Archive for August 2020
“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.”
###
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.
“If a ‘religion’ is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one”*…
In 1931, the Austrian logician Kurt Gödel pulled off arguably one of the most stunning intellectual achievements in history.
Mathematicians of the era sought a solid foundation for mathematics: a set of basic mathematical facts, or axioms, that was both consistent — never leading to contradictions — and complete, serving as the building blocks of all mathematical truths.
But Gödel’s shocking incompleteness theorems, published when he was just 25, crushed that dream. He proved that any set of axioms you could posit as a possible foundation for math will inevitably be incomplete; there will always be true facts about numbers that cannot be proved by those axioms. He also showed that no candidate set of axioms can ever prove its own consistency.
His incompleteness theorems meant there can be no mathematical theory of everything, no unification of what’s provable and what’s true. What mathematicians can prove depends on their starting assumptions, not on any fundamental ground truth from which all answers spring.
In the 89 years since Gödel’s discovery, mathematicians have stumbled upon just the kinds of unanswerable questions his theorems foretold. For example, Gödel himself helped establish that the continuum hypothesis, which concerns the sizes of infinity, is undecidable, as is the halting problem, which asks whether a computer program fed with a random input will run forever or eventually halt. Undecidable questions have even arisen in physics, suggesting that Gödelian incompleteness afflicts not just math, but — in some ill-understood way — reality…
A (relatively) simple explanation of the incompleteness theorem– which destroyed the search for a mathematical theory of everything: “How Gödel’s Proof Works.”
* John D. Barrow, The Artful Universe
###
As we noodle on the unknowable, we might spare a thought for Vilfredo Federico Damaso Pareto; he died on this date in 1923. An engineer, sociologist, economist, political scientist, and philosopher, he made several important contributions to economics, sociology, and mathematics.
He introduced the concept of Pareto efficiency and helped develop the field of microeconomics. He was also the first to discover that income follows a Pareto distribution, which is a power law probability distribution. The Pareto principle, named after him, generalized on his observations on wealth distribution to suggest that, in most systems/settings, 80% of the effects come from 20% of the causes– the “80-20 rule.” He was also responsible for popularizing the use of the term “elite” in social analysis.
As Benoit Mandelbrot and Richard L. Hudson observed, “His legacy as an economist was profound. Partly because of him, the field evolved from a branch of moral philosophy as practised by Adam Smith into a data intensive field of scientific research and mathematical equations.”
The future leader of Italian fascism Benito Mussolini, in 1904, when he was a young student, attended some of Pareto’s lectures at the University of Lausanne. It has been argued that Mussolini’s move away from socialism towards a form of “elitism” may be attributed to Pareto’s ideas.
Mandelbrot summarized Pareto’s notions as follows:
At the bottom of the Wealth curve, he wrote, Men and Women starve and children die young. In the broad middle of the curve all is turmoil and motion: people rising and falling, climbing by talent or luck and falling by alcoholism, tuberculosis and other kinds of unfitness. At the very top sit the elite of the elite, who control wealth and power for a time – until they are unseated through revolution or upheaval by a new aristocratic class. There is no progress in human history. Democracy is a fraud. Human nature is primitive, emotional, unyielding. The smarter, abler, stronger, and shrewder take the lion’s share. The weak starve, lest society become degenerate: One can, Pareto wrote, ‘compare the social body to the human body, which will promptly perish if prevented from eliminating toxins.’ Inflammatory stuff – and it burned Pareto’s reputation… [source]
“Rice is great if you’re really hungry and want to eat two thousand of something”*…
Rice is the most widely consumed staple food for a large part of the world’s population, especially in Asia and Africa. It is the third most widely-cultivated staple crop worldwide, after maize/corn and wheat… and it is notoriously difficult to prepare correctly on a stove…
Cooking rice on a stovetop can be fraught. Add too much water and you end up with porridge. Without a keen sense of timing, you end up with undercooked [pellet-like] grains…
The automatic rice cooker is a mid-century Japanese invention that made a Sisyphean culinary labor as easy as measuring out grain and water and pressing a button. These devices can seem all-knowing. So long as you add water and rice in the right proportions, it’s nearly impossible to mess up, as the machines stop cooking at exactly the right point for toothsome rice. But creating an automatic rice cooker was not so easy. In fact, it took decades of inventive leaps, undertaken by some of the biggest names in Japanese technology…
How the biggest names in Japanese technology fought to make rice easy: “The Battle to Invent the Automatic Rice Cooker.”
