“…deep down in the heart of piety lurks an insane and lunatic arbitrariness that knows that it has itself produced its God.”
Johannes Climacus (AKA Søren Kierkegaard)
It is claimed that Eratosthenes was known by his peers as Beta, because he was the second-best in the ancient Greek world at just about everything; he devised an algorithmic method for determining prime numbers which marked him out as the second-best mathematician, and his version of the myths about the constellations was some of the second-best poetry ancient Greece had ever heard. His poetry was good, but not so good that anyone ever bothered to write much of it down, so the vast majority of his work has long been lost. However, Eratosthenes is reputed to have been the first person to use the term ‘geography’ and was the first to measure the circumference of the Earth. He did so with an amazing degree of accuracy, although it is unclear exactly how accurate his measurement was because units of measurement were yet to be standardised. Standardised units of measurement were not invented for another two millennia.
Beta made his calculation of the Earth’s circumference without leaving his home city of Alexandria. He was employed as the head of the Library of Alexandria, while there he read that in Swenet, which occupies the site where Aswan is today which sits on the Tropic of Cancer, a vertical column or a pole set plumb in the ground will cast no shadow at noon on the longest day of the year, for at that moment the sun is directly overhead in the sky so that its light will reach the very bottom of the deepest well. Beta knew that the same was not true in Alexandria and he realised that by measuring the angle at which a vertical column casts a shadow at noon on the summer solstice in Alexandria he could ascertain how many degrees of the Earth’s circumference separated the two sites. All that was then needed for Beta to make a calculation of the total circumference of the planet was to know the distance from Alexandria to Swenet.
Beta approximated the distance by asking a travelling merchant how long the journey would take by camel. This is the kind of sloppiness that makes the difference between being first-best and being nicknamed Beta. It also suggests that Eratosthenes’ accurate calculation was an educated-guess benefitting from mutually compensating errors rather than the fruit of the rigorous application of scientific method.
However, for our purposes the accuracy of Eratosthenes' calculation is of secondary interest compared to the fact of his having set out to make the calculation in the first place and its implications for the our conception of the globe.
Around 250 years later, the Roman geographer Pomponius Mela drew a diagram of the planet Earth stratified into distinct zones; freezing polar regions - too cold to inhabit, the temperate area in which the Roman Empire was situated and an equatorial band which would be too hot to navigate across. Mela hypothesised that on the southern side of this equatorial zone there should be an antipodean temperate region mirroring our own which, in theory, could be home to un-contactable races of men. Later still, in the second century, Ptolemy wrote Geographia in which he gave instructions for the drawing up of maps of the known world. When he did so, Ptolemy knew (thanks to Eratosthenes) that the area he was describing represented only about one quarter of the surface of the globe. Eratosthenes’ measurement, to borrow a phrase from the amateur epistemologist Donald Rumsfeld, meant that the three quarters of the globe that were yet to be mapped had moved from being an unknown unknown, to being a known unknown; terra incognita awaiting exploration, conquest and exploitation.
That which can be measured can be ascribed a value, that which can be measured may be sold or speculated upon. Eratosthenes’ measurement of the globe was a catalyst for the beginning of globalisation. It would take until the seventeenth century before trade was sufficiently globalised that it became urgent to solve the problem of a universal unit of measurement, and when the metric system was developed it was as much a symptom of the revolutionary politics of the time as it was a response to necessity. In his 1668 essay Towards a Real Character and a Philosophical Language John Wilkins went further than proposing a universal system of weights and measures; he integrated it within a universal language that would allow merchants, scientists and philosophers from around the world to communicate without their meaning being corrupted by translation or by the fundamental arbitrariness of natural language.
Wilkins was influenced in the construction of his language by a misapprehension that the symbols of Chinese writing make up a form of pasigraphy in which each symbol represents a distinct self-defining concept. In Wilkins’ linguistic scheme everything in the universe is put into one of forty Genera, each Genera represented by a two-letter syllable. These Genera are subdivided into Differences by the addition of a third letter and then subdivided further into Species by the addition of a fourth. By learning the Genera, Differences and species, the speaker of Wilkins’ language may name any animal, mineral or vegetable they might encounter without having to learn what it is it first. Conversely, upon encountering a hitherto unknown word, the speaker may derive an objective definition of whatever it describes.
