Posts Tagged ‘perspective’
“Reality favors symmetry”*…
Emmy Noether showed that fundamental physical laws are themselves a consequence of simple symmetries. As Shalma Wegsman explains, a century later, her insights continue to shape physics…
In the fall of 1915, the foundations of physics began to crack. Einstein’s new theory of gravity seemed to imply that it should be possible to create and destroy energy, a result that threatened to upend two centuries of thinking in physics.
Einstein’s theory, called general relativity, radically transformed the meaning of space and time. Rather than being fixed backdrops to the events of the universe, space and time were now characters in their own right, able to curve, expand and contract in the presence of matter and energy.
One problem with this shifting space-time is that as it stretches and shrinks, the density of the energy inside it changes. As a consequence, the classical energy conservation law that previously described all of physics didn’t fit this framework. David Hilbert, one of the most prominent mathematicians at the time, quickly identified this issue and set out with his colleague Felix Klein to try to resolve this apparent failure of relativity. After they were stumped, Hilbert passed the problem on to his assistant, the 33-year-old Emmy Noether.
Noether was an assistant in name only. She was already a formidable mathematician when, in early 1915, Hilbert and Klein invited her to join them at the University of Göttingen. But other faculty members objected to hiring a woman, and Noether was blocked from joining the faculty. Regardless, she would spend the next three years prodding the fault line separating physics and mathematics, eventually setting off an earthquake that would shake the foundations of fundamental physics.
In 1918, Noether published the results of her investigations in two landmark theorems. One made sense of conservation laws in small regions of space, a mathematical feat that would later prove important for understanding the symmetries of quantum field theory. The other, now just known as Noether’s theorem, says that behind every conservation law lies a deeper symmetry.
In mathematical terms, a symmetry is something you can do to a system that leaves it unchanged. Consider the act of rotation. If you start with an equilateral triangle, you’ll find that you can rotate it by multiples of 120 degrees without changing how it looks. If you start with a circle, you can rotate it by any angle. These actions without consequences reveal the underlying symmetries of these shapes.
But symmetries go beyond shape. Imagine you do an experiment, then you move 10 meters to the left and do it again. The results of the experiment don’t change, because the laws of physics don’t change from place to place. This is called translation symmetry.
Now wait a few days and repeat your experiment again. The results don’t change, because the laws of physics don’t change as time passes. This is called time-translation symmetry.
Noether started with symmetries like these and explored their mathematical consequences. She worked with established physics using a common mathematical description of a physical system, called a Lagrangian.
This is where Noether’s insight went beyond the symbols on the page. On paper, symmetries seem to have no impact on the physics of the system, since symmetries don’t affect the Lagrangian. But Noether realized that symmetries must be mathematically important, since they constrain how a system can behave. She worked through what this constraint should be, and out of the mathematics of the Lagrangian popped a quantity that can’t change. That quantity corresponds to the physical property that’s conserved. The impact of symmetry had been hiding beneath the equations all along, just out of view.
In the case of translation symmetry, the system’s total momentum should never change. For time-translation symmetry, a system’s total energy is conserved. Noether discovered that conservation laws aren’t fundamental axioms of the universe. Instead, they emerge from deeper symmetries.
The conceptual consequences are hard to overstate. Physicists of the early 20th century were shocked to realize that a system that breaks time-translation symmetry can break energy conservation along with it. We now know that our own universe does this. The cosmos is expanding at an accelerating rate, stretching out the leftover light from the early universe. The process reduces the light’s energy as time passes…
… Noether’s theorem has shaped the quantum world too. In the 1970s, it played a big role in the construction of the Standard Model of particle physics. The symmetries of quantum fields dictate laws that restrict how fundamental particles behave. For instance, a symmetry in the electromagnetic field forces particles to conserve their charge.
The power of Noether’s theorem has inspired physicists to look toward symmetry to discover new physics. Over a century later, Noether’s insights continue to influence the way physicists think…
“How Noether’s Theorem Revolutionized Physics,” from @shalmawegs in @QuantaMagazine.
