Dimensionality (pronounced dih-men-shuhn-nal-i-tee or dahy-men-shuhn-nal-i-tee).
(1) The state or characteristic of
possessing dimensions.
(2) In mathematics, engineering, computing,
physics etc, the number of dimensions possessed or attributed to an object,
space or concept; the nature of the dimensions, considered, in relation to each
other or the external world.
(3) In architecture (usually in criticism
or theory), as super-dimensionality, micro-dimensionality, complimentary-dimensionality
et al, an expression used to critique the scale of designs.
Circa 1910: A coining of mathematicians said to date from
the early twentieth century (though actual use may pre-date this), the
construct was dimension + -ality. Dimension was from
late fourteenth century late Middle English dimensioun,
from the Anglo-French, from the Latin dīmēnsiōn-, from dīmēnsiō &
dīmēnsiōnem, from dīmensus
(measuring, measurement, dimension), perfect active participle of dīmētior (measured, regular), the
construct being dis- (part’ separate;
render asunder) + mētior (measure or estimate; distribute or mete out; traverse),
from the Proto-Italic mētis, from the
primitive Indo-European meh- (to
measure). The suffix –ality was a compound affix, the construct
being -al + -ity and equivalent to the French -alité and the Latin -ālitās. The -al suffix was from the Middle English -al, from the Latin adjectival suffix -ālis, or the French, Middle French and Old French –el & -al. It was use to denote
the sense "of or pertaining to", an adjectival suffix appended (most
often to nouns) originally most frequently to words of Latin origin, but since
used variously and also was used to form nouns, especially of verbal
action. The alternative form in English
remains -ual (-all being obsolete). 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.
The derived forms from mathematics and other
disciplines (extradimentionality et al) are sometimes hyphenated (extra-dimentionality
et al). Dimensionality is a noun; the
noun plural is dimensionalities.
Being inherently a thing of numbers, in both
pure and applied mathematics, dimensionality matters. There is equidimensionality
which, strictly speaking in the quality enjoyed by two (or more) dimensions exactly
the same but the term has also been used in architecture as (1) a fancy way to
say that things are (by mathematical standards) “roughly the same” and (2) a
synonym for symmetrical. Nobody seems to
have come up with “hetrodimensionality” or something like that, asymmetrical
apparently adequate. In psychiatry, unidimensionality
is the quality of measuring a single construct, trait, or other attribute; it's
a clinical tool, an example of which is a unidimensional personality scale
which would contain items related only to the respective concept of
interest. It's not the same as the pop-psychology
term "one-dimensional" which is an allusion to functional, intellectual,
emotional etc limitations in individuals or institutions. A particular use of that appeared in the book
One-Dimensional Man (1964) by
German-American philosopher Herbert Marcuse (1898–1979). Marcuse argued modern capitalism had reduced
culture to a technological rationality and individuals to mere economic units,
their value measured only by their industrial productivity. Moreover, the genius of this system was that
the false consciousness of the victims was manipulated to the point they became
defenders of their own oppression.
Superdimensionality on the beach: A gigantic Lindsay
Lohan.
Nondimensionality refers to quantity
or measurement with no physical units attached, often represented as a ratio of
two quantities that have the same units, such as the ratio of the diameter of a
circle to its circumference (which is represented by the nondimensional
quantity π, or pi). It’s not quite a revenge
on the physicists who have identified certain particles with dimensions yet no
mass, nondimensionality being useful in that relationships between different
physical quantities can be expressed without the need to have specific units of
measure. Unidimensionality (the opposite of multidimensionality) refers to a
measurement or quantity involving only one dimension or aspect; it is used not
to imply there is only one dimension but in situations where the critical
quality can be described using a single variable or dimension. The classic examples of unidimensionality are
the three dimensions length, width & breadth. Multidimensionality involves two or more
dimensions. The companion terms “curse of dimensionality” and “blessing of dimensionality” are both
commentaries of the volume of data available but reference not the data but the
processes applied to the information. The
curse of dimensionality is that in some cases there can be an unmanageable amount
of data; there is simply too much information even to assess what should be discarded. However, for other purposes, the same data
set could be invaluable, the volume making possible what once was not, thus the
blessing of dimensionality.