Wilkins and his contemporaries aimed to develop a system of measurement that would supersede old, arbitrary and inaccurate units of measurement such as the acre – which was originally defined as the area that can be tilled by a yoke of oxen within a single day – or the stadia – the unit of distance used by Eratosthenes – although it is unclear whether he adopted the Greek or the Egyptian stadia. The new metric system was to be arrived at scientifically. In Towards a Real Character and a Philosophical Language John Wilkins proposed a unit of length based on the length of a pendulum whose beat is precisely one second, an idea which he borrowed from Christopher Wren. However, the difficulty of accurately measuring one second complicated this apparently simple idea. A proposal made by Gabriel Mouton was adopted instead and, via a series of compromises, one metre came to be defined as one ten-millionth of the length of a meridian running between the North Pole and the equator on a line of longitude running through Paris.
The difficulty of accurately measuring the distance from the pole to the equator, not to mention the misshapen nature of the globe, resulted in the prototype one-metre bar, minted from gold in 1793, being too short by a fraction of a millimetre. Successively more accurate prototype metres have since been made using ever more (supposedly) objective definitions of the unit.
Like Eratosthenes, Jorge Luis Borges worked as a head librarian. It is easy to see similarities between Wilkins’ language and the Dewey Decimal System used in libraries, and it’s not too great a stretch to suppose that the librarian’s concern with the classification of knowledge contributed to Borges’ identification, in a well-known essay, of the central problem with Wilkins’ scheme of universal categorisation and measurement. While the structure of Wilkins’ language is systematic, there is a degree of arbitrariness in the divisions between each of his Genera, Differences and Species. As an example, Borges examines the eighth of Wilkins’ forty Genera; stones:
“Wilkins’ divides them into common (flint, gravel, slate); moderate (marble, amber, coral); precious (pearl, opal); transparent (amethyst, sapphire); and insoluble (coal, fuller’s earth, and arsenic). The ninth category is almost as alarming as the eighth. It reveals that metals can be imperfect (vermillion, quicksilver); artificial (bronze, brass); recremental (filings, rust); and natural (gold, tin, copper). The whale appears in the sixteenth category: it is a viparous, oblong fish…”
Before questioning the categorisation of the whale as a fish, it is worth asking how Wilkins defines the category fish itself.
As soon as any categorisation is attempted, arbitrariness, ambiguity and imprecision inevitably creep in. Borges suggests that Wilkins’ categories are as ridiculous as the cataloguing of all of the world’s animals that he quotes from the apocryphal Chinese encyclopaedia the Heavenly Emporium of Benevolent Knowledge:
“Those that belong to the emperor, Embalmed ones, Those that are trained, Suckling pigs, Mermaids (or Sirens), Fabulous ones, Stray dogs, Those that are included in this classification, Those that tremble as if they were mad, Innumerable ones, Those drawn with a very fine camel hair brush, Et cetera, Those that have just broken the flower vase, Those that, at a distance, resemble flies”
The measurement from which all of the units of the metric system are derived is no less absurd, no less arbitrary, than any of the categories found in the Heavenly Emporium of Benevolent Knowledge:
A unit equal to one ten-millionth of the distance between the North Pole and the equator along a line passing through the capital of France.
In fact, the criteria by which any division of space is defined; a valley, a river, a peninsula, a coastline or a desert, is necessarily arbitrary to some degree. Any atlas is necessarily incomplete, when compiling an atlas it must be accepted that the spaces which its entries describe cannot represent an exhaustive list of the places on the planet. And these spaces can only be described to within a reasonable degree of exactitude and their description can, at best, be anecdotal and refer only to individual cases rather than providing universal definitions. And this will be the case with each of the entries in this atlas, more of which will be added over time.
-The highest point on the planet
-The Parts of the Planet in Which it is Currently Dark
-The Area wherein a Particular Dialect Dominates over Others
-Geographically Distinct Regions whose Names Share Common Origins
-A Three-Dimensional Form with an Infinite Surface Area but a Finite Volume
-A Burial Ground
-Where do Ideas Come From?
-An International Border
-Alternative Routes to a Common Destination
-A Floating Island
Olympus Mons is the tallest mountain on any planet in the solar system. Mars has no sea-level against which to measure Olympus Mons, but sea-level is an inadequate base to measure against anyway as it is subject to perpetual change. Olympus Mons is a volcano standing about 21km above the approximate mean height of the surface of Mars. Measuring from the plain at the foot of the volcano to its summit gives a height of around 22km. Using these parameters, the volcano Mauna Kea is the tallest mountain on Earth; 10km from its base on the seabed to its summit.
