The seemingly random digits known as prime numbers are not nearly as scattershot as previously thought. A new analysis by Princeton University researchers has uncovered patterns in primes that are similar to those found in the positions of atoms inside certain crystal-like materials.
The researchers found a surprising similarity between the sequence of primes over long stretches of the number line and the pattern that results from shining X-rays on a material to reveal the inner arrangement of its atoms. The analysis could lead to predicting primes with high accuracy, said the researchers. The study was published Sept. 5 in the Journal of Statistical Mechanics: Theory and Experiment.
“There is much more order in prime numbers than ever previously discovered,” said Salvatore Torquato, Princeton’s Lewis Bernard Professor of Natural Sciences, professor of chemistry and the Princeton Institute for the Science and Technology of Materials. “We showed that the primes behave almost like a crystal or, more precisely, similar to a crystal-like material called a ‘quasicrystal.’”
Primes are numbers that can only be divided by 1 and themselves. Very large primes are the building blocks of many cryptography systems. Primes appear to be sprinkled randomly along the number line, although mathematicians have discerned some order. The first few primes are 2, 3, 5, 7 and 11, becoming more sporadic higher in the number line.
Torquato and his colleagues have found that that, when considered over large swaths of the number line, prime numbers are more ordered than previously believed, falling within the class of patterns known as “hyperuniformity.”
Hyperuniform materials have special order at large distances and include crystals, quasicrystals and special disordered systems. Hyperuniformity is found in the arrangement of cone cells in bird eyes, in certain rare meteorites, and in the large-scale structure of the universe. [Continue reading…]
Surprising hidden order unites prime numbers and crystal-like materials
Science, and government scientists, suffer under Trump
In an administration skilled in myth making, science suffers.
Consider findings from the Union of Concerned Scientists, a non-profit advocacy organization that surveyed thousands of scientific experts in the federal government. The first line of its new report paints a dismal picture of the place science holds under President Trump:
“A year and a half into the Trump administration, its record on science policy in several agencies and departments is abysmal.”
There are a couple of bright spots in the administration, however, so all is not lost. But responses from 4,200 scientists in 16 agencies present an alarming record of “studies cancelled, public-facing information altered or removed from websites, and scientists coming under political pressure.” Self-censorship, staffing cuts, low morale and management issues make the problem worse.
“At several federal agencies and departments, scientists reported that political and capacity pressures are compromising their ability to protect public health and the environment,” said Jacob Carter, a co-author of the report and a research scientist with the Union’s Center for Science and Democracy. “In many of the critical science agencies—especially the agencies that handle environmental regulation—scientists reported that they are having trouble doing their jobs because of political interference, staff reductions and a lack of qualified leadership.” [Continue reading…]
The nastiest feud in science
While the majority of her peers embraced the Chicxulub asteroid as the cause of the [dinosaurs’] extinction, [Gerta] Keller [a 73-year-old paleontology and geology professor at Princeton] remained a maligned and, until recently, lonely voice contesting it. She argues that the mass extinction was caused not by a wrong-place-wrong-time asteroid collision but by a series of colossal volcanic eruptions in a part of western India known as the Deccan Traps—a theory that was first proposed in 1978 and then abandoned by all but a small number of scientists. Her research, undertaken with specialists around the world and featured in leading scientific journals, has forced other scientists to take a second look at their data. “Gerta uncovered many things through the years that just don’t sit with the nice, simple impact story that Alvarez put together,” Andrew Kerr, a geochemist at Cardiff University, told me. “She’s made people think about a previously near-uniformly accepted model.”
Keller’s resistance has put her at the core of one of the most rancorous and longest-running controversies in science. “It’s like the Thirty Years’ War,” says Kirk Johnson, the director of the Smithsonian’s National Museum of Natural History. Impacters’ case-closed confidence belies decades of vicious infighting, with the two sides trading accusations of slander, sabotage, threats, discrimination, spurious data, and attempts to torpedo careers. “I’ve never come across anything that’s been so acrimonious,” Kerr says. “I’m almost speechless because of it.” Keller keeps a running list of insults that other scientists have hurled at her, either behind her back or to her face. She says she’s been called a “bitch” and “the most dangerous woman in the world,” who “should be stoned and burned at the stake.”
