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Posts Tagged ‘Mathematics

“Speed and acceleration are merely the dream of making time reversible”*…

In the early 20th century, there was Futurism…

The Italian Futurists, from the first half of the twentieth century… wanted to drive modernisation in turn-of-the-century Italy at a much faster pace. They saw the potential in machines, and technology, to transform the country, to demand progress. It was not however merely an incrementalist approach they were after: words like annihilation, destruction and apocalypse appear in the writings of the futurists, including the author of The Futurist Manifesto, Filippo Tomasso Marinetti. ‘We want to glorify war – the only cure for the world…’ Marinetti proclaimed – this was not for the faint hearted! That same Marinetti was the founder of the Partito Politico Futuristo in 1918, which became part of Mussolini’s Fascist party in 1919. Things did not go well after that.

Beautiful Ideas Which Kill: Accelerationism, Futurism and Bewilderment

And now, in the early 21st century, there is Accelerationism…

These [politically-motivated mass] killings were often linked to the alt-right, described as an outgrowth of the movement’s rise in the Trump era. But many of these suspected killers, from Atomwaffen thugs to the New Zealand mosque shooter to the Poway synagogue attacker, are more tightly connected to a newer and more radical white supremacist ideology, one that dismisses the alt-right as cowards unwilling to take matters into their own hands.

It’s called “accelerationism,” and it rests on the idea that Western governments are irreparably corrupt. As a result, the best thing white supremacists can do is accelerate their demise by sowing chaos and creating political tension. Accelerationist ideas have been cited in mass shooters’ manifestos — explicitly, in the case of the New Zealand killer — and are frequently referenced in white supremacist web forums and chat rooms.

Accelerationists reject any effort to seize political power through the ballot box, dismissing the alt-right’s attempts to engage in mass politics as pointless. If one votes, one should vote for the most extreme candidate, left or right, to intensify points of political and social conflict within Western societies. Their preferred tactic for heightening these contradictions, however, is not voting, but violence — attacking racial minorities and Jews as a way of bringing us closer to a race war, and using firearms to spark divisive fights over gun control. The ultimate goal is to collapse the government itself; they hope for a white-dominated future after that…

Accelerationism: the obscure idea inspiring white supremacist killers around the world” (and source of the image above)

See also: “A Year After January 6, Is Accelerationism the New Terrorist Threat?

For a look at the “intellectual” roots of accelerationism, see “Accelerationism: how a fringe philosophy predicted the future we live in.”

For a powerful articulation of the dangers of Futurism (and even more, Acclerationism), see “The Perils of Smashing the Past.”

And for a reminder of the not-so-obvious ways that movements like these live on, see “The Intentionally Scandalous 1932 Cookbook That Stands the Test of Time,” on The Futurist Cookbook, by Futurist Manifesto author Filippo Tommaso Marinetti… which foreshadowed the “food as fuel” culinary movements that we see today.

* Jean Baudrillard


As we slow down, we might send a “Alles Gute zum Geburtstag” to the polymathic Gottfried Wilhelm Leibniz, the philosopher, mathematician, and political adviser, who was important both as a metaphysician and as a logician, but who is probably best remembered for his independent invention of the calculus; he was born on this date in 1646.  Leibniz discovered and developed differential and integral calculus on his own, which he published in 1684; but he became involved in a bitter priority dispute with Isaac Newton, whose ideas on the calculus were developed earlier (1665), but published later (1687).

As it happens, Leibnitz was a wry and incisive political and cultural observer.  Consider, e.g…

If geometry conflicted with our passions and our present concerns as much as morality does, we would dispute it and transgress it almost as much–in spite of all Euclid’s and Archimedes’ demonstrations, which would be treated as fantasies and deemed to be full of fallacies. [Leibniz, New Essays, p. 95]



“It’s a recession when your neighbor loses his job; it’s a depression when you lose your own”*…

The “R word,” unpacked…

It’s being whispered and murmured about. The president is facing questions about it. Business leaders and investors are already bracing for it. The specter of recession is once again rearing its monstrous head.

