Posts Tagged ‘mobius’
“I think it’s much more interesting to live not knowing than to have answers which might be wrong… when we know that we actually do live in uncertainty, then we ought to admit it; it is of great value to realize that we do not know the answers to different questions.”*…
The immense complexity of the climate makes it impossible to model accurately. Instead, David Stainforth argues, we must use uncertainty to our advantage…
Today’s complex climate models aren’t equivalent to reality. In fact, computer models of Earth are very different to reality – particularly on regional, national and local scales. They don’t represent many aspects of the physical processes that we know are important for climate change, which means we can’t rely on them to provide detailed local predictions. This is a concern because human-induced climate change is all about our understanding of the future. This understanding empowers us. It enables us to make informed decisions by telling us about the consequences of our actions. It helps us consider what the future will be like if we act strongly to reduce greenhouse gas emissions, if we act only half-heartedly, or if we take no action at all. Such information enables us to assess the level of investment that we believe is worthwhile as individuals, communities and nations. It enables us to balance action on climate change against other demands on our finances such as health, education, security and culture.
For many of us, these issues are approached through the lens of personal experience and personal cares: we want to know what changes to expect where we live, in the places we know, and in the regions where we have our roots. We want local climate predictions – predictions conditioned on the choices that our societies make.
So, where do we get them? Well, nowadays most of these predictions originate from complicated computer models of the climate system – so-called Earth System Models (ESMs). These models are ubiquitous in climate change science. And for good reason. The increasing greenhouse gases in the atmosphere are driving the climate system into a never-before-seen state. That means the past cannot be a good guide to the future, and predictions based simply on historic observations can’t be reliable: the information isn’t in the observational data, so no amount of processing can extract it. Climate prediction is therefore about our understanding of the physical processes of climate, not about data-processing. And since there are so many physical processes involved – everything from the movement of heat and moisture around the atmosphere to the interaction of oceans with ice-sheets – this naturally leads to the use of computer models.
But there’s a problem: models aren’t equivalent to reality.
So, what can we do? One option is to make the models better. Make them more detailed and more complicated. That, though, raises an important question: when is a model sufficiently realistic to predict something as complex as climate change? When will the models be good enough? We don’t have an answer to this question. Indeed, scientists have hardly begun to study this problem, and some argue that these models might never be sufficiently accurate to make multi-decadal, local climate predictions.
Nevertheless, changing the way we use ESMs could provide a different and better way to generate the local climate information we seek. Doing so involves embracing uncertainty as a key part of our knowledge about climate change. It involves stepping back and accepting that what we want is not precise predictions but robust predictions, even if robustness involves accepting large uncertainties in what we can know about the future…
[Stainforth explains the current state of modeling, efforts to make them better, and the problems those efforts encounter…]
… focusing on high-resolution modelling is dangerous not only because we have no answer to the question of when a model is sufficiently realistic. Investing in this approach also means we don’t have the capacity to explore the uncertainties, which inevitably encourages overconfidence in the predictions that models make. This is a particular concern because Earth System Models are increasingly being used to guide decisions and investments across our societies. Overconfidence in model-based predictions therefore risks encouraging bad decisions: decisions that are optimised for the futures in our models rather than what we understand about the range of possible futures for reality.
By contrast, perturbed physics ensembles and storyline approaches focus on exploring and describing our uncertainties. Placing uncertainty front and centre is important. When we make an investment or a gamble, we don’t just base it on what we think is the most likely result. We consider the range of outcomes that we think are possible – ideally these are characterised by probabilities, although this isn’t always achievable. It’s the same with climate change. We should not only make plans based solely on our best estimate of what might happen. We should also consider the range of plausible outcomes we foresee. Our knowledge of uncertainty is also part of what we know about climate change. We should embrace this knowledge, expand it and use it.
