Brain Pickings

Posts Tagged ‘history’

17 APRIL, 2012

Magnificent Maps: Cartography as Power, Propaganda, and Art

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What the feats of Marco Polo have to do with medieval political propaganda and the history of tea.

Three of my great fascinations — cartography as art, propaganda design, and antique maps — converge in Magnificent Maps: Power, Propaganda and Art. The lavish tome collects cartographic curiosities from the golden age of display maps — the period between 1450 and 1800, when maps were as much a practical tool for navigation as they were works of art and affirmations of cultural hegemony or social status — culled from the formidable collection of the British Library.

Peter Barber, who heads the map collections at the British Library, and Tom Harper, BL’s Curator of Antiquarian Mapping, contextualize the maps with detailed descriptions of how and where they were used, from schoolrooms to bedchambers, and explore their parallel role as art and propaganda.

Fra Mauro World Map, 1450

This is an 1804 copy of perhaps the first ‘modern’ world map, made by the Venetian monk Fra Mauro in about 1450. It points south because 15th-century compasses were south-pointing. It shows the Portuguese discoveries in Africa and questioned the authority of medieval and classical sources. Intended for display in Venice, it emphasizes the feats of Marco Polo. The British East India Company commissioned this copy, thus implying that Britain was heir to the Portuguese empire.

The Americas by Diego Gutiérrez, 1562

This is a powerful celebration of Spain's New World Empire, beginning in the late 15th century. In the upper left-hand corner is the arms of King Philip II (reigned 1554-1598). In the sea, Philip appears on a chariot, riding through a turbulent Atlantic. The map aimed to strengthen Spain's political image in Europe and its claim to the Americas.

Psalter World Map (mappa mundi), 1265

Despite its small size, this is one of the ‘great’ medieval world maps. It is probably a copy of the lost map which adorned King Henry III's bedchamber in Westminster Palace from the mid-1230s. The original colors are intact. Showing east at the top, it is a visual encyclopedia, embracing ancient history, politics, scripture and ethnography as well as geography.

'The Island' by Stephen Walter, 2008

The Island satirizes the London-centric view of the English capital and its commuter towns as independent from the rest of the country. The artist, a Londoner with a love of his native city, offers up a huge range of local and personal information in words and symbols. Walter speaks in the dialect of today, focusing on what he deems interesting or mundane.

'Tea Revives the World' by MacDonald Gill, 1940

Commissioned by the International Tea Market Expansion Board, this map aimed to promote wartime strength, Allied resolve, and international trade during WWII through a celebration of Britain’s adopted national beverage and its pictorial history of tea.

Complementing Magnificent Maps is an interactive site from the British Library that lets you explore some of the maps with curatorial context.

For a related treat, see BBC’s fantastic The Beauty of Maps, which visits the British Library to explore five of the world’s most beautiful maps and their sociocultural context.

Images and captions courtesy of the British Library; thanks, Sonja

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16 APRIL, 2012

How 17 Equations Changed the World

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What Descartes has to do with C. P. Snow and the second law of thermodynamics.

When legendary theoretical physicist Stephen Hawking was setting out to release A Brief History of Time, one of the most influential science books in modern history, his publishers admonished him that every equation included would halve the book’s sales. Undeterred, he dared include E = mc², even though cutting it out would have allegedly sold another 10 million copies. The anecdote captures the extent of our culture’s distaste for, if not fear of, equations. And yet, argues mathematician Ian Stewart in In Pursuit of the Unknown: 17 Equations That Changed the World, equations have held remarkable power in facilitating humanity’s progress and, as such, call for rudimentary understanding as a form of our most basic literacy.

Stewart writes:

The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us… This is the story of the ascent of humanity, told in 17 equations.

From how the Pythagorean theorem, which linked geometry and algebra, laid the groundwork of the best current theories of space, time, and gravity to how the Navier-Stokes equation applies to modeling climate change, Stewart delivers a scientist’s gift in a storyteller’s package to reveal how these seemingly esoteric equations are really the foundation for nearly everything we know and use today.

Greek stamp showing Pythagoras's theorem

But the case for why we should even care about equations — and mathematics, and science in general — goes back much further. In 1959, physicist and novelist C. P. Snow lamented — as Jonah Lehrer did half a century later — the tragic divergence of the sciences and humanities in his iconic lecture, The Two Cultures:

A good many times I have been presented at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: ‘Have you ever read a work of Shakespeare’s?’