String theory: Lindsay Lohan in string
bikini, Mykonos, Greece, 2014.Extradimensionality
underlies string theory, a (highly) theoretical construct which has provided a
number of speculative frameworks in an attempt to unify what are still
considered the fundamental forces at work in the universe (gravity,
electromagnetism, and the strong and weak nuclear forces). The essence of string theory in that the
fabric of the universe is composed not of point-like particles in space but very
small, one-dimensional forms (the nature of which varies according to the version
of the theory) which act like “strings”, vibrating at different frequencies. The strings are said to exist in another dimensional
space-time than the four with which we are familiar (length, width, depth &
time) and some string theorists have suggested there may be ten or more
dimensions. The most significant aspect
of the behavior of the strings is said to be their interaction with both the
space in which they exist and other strings in other spaces (although on the
latter point some theorists differ). The
intricate equations describing the strings and their dimensions has allowed very
complex models to be built and from these, the handful of people of the planet
who understand both the mathematics and their implications have drawn a number
of inferences about the universe said variously to be “fascinating”, “speculative”
and “nonsensical” and one of the delights of string theory is that it can be neither
proved nor disproved. Word nerds however
can be grateful to the stringers because they adopted “compactified”, the word
describing the way the dimensions beyond the verifiable four are curled up (or
scrunched) at scales so small they remain unobservable with current technology.
Superdimentionality
Model of Germania, built to scale.Superdimentionality
is the application of exaggerated dimensions to designs, some of which actually
get built. It a popular motif for the kitsch
structures favored by tourist attractions of which Australia has many (the big
pineapple, big prawn, big golfball, big lobster, big gumboot et al) but for Adolf
Hitler (1889-1945; German head of government 1933-1945 & head of state
1934-1945), superdimentionality was the dominant concept for the entire Nazi empire;
reichism writ large. The idea was well
documented in the plans for Germania, the re-building of Berlin designed by a
team under Albert Speer (1905–1981; Nazi court architect 1934-1942; Nazi
minister of armaments and war production 1942-1945), the centerpiece of which
was the monumental Volkshalle (People's
Hall), sometimes referred to as the Große
Halle (Great Hall). The hall would
have seated 180,000 under a dome 16 times larger than that of St Peter's
Basilica in the Vatican and in its vastness was a classic example of the
representational architecture of the Third Reich. Although it’s obvious the structure as a
whole was intended to inspire awe, the details also conveyed the subliminal
messaging of much fascist propaganda, fixtures like doorways sometimes four times
the usual height, the disconnection from human scale emphasizing the
supremacy of the state.
German conceptual H-45 battleship.Hitler also thought the materiel supplied to
his military machine should be big. After
being disappointed by proposals for the successors to the Bismarck-class ships
to have the armament increased only from eight 15-inch (380 mm) to eight 16
inch (406 mm) canons, he ordered OKM (Oberkommando
der Marine; Naval High Command) to design bigger ships. Although none were ever built, Germany
lacking the facilities even to lay down the keels, the largest (the H-44) would
have had eight 20-inch (508 mm) cannons.
Even more to the Führer’s liking was the concept of the H-45, equipped
with eight 31.5 inch (800 mm) Gustav siege guns but the experience of surface
warfare at sea convinced Hitler the days of the big ships were over and he
would even try to persuade the navy to retire all their capital ships and
devote more resources to the submarines which, as late as 1945, he hoped might
still prolong the war. However, he never
lost faith in the promise of bigger and bigger tanks, an opinion share by none
of the tank commanders who were appalled at the designs of some of the
monstrosities he ordered prepared.
Hitler’s study in the Reich Chancellery
(1939) (left) and his (rarely used) big desk in the corner, the big doors
behind (right)
Perhaps surprisingly, there’s no record
Hitler ever complained the Mercedes-Benz built for his use were too small but
then they were by even by the standards to which popes, presidents and
potentates were accustomed, big. Certainly,
there’s no record of him asking Daimler-Benz for anything larger as Charles De
Gaulle (1890–1970; President of France 1958-1969), in 1965 aghast at the notion
the state car of France might be bought from Germany or the US (it’s not known
which idea he thought most appalling and apparently nobody bothered to suggest
buying British) requested of coachbuilder Henri Chapron (1886-1978). Le General’s only stipulations about his Citroën
DS Presidential were (1) it had to be longer than the extended Lincoln Continentals
then used by the White House for Lyndon Johnson (LBJ, 1908–1973; US president
1969-1969) and (2) the turning circle had to be tight enough to enter the
Elysée Palace’s courtyard from the rue du Faubourg Saint-Honoré and then pull
up at the steps in a single maneuver.
