(Roughly) Daily

Posts Tagged ‘Renaissance

“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



“In every grain of sand there is the story of the earth”*…

(Roughly) Daily has looked before (see here and here) at sand as a critical ingredient in the stuff of modern life. Today’s post features Steven Connor on the metaphorical power of sand…

Sand belongs to the great, diffuse class, undeclared, rarely described, but insistent and insinuating, of what may be called quasi-choate matters — among them mist, smoke, dust, snow, sugar, cinders, sleet, soap, syrup, mud, toffee, grit. Such pseudo-substances hover, drift, and ooze between consistency and dissolution, holding together even as they come apart from themselves. And, of all of these dishesive matters, sand is surely the most untrustworthy, the most shifting and shifty.

Nobody would seriously consider taking a stand on a cloud, but sand has betrayed many an architect and edifice. Sand is at once architectural and archiclastic. An eighteenth-century continuation of Baron Munchausen’s adventures describes how the Baron and his party survive a whirlwind of sand by scooping an igloo-style sand-chamber in which to shelter from the storm, and then digging a tunnel from their bunker back out into the light. Sand has the capacity to engulf and inundate, blearing contours, eroding and erasing every edge and eminence. As such it is the ultimate mockery of the permanence of stone, for it is no more than one of stone’s own moods, the manner in which stone, atomised, consumes itself. Shelley’s “Ozymandias” imagines the monumental statue of Rameses the Great dismembered on the Egyptian sands. The shattered chunks of head, legs, and pedestal portend a further, finer comminution, after the membra disjecta themselves will have been milled away into flatness: “Round the decay/Of that colossal wreck, boundless and bare,/The lone and level sands stretch far away.”

Sand is reversible. Only utter desiccation can attain to this pouring, milk-smooth liquefaction. Sand-baths were used in the ancient world both to draw out the damp ague of rheumatism and as a kind of sauna, to promote perspiration. Sand is the product of abrasion, but is also itself abrasive, used in sand-blasting to etch and burnish. Pliny tells us of the use of sand under a saw edge to make a clean cut in marble, and to polish it after it has been carved.

Sand signifies neutrality, indifference, and uniformity; yet it also has hairtrigger sensitivity and responsiveness. A grain of sand (in actual fact often a tiny parasite) is the irritant that provokes in the oyster the nacreous secretions that build into a pearl. Sand has a favoured relation to sound, putting a hoarse rattle in the throat of the wind, and is itself all ears. In 1787, the German physicist Ernst Chladni showed how drawing a violin bow over a metal plate could induce in the fine sand sprinkled on it hierophantic figurings of the sound, in quivering mandalas and ripple-fingered arpeggios. Though sand can disfigure and obliterate, it can also disclose the ghost wrist of wind and the perturbations of the earth. It is a detection and reception mechanism, forming ridged isobars, shivering musculature, oscilloscape of the air’s sculpting shoves and gusts.

Sand participates in dream and vision. The Sandman brings sleep by throwing or blowing sand into the eyes of children. But the sand does more than merely seal the eyes, for in many versions of this nursery tale, it is the very stuff that dreams are made on, the numb matter of sleep, swirling, particulate, that the sandman carries in his sack. The somnolence of sand is redoubled when in Top Hat (1935) Fred Astaire soothes Ginger Rogers to sleep in the hotel room below him by spreading sand on the floor and hush-dancing a susurrous soft-shoe shuffle. The origins of moon-walking are to be found in the novelty slides and scrapes across a sanded stage by music-hall acts like Wilson, Keppel and Betty. Specious it may be, but sand is also the secret stuff of omen and auspice, in the practice of divination through tossing and scrying handfuls of sand, known in Arabic as ilm al-raml, the science of the sand, or what might have been its Greek equivalent, psammomancy.

Sand is not only temporary, it is also the most temporised form of matter. It is the image or allegory of time, shifting, yet unshiftable. It seems a compiling of the minced, mounded years that go into its making, and grains of sand imitate the elementary atoms of time, moment upon pattering moment. Sand is featureless, without joints or divisions, even though it is nothing but division all the way down. Yet it is this very feature that makes it useful in the measurement of time, for, unlike other materials, sand will flow easily and regularly, even as its volume diminishes. Sand-glasses came into use in part because of the need to measure time at sea, far from any landmark; speed would be measured by counting the number of knots in a rope paid out from the back of the ship in the time it took for the sand to run through a half-minute glass. A half-hour period of watch, known as a “glass”, was also measured in this way. Grains of sand, in the form of quartz crystals, with their precise oscillations, still micro-regulate our time. In fact, the sand of hourglasses was often not quartz sand at all, but powdered marble, or eggshell. But we find it hard to give up the idea of the affinity of sand and the glass through which it runs, since silicates of sand are still the most important source of glass. George Herbert imagines this interfusion when he writes that “flesh is but the glasse, which holds the dust/That measures all our time; which also shall/Be crumbled into dust”, while for Gerard Manley Hopkins the soul itself is “soft sift/In an hourglass – at the wall/Fast, but mined with a motion, a drift,/And it crowds and it combs to the fall”…

From the mythical Sandman, through the grains in an hourglass, to an irritating mote lodged in the beachgoer’s eye, sand harbors unappreciated power: “The Dust That Measures All Our Time.”