Snow later added:

I now believe that if I had asked an even simpler question — such as, What do you mean by mass, or acceleration, which is the scientific equivalent of saying, ‘Can you read?’ — not more than one in ten of the highly educated would have felt that I was speaking the same language. So the great edifice of modern physics goes up, and the majority of the cleverest people in the western world have about as much insight into it as their Neolithic ancestors would have had.

It is no coincidence, then, that some of the most revolutionary of the breakthroughs Stewart outlines came from thinkers actively interested in both the sciences and the humanities. Take René Descartes, for instance, who is best remembered for his timeless soundbite, Cogito ergo sumI think, therefore I am. But Descartes’ interests, Stewart points out, extended beyond philosophy and into science and mathematics. In 1639, he observed a curious numerical pattern in regular solids — what was true of a cube was also true of a dodecahedron or an icosahedron, for all of which subtracting from the number of faces the number of edges and then adding the number of vertices equaled 2. (Try it: A cube has 6 faces, 12 edges, and 8 vertices, so 6 – 12 + 8 = 2.) But Descartes, perhaps enchanted by philosophy’s grander questions, saw the equation as a minor curiosity and never published it. Only centuries later mathematicians recognized it as monumentally important. It eventually resulted in Euler’s formula, which helps explain everything from how enzymes act on cellular DNA to why the motion of the celestial bodies can be chaotic.

So how did equations begin, anyway? Stewart explains:

An equation derives its power from a simple source. It tells us that two calculations, which appear different, have the same answer. The key symbol is the equals sign, =. The origins of most mathematical symbols are either lost in the mists of antiquity, or are so recent that there is no doubt where they came from. The equals sign is unusual because it dates back more than 450 years, yet we not only know who invented it, we even know why. The inventor was Robert Recorde, in 1557, in The Whetstone of Witte. He used two parallel lines (he used an obsolete word gemowe, meaning ‘twin’) to avoid tedious repetition of the words ‘is equal to’. He chose that symbol because ‘no two things can be more equal’. Recorde chose well. His symbol has remained in use for 450 years.

The original coinage appeared as follows:

To avoide the deiouse repetition of these woordes: is equalle to: I will sette as I doe often in woorke use, a paire of paralleles, or gemowe lines of one lengthe: =, bicause noe .2. thynges, can be moare equalle.

Far from being a mere math primer or trivia aid, In Pursuit of the Unknown is an essential piece of modern literacy, wrapped in an articulate argument for why this kind of knowledge should be precisely that.

Stewart concludes by turning his gaze towards the future, offering a kind of counter-vision to algo-utopians like Stephen Wolfram and making, instead, a case for the reliable humanity of the equation:

It is still entirely credible that we might soon find new laws of nature based on discrete, digital structures and systems. The future may consist of algorithms, not equations. But until that day dawns, if ever, our greatest insights into nature’s laws take the form of equations, and we should learn to understand them and appreciate them. Equations have a track record. They really have changed the world — and they will change it again.

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16 APRIL, 2012

The Geometry of God: The Striking Kaleidoscopic Patterns of European Cathedral Ceilings

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Photographer David Stephenson captures architectural triumphs at the intersection of art and mathematics.

If you’ve ever set foot in one of Europe’s Gothic or Romanesque cathedrals and looked up, you likely found yourself spellbound by the striking vaulted ceilings. If you haven’t, photographer David Stephenson allows you to do so vicariously with his Heavenly Vaults project — a series of magnificent kaleidoscopic photos that capture the singular blend of ethereal magic and patterned precision in these architectural triumphs at the intersection of art and mathematics, flattening the vaulted ceilings and distilling them to their essential shapes, recurring fractal-like patterns, and intricate detailing.

Many of these structures, particularly the Gothic cathedrals, were constructed in an era actively occupied with ordering the heavens and expressed in their mathematical nature was a microcosm model of the universe — perhaps a paradoxical proposition that rationality and logic could explain or convey the might of God to which these temples of worship aimed to attest.

Heavenly Vaults is a follow-up to Stephenson’s 2005 book, Visions of Heaven: The Dome in European Architecture. More of Stephenson’s stunning images can be seen on his site.

Visual News It’s Nice That

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