However, owing to the low profile of Olympus Mons’ slope, the view from the top is unlikely to be anything to write home about. The mountain’s slopes are shallow enough that, if we stood at the summit, the base would be over the horizon. If we were to stand at the top of the tallest mountain in the solar system we would have the impression that we were at the centre of a vast plain. Olympus Mons is not much of a mountain.
The highest point on Earth is the summit of the volcano Chimborazo, when measured from the centre of the planet. Being farthest from the centre, it is the point on the planet where gravity is weakest, so your rucksack will be lighter here than it was when you packed it at home. But it is unlikely you’ll appreciate the effect as the lack of oxygen at this altitude will mean you’re quite a lot weaker.
This is all because Chimborazo sits on the equator and the Earth bulges nearly 43km at the equator compared to the poles. Something Eratosthenes had not way of suspecting when he attempted to make his measurement of the globe. Presumably, Chimborazo is also the point on the planet nearest to the sun at noon and farthest from the sun at midnight.
Sir George Everest was Superintendant of the Great Trigonometric Survey of India between 1823 and 1843. His renowned pedantry and obsession with precision not only meant that he was well-suited to the task and also suggests that he would appreciate it being pointed out that his name is pronounced Eve-rest not Ever-est like the mountain.
The survey was conducted using huge theodolites, each of which required 12 men to carry it. Up to 700 men at a time worked on the survey which lasted from 1818 until 1921, despite the project originally being expected to take 5 years and almost bankrupting the East India Company. The survey measured heights above sea-level, making corrections to their measurements to compensate for the curvature of the Earth, the unevenness of its curvature and even the gravitational pull exerted on their equipment by nearby mountains.
By 1847, Andrew Waugh had taken over as superintendant, however, the survey had reached India’s northern border and could not proceed into Nepal. From Terai, well inside of Indian territory, Waugh made trigonometric measurements of the tallest known peak in the world, Kangchenjung, over the border in Nepal. He went on to measure Peak XV, which was at a distance of around 230km from his position. Many measurements and height estimates later, Waugh calculated the height of Peak XV as 29,000 feet above sea-level. However, he publicly announced a height of 29,002 feet so as to avoid the impression that he had made the figure up.
Waugh suggested that Peak VX should be renamed after his predecessor.
Ptolemy devised his own system for measuring latitude. The system used today gives latitude in degrees of arc; the equator at zero degrees and to poles at 90. Ptolemy’s system expresses latitude with reference to the length of midsummer day; 12 hours at the equator, 24 hours at the pole.
See also; The Globe
(Elements of the following chapter have appeared previously in the book Idioglossia, an art writing glossary)
I have an indistinct memory of visiting the Meadowhall shopping centre on the outskirts of Sheffield. My mental image of it is confused with the image of countless other shopping precincts; some around the edges of London, other strangely futuristic ones in the north of France, uncannily familiar ones in South America, the ubiquitous malls of American television.
According to popular, albeit disputed, folklore, Meadowhall was designed such that had it been a commercial failure, had it not proven an effective economic stimulus, it could have been easily converted into a prison. The evidence against this urban legend is pretty overwhelming, but there is something of the Panopticon in the layout of the centre.
Many years after my encounter with Meadowhall I found myself in an innocuous discussion about the ‘doughnut effect’; a description of the decline of town centres which is perceived to result from the development of out of town shopping and leisure centres, reducing cities to hollowed-out atolls of suburban sprawl. This particular discussion may have concerned the Merry Hill centre near Dudley in the Midlands. But on reflection I cannot remember whether it was Meadowhall or Merry Hill that I had visited, or for that matter, which of the two was being discussed in relation to doughnuts.
The two places are conflated in my memory; Meadowhall in Sheffield and Merry Hill in Dudley. And I am sure that this confusion arises not from them having similar names, and not because both places occupy ‘enterprise zones’ inaugurated on the sites of defunct steelworks or because upon opening they were the largest and second-largest shopping centres in the country. The confusion arises because I have heard locals refer to them by almost the same nickname; Meadow-Hell and Merry Hell respectively.
