Perimeter & Parameter

Perimeter (pronounced puh-rim-i-ter)

(1) A line bounding or marking off an area; any boundary around.

(2) The outermost limits.

(3) In geometry, the border or outer boundary of a two-dimensional figure (the sum of the lengths of the segments that form the sides of a polygon.

(4) The total length of such line; the total length of any such closed curve, such as the circumference of a circle.

(5) In military jargon a fortified boundary that protects a position.

(6) In clinical ophthalmology, an instrument for determining the peripheral field of vision.

(7) In basketball, a semicircular line on a basketball court surrounding the basket, outside of which field goals are worth three points rather than two (also called three-point line).

(8) The area outside this line (often used attributively).

1585–1595: From the French périmètre (circumference, outer boundary, or border of a figure or surface), from the feminine Latin form perimetros, from the neuter Greek perímetron (circumference), the construct being peri- (around; about) + -meter from metron (measure), from the primitive Indo-European root me- (to measure).  The military sense of “boundary of a defended position” is said by some sources to have come into use only by 1943 despite the tactic being probably the second oldest military procedure still in use (the attack presumably the first).  Whether coincidental or not, the ultimate failure of perimeter defense was what finally led to the success of the Soviet offensive against the Nazi Sixth Army in Stalingrad (now Volgagrad) in 1943.  The technical terms created by the use of perimeter as a modifier include perimeter check (a patrol which checks to ensure a defensive perimeter remains in place) & perimeter fence.  Perimeter & perimetry are nouns, perimetral, perimetric & perimetrical are adjectives and perimetrically is an adverb; the noun plural is perimeters.

Parameter (pronounced puh-ram-uh-tuhr (U) or puh-ram-i-ter (non-U)

(1) In mathematics, a constant or variable term in a function that determines the specific form of the function but not its general nature, as a in f(x) = ax, where a determines only the slope of the line described by f(x).  (A value kept constant during an experiment, equation, calculation or similar, but varied over other versions of the experiment, equation, calculation etc).

(2) In mathematics, one of the independent variables in a set of parametric equations.

(3) In geometry, in the ellipse and hyperbola, a third proportional to any diameter and its conjugate, or in the parabola, to any abscissa and the corresponding ordinate.

(4) In crystallography, the ratio of the three crystallographic axes which determines the position of any plane; the fundamental axial ratio for a given species.

(5) In statistics, a variable entering into the mathematical form of any distribution such that the possible values of the variable correspond to different distributions (any measured quantity of a statistical population that summarizes or describes an aspect of the population).

(6) In computing, a variable that must be given a specific value during the execution of a program or of a procedure within a program.

(7) Limits or boundaries; guidelines; specifications; any constant, definitional or limiting factor (usually in the plural parameters).

(8) Characteristic or a factor; an aspect or element.

(9) In computing syntax for various purposes, an input variable of a function definition, that become an actual value (argument) at execution time (an actual value given to such a formal parameter).

1650-1660: From the French paramètre, from the New Latin parametrum (parameter), the construct being the Ancient Greek παρα- (para-) (beside, subsidiary) + μέτρον (métron) (meter) (measure), from the primitive Indo-European root me- (to measure).  The words was almost exclusive to mathematics & geometry until the late 1920s when it came to be extended to “measurable factor(s) which help to define a particular system", hence the now common alternative meaning “boundary, limit, characteristic factor” (under the influence of perimeter which used a similar spelling and (at least conceptually) could be understood to enjoy some overlap of meaning.  Although the wider definition has been in use since the 1950s, purists have never approved.  Parameter is a noun and parametric & parametrical are adjectives; the noun plural is parameters.

Parameters and perimeters

The more modern ways “parameter” has been used since the early twentieth century does offend the linguistically more fastidious but it seems clear the innovations are here to stay.  Some do however just get it wrong and university lecturers in the social sciences seem to be those who bear the heaviest burden of training a certain number of their institution’s first year students in the correct use of “parameter” & “perimeter”.  That they are sometimes confused is understandable because the spellings are so close and there is some sense of overlap in the meanings, both able to be used in a way which defines limits.  The definitions can be reduced to: (1) perimeter refers to either something physical (a national border; a fence etc) or a representation of something physical (lines on a map; the four sides of a square etc) whereas (2) a parameter is an element of specification, a constant or variable value which can be either an absolute value or a range.  So, a perimeter may be drawn on the basis of certain parameters while the values of parameters will in some cases exist within certain perimeters.  Definitions such as that are vague enough for those so inclined to find contradictions but for the way most people, most of the time (correctly) use parameter & perimeter, it seems serviceable.

