Posts Tagged ‘disorder’
“Two dangers constantly threaten the world: order and disorder”*…
After two days of posts on the state of our civil society, a palette-cleanser: Jordana Cepelewicz with a possibly-consoling reminder…
When he died in 1930 at just 26 years old, Frank Ramsey [see here] had already made transformative contributions to philosophy, economics and mathematics. John Maynard Keynes sought his insights; Ludwig Wittgenstein admired him and considered him a close friend. In his lifetime, Ramsey published only eight pages on pure math: the beginning of a paper about a problem in logic. But in that work, he proved a theorem that ultimately led to a whole new branch of mathematics — what would later be called Ramsey theory.
His theorem stated that if a system is large enough, then no matter how disordered it might be, it’s always bound to exhibit some sort of regular structure. Order inevitably emerges from chaos; patterns are unavoidable. Ramsey theory is the study of when this happens — in sets of numbers, in collections of vertices and edges called graphs, and in other systems. The mathematicians Ronald Graham and Joel Spencer likened it to how you can always pick out patterns among the stars in the night sky…
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… In fact, Ramsey theory isn’t just about inevitable patterns found in graphs. Hidden structure emerges in lists of numbers, strings of beads and even card games. In 2019, for example, mathematicians studied collections of sets that can always be arranged to resemble the petals of a sunflower. That same year, Quanta reported on research into sets of numbers that are guaranteed to contain numerical patterns called polynomial progressions. And last year, mathematicians proved a similar result, about sets of integers that must always include three evenly spaced numbers, called arithmetic progressions.
In its hunt for patterns, Ramsey theory gets to the core of what mathematics is all about: finding beauty and order in the most unexpected places…
Finding order in chaos: “Why Complete Disorder Is Mathematically Impossible,” from @jordanacep in @QuantaMagazine.
* Paul Valery
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As we ponder patterns, we might send paradigm-shaping birthday greetings to a woman who found order and pattern of a different– and world-changing– sort: Rosalind Franklin; she was born on this date in 1920. A biophysicist and X-ray crystallographer, Franklin captured the X-ray diffraction images of DNA that were, in the words of Francis Crick, “the data we actually used” when he and James Watson developed their “double helix” hypothesis for the structure of DNA. Indeed, it was Franklin who argued to Crick and Watson that the backbones of the molecule had to be on the outside (something that neither they nor their competitor in the race to understand DNA, Linus Pauling, had understood). Franklin never received the recognition she deserved for her independent work– her paper was published in Nature after Crick and Watson’s, which barely mentioned her– and she died of cancer four years before Crick, Watson, and their lab director Maurice Wilkins won the Nobel Prize for the discovery.
“Nothing in life is certain except death, taxes and the second law of thermodynamics”*…
The second law of thermodynamics– asserting that the entropy of a system increases with time– is among the most sacred in all of science, but it has always rested on 19th century arguments about probability. As Philip Ball reports, new thinking traces its true source to the flows of quantum information…
In all of physical law, there’s arguably no principle more sacrosanct than the second law of thermodynamics — the notion that entropy, a measure of disorder, will always stay the same or increase. “If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations — then so much the worse for Maxwell’s equations,” wrote the British astrophysicist Arthur Eddington in his 1928 book The Nature of the Physical World. “If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.” No violation of this law has ever been observed, nor is any expected.
But something about the second law troubles physicists. Some are not convinced that we understand it properly or that its foundations are firm. Although it’s called a law, it’s usually regarded as merely probabilistic: It stipulates that the outcome of any process will be the most probable one (which effectively means the outcome is inevitable given the numbers involved).
Yet physicists don’t just want descriptions of what will probably happen. “We like laws of physics to be exact,” said the physicist Chiara Marletto of the University of Oxford. Can the second law be tightened up into more than just a statement of likelihoods?
A number of independent groups appear to have done just that. They may have woven the second law out of the fundamental principles of quantum mechanics — which, some suspect, have directionality and irreversibility built into them at the deepest level. According to this view, the second law comes about not because of classical probabilities but because of quantum effects such as entanglement. It arises from the ways in which quantum systems share information, and from cornerstone quantum principles that decree what is allowed to happen and what is not. In this telling, an increase in entropy is not just the most likely outcome of change. It is a logical consequence of the most fundamental resource that we know of — the quantum resource of information…
Is that most sacrosanct natural laws, second law of thermodynamics, a quantum phenomenon? “Physicists Rewrite the Fundamental Law That Leads to Disorder,” from @philipcball in @QuantaMagazine.
