Posts Tagged ‘Christopher Columbus’
“There’s no idea in economics more beautiful than Arrow’s impossibility theorem”*…
Tim Harford unpack’s Kenneth Arrow‘s Impossibility Theorem (which feels a bit like a socio-economic “Monty Hall Problem“) and considers it’s implications…
… if any group of voters gets to decide one thing, that group gets to decide everything, and we prove that any group of decisive voters can be pared down until there’s only one person in it. That person is the dictator. Our perfect constitution is in tatters.
That’s Arrow’s impossibility theorem. But what does it really tell us? One lesson is to abandon the search for a perfect voting system. Another is to question his requirements for a good constitution, and to look for alternatives. For example, we could have a system that allows people to register the strength of their feeling. What about the person who has a mild preference for profiteroles over ice cream but who loathes cheese? In Arrow’s constitution there’s no room for strong or weak desires, only for a ranking of outcomes. Maybe that’s the problem.
Arrow’s impossibility theorem is usually described as being about the flaws in voting systems. But there’s a deeper lesson under its surface. Voting systems are supposed to reveal what societies really want. But can a society really want anything coherent at all? Arrow’s theorem drives a stake through the heart of the very idea. People might have coherent preferences, but societies cannot…
On choice, law, and the paradox at the heart of voting: “Arrow’s Impossibility Theorem,” from @TimHarford in @WhyInteresting. Eminently worth reading in full.
* Tim Harford
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As we contemplate collective choice, we might send grateful birthday greetings to the man who “wrote the book” on perspective, Leon Battista Alberti; he was born on this date in 1404. The archetypical Renaissance humanist polymath, Alberti was an author, artist, architect, poet, priest, linguist, philosopher, cartographer, and cryptographer. He collaborated with Toscanelli on the maps used by Columbus on his first voyage, and he published the the first book on cryptography that contained a frequency table.
But he is surely best remembered as the author of the first general treatise– Della Pictura (1434)– on the the laws of perspective, which built on and extended Brunelleschi’s work to describe the approach and technique that established the science of projective geometry… and fueled the progress of painting, sculpture, and architecture from the Greek- and Arabic-influenced formalism of the High Middle Ages to the more naturalistic (and Latinate) styles of Renaissance.
“Nobody expects the Spanish Inquisition”*…
On the long-term effects of suppression and persecution…
From Imperial Rome to the Crusades, to modern North Korea or the treatment of Rohingya in Myanmar, religious persecution has been a tool of state control for millennia.
While its immediate violence and human consequences are obvious, less obvious is whether it leaves scars centuries after it ends.
In a new study we have attempted to examine the present day consequences of one of the longest-running and most meticulously documented persecutions of them all – the trials of the Spanish Inquisition between 1478 to 1834…
Details at “Extraordinarily, the effects of the Spanish Inquisition linger to this day.”
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As we tolerate, we might recall that it was on this date in 1492 that Catholic monarchs, King Ferdinand II of Aragon and Isabella I of Castile took control of the Emirate of Grenada (1238-1492), the last Moorish stronghold in Spain. King Boabdil surrendered to Spanish forces in the Alhambra palace, surrendering the key to the city– an event Christopher Columbus witnessed as he received the support of the monarchy to sail to the Indies.
Pursuant to the Inquisition, Ferdinand and Isabella had targeted Muslims and Sephardic Jews (also called the Megorashim), forcing them either to convert to Christianity or to leave Spain within four months without any possessions. Failure to leave resulted in torture and/or death.
“As long as the world is turning and spinning, we’re gonna be dizzy and we’re gonna make mistakes”*…
Observant fans of HG Wells have questioned how a new coin from the Royal Mint commemorating The War of the Worlds author could be released with multiple errors, including giving his “monstrous tripod” four legs.
The £2 coin is intended to mark 75 years since the death of Wells, and includes imagery inspired by The War of the Worlds and The Invisible Man.