It’s feasible that the economy could chug along without any bumps or crashes. But boom-and-bust cycles remain a seemingly inescapable feature of capitalist economies. Some countries have done well avoiding busts. Starting in 1991, Australia had a run of almost 29 years without a recession, the longest stretch of economic growth of any nation in modern history. That ended in 2020, when the pandemic led to a big contraction — and Australia (briefly) succumbed to the beast.

While Australia had zero recessions between 1991 and 2020, the United States had two, a mild one in 2001, amid the dotcom crash and the 9/11 terrorist attacks; and a catastrophic one known as the Great Recession, between 2007 and 2009. Since 1854, the first year for which we have official economic data, the United States has experienced 35 recessions.

The National Bureau of Economic Research’s Business Cycle Dating Committee is the official body that keeps track of recessions in the U.S. The committee has traditionally defined recessions as “a significant decline in economic activity that is spread across the economy and that lasts more than a few months.”…

Recessions– what they are, what they aren’t, and how they happen: “Fear The Vibe Shift: Are We Entering A Recession?,” from Greg Rosalsky (@elliswonk) at Planet Money (@planetmoney).

And for a dive into the vibe in question, see Derek Thompson‘s (@DKThomp) examination of why many Americans believe that they’re personally doing well, even as they feel that the country and the economy are going to hell: “Everything Is Terrible, but I’m Fine.”

See also: “There are 2 very different kinds of recessions—and the U.S. is likely headed for something totally different than 2008” in @FortuneMagazine (source of the image above), and “A recession in America by 2024 looks likely– It should be mild—but fear its consequences” in @TheEconomist.

* Harry S. Truman


As we batten the hatches, we might send carefully-considered birthday greetings to Robert Aumann; he was born on this date in 1930. An economist and mathematician, he is best known for his contributions to game theory, especially for his work on repeated games (situations in which players encounter the same situation over and over again). He developed the concept of correlated equilibrium in game theory, which is a type of equilibrium in non-cooperative games (like most of those in our economy), a more flexible version than the classical Nash equilibrium.

For these and related contributions to game theory, he shared the 2005 Nobel Prize in Economics.


“If you are confused by the underlying principles of quantum technology – you get it!”*…

A tour through the map above– a helpful primer on the origins, development, and possible futures of quantum computing…

From Dominic Walliman (@DominicWalliman) on @DomainOfScience.

* Kevin Coleman


As we embrace uncertainty, we might spare a thought for

Alan Turing; he died on this date in 1954. A British mathematician, he was a foundational computer science pioneer (inventor of the Turing Machine, creator of the “Turing Test” (perhaps to b made more relevant by quantum computing :), and inspiration for “The Turing Award“) and cryptographer (leading member of the team that cracked the Enigma code during WWII).  


“A nothing will serve just as well as a something about which nothing could be said”*…

Metaphysical debates in quantum physics don’t get at “truth,” physicist and mathematician Timothy Andersen argues; they’re nothing but a form of ritual activity and culture. After a thoughtful intellectual history of both quantum mechanics and Wittgenstein’s thought, he concludes…

If Wittgenstein were alive today, he might have couched his arguments in the vocabulary of cultural anthropology. For this shared grammar and these language games, in his view, form part of much larger ritualistic mechanisms that connect human activity with human knowledge, as deeply as DNA connects to human biology. It is also a perfect example of how evolution works by using pre-existing mechanisms to generate new behaviors.

The conclusion from all of this is that interpretation and representation in language and mathematics are little different than the supernatural explanations of ancient religions. Trying to resolve the debate between Bohr and Einstein is like trying to answer the Zen kōan about whether the tree falling in the forest makes a sound if no one can hear it. One cannot say definitely yes or no, because all human language must connect to human activity. And all human language and activity are ritual, signifying meaning by their interconnectedness. To ask what the wavefunction means without specifying an activity – and experiment – to extract that meaning is, therefore, as sensible as asking about the sound of the falling tree. It is nonsense.

