Author: Sam

How mathematicians still grapple with the issues Einstein confronted

Published by Sam

Albert Einstein released his general theory of relativity at the end of 1915. He should have finished it two years earlier. When scholars look at his notebooks from the period, they see the completed equations, minus just a detail or two. “That really should have been the final theory,” said John Norton, an Einstein expert and a historian of science at the University of Pittsburgh. But Einstein made a critical last-second error that set him on an odyssey of doubt and discovery — one that nearly cost him his greatest scientific achievement. The consequences of his decision continue to reverberate in math and physics today. Here’s the error. General relativity was meant to supplant Newtonian gravity. This meant it had to explain all the same physical phenomena Newton’s equations could, plus other phenomena that Newton’s equations couldn’t. Yet in mid-1913, Einstein convinced himself, incorrectly, that his new theory couldn’t account for scenarios where the force of gravity was weak — scenarios that Newtonian gravity handled well. “In retrospect, this is just a bizarre mistake,” said Norton. …

Questions about exploring outer space

Questions about exploring outer space

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Metallic shrapnel flying faster than bullets; the Space Shuttle smashed to pieces; astronauts killed or ejected into space. The culprit? Space debris – remnants of a Russian satellite blown up by a Russian missile. The one survivor, Ryan Stone, has to find her way back to Earth with oxygen supplies failing and the nearest viable spacecraft hundreds of miles away. Over on Mars, 20 years in the future, an exploration mission from Earth is going wrong. An epic dust storm forces the crew to abandon the planet, leaving behind an astronaut, Mark Watney, who is presumed dead. He has to figure out how to grow food while awaiting rescue. Hollywood knows how to terrify and inspire us about outer space. Movies like Gravity (2013) and The Martian (2015), present space as hostile and unpredictable – spelling danger for any intrepid human who dares to venture outside Earth’s hospitable confines. This is only part of the story, however – the bit with people centre stage. Sure, no one wants to see astronauts killed or stranded in space. And we all …

America’s declining relevance and China’s gains in the South China Sea

America’s declining relevance and China’s gains in the South China Sea

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At a top regional security forum on Saturday, US Defence Secretary Jim Mattis said China’s recent militarisation efforts in the disputed South China Sea were intended to intimidate and coerce regional countries. Mattis told the Shangri-La Dialogue that China’s actions stood in “stark contrast with the openness of [the US] strategy,” and warned of “much larger consequences” if China continued its current approach. As an “initial response”, China’s navy has been disinvited by the US from the upcoming 2018 Rim of the Pacific Exercise, the world’s largest international naval exercise. It is important to understand the context of the current tensions, and the strategic stakes for both China and the US. In recent years, China has sought to bolster its control over the South China Sea, where a number of claimants have overlapping territorial claims with China, including Vietnam, the Philippines and Taiwan. China’s efforts have continued unabated, despite rising tensions and international protests. Just recently, China landed a long-range heavy bomber for the first time on an island in the disputed Paracels, and deployed anti-ship and anti-air missile systems  to its outposts …

Our Time Has Come - Alyssa Ayres

Our Time Has Come – Alyssa Ayres

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How India is Making Its Place in the World Publisher –Oxford University Press     Release Date –Jan 2018   Pages –336    ISBN 978-0-190-49452-0 Over the last 25 years, India’s explosive economic growth has vaulted it into the ranks of the world’s emerging major powers. Long plagued by endemic poverty, India was hamstrung by a burdensome regulatory regime that limited its ability to compete on a global scale until the 1990s. Since then, however, the Indian government has gradually opened up the economy, and the results have been stunning. India’s middle class has grown by leaps and bounds, and the country’s sheer scale—its huge population and $2 trillion economy—means its actions will have a major global impact. From world trade to climate change to democratization, India now matters. While it is clearly on the path to becoming a great power, India has not abandoned all of its past policies: its economy remains relatively protectionist, and it still struggles with the legacy of its longstanding foreign policy doctrine of nonalignment. India’s vibrant democracy encompasses a vast array …

Finding links between the Standard Model of particle physics and the octonions

Finding links between the Standard Model of particle physics and the octonions

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In 2014, a graduate student at the University of Waterloo, Canada, named Cohl Furey rented a car and drove six hours south to Pennsylvania State University, eager to talk to a physics professor there named Murat Günaydin. Furey had figured out how to build on a finding of Günaydin’s from 40 years earlier — a largely forgotten result that supported a powerful suspicion about fundamental physics and its relationship to pure math. The suspicion, harbored by many physicists and mathematicians over the decades but rarely actively pursued, is that the peculiar panoply of forces and particles that comprise reality spring logically from the properties of eight-dimensional numbers called “octonions.” As numbers go, the familiar real numbers — those found on the number line, like 1, π and -83.777 — just get things started. Real numbers can be paired up in a particular way to form “complex numbers,” first studied in 16th-century Italy, that behave like coordinates on a 2-D plane. Adding, subtracting, multiplying and dividing is like translating and rotating positions around the plane. Complex …