* Jorge Luis Borges
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As we contemplate cosmology, we might send insightful birthday greetings to the man who “wrote the book” on perspective, Leon Battista Alberti; he was born on this date in 1404. The archetypical Renaissance humanist polymath, Alberti was an author, artist, architect, poet, priest, linguist, philosopher, cartographer, and cryptographer. He collaborated with Toscanelli on the maps used by Columbus on his first voyage, and he published the the first book on cryptography that contained a frequency table.
But he is surely best remembered as the author of the first general treatise– Della Pictura (1434)– on the the laws of perspective, which built on and extended Brunelleschi’s work to describe the approach and technique that established the science of projective geometry… and fueled the progress of painting, sculpture, and architecture from the Greek- and Arabic-influenced formalism of the High Middle Ages to the more naturalistic (and Latinate) styles of Renaissance.
“Nature does not hurry, yet everything is accomplished”*…
Paul Constance on a chain of dedicated scientists who are building data sets on the natural world around us, and how– coupled with emerging new nature apps that enable citizen scientists– they are expanding our ecological attention span into the long now…
Every two weeks from March to November, Chris Halsch walks a ten-mile loop near the Donner Pass, high up in California’s Sierra Nevada, for the sole purpose of counting butterflies.
It is one of five sites at various altitudes that Halsch, a PhD candidate at the University of Nevada, Reno, has been visiting with metronomic regularity for the past five years. At each one he retraces his steps, pausing every so often to jot down species and numbers in a notebook.
Along the way, he sometimes meets recreational birders or hikers who take photographs and use nature apps to identify species for fun. But unlike those random snapshots, Halsch’s notes are a coveted resource for scientists. Once he types them into a spreadsheet, each of his data points adds a new segment to a chain of observations that has been growing without interruption for half a century, in one the world’s longest-lived efforts to monitor butterfly populations. Like a relay runner, Halsch is extending a marathon of sustained attention that began 20 years before he was born.
Multi-decadal time-series of field observations are among the rarest and most valuable artifacts in ecosystem science because they help to overcome a peculiar weakness in our ability to perceive and interpret the natural world. Humans have developed powerful methods for reconstructing events in the distant past, from the birth of a galaxy to mass extinctions in the Devonian. We have built instruments that can parse the present down to the zeptosecond. But when it comes to the modest timescale of our own lifespans, we are like near-sighted moles.
Weren’t there more birds in this meadow when we were kids?
Doesn’t it seem like spring is a lot rainier than it used to be?
Are you sure it’s safe to eat fish from this river?
Our answers to these types of questions are notoriously unreliable. Think of the tendency to describe a single weather event as evidence for (or against) climate change, or the panic caused by invasive zebra mussels that, 20 years later, turns out to have been misplaced. Perceptions are distorted by selective memories, cognitive biases, political agendas and shifting baseline syndrome—the propensity of each generation to gradually forget past environmental conditions and accept present ones as normal. In an essay published in 01990, the zoologist John J. Magnuson wrote that this temporal myopia can trap us in the “invisible present,” a space where we fail to see slow changes and are unable to interpret effects that lag years behind their causes. “In the absence of the temporal context provided by long-term research, serious misjudgments can occur not only in our attempts to understand and predict change in the world around us, but also in our attempts to manage our environment,” he warned.
Magnuson was echoing a group of mid-century scientists who believed that some of the biggest questions in ecology could only be answered with field observations that were carefully structured and repeated at the same sites for at least two decades. The longer the time-series, the greater likelihood that the invisible present will “melt away,” exposing the complex and often unexpected dynamics of ecosystem change….
[Constance describes a variety of efforts underway…]
… Collectively, these efforts are widening the aperture of our ecological attention, enabling scientists to find and stitch together scattered fragments of temporal data into panoramas that tell a more illuminating story about the interactions that drive change. Unfortunately, the emerging picture is still largely focused on wealthy countries—particularly ones with long histories of field-based science. A map of the International LTER network, an association of 750 field stations that, like their U.S. counterparts, are making long-term observations, shows that more than two thirds are concentrated in Western Europe. Numerous countries in Asia, Africa and Latin America have no stations at all. Moreover, even as scientists like Moran and Grames are exploiting the new wealth of temporal evidence, it is not clear how this research will influence the wider culture, where the blinkered perceptions of the “invisible present” are still pervasive.