If we understand the uncertainties well, we can bring our values to bear on the risks we are willing to take. Uncertainty therefore needs to be at the core of adaptation planning while also being the lens through which we judge the value of climate policy and the energy transition. In my view, climate researchers and modellers wanting to support society should focus on understanding, characterising and quantifying uncertainty, and avoid the trap of seeking climate models that make reliable predictions. They may well never exist…
A more practical approach to preparing for climate change: “The model of catastrophe,” from @aeon.co
* Richard Feynman
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As we preference plausibility (over predictability), we might send never-ending birthday greetings to August Möbius; he was born on this date in 1790. An astronomer and mathematician, he studied under mathematician Carl Friedrich Gauss while Gauss was the director of the Göttingen Observatory. From there, he went on to study with Carl Gauss’s instructor, Johann Pfaff, at the University of Halle, where he completed his doctoral thesis The occultation of fixed stars in 1815. In 1816, he became Extraordinary Professor in the “chair of astronomy and higher mechanics” at the University of Leipzig, where he remained for the rest of his career. Möbius made many contributions to both astronomy and the math that underlay it: he was among the first to conceive the possibility of geometry in more than three dimensions; he introduced homogeneous coordinates into projective geometry; and he pioneered the barycentric coordinate system… all parts of the intellectual foundation of the complex system modeling described above.
But while he was an influential scholar and professor, he is best remembered for his creation of the “Möbius strip.”
“The ultimate hidden truth of the world is that it is something we make and could just as easily make differently”*…
As a new collection of his writing is published, Rebecca Solnit remembers her friend David Graeber, the late activist and anarchist who believed ordinary people have the power to change the world…
David Graeber was a joyful, celebratory person. An enthusiast, voluble, on fire with the possibilities in the ideas and ideologies he wrestled with. Every time we met – from New Haven in the early 00s to London a few years before his death in 2020 – he was essentially the same: beaming, rumpled, with a restless energy that seemed to echo the constant motion of his mind, words tumbling out as though they were, in their unstoppable abundance, overflowing. But he was also much respected in activist circles for being a good listener, and his radical egalitarianism was borne out in how he related to the people around him.
He was always an anthropologist. After doing fieldwork among traditional peoples in Madagascar, he just never stopped, but he turned his focus to his own society. Essays such as Dead Zones of the Imagination: On Violence, Bureaucracy, and ‘Interpretive Labor’ and his book Bullshit Jobs came from using the equipment of an anthropologist on stuff usually regarded as boring, or not regarded at all – the function and impact of bureaucracy. His 2011 bestseller on debt reminded us that money and finance are among the social arrangements that could be rearranged for the better.
He insisted, again and again, that industrialised Euro-American civilisation was, like other societies past and present, only one way of doing things among countless options. He cited times when societies rejected agriculture or technology or social hierarchy, when social groups chose what has often been dismissed as primitive because it was more free. And he rejected all the linear narratives that present contemporary human beings as declining from primordial innocence or ascending from primitive barbarism. He offered, in place of a single narrative, many versions and variations; a vision of societies as ongoing experiments, and human beings as endlessly creative. That variety was a source of hope for him, a basis for his recurrent insistence that it doesn’t have to be this way.
As Marcus Rediker wrote in his review of David’s posthumous book Pirate Enlightenment, “Everything Graeber wrote was simultaneously a genealogy of the present and an account of what a just society might look like.” He was concerned about inequality of all kinds, including gender inequality in this society and others, and the violence that enforces inequality and unfreedom, as well as how they might be delegitimised and where and when societies might have escaped them. He focused, in short, on freedom and its impediments…
…
… The way that, as he wrote, “The ultimate hidden truth of the world is that it is something we make and could just as easily make differently.” If you truly believe that, if you perceive a world that is constructed according to certain assumptions and values, then you see that it can be changed, not least by changing those assumptions and values.
