(Roughly) Daily

Posts Tagged ‘logic

“Advantage! What is advantage?”*…

Pradeep Mutalik unpacks the magic and math of how to win games when your opponent goes first…

Most games that pit two players or teams against each other require one of them to make the first play. This results in a built-in asymmetry, and the question arises: Should you go first or second?

Most people instinctively want to go first, and this intuition is usually borne out. In common two-player games, such as chess or tennis, it is a real, if modest, advantage to “win the toss” and go first. But sometimes it’s to your advantage to let your opponent make the first play.

In our February Insights puzzle, we presented four disparate situations in which, counterintuitively, the obligation to move is a serious and often decisive disadvantage. In chess, this is known as zugzwang — a German word meaning “move compulsion.”…

Four fascinating examples: “The Secrets of Zugzwang in Chess, Math and Pizzas,” from @PradeepMutalik.

* Fyodor Dostoyevsky, Notes from Underground

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As we play to win, we might recall that it was on this date in 2011 that scientists involved in the OPERA experiment (a collaboration between CERN and the Laboratori Nazionali del Gran Sasso) mistakenly observed neutrinos appearing to travel faster than light. OPERA scientists announced the results with the stated intent of promoting further inquiry and debate. Later the team reported two flaws in their equipment set-up that had caused errors far outside their original confidence interval: a fiber optic cable attached improperly, which caused the apparently faster-than-light measurements, and a clock oscillator ticking too fast; accounting for these two sources of error eliminated the faster-than-light results. But even before the sources of the error were discovered, the result was considered anomalous because speeds higher than that of light in a vacuum are generally thought to violate special relativity, a cornerstone of the modern understanding of physics for over a century.

The Large Hadron Collider at CERN

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Written by (Roughly) Daily

September 22, 2022 at 1:00 am

“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

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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]

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“In the sphere of thought, absurdity and perversity remain the masters of this world, and their dominion is suspended only for brief periods”*…

From a (somewhat sarcastic) 1896 essay (“The Art of Controversy”) by that gloomiest of philosophers, Arthur Schopenhauer, advice that (sadly) feels as appropriate today as it surely was then…

1. Carry your opponent’s proposition beyond its natural limits; exaggerate it. The more general your opponent’s statement becomes, the more objections you can find against it. The more restricted and narrow his or her propositions remain, the easier they are to defend by him or her.

2. Use different meanings of your opponent’s words to refute his or her argument.

3. Ignore your opponent’s proposition, which was intended to refer to a particular thing. Rather, understand it in some quite different sense, and then refute it. Attack something different than that which was asserted.

The first three of “Schopenhauer’s 38 Stratagems, or 38 Ways to Win an Argument.” Via @TheBrowser.

[Image above: source]

* Arthur Schopenhauer, “The Art of Controversy

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As we celebrate sophistry, we might recall that it was on this date (or near; scholars disagree) in 325 that Roman Emperor Constantine I convened a gathering in which all of Scopenhauer’s tricks were surely employed: the First Council of Nicaea. An ecumenical council, it was the first effort to attain consensus in the church through an assembly representing all Christendom. Its main accomplishments were settlement of the Christological issue of the divine nature of God the Son and his relationship to God the Father, the construction of the first part of the Nicene Creed, mandating uniform observance of the date of Easter, and the promulgation of early canon law.

Icon depicting the Emperor Constantine and the bishops of the First Council of Nicaea holding the Nicene Creed

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“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

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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.

220px-ClaudeShannon_MFO3807

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“No law of nature, however general, has been established all at once; its recognition has always been preceded by many presentiments.”*…

Laws of nature are impossible to break, and nearly as difficult to define. Just what kind of necessity do they possess?

… The natural laws limit what can happen. They are stronger than the laws of any country because it is impossible to violate them. If it is a law of nature that, for example, no object can be accelerated from rest to beyond the speed of light, then it is not merely that such accelerations never occur. They cannot occur.

There are many things that never actually happen but could have happened in that their occurrence would violate no law of nature. For instance, to borrow an example from the philosopher Hans Reichenbach (1891-1953), perhaps in the entire history of the Universe there never was nor ever will be a gold cube larger than one mile on each side. Such a large gold cube is not impossible. It just turns out never to exist. It’s like a sequence of moves that is permitted by the rules of chess but never takes place in the entire history of chess-playing. By contrast, if it is a law of nature that energy is never created or destroyed, then it is impossible for the total energy in the Universe to change. The laws of nature govern the world like the rules of chess determine what is permitted and what is forbidden during a game of chess, in an analogy drawn by the biologist T H Huxley (1825-95).

Laws of nature differ from one another in many respects. Some laws concern the general structure of spacetime, while others concern some specific inhabitant of spacetime (such as the law that gold doesn’t rust). Some laws relate causes to their effects (as Coulomb’s law relates electric charges to the electric forces they cause). But other laws (such as the law of energy conservation or the spacetime symmetry principles) do not specify the effects of any particular sort of cause. Some laws involve probabilities (such as the law specifying the half-life of some radioactive isotope). And some laws are currently undiscovered – though I can’t give you an example of one of those! (By ‘laws of nature’, I will mean the genuine laws of nature that science aims to discover, not whatever scientists currently believe to be laws of nature.)

What all of the various laws have in common, despite their diversity, is that it is necessary that everything obey them. It is impossible for them to be broken. An object must obey the laws of nature…

But although all these truisms about the laws of nature sound plausible and familiar, they are also imprecise and metaphorical. The natural laws obviously do not ‘govern’ the Universe in the way that the rules of chess govern a game of chess. Chess players know the rules and so deliberately conform to them, whereas inanimate objects do not know the laws of nature and have no intentions.

Scientists discover laws of nature by acquiring evidence that some apparent regularity is not only never violated but also could never have been violated. For instance, when every ingenious effort to create a perpetual-motion machine turned out to fail, scientists concluded that such a machine was impossible – that energy conservation is a natural law, a rule of nature’s game rather than an accident. In drawing this conclusion, scientists adopted various counterfactual conditionals, such as that, even if they had tried a different scheme, they would have failed to create a perpetual-motion machine. That it is impossible to create such a machine (because energy conservation is a law of nature) explains why scientists failed every time they tried to create one.

Laws of nature are important scientific discoveries. Their counterfactual resilience enables them to tell us about what would have happened under a wide range of hypothetical circumstances. Their necessity means that they impose limits on what is possible. Laws of nature can explain why something failed to happen by revealing that it cannot happen – that it is impossible.

We began with several vague ideas that seem implicit in scientific reasoning: that the laws of nature are important to discover, that they help us to explain why things happen, and that they are impossible to break. Now we can look back and see that we have made these vague ideas more precise and rigorous. In doing so, we found that these ideas are not only vindicated, but also deeply interconnected. We now understand better what laws of nature are and why they are able to play the roles that science calls upon them to play.

What is a Law of Nature?,” Marc Lange explains in @aeonmag.

* Dmitri Mendeleev (creator of the Periodic Table)

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As we study law, we might send inquisitive birthday greetings to Federico Cesi; he was born on this date in 1585. A scientist and naturalist, he is best remembered as the founder of the Accademia dei Lincei (Lincean Academy), often cited as the first modern scientific society. Cesi coined (or at least was first to publish/disseminate) the word “telescope” to denote the instrument used by Galileo– who was the sixth member of the Lincean Academy.

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