The trend that may ultimately overcome both of these limitations is driven, paradoxically, by smartphones. Non-scientists have long been a critical source of field labor for long time-series, most famously for the Audubon Society’s 122-year-old Christmas Bird Count, but also in hundreds of smaller projects that monitor other kinds of flora and fauna. Now, smartphones with powerful cameras and apps such as eBird, iNaturalist, Seek and Picture Insect have enabled millions of casual observers to supplement this pool of dedicated volunteers. Despite the lively debate on whether smartphone usage in the outdoors enhances or interferes with people’s appreciation of nature, one fact is clear: because nature apps automatically time-stamp, geo-reference and store each observation in a robust database, they are generating potential time-series at an unprecedented scale.
In the 20 years since the Cornell Lab of Ornithology launched eBird, the app has amassed more than one billion observations by 700,000 birders from every country in the world. Carrie Seltzer, who heads stakeholder engagement at iNaturalist, says that more than 2.4 million people have made observations on the app, at a rate that has grown between 50 percent and 100 percent per year since 02012… This torrent of raw field data vastly exceeds what even well-funded researchers could ever dream of gathering with traditional methods…
Understanding the world around us: “Peering into The Invisible Present,” from @presentbias and @longnow. Eminently worth reading in full– then browsing the other remarkable pieces available on the Long Now website.
* Lao Tzu
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As we take the long view, we might send insightful birthday greetings to a man who encourages us to see in different ways, M. C. Escher; he was born on this date in 1898. A graphic artist inspired by mathematics, he created woodcuts, lithographs, and mezzotints, that— while largely ignored by the art world in his lifetime, have become widely celebrated. He’s been recognized as an heir to Parmigianino, Hogarth, and Piranesi.
His work features mathematical objects and operations including impossible objects, explorations of infinity, reflection, symmetry, perspective, truncated and stellated polyhedra, hyperbolic geometry, and tessellations. And though Escher believed he had no mathematical ability, he interacted with the mathematicians George Pólya, Roger Penrose, and Donald Coxeter, and the crystallographer Friedrich Haag, and conducted his own research into tessellation.
For more on (and more examples of) Escher’s work, see here.
“Make visible what, without you, might perhaps never have been seen”*…
Lawrence Weschler is no stranger to controversy. In 2000 he published an article in The New Yorker, recounting a theory that David Hockey had shared with him, that ignited a fire storm in the art world– and that burns (or at least smolders) to this day.
And he’s at it again…
A few months back—in the lee of the Rijksmuseum’s epic Vermeer show and Ren’s [Wechsler’s] controversial Atlantic magazine article (featured in our Issue #39) on Vermeer and Benjamin Binstock’s intriguing contention that eight of the thirty-four paintings conventionally attributed to the Delft master were in fact by his daughter Maria—the eminent curator Helen Molesworth invited Ren and Claudia Swan (the historian behind Rarities of These Lands and other classics on the Dutch Golden Age) to engage in a conversation evaluating both that show and Binstock’s thesis for an episode of her ongoing Dialogues podcast, out of the David Zwirner Gallery. And indeed, that half-hour episode dropped yesterday—and we thought you might enjoy hearing it here. Spoiler alert: Two of the top people in the field seem decidedly open to Binstock’s theory…
Fascinating: “Vermeer’s Daughter?”
* Robert Bresson
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As we argue over attribution, we might send grateful birthday greetings to Leon Battista Alberti; he was born on this date in 1404. The archetypical Renaissance humanist polymath, Alberti was an author, artist, architect, poet, priest, linguist, philosopher, cartographer, and cryptographer. Indeed, with Johannes Trithemius, he is considered the father of cryptography. And he collaborated with Toscanelli on the maps used by Columbus on his first voyage.