We have to recognise that ideas are tools that we wield – and with them, some power. David wanted to put these tools in everyone’s hands, or remind them that they are already there. Which is part of why he worked hard at – and succeeded in – writing in a style that wasn’t always simple but was always as clear and accessible as possible, given the material. Egalitarianism is a prose style, too. Our mutual friend the writer, film-maker, and debt abolitionist Astra Taylor texted him: “Re-reading Debt. You are such a damn good writer. A rare skill among lefties.” He texted back that August, a month before his demise: “Why thanks! Well at least I take care to do so – I call it ‘being nice to the reader,’ which is an extension of the politics, in a sense.”
In order to believe that people can govern themselves in the absence of coercive institutions and hierarchies, anarchists must have great faith in ordinary people, and David did. A sentence Lyndsey Stonebridge wrote about Hannah Arendt could apply equally well to him: “To fixate on her exceptional mind is to miss something that is important about her lessons in thinking: thinking is ordinary, she teaches; that is its secret power.”…
An edited extract from Solnit’s foreword to The Ultimate Hidden Truth of the World by David Graeber: “‘It does not have to be this way’- the radical optimism of David Graeber,” from @RebeccaSolnit in @guardian.
* David Graeber
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As we promote possibility (and remember that on this date in 1973 then-President Richard Nixon averred in a speech that “I am not a crook”), we might send never-ending birthday greetings to August Möbius; he was born on this date in 1790. An astronomer and mathematician, he studied under mathematician Carl Friedrich Gauss while Gauss was the director of the Göttingen Observatory. From there, he went on to study with Carl Gauss’s instructor, Johann Pfaff, at the University of Halle, where he completed his doctoral thesis The occultation of fixed stars in 1815. In 1816, he became Extraordinary Professor in the “chair of astronomy and higher mechanics” at the University of Leipzig, where he remained for the rest of his career.
While he was an influential professor, he is best remembered for his creation of the “Möbius strip.”
“Reality is merely an illusion, albeit a very persistent one”*…
To look for the strange wave-like properties of quantum particles, physicists hurtle them through a long tunnel-like instrument known as an interferometer
Magnify a speck of dirt a thousand times, and suddenly it no longer seems to play by the same rules. Its outline, for example, won’t look well-defined most of the time and will resemble a diffuse, sprawling cloud. That’s the bizarre realm of quantum mechanics. “In some books, you’ll find they say a particle is in various places at once,” says physicist Markus Arndt of the University of Vienna in Austria. “Whether that really happens is a matter of interpretation.”
Another way of putting it: Quantum particles sometimes act like waves, spread out in space. They can slosh into each other and even back onto themselves. But if you poke at this wave-like object with certain instruments, or if the object interacts in specific ways with nearby particles, it loses its wavelike properties and starts acting like a discrete point—a particle. Physicists have observed atoms, electrons, and other minutiae transitioning between wave-like and particle-like states for decades.
But at what size do quantum effects no longer apply? How big can something be and still behave like both a particle and a wave? Physicists have struggled to answer that question because the experiments have been nearly impossible to design.
Now, Arndt and his team have circumvented those challenges and observed quantum wave-like properties in the largest objects to date—molecules composed of 2,000 atoms, the size of some proteins. The size of these molecules beats the previous record by two and a half times. To see this, they injected the molecules into a 5-meter-long tube. When the particles hit a target at the end, they didn’t just land as randomly scattered points. Instead, they formed an interference pattern, a striped pattern of dark and light stripes that suggests waves colliding and combining with each other…
One possibility physicists are exploring is that quantum mechanics might in fact apply at all scales. “You and I, while we sit and talk, do not feel quantum,” says Arndt. We seem to have distinct outlines and do not crash and combine with each other like waves in a pond. “The question is, why does the world look so normal when quantum mechanics is so weird?”…
A record-breaking experiment shows an enormous molecule is also both a particle and a wave—and that quantum effects don’t only apply at tiny scales: “Even Huge Molecules Follow the Quantum World’s Bizarre Rules.”
Read the paper published in Nature Physics by Arndt and his team here.
