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Posts Tagged ‘Mathematics

“We can judge our progress by the courage of our questions and the depth of our answers, our willingness to embrace what is true rather than what feels good”*…




If one takes Donald Trump and his administration to embody modern conservatism, it is easy to see in their response to the coronavirus pandemic the right’s final divorce from science and expertise. There was the case of Rick Bright, the Health and Human Services scientist who claims that the Trump administration retaliated against him when he objected to the administration’s rapid push to distribute anti-malaria drugs that were largely untested for treating coronavirus patients. There are reports that the president for months ignored his own intelligence experts’ warnings that the virus threatened our shores. There was the ongoing drama over whether Trump would fire Anthony Fauci, who has headed the National Institute of Allergy and Infectious Diseases since 1984. And there was the president’s daily passion play—the White House press briefings where he’d stand next to scientists who grimaced as he speculated that the death toll was exaggerated and that sunlight inside the body might kill the virus.

The White House’s sorry Covid-19 track record has sparked a chorus of dissent recently distilled by New York Times columnist Michelle Goldberg, who argues that the crisis displays conservatives’ long-standing “antipathy to science,” owing to “populist distrust of experts, religious rejection of information that undermines biblical literalism and efforts by giant corporations to evade regulation.” But this narrative is too pat. While something is plainly amiss in the relationship of the Trumpian right to science, it is hardly as principled as the religious objections of, say, creationists opposing evolutionary theory. Neither is it straightforwardly hostile.

What’s more curious about the response by the president and his allies to the virus is rather their embrace of scientific expertise of a sort…

The story of the crisis is not quite that of scientists who knew the answers and one political party that just wouldn’t listen to them. Rather, it is a story of fracture—of conflict and confusion, of experts earning mistrust, of each side cultivating its own class of experts to own the other’s. It is also a perverse story of how a group of self-styled truth-telling outsiders turned science’s mythology against its institutions, warping it from a tool to fight the virus into a tool to attack the establishment.

How did we get here?…

Ari Schulman (@AriSchulman) explains how a new class of outsider experts is exploiting institutional failures and destabilizing knowledge: “The Coronavirus and the Right’s Scientific Counterrevolution.”

TotH to Byrne Hobart, who notes (in his nifty newsletter, The Diff):

… this essay obviously takes a side, but it tries to be fair to the side it disagrees with. Which means there are two Straussian readings: maybe it’s an essay about how science is on one side in an American political context, and the other side only makes vague gestures towards empiricism. Alternatively, it could be an essay on how science never answers political questions, but politics corrupts science. (Why doesn’t science answer political questions? Because you can’t build a coalition out of stating the obvious, but you can build one from denying it—if your beliefs are crazy, you can spot members of the ingroup. So most scientific questions are irrelevant to politics, and when they’re relevant, politics wins by default in the short term, even if it loses long-term. To build a coherent and healthy ingroup, you need beliefs that are crazy but don’t lead to bad decisions.)

Pair with another of Hobart’s suggestions: “On Cultures That Build” (and the reasons why, the author argues. the U.S. is not one).

* Carl Sagan


As we commit to learning, we might note that today is the birthday of not one but two extraordinary mathematicians:  Gottfried Wilhelm Leibniz (1646; variants on his date of birth are due to calendar changes), the German  philosopher, scientist, mathematician, diplomat, librarian, lawyer, co-inventor, with Newton, of The Calculus, and “hero” (well, one hero) of Neal Stephenson’s Baroque Trilogy…  and  Alan Turing (1912), British mathematician, computer science pioneer (inventor of the Turing Machine, creator of “the Turing Test” and inspiration for “The Turing Prize”), and cryptographer (leading member of the team that cracked the Enigma code during WWII).

Go figure…

Turing (source: Univ. of Birmingham)

Giambattista Vico was also born on this date in 1668.  A political philosopher, rhetorician, historian, and jurist, Vico was one of the greatest Enlightenment thinkers.  Best known for the Scienza Nuova (1725, often published in English as New Science), he famously criticized the expansion and development of modern rationalism and was an apologist for classical antiquity.

He was an important precursor of systemic and complexity thinking (as opposed to Cartesian analysis and other kinds of reductionism); and he can be credited with the first exposition of the fundamental aspects of social science, though his views did not necessarily influence the first social scientists.  Vico is often claimed to have fathered modern philosophy of history (although the term is not found in his text; Vico speaks of a “history of philosophy narrated philosophically”). While he was not strictly speaking a historicist, interest in him has been driven by historicists (like Isaiah Berlin).