Time to look closer to home

Time to look closer to home

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Immigration is at the heart of the Brexit debate. It’s a large reason why economic arguments have failed to sway voters. Despite warnings of the high economic costs of leaving the EU (warnings supported by a majority of economists), immigration has continued to have a powerful influence – and is perhaps the major reason why the opinion polls have become so close in recent weeks. The immigration debate is quite polarised. On one side, the Remain campaign either ducks the issue or focuses on the benefits that immigration brings to the economy as a whole. On the other side, the Leave camp focuses on its costs and plays into fears (often in a cruel and cynical way) that migrants are putting pressure on public services that are already at breaking point. At least among Labour supporters intending to vote leave, immigration also appears to be a key issue. The need for a more even-handed assessment of the costs and benefits of immigration is sorely needed. While immigration brings undoubted benefits, it also places pressures on particular communities. It also feeds a sense of …

Challenges of keeping the masses moving

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Cities worldwide face the problems and possibilities of “volume”: the stacking and moving of people and things within booming central business districts. We see this especially around mass public transport hubs. As cities grow, they also become more vertical. They are expanding underground through rail corridors and above ground into the tall buildings that shape city skylines. Cities are deep as well as wide. The urban geographer Stephen Graham describes cities as both “vertically stacked” and “vertically sprawled”, laced together by vertical and horizontal transport systems. People flow in large cities is not only about how people move horizontally on rail and road networks into and out of city centres. It also includes vertical transport systems. These are the elevators, escalators and moving sidewalks that commuters use every day to get from the underground to the surface street level. Major transport hubs are where many vertical and horizontal transport systems converge. It’s here that people flows are most dense. But many large cities face the twin challenges of ageing infrastructure and increased volumes of people flowing through transport …

When Milky Way Collided With a Dwarf Galaxy

When Milky Way Collided With a Dwarf Galaxy

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As the Milky Way was growing, taking shape, and minding its own business around 10 billion years ago, it suffered a massive head-on collision with another, smaller galaxy. That cosmic cataclysm changed the Milky Way’s structure forever, shaping the thick spirals that spin out from the supermassive black hole at the galaxy’s core. Two new studies — one published earlier this month, another still under peer review — describe the evidence for this previously unnoticed event. “This is a big step forward,” said Elena D’Onghia, an astrophysicist at the University of Wisconsin who is unaffiliated with the new research. “It’s interesting because we can finally see what the history of the Milky Way is.” To uncover evidence of the collision so many eons later, astronomers have to work like galactic archaeologists, sifting through myriad sources of surviving information to piece together a story consistent with the available evidence. Both research teams relied on data from the European Space Agency’s Gaia space telescope, which has spent years gathering exceptionally rich biographies of millions of stars — …

How parents need to figure out how to talk to their kids without involving religion

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Emily Freeman, a writer in Montana, grew up unaffiliated to a religion — culturally Jewish on her father’s side, a smattering of churchgoing on her mother’s. She and her husband Nathan Freeman talked about not identifying as religious — but they didn’t really discuss how it would affect their parenting. “I think we put it in the big basket of things that we figured we had so much time to think about,” Emily joked. But then they had kids, and the kids came home from their grandfather’s house talking about Bible stories. Nathan acknowledges that this came from a good place, and his father was acting in concern. “He feels like these lessons encapsulate a blueprint for how to move through life. And so of course, why wouldn’t we want our children to have those lessons alongside them as they travel through the world?” But while Nathan and Emily wanted their kids to learn about love and compassion, they didn’t want them to hear Bible stories. When the boys were so young, the certainty of those stories …

The cognitive science of religion

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The cognitive science of religion (CSR) is a scientific approach to the study of religion that combines methods and theory from cognitive, developmental and evolutionary psychology with the sorts of questions that animate anthropologists and historians of religion. Specifically, CSR explores causal explanations of religious phenomena (thoughts, ideas, practices and experiences) across peoples and populations. It asks ‘How does ordinary human psychology inform and constrain religious expression?’ Four current prominent topics in CSR are introduced here: teleological reasoning about the natural world; children’s acquisition of God concepts; ‘minimal counterintuitiveness theory’; and religion and prosociality. Why is religion so common around the world? Why do some religious ideas and practices out-compete others? Why do religious practices take on common characteristics across cultures, and how deeply imbedded in human history and nature is religion? The cognitive science of religion (CSR) tackles questions such as these, attempting to understand the reasons for initial acquisition, recurrence, and continued transmission of religious concepts and behaviour. Psychologists – particularly scientific psychologists – have the training and tools to address such issues, …