* Albert Einstein
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As we dwell on duality, we might spare a thought for August Ferdinand Möbius; he died on this date in 1868. A German mathematician and theoretical astronomer, he is best remembered as a topologist, more specifically for his discovery of the Möbius strip (a two-dimensional surface with only one side… or more precisely, a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space).
“The cyclical rebirth of caste in America is a recurring racial nightmare”*…
Dorothy and Lillian Gish and D.W. Griffith at the White House, 1922. Library of Congress
The year 1915 marked the fiftieth anniversary of the end of the Civil War. Monuments to Confederate and Union heroes were being dedicated all over the country. Woodrow Wilson, a fan of Jim Crow laws, was president. He had allowed federal workplaces to segregate again.
Enter Thomas Dixon Jr., Wilson’s classmate from Johns Hopkins. A film had just been made of Dixon’s second novel, “the true story” of the South under Reconstruction. Would the president, he wondered, be interested in viewing it? (He would.)
“History written with lightning,” Wilson declared of The Clansman, the second film ever to be screened in the White House. It was an endorsement guaranteed to head off resistance from town censor boards charged with shutting down entertainment deemed unsuitable or incendiary to the public…
The Clansman was a silent movie with title cards. It depicted whites as victims and blacks as villains. Benevolent former masters were denied votes and subjugated by newly freed blacks taking over the country. In an early scene, black legislators sit at desks, shoeless and drunk, too busy stuffing their faces with fried chicken to work. The title card read: “An historical facsimile of the State House of Representatives of South Carolina in 1870.” South Carolina had been the first state to elect a majority-black legislature and that the card implied that the apish behavior depicted was historically accurate, too.
In a later scene, the white heroine (played by Lillian Gish) is threatened by a black man unable to contain his urge to “mongrelize” the white race. Before she is ravaged, a savior army rides in: The Ku Klux Klan. The title-card copy comes straight from the president’s five-volume History of the American People, published in 1902:
More of this sad story, and its aftermath, at “Hatred Endorsed by a President.”
The New Jim Crow: Mass Incarceration in the Age of Colorblindness
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As we ruminate on recurrence, we might send never-ending birthday greetings to August Ferdinand Möbius; he was born on this date in 1790. A German mathematician and theoretical astronomer, he is best remembered as a topologist, more specifically for his discovery of the Möbius strip (a two-dimensional surface with only one side… or more precisely, a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space). See ““It might help to think of the universe as a rubber sheet, or perhaps not.”
“It might help to think of the universe as a rubber sheet, or perhaps not”*…
You have most likely encountered one-sided objects hundreds of times in your daily life – like the universal symbol for recycling, found printed on the backs of aluminum cans and plastic bottles.
This mathematical object is called a Mobius strip. It has fascinated environmentalists, artists, engineers, mathematicians and many others ever since its discovery in 1858 by August Möbius, a German mathematician who died 150 years ago, on Sept. 26, 1868.
Möbius discovered the one-sided strip in 1858 while serving as the chair of astronomy and higher mechanics at the University of Leipzig. (Another mathematician named Listing actually described it a few months earlier, but did not publish his work until 1861. Indeed, it had already appeared in Roman mosaics from the third century CE.)…
The discovery of the Möbius strip in the mid-19th century launched a brand new field of mathematics: topology: “The Mathematical Madness of Möbius Strips and Other One-Sided Objects.”
Hogfather
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As we return from whence we came, we might wish a Joyeux Anniversaire to Denis Diderot, contributor to and the chief editor of the Encyclopédie (“All things must be examined, debated, investigated without exception and without regard for anyone’s feelings.”)– and thus towering figure in the Enlightenment; he was born on this date in 1713. Diderot was also a novelist (e.g., Jacques le fataliste et son maître [Jacques the Fatalist and his Master])… and no mean epigramist:
From fanaticism to barbarism is only one step.
We swallow greedily any lie that flatters us, but we sip only little by little at a truth we find bitter.
Man will never be free until the last king is strangled with the entrails of the last priest.
A thing is not proved just because no one has ever questioned it.
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