Written by LW

June 23, 2020 at 1:01 am

“Neoliberalization has meant, in short, the financialization of everything”*…




Investing and deal-making occupy an outsized role in popular depictions of “business” like HBO’s Succession and Showtime’s Billions. They also occupy an outsized share of our elite: Over the last five years, the nation’s top business schools have sent nearly thirty percent of their graduating classes into finance.

But the buying and selling of companies, the mergers and divestments, the hedging and leveraging, are not themselves valuable activity. They invent, create, build, and provide nothing. Their claim to value is purely derivative—by improving the allocation of capital and configuration of assets, they are supposed to make everyone operating in the real economy more productive. The practitioners are rewarded richly for their effort.

Does this work, or are the efforts largely wasted? One might default to the assumption that an industry attracting so much talent and generating so much profit must be creating enormous value. But the elaborate financial engineering of the 2000s, which attempted an alchemy-like conversion of high-risk loans into rock-solid assets, and then placed highly leveraged bets against their performance, led to the collapse of some established Wall Street institutions, massive bailouts for others, and a global economic meltdown. Mergers and acquisitions, meanwhile, appear largely to be exercises in wheel-spinning: “M&A is a mug’s game,” explains Roger Martin in the Harvard Business Review, “in which typically 70%–90% of acquisitions are abysmal failures.”…

Hedge funds and venture capital funds appear to badly underperform simple public market indexes, while buyout funds have performed roughly at par over the past decade. Of course, some funds deliver outsized returns in a given timeframe; even a random distribution has a right tail. And there are managers whose strong and consistent track records suggest the creation of real value.

In other words, most fund managers are generating the results that one might expect from an elaborate game of chance—placing bets in the market with odds similar to a coin flip. With enough people playing, some will always find themselves on winning streaks and claim the Midas touch, at least until the coin’s next flip. Except under these rules of “heads I win, tails you lose,” they collect their fees regardless…

In the U.S., finance, insurance and real estate (FIRE) sector now accounts for 20 percent of GDP– compared with only 10 percent in 1947.  The thorough and thoughtful analysis– and critique–  of the frothier components of that sector excerpted above is noteworthy, beyond its quality, for it’s origin; it is an early product of a new conservative think tank, American Compass.

Read it in full: “Coin-Flip Capitalism: A Primer.”

Pair with “What Kind of Country Do We Want?“, a resonant essay from the amazing Marilynne Robinson.

(image above: source)

* “Neoliberalization has meant, in short, the financialization of everything. There was unquestionably a power shift away from production to the world of finance… Neoliberalization has not been very effective in revitalizing global capital accumulation, but it has succeeded remarkably well in restoring, or in some instances (as in Russia and China) creating, the power of an economic elite. The theoretical utopianism of neoliberal argument has, I conclude, primarily worked as a system of justification and legitimation for whatever needed to be done to achieve this goal.”  — David Harvey, A Brief History of Neoliberalism


As we look beyond price to value, we might recall that it was on this date in 1936 that Alan Turing submitted his paper, “On Computable Numbers” for publication; its full title was “On Computable Numbers, with an Application to the Entscheidungsproblem.”  In answer to Hibert’s and Ackermann’s 1928 challenge, Turing demonstrated that some purely mathematical yes-no questions can never be answered by computation; more technically, that some decision problems are “undecidable” in the sense that there is no single algorithm that infallibly gives a correct “yes” or “no” answer to each instance of the problem.  In Turing’s own words: “…what I shall prove is quite different from the well-known results of Gödel … I shall now show that there is no general method which tells whether a given formula U is provable in K.”

Turing followed this proof with two others, both of which rely on the first. And all rely on his development of type-writer-like “computing machines” that obey a simple set of rules and his subsequent development of a “universal computing machine”– the “Turing Machine,” a key inspiration (to von Neumann and others) for the development of the digital computer.

220px-Alan_Turing_Aged_16 source


“Real randomness requires an infinite amount of information”*…




If you have ever tossed dice, whether in a board game or at the gambling table, you have created random numbers—a string of numbers each of which cannot be predicted from the preceding ones. People have been making random numbers in this way for millennia. Early Greeks and Romans played games of chance by tossing the heel bone of a sheep or other animal and seeing which of its four straight sides landed uppermost. Heel bones evolved into the familiar cube-shaped dice with pips that still provide random numbers for gaming and gambling today.

But now we also have more sophisticated random number generators, the latest of which required a lab full of laser equipment at the U.S. National Institute of Standards and Technology (NIST) in Boulder, CO. It relies on counterintuitive quantum behavior with an assist from relativity theory to make random numbers. This was a notable feat because the NIST team’s numbers were absolutely guaranteed to be random, a result never before achieved.