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

Frame

Frame (pronounced freym)

(1) A (sometimes intricate) border or case for enclosing a picture, mirror etc.

(2) A rigid structure formed of relatively slender pieces, joined so as to surround sizable empty spaces or non-structural panels, and generally used as a major support in building or engineering works, machinery, furniture etc.

(3) A body, especially a human body, with reference to its size or build; the physique of someone (often with a modifier (large frame, slight frame etc).

(4) A structure for admitting or enclosing something (doors, windows etc); other in the plural and used with a plural verb).

(5) In textile production, a machine or part of a machine over which yarn is stretched.

(6) In statistics, an enumeration of a population for the purposes of sampling, especially as the basis of a stratified sample

(7) In telecommunications and data transmission, one cycle of a regularly recurring number of pulses in a pulse train (frame relay etc); in networking, an independent chunk of data sent over a network.

(8) A constitution or structure in general; the system.

(9) In beekeeping, one of the sections of which a beehive is composed, especially one designed to hold a honeycomb

(10) In formal language teaching, a syntactic construction with a gap in it, used for assigning words to syntactic classes by seeing which words may “fill the gap”.

(11) In physical film stock, one of the successive pictures, the concept transferred to digital imagery.

(12) In television, a single traversal by the electron beam of all the scanning lines on a television screen.

(13) In computing, the information or image on a screen or monitor at any one time (dated).

(14) In computing (website design), a self-contained section that functions independently from other parts; by using frames, a website designer can make some areas of a website remain constant while others change according to the choices made by the internet user (an individually scrollable region of a webpage; “collapsible frames” a noted innovation).

(15) In philately, the outer decorated portion of a stamp's image, often repeated on several issues although the inner picture may change; the outer circle of a cancellation mark.

(16) In electronics (film, animation, video games), a division of time on a multimedia timeline.

(17) In bowling, one of the ten divisions of a game; one of the squares on the scorecard, in which the score for a given frame is recorded.

(18) In billiards and related games, the wooden triangle used to set up the balls; the balls when set up by the frame.

(19) In baseball, an inning.

(20) In underworld slang, as “frame-up” or “framed”, to incriminate (an innocent person) on the basis of fabricated evidence.

(21) In law enforcement slang as “in the frame”, being suspected by the authorities of having committed a offence.

(22) In publishing, enclosing lines (usually in the form of a square or rectangle), to set off printed matter in a newspaper, magazine, or the like; a box.

(23) The structural unit that supports the chassis of an automobile (X-Frame, ladder-Frame, perimeter-frame, space-frame et al).

(24) In nautical architecture, any of a number of transverse, rib-like members for supporting and stiffening the shell of each side of a hull; any of a number of longitudinal members running between web frames to support and stiffen the shell plating of a metal hull.

(25) In genetics, as “reading frame”, a way of dividing nucleotide sequences into a set of consecutive triplets.

(26) In mathematics, a complete lattice in which meets distribute over arbitrary joins.

(27) A machine or part of a machine supported by a framework, (drawing frame, spinning frame et al).

(28) In printing, the workbench of a compositor, consisting of a cabinet, cupboards, bins, and drawers, and having flat and sloping work surfaces on top.

(29) In bookbinding, an ornamental border, similar to a picture frame, stamped on the front cover of some books.

(30) One’s thoughts, attitude or opinion (usually as “frame of mind”).

(31) To form or make, as by fitting and uniting parts together; construct.

(32) To contrive, devise, or compose, as a plan, poem, piece of legislation etc.

(33) To conceive or imagine, as an idea.

(34) To provide with or put into a frame (painting, mirror et al).

(35) To give utterance to (typically as “frame an answer” etc).

(36) To form or seem to form (speech) with the lips, as if enunciating carefully (often used in speech therapy and elocution training).

(37) To fashion or shape (often a term used in sculpture).

(38) To shape or adapt to a particular purpose.

(39) To line up visually in a viewfinder or sight.

(40) To direct one's steps (archaic).

(41) To betake oneself; to resort (archaic).

(42) To prepare, attempt, give promise, or manage to do something (archaic).

