“By many measures of human flourishing the state of humanity has been improving,” renowned cognitive scientist Steven Pinker says, a view often in contrast to the highlights of the 24-hour news cycle and the recent “counter-enlightenment” movement of Donald Trump.
“Fewer of us are dying of disease, fewer of us are dying of hunger, more of us are living in democracies, were more affluent, better educated … these are trends that you can’t easily appreciate from the news because they never happen all at once,” he says.
Canadian-American thinker Steven Pinker is the author of Bill Gates’s new favourite book — Enlightenment Now — in which he maintains that historically speaking the world is significantly better than ever before.
But he says the media’s narrow focus on negative anomalies can result in “systematically distorted” views of the world.
Speaking to the ABC’s The World program, Mr Pinker gave his views on Donald Trump, distorted perceptions and the simple arithmetic that proves the world is better than ever before.
Donald Trump’s ‘counter-enlightenment’
“Trumpism is of course part of a larger phenomenon of authoritarian populism. This is a backlash against the values responsible for the progress that we’ve enjoyed. It’s a kind of counter-enlightenment ideology that Trumpism promotes. Namely, instead of universal human wellbeing, it focusses on the glory of the nation, it assumes that nations are in zero-sum competition against each other as opposed to cooperating globally. It ignores the institutions of democracy which were specifically implemented to avoid a charismatic authoritarian leader from wielding power, but subjects him or her to the restraints of a governed system with checks and balances, which Donald Trump seems to think is rather a nuisance to his own ability to voice the greatness of the people directly. So in many ways all of the enlightenment forces we have enjoyed, are being pushed back by Trump. But this is a tension that has been in play for a couple of hundred years. No sooner did the enlightenment happen that a counter-enlightenment grew up to oppose it, and every once in a while it does make reappearances.”
News media can ‘systematically distort’ perceptions
“If your impression of the world is driven by journalism, then as long as various evils haven’t gone to zero there’ll always be enough of them to fill the news. And if journalism isn’t accompanied by a bit of historical context, that is not just what’s bad now but how bad it was in the past, and statistical context, namely how many wars? How many terrorist attacks? What is the rate of homicide? Then our intuitions, since they’re driven by images and narratives and anecdotes, can be systematically distorted by the news unless it’s presented in historical and statistical context.
‘Simple arithmetic’: The world is getting better
“It’s just a simple matter of arithmetic. You can’t look at how much there is right now and say that it is increasing or decreasing until you compare it with how much took place in the past. When you look at how much took place in the past you realise how much worse things were in the 50s, 60s, 70s and 80s. We don’t appreciate it now when we concentrate on the remaining horrors, but there were horrific wars such as the Iran-Iraq war, the Soviets in Afghanistan, the war in Vietnam, the partition of India, the Bangladesh war of independence, the Korean War, which killed far more people than even the brutal wars of today. And if we only focus on the present, we ought to be aware of the suffering that continues to exist, but we can’t take that as evidence that things have gotten worse unless we remember what happened in the past.”
Don’t equate inequality with poverty
“Globally, inequality is decreasing. That is, if you don’t look within a wealthy country like Britain or the United States, but look across the globe either comparing countries or comparing people worldwide. As best as we can tell, inequality is decreasing because so many poor countries are getting richer faster than rich countries are getting richer. Now within the wealthy countries of the anglosphere, inequality is increasing. And although inequality brings with it a number of serious problems such as disproportionate political power to the wealthy. But inequality itself is not a problem. What we have to focus on is the wellbeing of those at the bottom end of the scale, the poor and the lower middle class. And those have not actually been decreasing once you take into account government transfers and benefits. Now this is a reason we shouldn’t take for granted, the important role of government transfers and benefits. It’s one of the reasons why the non-English speaking wealthy democracies tend to have greater equality than the English speaking ones. But we shouldn’t confuse inequality with poverty.”
Eles estão por toda parte. Nos formulários que preenchemos para vagas de emprego. Nas análises de risco a que somos submetidos em contratos com bancos e seguradoras. Nos serviços que solicitamos pelos nossos smartphones. Nas propagandas e nas notícias personalizadas que abarrotam nossas redes sociais. E estão aprofundando o fosso da desigualdade social e colocando em risco as democracias.