Why are random numbers worth so much effort? Random numbers are chaotic for a good cause. They are eminently useful, and not only in gambling. Since random digits appear with equal probabilities, like heads and tails in a coin toss, they guarantee fair outcomes in lotteries, such as those to buy high-value government bonds in the United Kingdom. Precisely because they are unpredictable, they provide enhanced security for the internet and for encrypted messages. And in a nod to their gambling roots, random numbers are essential for the picturesquely named “Monte Carlo” method that can solve otherwise intractable scientific problems…

Using entanglement to generate true mathematical randomness– and why that matters: “The Quantum Random Number Generator.”

* Tristan Perich


As we leave it to chance, we might send learned birthday greetings to Athanasius Kircher; he was born on this date in 1602.  A scholar, he published over 40 works. perhaps most notably on most notably in comparative religion, geology, and medicine, but over a range so broad that he was frequently compared to Leonardo Da Vinci (who died on the date in 1519) and was dubbed “Master of a Hundred Arts.”

For a look at one of his more curious works, see “Wonder is the beginning of wisdom.” And his take on The Plague (through which he lived in Italy in 1656), see here.

220px-Athanasius_Kircher_(cropped) source


“What is mathematics? It is only a systematic effort of solving puzzles posed by nature.”*…




In 1998, the Cloisters—the museum of medieval art in upper Manhattan—began a renovation of the room where the seven tapestries known as “The Hunt of the Unicorn” hang. The Unicorn tapestries are considered by many to be the most beautiful tapestries in existence. They are also among the great works of art of any kind. In the tapestries, richly dressed noblemen, accompanied by hunters and hounds, pursue a unicorn through forested landscapes. They find the animal, appear to kill it, and bring it back to a castle; in the last and most famous panel, “The Unicorn in Captivity,” the unicorn is shown bloody but alive, chained to a tree surrounded by a circular fence, in a field of flowers. The tapestries are twelve feet tall and up to fourteen feet wide (except for one, which is in fragments). They were woven from threads of dyed wool and silk, some of them gilded or wrapped in silver, around 1500, probably in Brussels or Liège, for an unknown person or persons, and for an unknown reason—possibly to honor a wedding. A monogram made from the letters “A” and “E” is woven into the scenery in many places; no one knows what it stands for. The tapestries’ meaning is mysterious: the unicorn was a symbol of many things in the Middle Ages, including Christianity, immortality, wisdom, lovers, marriage. For centuries, the tapestries were in the possession of the La Rochefoucauld family of France. In 1922, John D. Rockefeller, Jr., bought them for just over a million dollars, and in 1937 he gave them to the Cloisters. Their monetary value today is incalculable…

As the construction work got under way, the tapestries were rolled up and moved, in an unmarked vehicle and under conditions of high security, to the Metropolitan Museum of Art, which owns the Cloisters. They ended up in a windowless room in the museum’s textile department for cleaning and repair. The room has white walls and a white tiled floor with a drain running along one side. It is exceedingly clean, and looks like an operating room. It is known as the wet lab, and is situated on a basement level below the museum’s central staircase.

In the wet lab, a team of textile conservators led by a woman named Kathrin Colburn unpacked the tapestries and spread them out face down on a large table, one by one. At some point, the backs of the tapestries had been covered with linen. The backings, which protect the tapestries and help to support them when they hang on a wall, were turning brown and brittle, and had to be replaced. Using tweezers and magnifying lenses, Colburn and her team delicately removed the threads that held each backing in place. As the conservators lifted the backing away, inch by inch, they felt a growing sense of awe. The backs were almost perfect mirror images of the fronts, but the colors were different. Compared with the fronts, they were unfaded: incredibly bright, rich, and deep, more subtle and natural-looking. The backs of the tapestries had, after all, been exposed to very little sunlight in five hundred years. Nobody alive at the Met, it seems, had seen them this way…

Philippe de Montebello, the director of the museum, declared that the Unicorn tapestries must be photographed on both sides, to preserve a record of the colors and the mirror images. Colburn and her associates would soon put new backing material on them, made of cotton sateen. Once they were rehung at the Cloisters, it might be a century or more before the true colors of the tapestries would be seen again.

The manager of the photography studio at the Met is a pleasant, lively woman named Barbara Bridgers. Her goal is to make a high-resolution digital image of every work of art in the Met’s collections. The job will take at least twenty-five years; there are between two and two and a half million catalogued objects in the Met—nobody knows the exact number. (One difficulty is that there seems to be an endless quantity of scarab beetles from Egypt.) But, when it’s done and backup files are stored in an image repository somewhere else, then if an asteroid hits New York the Metropolitan Museum may survive in a digital copy.