Pre 1000: From the Middle English verb framen, fremen or fremmen (to prepare; to construct, build, strengthen, refresh, perform, execute, profit, avail), from the Old English framiae, fremian, fremman or framian (to avail, profit), from the Proto-West Germanic frammjan, from the Proto-Germanic framjaną (to perform, promote), from the primitive Indo-European promo- (front, forward) and cognate with the Low German framen (to commit, effect), the Danish fremme (to promote, further, perform), the Swedish främja (to promote, encourage, foster), the Icelandic fremja (to commit), the Old Frisian framia (to carry out), the Old Norse frama (to further) and the Old High German (gi)framōn (to do); the Middle English was derived from the verb.  Derived forms such as deframe, misframe, reframe, subframem unframe, beframe, enframe, full-frame, inframe, outframe, well-framed etc are created as needed.  Frame, framer & framableness are nouns, framed & framing are verbs, framable & frameable are adjectives, frameless is an adjective and framably is an adverb; the noun plural is frames.

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

In Middle English, the sense of the verb evolved from the mid-thirteenth century “make ready” to “prepare timber for building” by the late 1300s and the meaning “compose, devise” was in use by at least the 1540s. The criminal slang (“framed”; a “frame up” etc) made familiar in popular fiction all revolved around the idea of corrupt or unscrupulous police fabricating evidence to “blame an innocent person” seems not to have been in use until the 1920s (although the dubious policing practices would have had a longer history) and all forms are thought to have been a development of the earlier sense of “plot in secret”, noted since the turn of the twentieth century, that possibly and evolution from the meaning “fabricate a story with evil intent”, first attested early in the sixteenth century.  The use of the noun in the early thirteenth century to mean “profit, benefit, advancement” developed from the earlier sense of “a structure composed according to a plan”, developed from the verb and was influenced by Scandinavian cognates (the Old Norse frami meant “advancement”).

Like its predecessor the 300 SL Gullwing (W198; 1954-1957), the Mercedes-Benz 300 SL Roadster (W198; 1957—1963) was built on a tubular space-frame.

The use in engineering “sustaining parts of a structure fitted together” emerged circa 1400 while the general sense of “an enclosing border” of any kind came some two centuries later.  Surprisingly, the familiar form of a “border or case for a picture or pane of glass” seems to have come into use only in the mid-seventeenth century while the use “human body” (ie large frame, slight frame etc) was in use by the 1590s.  Of bicycles it was used from 1871 and of motor cars by 1900 although the early use referred often to what would now be understood as sub-frames, structures which attached to the chassis to support drive-train components, coach-work etc.  The meaning “separate picture in a series from a film” dates from 1960 and was purely descriptive because the individual “frames” on film-stock resembled framed photographs attached in a continuous roll.  The idea of a frame being a “specific state” was in use in the 1660s, the “particular state” (in the sense of “one’s frame of mind”) appears in the medical literature in the 1710s.  The “frame of reference” was coined for use in mechanics and graphing in 1897; the figurative sense coming into use by at least 1924.  As an adjective, frame was in use in architecture & construction by the late eighteenth century.  The A-Frame (a type of framework shaped like the capital letter "A") was an established standard by the 1890s and a vogue for buildings in this shape was noted in the 1930s.

Faster and smaller: By 1964 the IBM 360 mainframe (left) had outgrown its cabinet (the original “main frame”) and had colonized whole rooms.  By 2022, the IBM z16 mainframe (right) was sufficiently compact to return to a cabinet.  

In computing, the word “frame” was used in a variety of ways.  The mainframe (central processor of a computer system) was first described as such in 1964, the construct being main +‎ frame and the reference simply was to the fact the core components were stored in a cabinet which had the largest frame in the room, other, small cabinets being connected with wires and cables.  Mainframes were the original “big machines” in commercial computing and still exist; incomparably good for some purposes, less satisfactory for others.  Frame Relay also still exists as a standardized wide-area network (WAN) technology although it’s importance in the industry has declined since its heyday during the last two decades of the twentieth century.  A packet-switching protocol used for transmitting data across a network, Frame Relay operates at the data link layer of the OSI (Open Systems Interconnection) model, which is the second layer in the seven-layer model.  In a Frame Relay network, data is divided into frames, which are then transmitted between network devices (such as routers), over a shared communication medium and it was this latter aspect which accounted for its widespread adoption: unlike traditional circuit-switching networks (in which a dedicated physical circuit is established for the duration of a communication session), Frame Relay allows multiple logical connections to share the same physical resources so for all but the largest organizations, the potential for cost-saving was considerable.  Importantly too, integral to the protocol’s design was the use of packet switching (which means data is transmitted in variable-sized packets (ie frames) allowing the optimal use of available network bandwidth.  Frame Relay had the advantage also of not adding layers of complexity to the network architecture, relying on the underlying physical layer for error detection and correction rather than including error recovery mechanisms (a la a protocol like X.25 which operate at the network layer).  All of this made Frame Relay scalable and adaptable to various network topologies, making it an attractive “bolt-on” for system administrators and accountants alike.  However, while it still exists in some relatively undemanding niches, the roll-out of the infrastructure required to support internet traffic mean it has substantially been supplanted by newer technologies such as Multiprotocol Label Switching (MPLS).