As a scientist and mathematician, Wittgenstein has challenged my own tendency to seek out interpretations of phenomena that have no scientific value – and to see such explanations as nothing more than narratives. He taught that all that philosophy can do is remind us of what is evidently true. It’s evidently true that the wavefunction has a multiverse interpretation, but one must assume the multiverse first, since it cannot be measured. So the interpretation is a tautology, not a discovery.

I have humbled myself to the fact that we can’t justify clinging to one interpretation of reality over another. In place of my early enthusiastic Platonism, I have come to think of the world not as one filled with sharply defined truths, but rather as a place containing myriad possibilities – each of which, like the possibilities within the wavefunction itself, can be simultaneously true. Likewise, mathematics and its surrounding language don’t represent reality so much as serve as a trusty tool for helping people to navigate the world. They are of human origin and for human purposes.

To shut up and calculate, then, recognizes that there are limits to our pathways for understanding. Our only option as scientists is to look, predict and test. This might not be as glamorous an offering as the interpretations we can construct in our minds, but it is the royal road to real knowledge…

A provocative proposition: “Quantum Wittgenstein,” from @timcopia in @aeonmag.

* Ludwig Wittgenstein, Philosophical Investigations


As we muse on meaning, we might recall that it was on this date in 1954 that the official ground-breaking for CERN (Conseil européen pour la recherche nucléaire) was held. Located in Switzerland, it is the largest particle physics laboratory in the world… that’s to say, a prime spot to do the observation and calculation that Andersen suggests. Indeed, it’s been the site of many breakthrough discoveries over the years, maybe most notably the 2012 observation of the Higgs Boson.

Because researchers need remote access to these facilities, the lab has historically been a major wide area network hub. Indeed, it was at CERN that Tim Berners-Lee developed the first “browser”– and effectively fomented the emergence of the web.

CERN’s main site, from Switzerland looking towards France

“One of the most singular characteristics of the art of deciphering is the strong conviction possessed by every person, even moderately acquainted with it, that he is able to construct a cipher which nobody else can decipher.”*…

And yet, for centuries no one has succeeded. Now, as Erica Klarreich reports, cryptographers want to know which of five possible worlds we inhabit, which will reveal whether truly secure cryptography is even possible…

Many computer scientists focus on overcoming hard computational problems. But there’s one area of computer science in which hardness is an asset: cryptography, where you want hard obstacles between your adversaries and your secrets.

Unfortunately, we don’t know whether secure cryptography truly exists. Over millennia, people have created ciphers that seemed unbreakable right until they were broken. Today, our internet transactions and state secrets are guarded by encryption methods that seem secure but could conceivably fail at any moment.

To create a truly secure (and permanent) encryption method, we need a computational problem that’s hard enough to create a provably insurmountable barrier for adversaries. We know of many computational problems that seem hard, but maybe we just haven’t been clever enough to solve them. Or maybe some of them are hard, but their hardness isn’t of a kind that lends itself to secure encryption. Fundamentally, cryptographers wonder: Is there enough hardness in the universe to make cryptography possible?

In 1995, Russell Impagliazzo of the University of California, San Diego broke down the question of hardness into a set of sub-questions that computer scientists could tackle one piece at a time. To summarize the state of knowledge in this area, he described five possible worlds — fancifully named Algorithmica, Heuristica, Pessiland, Minicrypt and Cryptomania — with ascending levels of hardness and cryptographic possibility. Any of these could be the world we live in…

Explore each of them– and their implications for secure encryption– at “Which Computational Universe Do We Live In?” from @EricaKlarreich in @QuantaMagazine.

Charles Babbage


As we contemplate codes, we might we might send communicative birthday greetings to a frequentlyfeatured hero of your correspondent, Claude Elwood Shannon; he was born on this date in 1916.  A mathematician, electrical engineer– and cryptographer– he is known as “the father of information theory.”  But he is also remembered for his contributions to digital circuit design theory and for his cryptanalysis work during World War II, both as a codebreaker and as a designer of secure communications systems.



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