Popular local legend has it that Blackheath in South London owes its name to the plague pits, mass graves of victims of the Black Death that supposedly lie beneath its surface. This legend is given credence, of sorts, by the gangs of carrion crows that congregate on the heath by day in their little plague doctor costumes.
However, the legend is fatally undermined when we consider that the name Blackheath is recorded as long ago as the twelfth century, while the Black Death did not reach England until two hundred years later.
Outside of this legend, the name is often considered possibly to be a corruption of bleak-heath or to derive from an Old English descriptive name combining a term meaning dark-coloured earth with the word for heathland. In reality, the topsoil on the heath is light in colour, not dark, and the ground beneath is gravelly. At the edge of the heath there is a series of pits from which this gravel was once extracted and carried down the hill to Ballast Quay on the River Thames. Here, as the name suggests, the gravel was loaded onto ships as ballast. This ballast would be discarded wherever the boats loaded up with cargo. So it is likely that little bits of the heath may be found scattered right across the globe.
Further downstream where the Thames opens into an estuary is the town of Gravesend, which is linked directly to Blackheath by an old Roman road. A modern A-road now follows the route of that Roman road. Another popular local legend has it that the name Gravesend refers to it being either the site of the last recorded case of the Black Death in England or the place from which corpses were taken for mass burial at sea.
As is the case with Blackheath, variations of the name Gravesend predate the Black Death by centuries; appearing as Gravesham in 1086 where it is listed in the Domesday Book, by 1100 it is referred to as Gravesende.
To be fair to these legends, the Black Death had a rate of attrition so great – killing perhaps half of England’s population – that plague pits must have appeared in every town. The Black Death forms as great a part of the country’s national myth as any war or conquest. But while wars are officially glorified in this myth the Black Death is a subterranean presence.
Gravesend’s most notorious real grave is that of the Native American Indian Pocahontas who died there in 1617, having been one of the first natives of the New World to visit the Old. It seems that Pocahontas' presence in London was a marketing stunt pulled by white settlers from Jamestown Virginia. And it is likely she died from exposure to Old-World diseases rather than from a broken heart, as the Disney version of her story suggests she did.
See also; A burial Ground
Zeno’s paradox of Achilles and the Tortoise, formulated in support of the Elean doctrine that no movement is possible and the universe is eternally static and unchanging, has implications so radically opposed to everyday experience that they can be easily dismissed, even if the logic of the paradox is unassailable. There is something more hideous altogether about Gabriel’s Horn; a three-dimensional shape with a finite volume, but an infinite surface area. Yet such a shape exists, on paper at least.
Its outline can be drawn by tracing a line on an x/y axis where y=1/x and x>1...
...and then rotating this line 360 degrees around the x-axis.
Put more straightforwardly it looks like a horn, or a vuvuzela of infinite length which tapers to become infinitesimally narrow and infinitely long.
The idea of the horn’s infinite surface area is conceivable, if not really graspable; Gabriel’s Horn runs on to an infinite length, never ending, getting narrower and narrower. However, understanding how the horn can have a finite volume, despite its infinite surface area, is altogether more difficult.
In order to correctly work out the volume of Gabriel’s Horn it is necessary to imagine cutting it up into pancake-like slices, then calculating the combined volume of these slices...
Adding together the volume of these slices is analogous to adding up the infinite series of fractions 1/2+1/4+1/8+1/16+1/32… then half as much again and again ad infinitum. In this case, just as Achilles can never catch up with the tortoise, the sum of the fractions can never exceed 1, no matter how long we continue adding half as much again.
Where the radius of the wide end of the horn is one unit, its volume can never exceed pi cubic units. Pi is irrational, transcendent, no more graspable than Gabriel’s Horn is playable, but it is finite nonetheless.
Thomas Hobbes reasoned that to understand this shape with finite volume but infinite surface area one need not be a mathematician or geometrician, but rather, one needs to be mad. The infinite can be accepted even when it cannot be fully comprehended, but the finite volume of Gabriel’s Horn is far more vertiginous than any bottomless pit; every iota of confined space enclosing infinitely many infinitely small subdivisions of space. I could be bounded in a nutshell, and count myself a king of infinite space.