Unfortunately, it strays from Wells’s vision of his creations. “As someone who particularly likes one of his very famous stories, can I just note that the big walking machine on the coin has four legs? Four legs. The man famous for creating the Martian TRIpod,” wrote artist Holly Humphries. “How many people did this have to go through? Did they know how to count?”
Science fiction novelist and professor of 19th-century literature Adam Roberts, who is author of a biography of Wells and vice president of the HG Wells Society, also criticised the depiction of the Invisible Man, shown in a top hat; in the book he arrives at Iping under a “wide-brimmed hat”.
“It’s nice to see Wells memorialised, but it would have been nicer for them to get things right,” Roberts said. “A tripod with four legs is hard to comprehend (tri: the clue is in the name), and Wells’s (distinctly ungentlemanly) invisible man, Griffin, never wore a top hat … I’d say Wells would be annoyed by this carelessness: he took immense pains to get things right in his own work – inviting translators of his book to stay with him to help the process and minimise errors and so on.”…
The Wells slip-up is not the first mistake immortalised in legal tender. In 2013, Ireland’s Central Bank misquoted James Joyce on a commemorative coin intended to honour the author. While Joyce wrote in Ulysses: “Ineluctable modality of the visible: at least that if no more, thought through my eyes. Signatures of all things I am here to read …”, the Central Bank included an extra “that” in the final sentence, with its coin reading: “Signatures of all things that I am here to read.” The bank later claimed the coin was intended to be “an artistic representation of the author and text and not intended as a literal representation”.
Later that year, a new £10 note featured Jane Austen with the quote “I declare after all there is no enjoyment like reading!” However, the line is spoken by Caroline Bingley, described by academic John Mullan as “a woman who has no interest in books at all”. “You can imagine being the Bank of England employee given the task of finding the telling Austen quotation. Something about reading, perhaps? A quick text search in Pride and Prejudice turns up just the thing,” wrote Mullan at the time…
Memorializing mistakes in metal: “HG Wells fans spot numerous errors on Royal Mint’s new £2 coin.“
* Mel Brooks
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As we cast with care, we might recall that it was on this date in 1493 that Christopher Columbus, having sailed from Spain six months earlier and arrived in the Caribbean, off the shores of (what we now know as) the Dominican Republic, saw three “mermaids,” described in his diary as “not half as beautiful as they are painted.” Mermaids, mythical half-female, half-fish creatures, had persistently been reported in seafaring cultures at least since the time of the ancient Greeks. Mermaid sightings by sailors, when they weren’t made up, were most likely manatees (sea cows), dugongs or Steller’s sea cows (which became extinct by the 1760s due to over-hunting).
“Geographers never get lost. They just do accidental field work.”*…
An image from The Catalan Atlas, 1375
When Christopher Columbus first set foot in what’s now the Bahamas, it was the lucky sum of a 1,400-year-old cartographical error and Columbus’s own miscalculations of the globe. The Genoese explorer believed the Eurasian landmass to cover nearly 2/3 of the earth’s circumference—the actual distance from Spain eastward to his target of eastern Asia was closer to 1/3 of the circumference.
Columbus’s image of the world was based on ancient maps that greatly overestimated the size of the Eurasian continent and depicted the planet’s circumference some 25 percent smaller than it actually was—a misjudgment compounded by his own wishful thinking and erroneous math. By his calculation, India lay within a 2,500-mile voyage west of Spain. He was off by about 8,000 miles.
Columbus’s errors are only a chapter in a series of discoveries, theories, and mistakes that tell the story of maps and mapmaking. Maps are a 10,000-year journey of humans trying to understand Earth. In 1492, most people had no idea what the world looked like; even some impressively accurate maps were full of myths and mistakes, from fantastical monsters to entire missing continents to swaths of terra incognita, or “unknown territory.”
Over time, errors were corrected and empty spaces were filled in, and today, much of the population walks around with a map of the entire Earth in their pocket that’s so detailed you can see your own front door…
Eight maps, from antiquity to today, that changed how we see the world: “Why Maps Are Civilization’s Greatest Tool.”