Definitivamente, não é com entusiasmo que a americana Cathy O’Neil enxerga a revolução dos algoritmos, sistemas capazes de organizar uma quantidade cada vez mais impressionante de informações disponíveis na internet, o chamado Big Data.
Matemática com formação em Harvard e Massachussetts Institute of Technology (MIT), duas das mais prestigiadas universidades do mundo, ela abandonou em 2012 uma bem-sucedida carreira no mercado financeiro e na cena das startups de tecnologia para estudar o assunto a fundo.
Quatro anos depois, publicou o livro Weapons of Math Destruction (Armas de Destruição em Cálculos, em tradução livre, um trocadilho com a expressão “armas de destruição em massa” em inglês) e tornou-se uma das vozes mais respeitadas no país sobre os efeitos colaterais da economia do Big Data.
A obra é recheada de exemplos de modelos matemáticos atuais que ranqueiam o potencial de seres humanos como estudantes, trabalhadores, criminosos, eleitores e consumidores. Segundo a autora, por trás da aparente imparcialidade desses sistemas, escondem-se critérios nebulosos que agravam injustiças.
É o caso dos seguros de automóveis nos Estados Unidos. Motoristas que nunca tomaram uma multa sequer, mas que tinham restrições de crédito por morarem em bairros pobres, pagavam valores consideravelmente mais altos do que aqueles com facilidade de crédito, mas já condenados por dirigirem embriagados. “Para a seguradora, é um ganha-ganha. Um bom motorista com restrição de crédito representa um risco baixo e um retorno altíssimo”, exemplifica.
Confira abaixo os principais trechos da entrevista:
BBC Brasil – Há séculos pesquisadores analisam dados para entender padrões de comportamento e prever acontecimentos. Qual é novidade trazida pelo Big Data?
Cathy O’Neil – O diferencial do Big Data é a quantidade de dados disponíveis. Há uma montanha gigantesca de dados que se correlacionam e que podem ser garimpados para produzir a chamada “informação incidental”. É incidental no sentido de que uma determinada informação não é fornecida diretamente – é uma informação indireta. É por isso que as pessoas que analisam os dados do Twitter podem descobrir em qual político eu votaria. Ou descobrir se eu sou gay apenas pela análise dos posts que curto no Facebook, mesmo que eu não diga que sou gay.
A questão é que esse processo é cumulativo. Agora que é possível descobrir a orientação sexual de uma pessoa a partir de seu comportamento nas redes sociais, isso não vai ser “desaprendido”. Então, uma das coisas que mais me preocupam é que essas tecnologias só vão ficar melhores com o passar do tempo. Mesmo que as informações venham a ser limitadas – o que eu acho que não vai acontecer – esse acúmulo de conhecimento não vai se perder.
BBC Brasil – O principal alerta do seu livro é de que os algoritmos não são ferramentas neutras e objetivas. Pelo contrário: eles são enviesados pelas visões de mundo de seus programadores e, de forma geral, reforçam preconceitos e prejudicam os mais pobres. O sonho de que a internet pudesse tornar o mundo um lugar melhor acabou?
O’Neil – É verdade que a internet fez do mundo um lugar melhor em alguns contextos. Mas, se colocarmos numa balança os prós e os contras, o saldo é positivo? É difícil dizer. Depende de quem é a pessoa que vai responder. É evidente que há vários problemas. Só que muitos exemplos citados no meu livro, é importante ressaltar, não têm nada a ver com a internet. As prisões feitas pela polícia ou as avaliações de personalidade aplicadas em professores não têm a ver estritamente com a internet. Não há como evitar que isso seja feito, mesmo que as pessoas evitem usar a internet. Mas isso foi alimentado pela tecnologia de Big Data.
Por exemplo: os testes de personalidade em entrevistas de emprego. Antes, as pessoas se candidatavam a uma vaga indo até uma determinada loja que precisava de um funcionário. Mas hoje todo mundo se candidata pela internet. É isso que gera os testes de personalidade. Existe uma quantidade tão grande de pessoas se candidatando a vagas que é necessário haver algum filtro.
BBC Brasil – Qual é o futuro do trabalho sob os algoritmos?
O’Neil – Testes de personalidade e programas que filtram currículos são alguns exemplos de como os algoritmos estão afetando o mundo do trabalho. Isso sem mencionar os algoritmos que ficam vigiando as pessoas enquanto elas trabalham, como é o caso de professores e caminhoneiros. Há um avanço da vigilância. Se as coisas continuarem indo do jeito como estão, isso vai nos transformar em robôs.
