probably didn’t surprise Freud but doubtless we disappointed Marcuse.  Finally, there is “stoic” which traces back to the Hellenic school of stoicism, a philosophy with a great following in Antiquity which was intended always to be practical, a way to help citizens live good lives rather than anything concerned with abstractions.  In its pure form it survives in that form but the modern re-purposing of the word means it’s now used to mean something like “suffering in silence”.  “Callosity” then is one of many ways to refer to the “unfeeling” and its use in this context is based on the use in medicine, a callosity (ie a callus) being “skin of abnormal hardness & thickness” which can be poked or pricked with the subject barely feeling the intrusion.  In that it’s subtly different from “thick skinned” which usually means “not easily offended”.

Fragile

Fragile (pronounced fraj-uhl (U) or fraj-ahyl (non-U))

(1) Easily broken, shattered, or damaged; delicate; brittle; frail.

(2) Vulnerably delicate, as in appearance.

(3) Lacking in substance or force; flimsy.

1505–1515: From the Middle English fragile (liable to sin, morally weak), from the Middle French fragile, from the fourteenth century Old French fragele, from the Latin fragilis (easily broken) (doublet of frêle), the construct being frag- (variant stem of the verb frangere (break), from the primitive Indo-European root bhreg- (to break) + -ilis.  The -ilis (neuter -ile) suffix was from the Proto-Italic -elis, from the primitive Indo-European -elis, from -lós; it was used to form an adjective noun of relation, frequently passive, to the verb or root.  It was cognate with fraction & fracture and doublet of frail.  The original meaning from circa 1510 (liable to sin, morally weak) by circa 1600 extended to "liable to break" as a back-formation from fragility which was actually an adoption of the sense in Latin.  The transferred sense "of frail constitution" (of persons) dates from 1858.  The companion adjective frail emerged in the mid fourteenth century in the sense of "morally weak", from the twelfth century Old French fraile & frele (weak, frail, sickly, infirm) (enduring in Modern French as frêle), from the Latin fragilis.  The US slang noun meaning "a woman" is documented from 1908 and although there’s no evidence, etymologists have noted Shakespeare's "Frailty, thy name is woman" (Hamlet, Act I, Scene 2).  The comparative fragiler and the superlative fragilest are both correct but the more elegant “more fragile” and “most fragile” tend to be preferred.  Fragile is used usually as an adjective but can be applied as a noun (typically by folk like furniture movers) or in the same way as “exquisite”.  Fragilely is an adverb and fragility is a noun; the noun plural is fragiles.

Words which are either synonyms or close in meaning include delicate, feeble, frail, weak, brittle, crisp, crumbly, decrepit, fine, flimsy, fracturable, frangible, friable, infirm, insubstantial, shivery, slight & unsound.  The antonym most often used to suggest the opposite quality to fragile is “robust” (evincing strength and health; strong).  Robust dates from circa 1545 and was a learned borrowing from circa 1400 Medieval Latin rōbustus (oaken, hard, strong), the construct being rōbus- (stem of rōbur (oak, strength) + -tus (the adjectival suffix).

Lindsay Lohan looking fragile: Lindsay (2019) by Sam McKinniss (b 1985) (left), from a reference photograph taken 22 July 2012, leaving the Chateau Marmont in West Hollywood, LA (right).

However, fragile and robust, although often used as antonyms (and in general use usefully so because the meanings are so well conveyed and understood) are really not opposites but simply degrees of the same thing.  In the narrow technical sense an expression of robustness or fragility is a measure of the same thing; a degree of strength.  The traditions of language obscure this but it becomes clear if measures of fragility or robustness are reduced to mathematics and expressed as comparative values in numbers.  It's true that on such a continuum a point could be set at which point something is regarded as no longer robust and becomes defined as fragile (indeed this is the essence of stress-testing) but this doesn't mean one is the antonym of the other.

The opposite of fragile is actually antifragile (the anti prefix was from the Ancient Greek ἀντι- (anti-) (against, hostile to, contrasting with the norm, opposite of, reverse (also "like, reminiscent of"))).  The concept is well known in physiology and part of the object in some forms of strength training is to exploit the propensity of muscles to tear at stress points, relying on the body to repair these tears in a way that doesn’t restore them to their original form but makes them stronger so that if subjected again to the same stress, a tear won’t happen.  It’s thus an act of antifragility, the process illustrated also by the calluses which form on the hands after the skin blisters in response to work.  Fragile and robust merely express points on a spectrum and are used according to emphasize the extent of strength; antifragile is the true opposite.

The idea of antifragile was introduced by Lebanese-born, US-based mathematician and trader Nassim Nicholas Taleb (b 1960) in the book Antifragile: Things That Gain From Disorder (2012), the fourth of five works which explore his ideas relation to uncertainty, randomness & probability, the best-known and most influential was The Black Swan: The Impact of the Highly Improbable (2007).  His work was thoughtful, intriguing and practical and was well received although the more accessible writing he adopted for the later volumes attracted criticism from some who felt an academic style more suited to the complex nature of his material; probably few who read the texts agreed with that.  Apart from the ideas and the use to which they can be put, his deconstruction of many suppositions is also an exploration of the rigidities of thought we allow our use of language to create.