* “Nothing in life is certain except death, taxes and the second law of thermodynamics. All three are processes in which useful or accessible forms of some quantity, such as energy or money, are transformed into useless, inaccessible forms of the same quantity. That is not to say that these three processes don’t have fringe benefits: taxes pay for roads and schools; the second law of thermodynamics drives cars, computers and metabolism; and death, at the very least, opens up tenured faculty positions.” — Seth Lloyd
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As we get down with disorder, we might spare a thought for Francois-Marie Arouet, better known as Voltaire; he died on this date in 1778. The Father of the Age of Reason, he produced works in almost every literary form: plays, poems, novels, essays, and historical and scientific works– more than 2,000 books and pamphlets (and more than 20,000 letters). He popularized Isaac Newton’s work in France by arranging a translation of Principia Mathematica to which he added his own commentary.
A social reformer, Voltaire used satire to criticize the intolerance, religious dogma, and oligopolistic privilege of his day, perhaps nowhere more sardonically than in Candide.
“No structure, even an artificial one, enjoys the process of entropy. It is the ultimate fate of everything, and everything resists it.”*…
A 19th-century thought experiment that motivates physicists– and information scientists– still…
The universe bets on disorder. Imagine, for example, dropping a thimbleful of red dye into a swimming pool. All of those dye molecules are going to slowly spread throughout the water.
Physicists quantify this tendency to spread by counting the number of possible ways the dye molecules can be arranged. There’s one possible state where the molecules are crowded into the thimble. There’s another where, say, the molecules settle in a tidy clump at the pool’s bottom. But there are uncountable billions of permutations where the molecules spread out in different ways throughout the water. If the universe chooses from all the possible states at random, you can bet that it’s going to end up with one of the vast set of disordered possibilities.
Seen in this way, the inexorable rise in entropy, or disorder, as quantified by the second law of thermodynamics, takes on an almost mathematical certainty. So of course physicists are constantly trying to break it.
One almost did. A thought experiment devised by the Scottish physicist James Clerk Maxwell in 1867 stumped scientists for 115 years. And even after a solution was found, physicists have continued to use “Maxwell’s demon” to push the laws of the universe to their limits…
A thorny thought experiment has been turned into a real experiment—one that physicists use to probe the physics of information: “How Maxwell’s Demon Continues to Startle Scientists,” from Jonathan O’Callaghan (@Astro_Jonny)
* Philip K. Dick
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As we reconsider the random, we might send carefully-calculated birthday greetings to Félix Édouard Justin Émile Borel; he was born on this date in 1871. A mathematician (and politician, who served as French Minister of the Navy), he is remembered for his foundational work in measure theory and probability. He published a number of research papers on game theory and was the first to define games of strategy.
But Borel may be best remembered for a thought experiment he introduced in one of his books, proposing that a monkey hitting keys at random on a typewriter keyboard will – with absolute certainty – eventually type every book in France’s Bibliothèque Nationale de France. This is now popularly known as the infinite monkey theorem.
A place for every thing, and everything in its place…
Swiss artist Ursus Wehrli is the epitome of neatness. His new book, The Art of Clean Up, takes everyday scenes of disorder and… well, orders them.
Readers can find more of Wehrli’s “chaos conquered” at Jeannie Huang’s nifty blog Jeannie, Jeannie— and see Wehrli’s tidiness applied to high culture in his Tidying Up Art books…
As we resolve to straighten up and fly right, we might recall that it was on this date in 1993 that that America’s favorite neat freak got his own show, when Cheers spin-off Frasier debuted on NBC. Kelsey Grammar created the Frasier Crane character (in 1984) for what was supposed to be a short-arc as Diane’s boyfriend on Cheers. But the character was such a hit that he became a regular, then anchored his own series for 11 years. Grammar appeared in character as Dr. Crane on the NBC series Wings— and became the only actor ever nominated for Emmys for portraying the same character on three different series.
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