Mas eu não quero pensar nisso como um fato inevitável – que os algoritmos vão transformar as pessoas em robôs ou que os robôs vão substituir o trabalho dos seres humanos. Eu não quero admitir isso. Isso é algo que podemos decidir que não vai acontecer. É uma decisão política. Essa ideia de que os robôs vão substituir o trabalho humano é muito fatalista. É preciso reagir e mostrar que essa é uma batalha política. O problema é que estamos tão intimidados pelo avanço dessas tecnologias que sentimos que não há como lutar contra.
BBC Brasil – E no caso das companhias de tecnologia como a Uber? Alguns estudiosos usam o termo “gig economy” (economia de “bicos”) para se referir à organização do trabalho feita por empresas que utilizam algoritmos.
O’Neil – Esse é um ótimo exemplo de como entregamos o poder a essas empresas da gig economy, como se fosse um processo inevitável. Certamente, elas estão se saindo muito bem na tarefa de burlar legislações trabalhistas, mas isso não quer dizer que elas deveriam ter permissão para agir dessa maneira. Essas companhias deveriam pagar melhores remunerações e garantir melhores condições de trabalho.
No entanto, os movimentos que representam os trabalhadores ainda não conseguiram assimilar as mudanças que estão ocorrendo. Mas essa não é uma questão essencialmente algorítmica. O que deveríamos estar perguntando é: como essas pessoas estão sendo tratadas? E, se elas não estão sendo bem tratadas, deveríamos criar leis para garantir isso.
Eu não estou dizendo que os algoritmos não têm nada a ver com isso – eles têm, sim. É uma forma que essas companhias usam para dizer que elas não podem ser consideradas “chefes” desses trabalhadores. A Uber, por exemplo, diz que os motoristas são autônomos e que o algoritmo é o chefe. Esse é um ótimo exemplo de como nós ainda não entendemos o que se entende por “responsabilidade” no mundo dos algoritmos. Essa é uma questão em que venho trabalhando há algum tempo: que pessoas vão ser responsabilizadas pelos erros dos algoritmos?
BBC Brasil – No livro você argumenta que é possível criar algoritmos para o bem – o principal desafio é garantir transparência. Porém, o segredo do sucesso de muitas empresas é justamente manter em segredo o funcionamento dos algoritmos. Como resolver a contradição?
O’Neil – Eu não acho que seja necessária transparência para que um algoritmo seja bom. O que eu preciso saber é se ele funciona bem. Eu preciso de indicadores de que ele funciona bem, mas isso não quer dizer que eu necessite conhecer os códigos de programação desse algoritmo. Os indicadores podem ser de outro tipo – é mais uma questão de auditoria do que de abertura dos códigos.
A melhor maneira de resolver isso é fazer com que os algoritmos sejam auditados por terceiros. Não é recomendável confiar nas próprias empresas que criaram os algoritmos. Precisaria ser um terceiro, com legitimidade, para determinar se elas estão operando de maneira justa – a partir da definição de alguns critérios de justiça – e procedendo dentro da lei.
BBC Brasil – Recentemente, você escreveu um artigo para o jornal New York Times defendendo que a comunidade acadêmica participe mais dessa discussão. As universidades poderiam ser esse terceiro de que você está falando?
O’Neil – Sim, com certeza. Eu defendo que as universidades sejam o espaço para refletir sobre como construir confiabilidade, sobre como requerer informações para determinar se os algoritmos estão funcionando.
BBC Brasil – Quando vieram a público as revelações de Edward Snowden de que o governo americano espionava a vida das pessoas através da internet, muita gente não se surpreendeu. As pessoas parecem dispostas a abrir mão da sua privacidade em nome da eficiência da vida virtual?
O’Neil – Eu acho que só agora estamos percebendo quais são os verdadeiros custos dessa troca. Com dez anos de atraso, estamos percebendo que os serviços gratuitos na internet não são gratuitos de maneira alguma, porque nós fornecemos nossos dados pessoais. Há quem argumente que existe uma troca consentida de dados por serviços, mas ninguém faz essa troca de forma realmente consciente – nós fazemos isso sem prestar muita atenção. Além disso, nunca fica claro para nós o que realmente estamos perdendo.
