Posts Tagged ‘Toscanelli’
“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.
“When I was shown the charts and diagrams… How soon unaccountable I became tired and sick”*…
How meta is this?! An infographic on infographics…
* When I heard the learn’d astronomer,
When the proofs, the figures, were ranged in columns before me,
When I was shown the charts and diagrams, to add, divide, and measure them,
When I sitting heard the astronomer where he lectured with much applause in the lecture-room,
How soon unaccountable I became tired and sick,
Till rising and gliding out I wander’d off by myself,
In the mystical moist night-air, and from time to time,
Look’d up in perfect silence at the stars.
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As we ponder pictograms, we might spare a grateful thought for the man who wrote the book on perspective, Leon Battista Alberti; he died on this date in 1472. 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 Leon Battista Alberti, Della Pictura
Odds are…
On the heels of the cosmic coincidence of a flaming fireball over Russia and a close approach by a larger asteroid, The Economist offers a comparative chart sketching the mortal risks one faces this year…
Of course, as astronaut Rusty Schweickart reminds us, the odds of an asteroid strike over a materially-longer period are much higher; over the next 100,000 years…
– There’s a 10% chance of an asteroid causing planet-scale damage with 100,000 megatons of energy released.
– There’s a 50-50 chance of a 500-meter asteroid that could destroy an area the size of Texas with a 6,000 megaton explosion—100 times the USSR’s biggest bomb.
– There will be about TEN 200-meter asteroid impacts, good for 400 megatons.
– There will be about A HUNDRED 70-meter-diameter asteroids, each causing 15 megatons of damage (i.e. worse than the Tunguska explosion, which would have wiped out all of London if it had hit there instead of the remote wilderness).
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As we struggle to keep this all in perspective, 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 Leon Battista Alberti, Della Pictura
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