Pop-art painting of Lindsay Lohan in a mid-eighteenth century frame by Jean Cherin (circa 1734-1785), Paris, France.  This is an intricately carved example of the transitional Louis XV-style gilt double sweep frame, ornamented with shell centres, acanthus fan corners, and a top crested with a ribbon-tied leaf & flower cluster atop a cabochon.

Xmas

Xmas (pronounced kris-muhs (u) or eks-muhs (non-U))

An abbreviation for Christmas which, despite a long history of uncontroversial use, is increasingly labelled offensive by fundamentalist Christians.

1755: The construct was X- (the Greek letter χι (chi)) + Christ (our Lord and Savior Jesus Christ) + mas (Eucharistic service) from the Middle English messe & masse, from the Old English mæsse (the mass, church festival), from the Vulgar Latin messa (Eucharistic service (literally "dismissal”)), from the Late Latin missa (dismissal), the feminine past participle of mittere (to let go, send).  The connection is X being the initial letter in the Ancient Greek word Χριστός (Chrīstos) (Christ) although it’s speculated the physical resemblance between X and the cross on which Christ was crucified may at least have strengthened the association.  It sometimes appears as X-mas but Xtmas is long archaic; the plural is Xmases and there’s also the occasional appearance Xmassy (ie an (X- +) abbreviation of the adjective Christmassy) but it’s non-standard.  As a point of usage, Xmas should be pronounced kris-muhs, eks-muhs both non-U and a misplaced spoken tribute to the written although, it’s permissible if being used in the context of complaining about the use of the spelling Xmas.

The seemingly strange connection of the element –mas between a ritual of churches and the Latin root meaning “dismissal” is thought to lie in the concluding words of the service: Ite, missa est (“Go, (the prayer) has been sent" or "Go, it is the dismissal”)).  In Old English use, the Latin was sometimes glossed sendnes (send-ness) and the meaning "musical setting of certain parts of the Roman Catholic and Anglican liturgies” emerged in the 1590s.  Variations of mass are common in European languages including the Dutch mis, German Messe, Danish messe, Swedish mässa & Icelandic messa.

Xmas spirit: Lindsay Lohan, Santa Monica beach, Christmas, 2009.

Xmas was apparently first used in 1755 as a modification of the earlier abbreviation X'temmas, attested from 1551 where X was for Christ, the English letter X being identical in form (but not sound signification) to Greek χι (chi), the first letter of Ancient Greek Χριστός (Chrīstos) (Christ).  Earlier, the convention in English when abbreviating Christmas was to use Xp- or Xr- (corresponding to the "Chr-" in the Greek Χριστος), the spelling Χp̃es mæssa (Christmas) is in the Anglo-Saxon Chronicle (a circa 1100 compilation of documents chronicling the history of the Anglo-Saxons, the original text dating from late in the reign of Alfred the Great (circa-899, king of the West Saxons from 871-circa 886 of the Anglo-Saxons circa 886-899)) and that was from Cristes mæsse, again with the abbreviation of Cristes provided by the symbol X, an orthographic borrowing from Ancient Greek χι (chi).  Scholars seem generally to agree the first known proto-Xmas appeared in 1021 when an Anglo-Saxon scribe saved some space with the multiple repetitions of Xpmas in a document; parchment was then expensive as the letters on telegrams would a millennium-odd later be.  Just to save space then, the same imperative that would later result in the anti-climatic Y2K bug, computer memory address space briefly the scarce parchment of its time.   

Use Xmas instead of Christmas and go straight to Hell.

Xmas was for centuries an accepted and uncontroversial abbreviation for Christmas, one found in the archives of both the Vatican and Lambeth Palace, for years used especially with technologies like telegrams and telexes which sometimes charged the sender by the letter and the thousand-odd year history of X as a substitute for “Christ” includes the words of men of letters Samuel Taylor Coleridge (1772–1834), Lord Byron (1788-1824), Lewis Carroll (1832-1898), TS Eliot (1888–1965) and the theologians amateur & professional, CS Lewis (1898–1963) & Karl Barth (1886–1968).  In the twentieth century however, the attitudes of fundamental Christians hardened as the new spirit of intolerance washed around the planet, the trend intensified in recent years by technologies which both amplified extreme views and gave them an unprecedented opportunity of dissemination.  At its core was a concern nominally or established Christian nations were having imposed on them the double threat of chauvinistic multiculturalism and creeping secularization with Xmas (“taking Christ out of Christmas”) a blatant insult to the faithful.  Even before social media however, there had been objections; as early as the 1940s, books of etiquette and style guides from the usual subjects suggested Xmas should be avoided in formal writing and banned absolutely from appearing on Christmas cards.  Telegrams still being a thing, it was acknowledged there was a place for Xmas but that place was mostly in the squalid business of commerce, advertising the place it belonged; elsewhere it was inelegant though hardly an attack on Christendom.  Even those such as Robert Hudson (b 1938) who in Christian Writer's Manual of Style (2004) documented the etymology and acknowledged the ancient history of respectful use, said it should be avoided if possible and never appear in formal writing.  It’s now common for certain factions of Christianity to label the use of Xmas a blasphemy.  Fox News definitely avoid it.