* Mitch Hedberg
###
As we ponder the pursuit of perfection, we might recall that today is National Potato Day– a celebration of the fourth most-widely cultivated staple crop.
“If you are not completely confused by quantum mechanics, you do not understand it”*…
If we can harness it, quantum technology promises fantastic new possibilities. But first, scientists need to coax quantum systems to stay yoked for longer than a few millionths of a second.
A team of scientists at the University of Chicago’s Pritzker School of Molecular Engineering announced the discovery of a simple modification that allows quantum systems to stay operational—or “coherent”—10,000 times longer than before. Though the scientists tested their technique on a particular class of quantum systems called solid-state qubits, they think it should be applicable to many other kinds of quantum systems and could thus revolutionize quantum communication, computing and sensing…
Down at the level of atoms, the world operates according to the rules of quantum mechanics—very different from what we see around us in our daily lives. These different rules could translate into technology like virtually unhackable networks or extremely powerful computers; the U.S. Department of Energy released a blueprint for the future quantum internet in an event at UChicago on July 23. But fundamental engineering challenges remain: Quantum states need an extremely quiet, stable space to operate, as they are easily disturbed by background noise coming from vibrations, temperature changes or stray electromagnetic fields.
Thus, scientists try to find ways to keep the system coherent as long as possible…
“This breakthrough lays the groundwork for exciting new avenues of research in quantum science,” said study lead author David Awschalom, the Liew Family Professor in Molecular Engineering, senior scientist at Argonne National Laboratory and director of the Chicago Quantum Exchange. “The broad applicability of this discovery, coupled with a remarkably simple implementation, allows this robust coherence to impact many aspects of quantum engineering. It enables new research opportunities previously thought impractical.”…
Very big news at a very small scale: “Scientists discover way to make quantum states last 10,000 times longer.”
###
As we strive for stability, we might send calculated birthday greetings to Brook Taylor; he was born on this date in 1685. A mathematician, he is best known for his work in describing and understanding oscillation. In 1708, Taylor produced a solution to the problem of the center of oscillation. His Methodus incrementorum directa et inversa (“Direct and Indirect Methods of Incrementation,” 1715) introduced what is now called the calculus of finite differences. Using this, he was the first to express mathematically the movement of a vibrating string on the basis of mechanical principles. Methodus also contained Taylor’s theorem, later recognized by Joseph Lagrange as the basis of differential calculus.
A gifted artist, Taylor also wrote on the basic principles of perspective, including the first general treatment of the principle of vanishing points.
“As names have power, words have power”*…
My book club was reading The Wise Man’s Fear by Patrick Rothfuss. In the middle of an otherwise unremarkable plot, we found a 35-page interlude about a highly attractive fairy, describing her body in minute, eye-rolling detail.
After slogging through that book, I began paying attention to similarly stereotyped descriptions of bodies in other books. Women are all soft thighs and red lips. Men, strong muscles and rough hands.
I was frustrated by this lazy writing. I want to read books that explore the full humanity of their characters, not stories that reduce both men and women to weak stereotypes of their gender.
Before getting too upset, I wanted to see if this approach to writing was as widespread as it seemed, or if I was succumbing to selective reading. Do authors really mention particular body parts more for men than for women? Are women’s bodies described using different adjectives than those attributed to men?
To do this, I selected 2,000 books spanning Pulitzer-winning classics to pulpy best-sellers, and ran them through a parser that identified sentences mentioning body parts. I then extracted the owner of the body parts and any adjectives describing them…
It’s easy to dismiss or overlook the differences in the way men’s and women’s bodies are depicted because they can be subtle and hard to discern in one particular book—one or two extra mentions of “his bushy hair” may not register over 300 pages.
But when you zoom out and look at thousands of books, the patterns are clear…
All the details from Erin Davis (@erindataviz) in The Pudding: “The physical traits that define men & women in literature.”
(Via Walt Hickey at Numlock, who observes, “honestly, now I just want to read a book about a women who’s all knuckles and a dude who’s got rockin’ hips.”)
* The Name of the Wind
###
As we lose the lens, we might send fictional birthday greetings to award-winning journalist Lois Lane; she was “born” on this date (according to the 1976 DC Comics Calendar). She has been wildly differently depicted through the years, as one can see here (among other places).
The Golden Age Lois Lane and Superman, from the cover of Superman #27 (March–April 1944), art by Wayne Boring.
You must be logged in to post a comment.