Atop the gateposts at the western entrance of St Nicholas’ Church graveyard in Deptford there sits a pair of carved stone skulls resting on crossed bones. A plaque on the outside of the churchyard wall informs us that a church has occupied this site since at least the 12th century, but offers no more information than that.
Locally it is believed that this graveyard has an association with piracy, being the burial place of many executed pirates. This seems perfectly plausible; pirates certainly were hung, or subjected to even more grisly punishments, not far from here.
The tradition associating St Nicolas’ with piracy also holds that the skulls and crossed bones on the gateposts are the original inspiration for the design of the Jolly Roger flag. There seems to be no evidence to back up this idea.
St Olave’s Church in the City of London has a similarly morbid memento-mori above the gates of its small graveyard. This one depicts three skulls grimacing, or maybe laughing. A sign on the outside wall of this graveyard tells us that St Olave’s is one of the only medieval churches to have survived the Great Fire and that Samuel Pepys was buried here in 1703. Furthermore, the sign tells us, there are 365 names of plague victims on the burial register of 1665, and Mother Goose was buried here on September 14th 1586. No further information is given regarding this bizarre final claim.
Back at St Nicolas’ in Deptford, there is another mystery. At the eastern entrance to the graveyard, the far side from the skulls, on the inside of each of the gateposts there are embedded three gold balls in a triangular formation. The only place that this symbol is normally seen is outside a pawnbroker. Its presence here is puzzling. Perhaps this symbol is intended to remind us that life is borrowed, that wealth and status are mere worldly things. In this case, the three gold balls are indicators of the original meaning of the memento-mori; a symbol of piety rather than something gruesome.
In Sheffield's bakeries a small savoury bread roll called a breadcake is commonly sold. A Sheffield resident venturing west to Rochdale or Oldham will find a small savoury bread roll called a muffin is preferred there. This is not to be confused with an English muffin or an American muffin, which are sweet baked goods. In parts of Lancashire, bakeries sell a small savoury bread roll called an oven-bottom, whereas in other areas of that county a small savoury bread roll known as a barm cake is served. Throughout both Lancashire and Yorkshire it is not uncommon to find small savoury bread rolls called teacakes. This is not to be confused with a tea cake, which is a sweet bun containing fruit. If our traveller from Sheffield were to head south into the East Midlands, confusion may arise where bakeries stock a small savoury bread roll known as a cob (the name is taken from its being the shape of a cobble stone) which is very similar in appearance to a breadcake, oven-bottom, barm cake or teacake. In the West Midlands yet another small savoury bread roll is sold, here it is called a batch. A small savoury bread roll known as a batch can also be found in Liverpool. In Liverpool, a small savoury bread roll called a nudger is commonly eaten as well, however, in other parts of Merseyside a small savoury bread roll called a bin lid is sold instead. In the north east of England a small savoury bread roll is known as a bun and is sold alongside a slightly larger variety called a stottie.
That such a huge variety of breads has risen in such a small area provokes an interesting question; was each of these products invented independently of one another or do they all derive from a single ur-bread roll? Were the tortilla, chapatti and oatcake all invented in isolation or do they share common origins and owe their variation only to differences in local needs and resources? In other words, how many times has bread been invented?
If bread was invented more than once there is no reason to suppose it hasn't been invented many times again. The grinding of grain to produce dough is such a simple process, it is not difficult to imagine that it has been invented, by accident or through experimentation, on many separate occasions. A similar thing can be said of agriculture; the earliest manifestations of agriculture occurred in the Middle East and western Asia, however, maize, rice and wheat have all been domesticated independently by different peoples who were not in communication with one another.On the other hand, in these same regions there is archaeological evidence of wild grains being ground to produce bread dough predating the earliest agricultural societies by tens of thousands of years. Bread could be at least as old as civilisation. In which case it might have spread around the globe with it. If the invention of bread is as old as human language this could account for the depths to which it is incorporated into everyday metaphor; breadwinner, daily bread, bread as slang for money, putting bread on the table... Many cultures separated by vast expanses of time and space share common creation myths in which god(s) baked the first humans from dough. Bread has ceremonial and sacrificial roles in many religions around the world.
The exchange of traditions and technologies between societies obscures the origins of any particular type of bread. For instance, elaborately topped pizzas are a North American reinvention of a traditionally Italian bread. What is now recognised as pizza is an American innovation, yet it is commonly regarded as a quintessentially Italian food.