Malcolm X (1925-1965).

The linguistic link between “X” and “Christ” was unrelated to it being the choice of family name by African-American civil rights activist Malcolm X.  Malcolm X was politically the most interesting activist of the era and renounced the family name of his birth because he thought it a legacy of something imposed on his forebears by a slave-owner, “X” used in the sense it’s applied in mathematics to represent an unknown variable, his true family name from Africa which could never be known.  The abandonment of family names was the practice of the Nation of Islam (founded 1930), theologically a distinct branch of the faith with a particular emphasis on an overtly political ideology.  Malcolm X joined the Nation of Islam around 1949 and the teaching of its then leader, Elijah Muhammad (1897–1975), was that their “true names would in future be revealed” although he made more than one explanation of the circumstances in which this would happen.

Wonder

Wonder (pronounced wuhn-der)

(1) To think or speculate curiously.

(2) To be filled with admiration, amazement, or awe; marvel (often followed by at).

(3) Something strange and surprising; a cause of surprise, astonishment, or admiration.

(4) The emotion excited by what is strange and surprising; a feeling of surprised or puzzled interest, sometimes tinged with admiration.

(5) A miraculous deed or event; remarkable phenomenon.

(6) As a modifier, exciting wonder by virtue of spectacular results achieved, feats performed etc; wonder drug; wonder horse; seven wonders of the ancient world et al.

Pre 900: A Middle English nouns wonder & wunder from the Old English wundor (marvelous thing, miracle, object of astonishment), from the Proto-Germanic wundrą.  It was cognate with the Scots wunner (wonder), the West Frisian wonder & wûnder (wonder, miracle), the Dutch wonder (miracle, wonder), the Low German wunner & wunder (wonder), the German Wunder (miracle, wonder), the Danish, Norwegian & Swedish under (wonder, miracle), the Icelandic undur (wonder) and the Old Norse undr (wonder).  In Middle English, by the late thirteenth century, it came also to mean the emotion associated with such a sight.  The original wonder drug (1939) was Sulfanilamide, one of the first generation of sulfonamide antibiotics and best known as M&B (after the British manufacturer May & Baker); it was later largely superseded by penicillin and other sulfonamides.  The verb (derivative of the noun), was from the Middle English wondren & wonderen, from the Old English wundrian (be astonished; admire; make wonderful, magnify), from the Proto-Germanic wundrōną.  It was cognate with the Saterland Frisian wunnerje, the West Frisian wûnderje, the Dutch wonderen, the German Low German wunnern, the German wundern, the Old High German wuntaron and the Swedish & Icelandic undra.  The sense of "entertain some doubt or curiosity" dates from the late thirteenth century.

Exactly or vaguely synonymous are conjecture, meditate, ponder, question, marvel, surprise, amazement, bewilderment, awe, scepticism, reverence, fascination, confusion, shock, admiration, doubt, astonishment, curiosity, uncertainty, surprise, fear, phenomenon, oddity, miracle, spectacle & speculate.  The noun wonderment is a noun has been in use since the 1530s while wonderful was drawn from the late Old English wunderfoll and wondrous emerged circa 1500, derived (it would seem) from the Middle English adjective wonders which was first noted in the early fourteenth century, originally genitive of the noun wonder, the suffix altered by the influence of such as marvelous etc; it existed as an adverb from the 1550s, the evolution related to wondrously & wondrousness.  Wonder is a noun & verb, wonderer & wonderment are nouns, wonderless is an adjective, wondrous is an adjective & adverb, wonderful is an adjective & adverb (and a non-standard noun) and wondrously is an adverb; the noun plural is wonders. 