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) mammaplasty (breast reduction).  Never has satisfactorily it been explained why this procedure seems to be lawful in all 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 lightweight and robust unit which began life powering 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 intended 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 no more metal could be removed from the structure without dangerously compromising safety; in engineering (and other fields), there is a point at which further reduction becomes at least counter-productive and often dangerouw.  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 (unobtainable) 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.

Secretary of Defence the younger (left) and elder (right).  Donald Rumsfeld (left) with Gerald Ford (1913–2006; US president 1974-1977) and George W Bush (George XLIII, b 1946; US president 2001-2009).

Donald Rumsfeld (1932–2021; US Secretary of Defense 1975-1977 & 2001-2006) may or may not have been evil but his mind could sparkle and his marvellously reductionist principles can be helpful.  His classification of knowledge was often derided but it remains a useful framework:

(1) Known unknowns.
(2) Known knowns.
(3) Unknown unknowns.
(4) (most intriguingly) Unknown knowns.

A expert reductionist, he reminded us also there are only three possible answers to any question and while there's a cultural reluctance to say “don’t know”, sometimes it is best:

(1) I know and I’m going to tell you.
(2) I know and I’m not going to tell you.
(3) Don’t know.

While (1) known unknowns, (2) known knowns and (3) unknown unknowns are self-explanatory, examples of (4) unknown knowns are of interest and a classic one was the first “modern” submarine, developed by the Germans during the last months of World War II (1939-1945).

German Type XII Elektroboot (1945).

In World War II, the course of the war could have been very different had OKM (Oberkommando der Marine (the Kriegsmarine's (German Navy) high command)) followed the advice of the commander of the submarines and made available a fleet of 300 rather than building a surface fleet which wasn’t large enough to be a strategic threat but of sufficient size to absorb resources which, if devoted to submarines, could have been militarily effective.  With a fleet of 300, it would have been possible permanently to maintain around 100 at sea but at the outbreak of hostilities, only 57 active boats were on the navy’s list, not all of which were suitable for operations on the high seas so in the early days of the conflict, it was rare for the Germans to have more than 12 committed to battle in the Atlantic.  Production never reached the levels necessary for the numbers to achieve critical mass but even so, in the first two-three years of the war the losses sustained by the British were considerable and the “U-Boat menace” was such a threat that much attention was devoted to counter-measures and by 1943 the Allies could consider the battle of the Atlantic won.  The Germans’ other mistake was not building a true submarine capable of operating underwater (and therefore undetected) for days at a time.

It was only in 1945 when Albert Speer (1905–1981; Nazi court architect 1934-1942; Nazi minister of armaments and war production 1942-1945) and Grand Admiral Karl Dönitz (1891–1980; head of the German Navy 1943-1945, German head of state 1945) were assessing the “revolutionary” new design that they concluded there was no reason why such craft couldn’t have been built in the late 1930s because the engineering capacity and technology existed even then (although the industrial and labor resources did not).  It was a classic case of what Donald Rumsfeld (1932–2021: US defense secretary 1975-1977 & 2001-2006) would later call an “unknown known”: The Germans in 1939 knew how to build a modern submarine but didn’t “know that they knew”.  Despite the improvements however, military analysts have concluded that even if deployed in numbers, such was the strength of forces arrayed against Nazi Germany that by 1945, not even such a force could have been enough to turn the tide of war.  However, had the German navy in 1939-1940 had available a fleet of even 100 such submarines (about a third what OKM (Oberkommando der Marine (the Kriegsmarine's (German Navy) high command) calculated was the critical strategic size given at any point only a third would be at sea with the others either in transit or docked), the battle in the Atlantic would have been much more difficult for the British.

Mr Rumsfeld however neglected to mention another class of knowledge: the “lost known”, examples of which have from time-to-time appeared and there may be more still to be discovered.  The best known were associated with the knowledge lost after the fall in the fifth century of the Western Roman Empire when Europe entered the early medieval period, once popularly known as the “Dark Ages”.  The lost knowns included aspects of optics such as lens grinding and the orthodoxy long was the knowledge was not “re-discovered” or “re-invented” until perfected in Italy during the late thirteenth century although it’s now understood that in the Islamic world lens continued during the late Medieval period to be ground and it’s suspected it was from Arabic texts the information reached Europe.

What really was a lost known was how the Romans of Antiquity made their long-lasting opus caementicium (concrete) so famously “sticky” and resistant to the effects of salt water.  Unlike modern concrete, made using Portland cement & water, Roman concrete was a mix of volcanic ash & lime, mixed with seawater, the later ingredient inducing a chemical reaction creating a substance stronger and more durable.  When combined with volcanic rocks, it formed mineral crystalline structures called aluminum tobermorite which lent the mix great strength and resistance to cracking.  After the fall of Rome, the knowledge was lost and even when a tablet was discovered listing the mix ratios, caementicium couldn’t be replicated because the recipe spoke only of “water” and not “sea water”, presumably because that was common knowledge.  It was only modern techniques of analysis which allowed the “lost known” to again become a “known known”.