Understanding the cause of the mass extinction is not an esoteric academic endeavor. Dinosaurs are what paleontologists call “charismatic megafauna”: sexy, sympathetic beasts whose obliteration transfixes pretty much anyone with a pulse. The nature of their downfall, after 135 million years of good living, might offer clues for how we can prevent, or at least delay, our own end. “Without meaning to sound pessimistic,” the geophysicist Vincent Courtillot writes in his book Evolutionary Catastrophes, “I believe the ancient catastrophes whose traces geologists are now exhuming are worthy of our attention, not just for the sake of our culture or our understanding of the zigzaggy path that led to the emergence of our own species, but quite practically to understand how to keep from becoming extinct ourselves.” [Continue reading…]
Thinking about emergence
If you construct a Lego model of the University of London’s Senate House – the building that inspired the Ministry of Truth in George Orwell’s novel Nineteen Eighty-Four – the Lego blocks themselves remain unchanged. Take apart the structure, reassemble the blocks in the shape of the Great Pyramid of Giza or the Eiffel Tower, and the shape, weight and colour of the blocks stay the same.
This approach, applied to the world at large, is known as atomism. It holds that everything in nature is made up of tiny, immutable parts. What we perceive as change and flux are just cogs turning in the machine of the Universe – a huge but ultimately comprehensible mechanism that is governed by universal laws and composed of smaller units. Trying to identify these units has been the focus of science and technology for centuries. Lab experiments pick out the constituents of systems and processes; factories assemble goods from parts composed of even smaller parts; and the Standard Model tells us about the fundamental entities of modern physics.
But when phenomena don’t conform to this compositional model, we find them hard to understand. Take something as simple as a smiling baby: it is difficult, perhaps impossible, to explain a baby’s beaming smile by looking at the behaviour of the constituent atoms of the child in question, let alone in terms of its subatomic particles such as gluons, neutrinos and electrons. It would be better to resort to developmental psychology, or even a narrative account (‘The father smiled at the baby, and the baby smiled back’). Perhaps a kind of fundamental transformation has occurred, producing some new feature or object that can’t be reduced to its parts.
The notion of emergence can help us to see what’s going on here. While atomism is all about burrowing down to basic building blocks, emergence looks upward and outward, to ask whether strange new phenomena might pop out when things get sufficiently large or complex. [Continue reading…]
Anthropocene vs Meghalayan: Why geologists are fighting over whether humans are a force of nature
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By Mark Maslin, UCL and Simon Lewis, UCL
The Earth discovered it was living in a new slice of time called the Meghalayan Age in July 2018. But the announcement by the International Union of Geological Sciences (IUGS) confused and angered scientists all around the world.
In the 21st century, it claimed, we are still officially living in the Holocene Epoch, the warm period that began 11,700 years ago after the last ice age. But not only that: within the Holocene, we are also living in this new age – the Meghalayan – and it began 4,250 years ago.
Over the past decade, more and more scientists have agreed that human impact on Earth is so significant that we have entered a completely new geological phase, called the Anthropocene, including a group convened to agree a formal definition. The world of science was expecting an official announcement acknowledging this Anthropocene Epoch, not the unheard-of Meghalayan Age. It was so unexpected it turned up zero hits on Google when first reported. So what’s going on?
Science and the Loss of Confidence Project
In September 2016, the psychologist Dana Carney came forward with a confession: She no longer believed the findings of a high-profile study she co-authored in 2010 to be true. The study was about “power-posing” — a theory suggesting that powerful stances can psychologically and physiologically help one when under high-pressure situations. Carney’s co-author, Amy Cuddy, a psychologist at Harvard University, had earned much fame from power poses, and her 2012 TED talk on the topic is the second most watched talk of all time.
Carney, now based at the University of California, Berkeley, had, however, changed her mind. “I do not believe that ‘power pose’ effects are real,” she wrote on her website in 2016. The reason, she added, was that “since early 2015 the evidence has been mounting suggesting there is unlikely any embodied effect of nonverbal expansiveness.” Other researchers, it turned out, could not replicate the power pose results, and withering scrutiny of the Carney and Cuddy study by fellow scientists mounted.
Carney’s assertions and Cuddy’s responses were widely covered in the media. (Earlier this year, Forbes reported that Cuddy had successfully refuted criticism of the power-posing study.) And despite her own eventual refutation of the findings, Carney did not believe the original paper warranted a full retraction, because it “was conducted in good faith based on phenomena thought to be true at the time,” she told the research integrity blog Retraction Watch. [Continue reading…]