Chapron managed to fulfill both requirements although the contrast
between the Citroën’s rather agricultural 2.3 litre (140 cubic inch) four-cylinder
engine and the Lincoln’s 7.0 (430) V8 was remarkable, De Gaulle probably
regarding the Lincoln’s additional displacement as typical American vulgarity.
Mercedes-Benz 770K (W150), Berlin 1939.
Hitler though would have been impressed by
the big V8 although he would doubtless have pointed out the 7.7 litre (468
cubic inch) straight-8 in his Mercedes-Benz 770K was not only bigger but also
supercharged and he’d have found nothing vulgar in any of the American machine’s
dimensions. The 770Ks used by the Führer
were produced in two series (W07 (1930-1939) & W150 (1939-1943)) of what
the factory called the Grosser Mercedes (the Grand Mercedes) and while the earlier
cars were available to anyone with the money (seven between 1932-1935 purchased
by the Japanese Imperial household for the emperor’s fleet and adorned with the
family’s gold chrysanthemum), the W150s were made exclusively for the upper echelons of the Nazi Party although to smooth the path of foreign policy, some did end
up in foreign hands such as António Salazar (1889–1970) dictator of Portugal
1932-1968), Generalissimo Francisco Franco (1892-1975; Caudillo of Spain
1939-1975) & Field Marshal Mannerheim (commander-in-chief of Finnish defense
force 1939–1945 and president of Finland (1944–1946). Though large and impressive, by 1938 the
W07 was something of a engineering relic and although the demands of the military
were paramount in the economy, resources were found to update the Grosser to
the technical level of the more modern 540K by adopting a lower tubular chassis
with revised suspension (the de Dion axle at the rear something which should
have appeared on the post-war cars) and a new, five-speed, all synchromesh gearbox. Making the selection of first gear effortless was of
some significance because so much of the 770K’s time was spent at crawling
speed on parade duty but, despite the bulk (and the weight of the armored
versions with 1¾ inch (45 mm) glass could exceed 5500 kg (12,000
lb), speeds in excess of 160 km/h (100 mph) could be achieved provided one had
enough autobahn ahead although at that pace, even the 195 litre (52 US gallon,
43 Imperial gallon) fuel tank would soon have been drained. Some sources also claim five were built with
two superchargers, raising the top speed to 190 km/h (118 mph) but the tale may
be apocryphal.
Mercedes-Benz G4 during Hitler’s entry in Vienna
following the Anschluss (the absorption of Austral into the Reich), 14 March
1938. The statue in the background is of
the Archduke Charles Louis John Joseph Laurentius of Austria, Duke of Teschen
(1771–1847) and often referred to as “Archduke Karl”, mounted on the Heldenplatz.
Also appealing to Hitler was the big, three-axle
G4 (W31). The factory developed six-wheel
(and ten-wheel for those with dual rear wheels) cross-country vehicles for
military use during the 1920s but after testing a number of the prototype G1s,
the army declined to place an order, finding them too big, too expensive and
too heavy for their intended purpose. Hitler
however, as drawn to big, impressive machines as he was to huge,
representational architecture, ordered them adopted as parade vehicles and the
army soon acquired a fleet of the updated G4, used eventually not only on
ceremonial occasions but also as staff and command vehicles, several known to have been specially
configured, some as baggage cars and at least one as a mobile communications centre,
packed with radio-telephony. Eventually,
between 1934-1939, fifty-seven were built, originally exclusively for the OKW (Oberkommando der Wehrmacht (Armed Forces
High Command)) and OKH (Oberkommando des
Heeres (Army High Command)) but one was gift from Hitler to Franco and the Spanish
G4, one of few which still exists, was restored and remains in the royal garage
in Madrid. According to factory records,
all were built with 5.0, 5.3 & 5.4 litre straight-eight engines but there
is an unverified report of interview with Hitler’s long-time chauffeur, Erich
Kempka (1910-1975), suggesting one for the Führer’s exclusive use was built
with the 7.7 litre straight-eight used in the 770K Grosser. Most of the 770s were supercharged so, if
true, it's a tantalizing prospect but this story is widely thought apocryphal,
no evidence of such a one-off ever having been sighted.