But he is surely best remembered as the man who “wrote the book” on perspective: he authored of the first general treatise– De Pictura (1434)– on the the laws of perspective, which built on and extended Brunelleschi’s work to describe the approach and technique that established the science of projective geometry… and fueled the progress of painting, sculpture, and architecture from the Greek- and Arabic-influenced formalism of the High Middle Ages to the more naturalistic (and Latinate) styles of Renaissance.
“People overestimate what they can do in one year and underestimate what they can do in 10 years”*…
This is especially true, argue Sam Butler-Sloss and Kingsmill Bond of the Rocky Mountain Institute, when it comes to assessing our progress in addressing the challenges of climate change with renewable energy solutions…
The renewable revolution is advancing at remarkable speed. In fact, the speed of the renewable revolution has defied many leading energy commentators who have continuously underestimated its true trajectory. They have suffered from what statisticians call a systematic bias, that is, an error that consistently skews in one direction. Noise, or a random error, is inherent to forecasting; bias, however, requires a deeper explanation.
So why do so many intelligent people undersell the pace and dynamism of the renewable revolution? Leaving aside the inherent bias of those seeking to prop up the fossil fuel system in order to enjoy the largesse of its annual $2 trillion in rents, we identify eight deadly sins of the energy transition.
Whether intentional or unwitting, these eight general errors of perspective are holding back understanding, wasting time and capital, and fueling unproductive climate pessimism…
The renewable revolution is plainly gaining speed and impact. Read on to learn why are so many analysts so wrong about the pace and scale of innovation: “The Eight Deadly Sins of Analyzing the Energy Transition,” from @SamButl3r and @KingsmillBond at @RockyMtnInst. (TotH to friend MZ)
See also: “When Idiot Savants Do Climate Economics.”
* Bill Gates
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As we contemplate compounding, we might recall that it was on this date in 1896 that Nikola Tesla and Westinghouse Electric achieved the first long-distance transmission of hydroelectricity: from the Niagara Falls Power Company to Buffalo, N.Y., 26 miles away.
“I was a peripheral visionary. I could see the future, but only way off to the side.”*…
As Niels Bohr said, “prediciton is hard, especially about the future.” Still, we can try…
While the future cannot be predicted with certainty, present understanding in various scientific fields allows for the prediction of some far-future events, if only in the broadest outline. These fields include astrophysics, which studies how planets and stars form, interact, and die; particle physics, which has revealed how matter behaves at the smallest scales; evolutionary biology, which studies how life evolves over time; plate tectonics, which shows how continents shift over millennia; and sociology, which examines how human societies and cultures evolve.
The far future begins after the current millennium comes to an end, starting with the 4th millennium in 3001 CE, and continues until the furthest reaches of future time. These timelines include alternative future events that address unresolved scientific questions, such as whether humans will become extinct, whether the Earth survives when the Sun expands to become a red giant and whether proton decay will be the eventual end of all matter in the Universe…
A new pole star, the end of Niagara Falls, the wearing away of the Canadian Rockies– and these are just highlights from the first 50-60 million years. Read on for an extraordinary outline of what current science suggests is in store over the long haul: “Timeline of the far future,” a remarkable Wikipedia page.
Related pages: List of future astronomical events, Far future in fiction, and Far future in religion.
* Steven Wright
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As we take the long view, we might send grateful birthday greetings to the man who “wrote the book” on perspective (a capacity analogically handy in the endeavor featured above), Leon Battista Alberti; he was born on this date in 1404. The archetypical Renaissance humanist polymath, Alberti was an author, artist, architect, poet, priest, linguist, philosopher, cartographer, and cryptographer. He collaborated with Toscanelli on the maps used by Columbus on his first voyage, and he published the the first book on cryptography that contained a frequency table.
But he is surely best remembered as the author of the first general treatise– De Pictura (1434)– on the the laws of perspective, which built on and extended Brunelleschi’s work to describe the approach and technique that established the science of projective geometry… and fueled the progress of painting, sculpture, and architecture from the Greek- and Arabic-influenced formalism of the High Middle Ages to the more naturalistic (and Latinate) styles of Renaissance.
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