To make a digital image of the Unicorn tapestries was one of the most difficult assignments that Bridgers had ever had. She put together a team to do it, bringing in two consultants, Scott Geffert and Howard Goldstein, and two of the Met’s photographers, Joseph Coscia, Jr., and Oi-Cheong Lee. They built a giant metal scaffolding inside the wet lab, and mounted on it a Leica digital camera, which looked down at the floor. The photographers were forbidden to touch the tapestries; Kathrin Colburn and her team laid each one down, underneath the scaffold, on a plastic sheet. Then the photographers began shooting. The camera had a narrow view; it could photograph only one three-by-three-foot section of tapestry at a time. The photographers took overlapping pictures, moving the camera on skateboard wheels on the scaffolding. Each photograph was a tile that would be used to make a complete, seamless mosaic of each tapestry…

It took two weeks to photograph the tapestries. When the job was done, every thread in every tile was crystal-clear, and the individual twisted strands that made up individual threads were often visible, too. The data for the digital images, which consisted entirely of numbers, filled more than two hundred CDs. With other, smaller works of art, Bridgers and her team had been able to load digital tiles into a computer’s hard drives and memory, and then manipulate them into a complete mosaic—into a seamless image—using Adobe Photoshop software. But with the tapestries that simply wouldn’t work. When they tried to assemble the tiles, they found that the files were too large and too complex to manage. “We had to lower the resolution of the images in order to fit them into the computers we had, and it degraded the images so much that we just didn’t think it was worth doing,” Bridgers said. Finally, they gave up. Bridgers stored the CDs on a shelf and filed the project away as an unsolved problem…

Enter Gregory and David Chudnovsky, brothers whose work was so intertwined that they considered themselves a single mathematician.  Over four months– and after 30 hours of continuous running– their self-designed supercomputer successfully performed the 7.7 quadrillion calculations needed to produce the image for the Met.

Richard Preston tells the genuinely-fascinating story: “Capturing the Unicorn.”

It was a return of sorts for Preston, who, thirteen years earlier, had profiled the brothers and their successful quest to resolve pi to a record number of decimal places: “The Mountains of Pi.”

More on the Chudnovskys here.

* Shakuntala Devi


As we muse of the merger of art and science, we might recall that it was on this date in 1886 that Coca Cola was concocted in an Atlanta, Georgia backyard as a “brain tonic” that could cure hangovers, stomach aches and headaches.  The original formula included caffeine and five ounces of coca leaf (from which cocaine is derived) per gallon.  The creator, pharmacist John Pemberton, took his syrup a few doors down to Jacobs’ Pharmacy, where he mixed it with carbonated water and shared it with customers.  The pharmacy began marketing it on May 8 as a patent medicine for 5¢ a glass.  It spread first through the other Jacobs outlets in Atlanta, and then around the world.

“The valuable tonic and nerve stimulant properties of the coca plant and cola nuts …”

– John Pemberton





“All you really need to know for the moment is that the universe is a lot more complicated than you might think, even if you start from a position of thinking it’s pretty damn complicated in the first place”*…




When you gaze out at the night sky, space seems to extend forever in all directions. That’s our mental model for the universe, but it’s not necessarily correct. There was a time, after all, when everyone thought the Earth was flat, because our planet’s curvature was too subtle to detect and a spherical Earth was unfathomable.

Today, we know the Earth is shaped like a sphere. But most of us give little thought to the shape of the universe. Just as the sphere offered an alternative to a flat Earth, other three-dimensional shapes offer alternatives to “ordinary” infinite space.

We can ask two separate but interrelated questions about the shape of the universe. One is about its geometry: the fine-grained local measurements of things like angles and areas. The other is about its topology: how these local pieces are stitched together into an overarching shape.

Cosmological evidence suggests that the part of the universe we can see is smooth and homogeneous, at least approximately. The local fabric of space looks much the same at every point and in every direction. Only three geometries fit this description: flat, spherical and hyperbolic…

Alternatives to “ordinary” infinite space: “What Is the Geometry of the Universe?

* Douglas Adams, The Hitchhiker’s Guide to the Galaxy


As we tinker with topology, we might recall that it was on this date in 1811 that Percy Bysshe Shelley was expelled from the University of Oxford for publishing the pamphlet The Necessity of Atheism.  Shelley, of course, went on to become a celebrated lyric poet and one of the leaders of the English Romantic movement… one who had a confident (if not to say exalted) sense of his role in society:

Poets are the hierophants of an unapprehended inspiration; the mirrors of the gigantic shadows which futurity casts upon the present; the words which express what they understand not; the trumpets which sing to battle, and feel not what they inspire; the influence which is moved not, but moves. Poets are the unacknowledged legislators of the world.

220px-Percy_Bysshe_Shelley_by_Alfred_Clint source


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