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As we find our way, we might might recall that it was on this date in 1415 that Henry the Navigator led Portuguese forces to victory over the Marinids at the Battle of Ceuta, the Muslim port on the North African coast across the Straits of Gibraltar from the Iberian Peninsula– which marked the beginning of the Portuguese Empire in Africa. Henry remained a central figure in the early days of the Portuguese Empire and was a key driver of the 15th-century European maritime discoveries and maritime expansion. Through his administrative direction– including his patronage of cartographers– he is regarded as the main initiator of what would be known as the Age of Discovery.
“Christopher Columbus, as everyone knows, is honored by posterity because he was the last to discover America”*…
The Mali Empire in 1337
Abubakari II was a Malian who ascended to the throne in 1310. He controlled most of western Africa and an incredibly wealthy state with more than one million subjects. He (his navy) may have sailed to the Americas in 1311:
More than a hundred years before the Portuguese had cleared Cape Bojador in the Western Sahara, and almost two hundred before Columbus ‘discovered’ the Americas, there is some evidence to suggest that Abubakari II, Emperor of Mali, crossed the Atlantic and visited the Americas. The idea even received support from Columbus himself, who wrote in his journal about African journeys from the Guinea coast to the Americas and supposed this was how the South Americans had learned techniques of alloying gold.
At the time, the Malian empire was arguably the richest state on earth. Founded in 1235, by 1310 when Abubakari II came to the throes it had control of most of western Africa, form the inland trading cities of Timbuktu and Gao on the fringes of the Sahara to the Guinea coast. The empire ruled millions of subjects, its three gold mines were responsible for producing more than half of the Old World’s gold and it also profited from the extremely lucrative salt trade. …
[It is from] Inslamic historian al-Umari’s conversations with Mansa Musa [Abubakari II’s successor] that we have our best account of Abubakari’s mission. Apparently, when Abubakari came to the throne in 1310, he ordered two hundred boats to set out to check whether, like the Niger River, the Atlantic Ocean had a far bank. Inorder to maximise the chances of success, a variety of boats was constructed.
Some of them would have been pirogues, which resembled a canoe, while others were probably based on Arab boats such as the dhow. Each of the two hundred vessels had a supply barge attached, with enough dried meat grain and preserved fruit in ceramic jars to last for two years, as well as cotton goods and gold for trade.
Of the two hundred vessels that departed only one returned. The captain reported to the mansa that:
we sailed for a long time, up to the moment when we encountered in mid-ocean something like a river with a violent current. My ship was lost. The others sailed on, and gradually each of them entered this place, the disappeared and did not come back. We did not know what had happened to them. As for me, I returned to where I was and did not enter the current.
It seems that most of the fleet was destroyed in a giant whirlpool. Yet Abubakari II’s curiosity was not diminished by this tale of natural disaster. He determined to make the voyage himself. In 1311 he abdicated, leaving matters of state in the hands of his younger half-brother Musa, and set off at the head of an expedition whose two thousand ships and their supply barges made it ten times as large as the previous one. They sailed off into the Atlantic from where The Gambia is today and were never heard from again.
Powerful but inconclusive arguments have been made to suggest that at least some of the fleet landed in America. The locations usually suggested are Recife in Brazil, or the Caribbean, where the Garifuna, a tribe known to the Europeans as Black Caribs, claimed pre-Columbian African ancestry. Arguments for a pre-Columbian Malian presence in the Americas include the prevalence of the bottle gourd, a native African plant, in South American cultures; the composition of spearheads, indicating the use of Malian gold; linguistic traces of Mandinka languages in the regions where the fleet may have landed; and Columbus’s assertion that he saw black traders working in the Americas when he arrived…
An excerpt from Ed Wright’s The Lost Explorers: Adventurers Who Disappeared Off the Face of the Earth, via the ever-illuminating Delanceyplace.com.
* James Joyce
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As we investigate the initial, we might note that this leap-day (like every “last day in February”) is Rare Disease Day— an occasion devoted to raising awareness of and encouraging action on the too-often horrifying ailments that fall outside the spotlight, but that cumulatively are all-too-common. It’s a great day to adopt an orphan (disease).
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