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Posts Tagged ‘Brunelleschi

“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


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.

from Della Pictura



“I propose to build for eternity”*…

Florence Duomo as seen from Michelangelo hill

Sent back in time 600 years and tasked with building the world’s largest dome, how would most of us fare? Most of us, of course, are not trained architects or engineers, but then, neither was Filippo Brunelleschi. Known at the time as a goldsmith, Brunelleschi ended up winning the commission to build just such a colossal dome atop Florence’s Cattedrale di Santa Maria del Fiore, which itself had already been under construction for well over a century. The year was 1418, the dawn of the Italian Renaissance, but a break with medieval building styles had already been made, not least in the rejection of the kind of flying buttresses that had held up the stone ceilings of previous cathedrals. Brunelleschi had thus not just to build an unprecedentedly large dome, in accordance with a design drawn up 122 years earlier, but also to come up with the technology required to do so.

“He invented an ox-driven hoist that brought the tremendously heavy stones up to the level of construction,” architect David Wildman tells HowStuffWorks. Noticing that “marble for the project was being damaged as it was unloaded off of boats,” he also “invented an amphibious boat that could be used on land to transport the large pieces of marble to the cathedral.”

These and other new devices were employed in service of an ingenious structure using not just one dome but two, the smaller inner one reinforced with hoops of stone and chain. Built in brick — the formula for the concrete used in the Pantheon having been lost, like so much ancient Roman knowledge — the dome took sixteen years in total, which constituted the final stage of the Cattedrale di Santa Maria del Fiore’s generations-long construction.

Brunelleschi’s masterpiece, still the largest masonry dome in the world, has yet to quite yield all of its secrets: “There is still some mystery as to how all of the components of the dome connect with each other,” as Wildman puts it, thanks to Brunelleschi’s vigilance about concealing the nature of his techniques throughout the project. But you can see some of the current theories visualized (and, in a shamelessly fake Italian accent, hear them explained) in the National Geographic video [below]. However he did it, Brunelleschi ensured that every part of his structure fit together perfectly — and that it would hold up six centuries later, when we can look at it and see not just an impressive church, but the beginning of the Renaissance itself…

How Filippo Brunelleschi, untrained in architecture or engineering, built the world’s largest dome at the dawn of the Renaissance.

For more on the dome, see Ross King’s marvelous 2013 book, Brunelleschi’s Dome: How a Renaissance Genius Reinvented Architecture.

And for more on Brunelleschi— whose other accomplishments include the first precise system of linear perspective, which revolutionized painting and opened the way for the naturalistic styles of Renaissance art– see here.

* Filippo Brunelleschi


As we go big, we might recall that it was on this date in 330 that Roman Emperor Constantine the Great consecrated Constantinople (on the site of what had been the ancient city of Byzantium; today, Istanbul). Constantine identified the site of Byzantium as a place where an emperor could sit, readily defended, with easy access to the Danube or the Euphrates frontiers, his court supplied from the rich gardens and sophisticated workshops of Roman Asia, his treasuries filled by the wealthiest provinces of the Empire.

The city became famous for its architectural masterpieces, such as Hagia Sophia, the cathedral of the Eastern Orthodox Church. Built by the eastern Roman emperor Justinian I as the Christian cathedral of Constantinople for the state church of the Roman Empire between 532 and 537, the church was then the world’s largest interior space and among the first to employ a fully pendentive dome. It is considered the epitome of Byzantine architecture and is said to have “changed the history of architecture”… It set the bar for Brunelleschi.

Hagia Sophia


“I’d rather create a miniature painting than a Taj Mahal of a book”*…


South African artist Lorraine Loots agrees…

365 Postcards for Ants is the second phase of a project started on 1 January 2013, which involved me creating a miniature painting every single day for the entire year.

In celebration of our city’s designation as World Design Capital 2014, I’ve decided to do it all over again, and this time all the paintings will be Cape Town themed…

Learn- and see– more at Lustik, at her site, and on Loots’ Tumblr.

Mohsin Hamid


As we get small, we might send patronizing birthday greetings to Cosimo di Medici; he was born on this date in 1389.  The first of the Medici political dynasty, de facto rulers of Florence during much of the Italian Renaissance;, he was known as “Cosimo ‘the Elder'” (“il Vecchio”) and “Cosimo Pater Patriae” (“father of the nation”).  A fabulously-wealthy banker, he was a powerful patron of learning; he funded Ficino’s Latin translation of the complete works of Plato, and supported the work of scholars like Niccolo Niccoli and Leonardo Bruni.  But he is perhaps best remembered as a patron of the arts: he supported Fra Angelico, Fra Filippo Lippi, and Donatello, whose David and Judith Slaying Holofernes were Medici commissions; he commissioned Michelozzo Michelozzi‘s Palazzo Medici; and he enabled Brunelleschi to complete the magnificent dome of Santa Maria del Fiore (the “Duomo“).

Bronzino’s (posthumous) portrait of Cosimo de’ Medici



Written by (Roughly) Daily

September 27, 2014 at 1:01 am

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