Mas não é pelo fato de a NSA (sigla em inglês para a Agência de Segurança Nacional) nos espionar que estamos entendendo os custos dessa troca. Isso tem mais a ver com os empregos que nós arrumamos ou deixamos de arrumar. Ou com os benefícios de seguros e de cartões de crédito que nós conseguimos ou deixamos de conseguir. Mas eu gostaria que isso estivesse muito mais claro.
No nível individual ainda hoje, dez anos depois, as pessoas não se dão conta do que está acontecendo. Mas, como sociedade, estamos começando a entender que fomos enganados por essa troca. E vai ser necessário um tempo para saber como alterar os termos desse acordo.
BBC Brasil – O último capítulo do seu livro fala sobre a vitória eleitoral de Donald Trump e avalia como as pesquisas de opinião e as redes sociais influenciaram na corrida à Casa Branca. No ano que vem, as eleições no Brasil devem ser as mais agitadas das últimas três décadas. Que conselho você daria aos brasileiros?
O’Neil – Meu Deus, isso é muito difícil! Está acontecendo em todas as partes do mundo. E eu não sei se isso vai parar, a não ser que fechem o Facebook – o que, a propósito, eu sugiro que façamos. Agora, falando sério: as campanhas políticas na internet devem ser permitidas, mas não deveriam ser permitidos anúncios personalizados, customizados – ou seja, todo mundo deveria receber os mesmos anúncios. Eu sei que essa ainda não é uma proposta realista, mas acho que deveríamos pensar grande porque esse problema é grande. E eu não consigo pensar em outra maneira de resolver essa questão.
É claro que isso seria um elemento de um conjunto maior de medidas porque nada vai impedir pessoas idiotas de acreditar no que elas querem acreditar – e de postar sobre isso. Ou seja, nem sempre é um problema do algoritmo. Às vezes, é um problema das pessoas mesmo. O fenômeno das fake news é um exemplo. Os algoritmos pioram a situação, personalizando as propagandas e amplificando o alcance, porém, mesmo que não existisse o algoritmo do Facebook e que as propagandas políticas fossem proibidas na internet, ainda haveria idiotas disseminando fake news que acabariam viralizando nas redes sociais. E eu não sei o que fazer a respeito disso, a não ser fechar as redes sociais.
Eu tenho três filhos, eles têm 17, 15 e 9 anos. Eles não usam redes sociais porque acham que são bobas e eles não acreditam em nada do que veem nas redes sociais. Na verdade, eles não acreditam em mais nada – o que também não é bom. Mas o lado positivo é que eles estão aprendendo a checar informações por conta própria. Então, eles são consumidores muito mais conscientes do que os da minha geração. Eu tenho 45 anos, a minha geração é a pior. As coisas que eu vi as pessoas da minha idade compartilhando após a eleição de Trump eram ridículas. Pessoas postando ideias sobre como colocar Hilary Clinton na presidência mesmo sabendo que Trump tinha vencido. Foi ridículo. A esperança é ter uma geração de pessoas mais espertas.
By fetishising mathematical models, economists turned economics into a highly paid pseudoscience
04 April, 2016
Alan Jay Levinovitz is an assistant professor of philosophy and religion at James Madison University in Virginia. His most recent book is The Gluten Lie: And Other Myths About What You Eat (2015).Edited by Sam Haselby
What would make economics a better discipline?
Since the 2008 financial crisis, colleges and universities have faced increased pressure to identify essential disciplines, and cut the rest. In 2009, Washington State University announced it would eliminate the department of theatre and dance, the department of community and rural sociology, and the German major – the same year that the University of Louisiana at Lafayette ended its philosophy major. In 2012, Emory University in Atlanta did away with the visual arts department and its journalism programme. The cutbacks aren’t restricted to the humanities: in 2011, the state of Texas announced it would eliminate nearly half of its public undergraduate physics programmes. Even when there’s no downsizing, faculty salaries have been frozen and departmental budgets have shrunk.
But despite the funding crunch, it’s a bull market for academic economists. According to a 2015 sociological study in the Journal of Economic Perspectives, the median salary of economics teachers in 2012 increased to $103,000 – nearly $30,000 more than sociologists. For the top 10 per cent of economists, that figure jumps to $160,000, higher than the next most lucrative academic discipline – engineering. These figures, stress the study’s authors, do not include other sources of income such as consulting fees for banks and hedge funds, which, as many learned from the documentary Inside Job (2010), are often substantial. (Ben Bernanke, a former academic economist and ex-chairman of the Federal Reserve, earns $200,000-$400,000 for a single appearance.)