It is certain that appropriation, importation and export of breads has contributed to the variety of available examples, Naan bread takes its name from a Persian term for bread. The influence of this word has spread throughout India, Pakistan and Bangladesh. Persian food had an equally strong influence on mediaeval Spanish cuisine via Moorish culture. However, by the time the conquistadors arrived in Mesoamerica, they found flatbreads already being baked there from maize flour.
When white settlers arrived in Australia they found a well-established tradition of Aboriginal bread-making; a small savoury bread roll which has become known as bush bread is cooked on hot coals from dough made by the grinding of seeds. The technique by which bush bread is baked was quickly adopted by settlers to produce a small savoury bread roll called damper. Australian Aborigines arrived on that continent even more tens of thousands of years before the earliest evidence of bread-making in the Old World. This suggests that they may have invented baking independently. Unless, of course, bread-making is an even older technology than it is likely it could ever be proven to be. In which case its origins are irretrievably lost in prehistory.See also; The Area wherein a Particular Dialect Dominates over Others
Cartography did not exist as a single recognisable discipline in Medieval Europe, rather there were many forms of map-making each with a different purpose. Generally these maps were schematic rather than being accurate representations of space. For example, portolan charts were used for coastal navigation but their depictions of coastlines were approximate at best, showing exaggerated renditions of distinctive geographical features. The useful data on a portolan chart comes as a list of place names lining that coast and annotated with the compass bearings that sailors would need to set in order to navigate between them: "So, nor-nor'west you are to steer, till Brimstone Head doth appear."
Similarly, medieval land maps acted as sets of instructions for getting from A to B and did not aspire to accurately represent the ground itself. Mappaemundi were also schematic, but depicted both space and time, and more importantly, they told biblical and classical narratives.
Such systems of map-making suited the feudal world, where territories were rarely defined in precise geographic terms but according to ad-hoc, approximate or overlapping fiefdoms, communes and cities, each of which was regarded as an atomised entity. The feudal medieval conception of territory was textual rather than geometric; the Domesday Book, compiled in 1086, did not contain any maps of properties just written descriptions of territories and an inventory of their contents.
The available methods for the representation of physical space influence how that space is perceived, and ultimately how ownership of that space can be organised. Latin translations of Ptolemy's Geographia became available in Europe in the early 15th century, and provided a novel way of representing space. By this time, none of Ptolemy's original maps survived, however, his work contained an explanation of his grid system of lines of latitude and longitude as well as instructions for producing accurate map projections of the globe.
Portolan charts remained easier to use for the purposes of navigation and written works like the Domesday Book were more useful than any map for making inventories of who owns what. So Ptolemy's methods were slow to catch on.
It was not until the 16th Century that rulers began commissioning accurate maps of their domains. Owning such a map was a much more efficient method of claiming ownership over a territory than riding out on horseback to construct a verbal description of its extent. So, drawing a border on a map became the default mode of defining a territory.
Where ownership had previously been expressed textually in terms of acreage, households, taxable contents and resources it could now be easily represented geometrically in relation to arbitrary grid references according to lines of latitude and longitude. When warring European powers met at the 1646-1648 Conference of Westphalia, the ability to accurately define a territory in relation to borders drawn on a map meant that it was possible for countries to recognise each-other's sovereignty over that area and for the idea of the nation-state to be developed.
When the representatives of these European nation-states met again at the 1884-1885 Berlin Conference, this ability to define borders geometrically enabled Europeans to divide the continent of Africa between themselves without even having to visit in person.
Now, however, paper maps have been replaced by digitised equivalents. Once again space is more easily represented textually rather than geometrically; portolan charts have a contemporary equivalent in GPS, which does not require its user to know where they are on any map. Terrestrial maps have been replaced by journey planner apps. National territory is expressed as a top-level domain name and the business of government enfeoffed to private tenure while state sovereignty is bypassed by multinational commerce, enterprise zones and tax havens. And war between states is superseded by international civil war without borders.
Vienna, 1929; the Logical Positivists were determined to present their philosophy as radically new, a renunciation of superstition and of metaphysics and a departure from everything else that had preceded it. This may account for the surprising vigour with which the group not only denounced, but actively suppressed the 1911 book Die Philosophie des Als Ob (the Philosophy of As If) in which its author Hans Vaihinger first coined the term Logical Positivism.