The Wonderbra

The “wonder” in the portmanteau word Wonderbra underwent a bit of a meaning shift, decades after the product was released.  Although best-known for the illusory enhancement the structural engineering made possible, “wonder” was originally an allusion to the comfort offered compared with the usually more uncompromising alternatives of the time.  Wonderbra, marketed with an emphasis on the practicality and comfort made possible by innovations in construction, was first trademarked in 1939 by the Canadian Lady Corset Company and was for some years available only in Canada.  Not trademarked in the US until 1955, it wasn’t until 1961 (with the model 1300) that the now familiar, gravity-defying, design was released.

Even then, although the 1300 became the brand’s most popular product, it was thirty years before worldwide success was realized; although it had been on sale in the UK since 1964, sales boomed only in 1992, a success repeated in Europe the next season.  The Wonderbra was launched in the US in 1994 and, assisted by a minimalist advertising campaign featuring Czech model Eva Herzigová (b 1973), became not only a best-seller but part of the cultural lexicon.  The engineering of the Wonderbra wasn’t difficult to emulate and other manufacturers released clones, each with a portmanteau at least as suggestive of “wonder” as it had come to be understood in this context, Gossard offering an Ultrabra and Victoria's Secret a Miracle Bra.  Wonderbra responded to the competition with a novel technical innovation, the Air Wonder, inflatable for "high altitude cleavage".  Included with the Air Wonder was a mini-pump, small enough to fit in a handbag and be thus available for adjustments as circumstances demanded.

Wonderment: Lindsay Lohan as an enhanced Hermione Granger (a fictional character in JK Rowling's (b 1965) Harry Potter series), Saturday Night Live (season 29 episode 18), 1 May 2004.

The Seven Wonders of the Ancient World

The pyramid today: it's the only of the seven wonders which still stands.

The Great Pyramid of Giza was built in 2570 BC and still stands, debate continuing about how it was built, how long the construction took and how many workers were required.  Built as a tomb for the fourth dynasty Egyptian pharaoh Khufu, it was part of a complex which included temples and many smaller pyramids.  Originally, the outermost stones were a highly polished white limestone, many of which were loosened by an earthquake some 600 years ago and over time, all were removed and used in the structures of cities and mosques.  As well as being of interest to architects, Egyptologists and archaeologists in general, the Great Pyramid has attracted cosmologists and mathematicians because of references to the Moon, the Orion constellation, continental gravity and other features of the heavens.  Each side of the pyramid is almost perfectly aligned with the four cardinal points of the compass while the dimensions convert to a ratio that equates to 2π with nearly perfect accuracy.

In the absence of evidence, artists can make of the gardens what they will.

According to legend, the Walls and Hanging Gardens of Babylon were built in 600 BC and stood until destroyed by earthquake in 226 BC but among historians there has long been debate about (1) whether the gardens ever existed and (2) if they did could they possibly have been the form usually described.  None of that ever bothered medieval story-tellers or poets, some of whom embellished the legend as they went.  Most tales recount how they were by King Nebuchadrezzar II because his wife missed the lush, green gardens of her home and in the medieval imagination they were represented sometimes as a cascading series of rooftops and sometimes dangling from structures built into the walls of the royal palace.  A more recent theory, noting the difficulties which would have existed in creating an irrigation system speculate that the myth may be based on gardens planted not in Babylon but close to Sennacherib at the eastern bank of the river Tigris.

Zeus: Because of the well documented contemporary descriptions, the renditions since are at least conceptually accurate.

The Statue of Zeus at Olympia (Δίας μυθολογία) was built in 430 BC and was destroyed by fire in 426 AD. Carved from ivory, on a throne of cedarwood, the statue in its right hand held a life-size statue of Nike, the goddess of victory, and in its left a large sceptre topped with an eagle. Said to be some 12 metres (40 feet) tall, contemporary accounts say it occupied the whole width of one of the temple’s aisles, its head reaching to the ceiling.  Debate has long surrounded the fate of the statue, some saying the structure was lost in the fire while others had it moved to Constantinople (modern day Istanbul) where if remained for decades before being destroyed.  Evidence about its appearance is fragmentary and unreliable; although there’s no doubt many copies at various scales were created during the 800-odd years it stood, none are known to have survived.

Before the fire: The Temple of Artemis is a popular model for modern re-creations.