Unlike engineers and chemists, economists cannot point to concrete objects – cell phones, plastic – to justify the high valuation of their discipline. Nor, in the case of financial economics and macroeconomics, can they point to the predictive power of their theories. Hedge funds employ cutting-edge economists who command princely fees, but routinely underperform index funds. Eight years ago, Warren Buffet made a 10-year, $1 million bet that a portfolio of hedge funds would lose to the S&P 500, and it looks like he’s going to collect. In 1998, a fund that boasted two Nobel Laureates as advisors collapsed, nearly causing a global financial crisis.
The failure of the field to predict the 2008 crisis has also been well-documented. In 2003, for example, only five years before the Great Recession, the Nobel Laureate Robert E Lucas Jr told the American Economic Association that ‘macroeconomics […] has succeeded: its central problem of depression prevention has been solved’. Short-term predictions fair little better – in April 2014, for instance, a survey of 67 economists yielded 100 per cent consensus: interest rates would rise over the next six months. Instead, they fell. A lot.
Nonetheless, surveys indicate that economists see their discipline as ‘the most scientific of the social sciences’. What is the basis of this collective faith, shared by universities, presidents and billionaires? Shouldn’t successful and powerful people be the first to spot the exaggerated worth of a discipline, and the least likely to pay for it?
In the hypothetical worlds of rational markets, where much of economic theory is set, perhaps. But real-world history tells a different story, of mathematical models masquerading as science and a public eager to buy them, mistaking elegant equations for empirical accuracy.
As an extreme example, take the extraordinary success of Evangeline Adams, a turn-of-the-20th-century astrologer whose clients included the president of Prudential Insurance, two presidents of the New York Stock Exchange, the steel magnate Charles M Schwab, and the banker J P Morgan. To understand why titans of finance would consult Adams about the market, it is essential to recall that astrology used to be a technical discipline, requiring reams of astronomical data and mastery of specialised mathematical formulas. ‘An astrologer’ is, in fact, the Oxford English Dictionary’s second definition of ‘mathematician’. For centuries, mapping stars was the job of mathematicians, a job motivated and funded by the widespread belief that star-maps were good guides to earthly affairs. The best astrology required the best astronomy, and the best astronomy was done by mathematicians – exactly the kind of person whose authority might appeal to bankers and financiers.
In fact, when Adams was arrested in 1914 for violating a New York law against astrology, it was mathematics that eventually exonerated her. During the trial, her lawyer Clark L Jordan emphasised mathematics in order to distinguish his client’s practice from superstition, calling astrology ‘a mathematical or exact science’. Adams herself demonstrated this ‘scientific’ method by reading the astrological chart of the judge’s son. The judge was impressed: the plaintiff, he observed, went through a ‘mathematical process to get at her conclusions… I am satisfied that the element of fraud… is absent here.’
Romer compares debates among economists to those between 16th-century advocates of heliocentrism and geocentrism
The enchanting force of mathematics blinded the judge – and Adams’s prestigious clients – to the fact that astrology relies upon a highly unscientific premise, that the position of stars predicts personality traits and human affairs such as the economy. It is this enchanting force that explains the enduring popularity of financial astrology, even today. The historian Caley Horan at the Massachusetts Institute of Technology described to me how computing technology made financial astrology explode in the 1970s and ’80s. ‘Within the world of finance, there’s always a superstitious, quasi-spiritual trend to find meaning in markets,’ said Horan. ‘Technical analysts at big banks, they’re trying to find patterns in past market behaviour, so it’s not a leap for them to go to astrology.’ In 2000, USA Today quoted Robin Griffiths, the chief technical analyst at HSBC, the world’s third largest bank, saying that ‘most astrology stuff doesn’t check out, but some of it does’.