As a result, Vaihinger’s ideas are largely forgotten even though they form the basis of Logical Positivism, not to mention much of 20th century philosophy of science. Vaihinger’s work is even capable of evading the problem of the Incompleteness Theorems introduced by Kurt Gödel which finally and fatally undermined the Logical Positivist project. A Neo-Kantian, Vaihinger argued that, being unable to ever know the fundamental nature of reality, human beings live according to convenient fictions and semi-fictions - acting “as if” they were true. In the Philosophy of As If Vaihinger identifies such fictions at work in the practise of biology, mathematics, philosophy, political theory, psychology and religion.
Atomic theory (as it stood in the early twentieth century) provides Vaihinger with one of his prime examples. Atoms had not been directly observed and existing descriptions of their structure contradicted established scientific principles. Nevertheless, the picture of the atom with its nucleus and orbiting electrons is useful in explaining and predicting the properties of elements and their compounds. According to Vaihinger’s criteria atomic theory qualifies as a semi-fiction. A more current example may be the Standard Model of particle physics with its quarks, leptons and gauge bosons. These subatomic particles are treated like tiny snooker balls that can be fired towards one another around a particle accelerator, yet no physicist really believes that quarks, leptons and gauge bosons exist as particles at all. The Standard Model is no different to any other type of model; a model can never be identical to whatever it models, it is simply a representation with predictive power. The Standard Model, therefore, qualifies as a semi-fiction.
The commonest argument against Vaihinger (but by no means the most elegant one) is that, being besotted with his own theory, he finds fictions everywhere he looks and sorts them into arbitrary and unfixed categories. Even Vaihinger’s three main categories; hypotheses, semi-fictions and real-fictions are not particularly concrete. What is a hypothesis one day may, in the light of new data, become a heuristic semi-fiction a week later. A legal fiction may, in a different set of circumstances, be seen as a practical or ethical fiction instead.
Aristotle introduced the notion that the continents of the Northern Hemisphere must be ‘balanced’ by a landmass of similar extent in the south. Ptolemy incorporated this idea into his own work, through which it was introduced to European geographers. The Terra Australis Incognita depicted on the globes built by Johannes Schöner in the 1520s (three hundred years before any such land was ever sighted) qualifies as a (non-fiction) hypothesis - being verifiable by likely future observation.
When the southern continent was first seen by humans in 1820 it was assigned the name Antarctica because, by this time, the name Australia had already been taken. Modern maps of Antarctica are useful semi-fictions (a useful or virtuous fiction is distinguished from a vicious fiction if it is understood as being fictitious when it is introduced). While internally consistent (which qualifies them as semi-, rather than real-fictions) it is understood that maps are inconsistent with reality, being subject to the distortions of scale and reduction in detail that are inherent to the map-making process.
School is derived from the Latin word schola, which can be translated as leisure. The eventual root of the word is the Greek skhole which translates – lazy students might be happy to learn – more or less, as idleness.
It is tempting to presume a direct link between school; meaning a gathering of students, and school; meaning a gathering of fish. But such a presumption would be misguided. School (of fish) is an entirely different word with a Germanic root; skulo, meaning multitude, or perhaps troop.
The development of a language is generally assumed to be divergent; the number of words in a language tends to increase over time. A single word accrues additional new meanings throughout its life, and related languages become more distinct from one another as they develop. However, school is an example of the opposite occurring.
In this case, two distinct word roots have led to two identical spellings and two homophonous sounds. So, while we might assume that school (teacher) and school (of fish) are the same word, they are not.
Two paths from disparate origins appear to converge. But while the end points of the paths coincide precisely, they are, in fact, distinct.
Floating islands have always fascinated futurists and utopianists. Their imagined schemes combine the benefits of a nomadic lifestyle with the benefits gained through colocation in cities; a composite of a romanticised imaginary past and an ideal impossible future. The Uru people have lived on floating islands on Lake Titicaca for thousands of years. They were never conquered by the Inca Empire and they survived the conquistadors. In times of war the Uros float their islands out over the lake and thumb their noses at their attackers. A single variety of reed provides the Uros with material for their boats, their buildings and the islands themselves. New reeds are added to the top of the islands as the old reeds rot away from the bottom. The reeds are edible, but the Uros seldom resort to using them as a food source because the lake provides ample better alternatives.
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