Rachel Carson


As we muse on metaphor, we might send ideal birthday greetings to Marsilio Ficino; he was born on this date in 1433.  An Italian scholar and Catholic priest, he was one of the most influential humanist philosophers of the early Italian Renaissance.  The first translator of Plato’s complete extant works into Latin, he was important in the revival of Neoplatonism, and was in touch with every major academic thinker and writer of his day. His Florentine Academy was an attempt to revive Plato’s Academy, and influenced both the direction and the tenor of the Italian Renaissance and thus the development of European philosophy.

Ficino was also an astrologer, and is credited with having inspired the Tarot card deck– the Tarot of Marseilles– that was the pattern from which many subsequent tarot decks derive.

Marsilio Ficino, from a fresco painted by Domenico Ghirlandaio in the Tornabuoni Chapel, Santa Maria Novella, Florence


“Without a map who would attempt to study geography?”*…

History and maps!…

Imagine creating a timeline of your country’s whole history stretching back to its inception.

It would be no small task, and simply weighing the relative importance of so many great people, technological achievements, and pivotal events would be a tiny miracle in itself.

While that seems like a challenge, imagine going a few steps further. Instead of a timeline for just one country, what about creating a graphical timeline showing the history of the entire world over a 4,000 year time period, all while having no access to computers or the internet?…

John B. Sparks maps the ebb and flow of global power going all the way back to 2,000 B.C. on one coherent timeline.

Histomap, published by Rand McNally in 1931, is an ambitious attempt at fitting a mountain of historical information onto a five-foot-long poster. The poster cost $1 at the time, which would equal approximately $18 when accounting for inflation.

Although the distribution of power is not quantitatively defined on the x-axis, it does provide a rare example of looking at historic civilizations in relative terms. While the Roman Empire takes up a lot of real estate during its Golden Age, for example, we still get a decent look at what was happening in other parts of the world during that period.

The visualization is also effective at showing the ascent and decline of various competing states, nations, and empires. Did Sparks see world history as a zero-sum exercise; a collection of nations battling one another for control over scarce territory and resources?

Crowning a world leader at certain points in history is relatively easy, but divvying up influence or power to everyone across 4,000 years requires some creativity, and likely some guesswork, as well. Some would argue that the lack of hard data makes it impossible to draw these types of conclusions (though there have been other more quantitative approaches.)

Another obvious criticism is that the measures of influence are skewed in favor of Western powers. China’s “seam”, for example, is suspiciously thin throughout the length of the timeline. Certainly, the creator’s biases and blind spots become more apparent in the information-abundant 21st century.

Lastly, Histomap refers to various cultural and racial groups using terms that may seem rather dated to today’s viewers.

John Spark’s creation is an admirable attempt at making history more approachable and entertaining. Today, we have seemingly limitless access to information, but in the 1930s an all encompassing timeline of history would have been incredibly useful and groundbreaking. Indeed, the map’s publisher characterized the piece as a useful tool for examining the correlation between different empires during points in history.

Critiques aside, work like this paved the way for the production of modern data visualizations and charts that help people better understand the world around them today…

Histomap: a 1931 attempt to visualize the 4,000 year history of global power. (via Visual Capitalist)

* John B. Sparks, creator of Histomap


As we ponder patterns in the past, we might spare a thought for Carl Jacob Christoph Burckhardt; he died on this date in 1897. Probably best known for The Civilization of the Renaissance in Italy (which established that period as the vaunted subject it has become), he was a historian of art and culture and an influential figure in the historiography of both fields. Indeed, he is considered one the the founders of cultural history.

Sigfried Giedion said of Burckhardt’s achievement: “The great discoverer of the age of the Renaissance, he first showed how a period should be treated in its entirety, with regard not only for its painting, sculpture and architecture, but for the social institutions of its daily life as well.”


“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


“Everyone should be able to do one card trick, tell two jokes, and recite three poems, in case they are ever trapped in an elevator”*…

Two things make tall buildings possible: the steel frame and the safety elevator. The elevator, underrated and overlooked, is to the city what paper is to reading and gunpowder is to war. Without the elevator, there would be no verticality, no density, and, without these, none of the urban advantages of energy efficiency, economic productivity, and cultural ferment. The population of the earth would ooze out over its surface, like an oil slick, and we would spend even more time stuck in traffic or on trains, traversing a vast carapace of concrete. And the elevator is energy-efficient—the counterweight does a great deal of the work, and the new systems these days regenerate electricity. The elevator is a hybrid, by design…

The history, design, economics, and psychology of the technology that made modern cities possible– the lives of elevators: “Up and Then Down.”

* Daniel Handler


As we press the button, we might recall that it was on this date in 1527, during the War of the League of Cognac, that an estimated 20,000 mutinous troops of Charles V, Holy Roman Emperor (angered over unpaid wages) carried out the Sack of Rome (which was then part of the papal States). For three days, they pillaged the city, grabbing valuables and demanding tributes. They overpowered (and killed most of) the Swiss Guard, and took Pope Clement VII hostage (in Castel Sant’Angelo); he was freed only after a hefty ransom was paid. Benvenuto Cellini, witnessed the Sack and described the it in his works.

In the aftermath, Rome– which had been the center of Italian High Renaissance culture– never recovered its momentum. Indeed, many historians consider the Sack of Rome the end of the Renaissance.

The Sack of Rome, by Johannes Lingelbach (17th century)


Written by (Roughly) Daily

May 6, 2021 at 1:01 am

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