Ultimately, the problem isn’t with worshipping models of the stars, but rather with uncritical worship of the language used to model them, and nowhere is this more prevalent than in economics. The economist Paul Romer at New York University has recently begun calling attention to an issue he dubs ‘mathiness’ – first in the paper ‘Mathiness in the Theory of Economic Growth’ (2015) and then in a series of blog posts. Romer believes that macroeconomics, plagued by mathiness, is failing to progress as a true science should, and compares debates among economists to those between 16th-century advocates of heliocentrism and geocentrism. Mathematics, he acknowledges, can help economists to clarify their thinking and reasoning. But the ubiquity of mathematical theory in economics also has serious downsides: it creates a high barrier to entry for those who want to participate in the professional dialogue, and makes checking someone’s work excessively laborious. Worst of all, it imbues economic theory with unearned empirical authority.
‘I’ve come to the position that there should be a stronger bias against the use of math,’ Romer explained to me. ‘If somebody came and said: “Look, I have this Earth-changing insight about economics, but the only way I can express it is by making use of the quirks of the Latin language”, we’d say go to hell, unless they could convince us it was really essential. The burden of proof is on them.’
Right now, however, there is widespread bias in favour of using mathematics. The success of math-heavy disciplines such as physics and chemistry has granted mathematical formulas with decisive authoritative force. Lord Kelvin, the 19th-century mathematical physicist, expressed this quantitative obsession:
When you can measure what you are speaking about and express it in numbers you know something about it; but when you cannot measure it… in numbers, your knowledge is of a meagre and unsatisfactory kind.
The trouble with Kelvin’s statement is that measurement and mathematics do not guarantee the status of science – they guarantee only the semblance of science. When the presumptions or conclusions of a scientific theory are absurd or simply false, the theory ought to be questioned and, eventually, rejected. The discipline of economics, however, is presently so blinkered by the talismanic authority of mathematics that theories go overvalued and unchecked.
Romer is not the first to elaborate the mathiness critique. In 1886, an article in Science accused economics of misusing the language of the physical sciences to conceal ‘emptiness behind a breastwork of mathematical formulas’. More recently, Deirdre N McCloskey’s The Rhetoric of Economics(1998) and Robert H Nelson’s Economics as Religion (2001) both argued that mathematics in economic theory serves, in McCloskey’s words, primarily to deliver the message ‘Look at how very scientific I am.’
After the Great Recession, the failure of economic science to protect our economy was once again impossible to ignore. In 2009, the Nobel Laureate Paul Krugman tried to explain it in The New York Times with a version of the mathiness diagnosis. ‘As I see it,’ he wrote, ‘the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.’ Krugman named economists’ ‘desire… to show off their mathematical prowess’ as the ‘central cause of the profession’s failure’.
The mathiness critique isn’t limited to macroeconomics. In 2014, the Stanford financial economist Paul Pfleiderer published the paper‘Chameleons: The Misuse of Theoretical Models in Finance and Economics’, which helped to inspire Romer’s understanding of mathiness. Pfleiderer called attention to the prevalence of ‘chameleons’ – economic models ‘with dubious connections to the real world’ that substitute ‘mathematical elegance’ for empirical accuracy. Like Romer, Pfleiderer wants economists to be transparent about this sleight of hand. ‘Modelling,’ he told me, ‘is now elevated to the point where things have validity just because you can come up with a model.’
The notion that an entire culture – not just a few eccentric financiers – could be bewitched by empty, extravagant theories might seem absurd. How could all those people, all that math, be mistaken? This was my own feeling as I began investigating mathiness and the shaky foundations of modern economic science. Yet, as a scholar of Chinese religion, it struck me that I’d seen this kind of mistake before, in ancient Chinese attitudes towards the astral sciences. Back then, governments invested incredible amounts of money in mathematical models of the stars. To evaluate those models, government officials had to rely on a small cadre of experts who actually understood the mathematics – experts riven by ideological differences, who couldn’t even agree on how to test their models. And, of course, despite collective faith that these models would improve the fate of the Chinese people, they did not.
Astral Science in Early Imperial China, a forthcoming book by the historian Daniel P Morgan, shows that in ancient China, as in the Western world, the most valuable type of mathematics was devoted to the realm of divinity – to the sky, in their case (and to the market, in ours). Just as astrology and mathematics were once synonymous in the West, the Chinese spoke of li, the science of calendrics, which early dictionaries also glossed as ‘calculation’, ‘numbers’ and ‘order’. Li models, like macroeconomic theories, were considered essential to good governance. In the classic Book of Documents, the legendary sage king Yao transfers the throne to his successor with mention of a single duty: ‘Yao said: “Oh thou, Shun! The li numbers of heaven rest in thy person.”’