The Temple of Artemis at Ephesus (Ἀρτεμίσιον) was built in 550 BC and was destroyed by fire in 356 BC though as was the practice then, the structure was rebuilt several times over the centuries.  Unusually by the architectural conventions of the time, it was built substantially of marble and glittered with gold. The scale was impressive: from the high platform over a hundred sculptured columns supported the roof and being at least twice the size of the Parthenon, it was so breathtaking it was said to “rise to the clouds” which literally was rarely true but an example of how exaggeration in social media is nothing new.  The temple functioned also as an art gallery but the centrepiece was of course the statue of Artemis and if the legends are believed it was covered with gold and colourful stones, the legs adorned with carving of bees and animals with the top of the body adorned with breasts, symbolizing fertility.  It was destroyed in an act of arson by a malcontent called Herostratus who wished to secure a place in history by any means and the word herostatic (one who seeks fame at any cost) has endured.  Although made of marble, like the steel & glass Crystal Palace in London, the structure was packed with flammable materials and oils so it burned well.  There exists also a conspiracy theory that the act was a kind of inside job by the temple’s priests who had their own reasons for wanting a new building but neither that nor a reference to the writings of Aristotle which offers a lightning strike as the catalyst for the conflagration have much support among historians.

How to be remembered: The Mausoleum at Halicarnassus.

The Mausoleum at Halicarnassus (Μαυσωλεῖον Ἁλικαρνασσεύς), built as a tomb for Mausolus, a governor in the Persian Empire, was constructed in 352 BC and destroyed by earthquake in 1404 AD.  Said to be extravagant even by the standards of personal aggrandizement known throughout antiquity, the work included sculptural reliefs for each of the four sides of the building, commissioned from the leading Greek architects and artists; these soon became something of a tourist attraction.  Almost perfectly square and some 14 stories tall, the base covered some 10,000 square feet (900+ m²) while on each side of the tomb stood nine massive columns supporting a stepped pyramid on which stood by a four-horse marble chariot in which sat carvings of Mausolus and his Artemisia (who supervised the construction).  So famous was the tomb that Mausolus's name became the root for the word for large tombs in many languages.

Pleasing lines: The Lighthouse of Alexandria.

The Lighthouse of Alexandria (ὁ Φάρος τῆς Ἀλεξανδρείας) was built in 280 BC and was destroyed by earthquake in 1323 AD.  It sat on the island of Pharos in the harbor of Alexandria and was the world’s first “famous lighthouse” although it was architecturally different to modern structures, built in three stages, all sloping inward.  Built with marble blocks suing lead as mortar, the lowest was square, the middle octagonal and the top cylindrical.  Within the lighthouse was a ramp and “dumb-waiter” used to transport the wood for the fire which burned during the night.  On the lantern floor, a large, curved mirror reflected the sunlight during the day and the fire at night and in clear weather it’s said seafarers could see the light even at a distance of 50 kilometres (30 miles).  The earth’s curvature makes this seem improbable but under certain atmospheric conditions (such as the light reflecting from clouds), it may have been possible.  Also plausible is the legend the light generated by the mirror was so bright and hot it could be used as a weapon of coastal defense to set fire to an enemy’s ships.  Under controlled conditions, because such ships were sometimes coated with flammable, tar-like substances (for water-proofing & timber preservation), it might have been possible but it would have been challenging to achieve this against a moving target.  Such was the power of the legend of the Pharos that the word remains the root for “lighthouse” in a number of languages.

Vaguely plausible rendering of how The Colossus of Rhodes may have appeared.

The Colossus of Rhodes was a very big statue, erected somewhere near the port of the city of Rhodes, the biggest settlement on what is the one of the larger Greek islands of the same name which lies off what is now Turkey’s Aegean coast.  Taking a dozen years to complete, the statue, construction of which began in 292 BC, was erected to honor Elios, the God of the Sun, who brought the inhabitants victory over Demetrius Poliorcetes (Demetrius I of Macedon; “The Besieger" 337–283 BC) who laid siege to Rhodes in 305-304 BC.  It stood for only sixty-odd years, collapsing during a severe earthquake which struck in 226 BC, contemporary reports indicating the structure fractured at both knees before toppling.  Remarkably, the mostly bronze wreckage was left substantially undisturbed for some eight-hundred years, becoming something of a tourist attraction before, in 654, it was salvaged by Arab invaders under the Muslim caliph Mu'awiya I (معاوية بن أبي سفيان‎, Muʿāwiya ibn Abī Sufyān; circa 600–680) who sold it to someone described as “a Jewish merchant from Damascus” who is said to have carted it off on a camel train of almost “a thousand beasts”.

Demetrios the Besieger had a scandalous private life but had a flair for military matters, noted too for innovations in engineering such as the machines and devices built by his armies as siege engines.  However, even the forces he was able at deploy in 305-304 BC weren’t sufficient to defeat the fortifications of Rhodes and eventually, Demetrios was compelled to retreat, abandoning the siege machinery on the island.  To give thanks to the Sun God, the Rhodians granted the commission to build a triumphal statue to Helios to the sculptor Chares of Lindos (Χάρης ὁ Λίνδιος, circa 330 BC-circa 280 BC), a pupil of Lysippos (Λύσιππος; fourth century BC) and, in the dozen years between 304-292 BC, he supervised the construction.

Logo of Lindsay Lohan's Beach House at Rhodes.

Structurally, the build was executed along the well-understood engineering principles of the age, the base of white marble first installed to which were affixed the feet and ankles, an iron and stone framework gradually formed as scaffolding and structure proceeded in unison upwards.  To permit the workers to reach the highest levels, an earth ramp was built because the heights involved meant a free-standing system of scaffolding would lack the needed stability; when the work was complete, the earth ramp was demolished and the soil carted off.  While the superstructure was built, workers cast the outer skin in bronze using plates, the metal formed with copper melted in large ovens, to which iron, making 10-20% of the mix, was added.  Then the mouton metal mixture was moved in large ladles to be distributed in clay molds, flat structures used to form sheets varying in thickness according to need. Once cast, the rough edges were ground away and the plates polished before they were transported to the building site where they were hammered to the desired shape to be attached to the iron structure,  The thickest and heaviest plates were those rendered for the feet and ankles, complex in the shape of their curves and needing more mass to afford greater stability.  Thus for a dozen years, the thin bronze skin was added to the growing body of stone, each plate fixed to the iron frame and then to the neighboring plate.  Once finished, it was polished to reflect the rays of the Sun so it would shine as intensely as possible, better to honor Helios. 

How engineers would today build a 122 m (400 feet) high Colossus using modern techniques of structural engineering.  An interesting exercise although the Greek exchequer may have other fiscal priorities.

From the laying of the first stone to its toppling, building its destruction lies a time span of but sixty-seven years but the Colossus ranks as one of the seven wonders of the ancient world with Great Pyramid of Giza which still stands after almost five-thousand.  Such was the scale of the Colossus that the ruins still impressed, “…even lying on the ground, it is a marvel" wrote Pliny the Elder (24-79) who noted few men could wrap their arms around the fallen thumb and each finger alone would have stood taller than most other statues.  The earthquake which so damaged the city 226 BC broke the Colossus at its narrowest and thus weakest points, the knees, and given the mass which existed above, there was no chance it could survive.  Although it would be centuries before the list of the seven wonders would exist as the codified canon now familiar, the stature was already famous and the an offer to the pay the cost of restoration was extended by Ptolemy III Euergetes (Πτολεμαῖος Εὐεργέτης, Ptolemy the Benefactor; circa 280–222 BC) of Egypt.  However, an oracle was consulted and their judgement forbade any re-construction so the offer was declined.  Details of the oracle’s pronouncement are lost but it’s speculated the conclusion may have been the earthquake was the act of a wrathful Helios and the ruins should be left where they fell, lest anger again be aroused.  There is no otherwise compelling explanation to account for why so much valuable bronze wouldn’t for centuries be recycled.

A (fanciful) engraving of the Colossus of Rhodes (circa 1540) by Martin Heemskerck (1498-1574).

The exact location remains uncertain but the notion the Colossus straddled the entrance to Rhodes harbor with ships passing between its legs was a figment of medieval imagination, a thing famously vivid.  Given its method of construction, such a thing would have collapsed under its own weight even before it was complete and, had it stood over the water, not only would construction have been challenging but when it fell, it would have blocked the entrance to the Mandraki harbor.  Despite that, in the early 1980s when a large piece of rubble was discovered in the water, there were still romantics who hoped this might vindicate the medieval theory.  There’s little doubt the story of a 60m (200 feet) tall Colossus straddling the entrance to the harbor was the work of opportunist poets and artists, the engineers and architects of the time sufficiently acquainted with physics and metallurgy to have assured all of the impossibility of their vision yet it seems long to have captured the medieval imagination.  Despite all that, it still influenced many even at the dawn of modernity, being one of the inspirations for the Statue of Liberty but that was designed in a way to ensure greater strength and stability, the weight distribution and the dimensions of the base entirely different.  There’s no doubt the statue stood somewhere in the proximity of Rhodes harbor but archaeological excavations have thus far revealed nothing, not unsurprising given the footprint of a vertical structure is much less than a temple or other building, and the urbanization of Rhodes over two millennia mean the site may long ago have been built-over.  The Colossus though would have shared one noted characteristic with the Statue of Liberty: When copper rubs on iron, it creates electricity, especially in a costal environment with salty air.  Like Liberty, the Colossus of Rhodes made its own electricity.