China’s oldest mathematical text invokes astronomy and divine kingship in its very title – The Arithmetical Classic of the Gnomon of the Zhou. The title’s inclusion of ‘Zhou’ recalls the mythic Eden of the Western Zhou dynasty (1045–771 BCE), implying that paradise on Earth can be realised through proper calculation. The book’s introduction to the Pythagorean theorem asserts that ‘the methods used by Yu the Great in governing the world were derived from these numbers’. It was an unquestioned article of faith: the mathematical patterns that govern the stars also govern the world. Faith in a divine, invisible hand, made visible by mathematics. No wonder that a newly discovered text fragment from 200 BCE extolls the virtues of mathematics over the humanities. In it, a student asks his teacher whether he should spend more time learning speech or numbers. His teacher replies: ‘If my good sir cannot fathom both at once, then abandon speech and fathom numbers, [for] numbers can speak, [but] speech cannot number.’
Modern governments, universities and businesses underwrite the production of economic theory with huge amounts of capital. The same was true for li production in ancient China. The emperor – the ‘Son of Heaven’ – spent astronomical sums refining mathematical models of the stars. Take the armillary sphere, such as the two-metre cage of graduated bronze rings in Nanjing, made to represent the celestial sphere and used to visualise data in three-dimensions. As Morgan emphasises, the sphere was literally made of money. Bronze being the basis of the currency, governments were smelting cash by the metric ton to pour it into li. A divine, mathematical world-engine, built of cash, sanctifying the powers that be.
The enormous investment in li depended on a huge assumption: that good government, successful rituals and agricultural productivity all depended upon the accuracy of li. But there were, in fact, no practical advantages to the continued refinement of li models. The calendar rounded off decimal points such that the difference between two models, hotly contested in theory, didn’t matter to the final product. The work of selecting auspicious days for imperial ceremonies thus benefited only in appearance from mathematical rigour. And of course the comets, plagues and earthquakes that these ceremonies promised to avert kept on coming. Farmers, for their part, went about business as usual. Occasional governmental efforts to scientifically micromanage farm life in different climes using li ended in famine and mass migration.
Like many economic models today, li models were less important to practical affairs than their creators (and consumers) thought them to be. And, like today, only a few people could understand them. In 101 BCE, Emperor Wudi tasked high-level bureaucrats – including the Great Director of the Stars – with creating a new li that would glorify the beginning of his path to immortality. The bureaucrats refused the task because ‘they couldn’t do the math’, and recommended the emperor outsource it to experts.
The equivalent in economic theory might be to grant a model high points for success in predicting short-term markets, while failing to deduct for missing the Great Recession
The debates of these ancient li experts bear a striking resemblance to those of present-day economists. In 223 CE, a petition was submitted to the emperor asking him to approve tests of a new li model developed by the assistant director of the astronomical office, a man named Han Yi.
At the time of the petition, Han Yi’s model, and its competitor, the so-called Supernal Icon, had already been subjected to three years of ‘reference’, ‘comparison’ and ‘exchange’. Still, no one could agree which one was better. Nor, for that matter, was there any agreement on how they should be tested.
In the end, a live trial involving the prediction of eclipses and heliacal risings was used to settle the debate. With the benefit of hindsight, we can see this trial was seriously flawed. The helical rising (first visibility) of planets depends on non-mathematical factors such as eyesight and atmospheric conditions. That’s not to mention the scoring of the trial, which was modelled on archery competitions. Archers scored points for proximity to the bullseye, with no consideration for overall accuracy. The equivalent in economic theory might be to grant a model high points for success in predicting short-term markets, while failing to deduct for missing the Great Recession.
None of this is to say that li models were useless or inherently unscientific. For the most part, li experts were genuine mathematical virtuosos who valued the integrity of their discipline. Despite being based on inaccurate assumptions – that the Earth was at the centre of the cosmos – their models really did work to predict celestial motions. Imperfect though the live trial might have been, it indicates that superior predictive power was a theory’s most important virtue. All of this is consistent with real science, and Chinese astronomy progressed as a science, until it reached the limits imposed by its assumptions.
However, there was no science to the belief that accurate li would improve the outcome of rituals, agriculture or government policy. No science to the Hall of Light, a temple for the emperor built on the model of a magic square. There, by numeric ritual gesture, the Son of Heaven was thought to channel the invisible order of heaven for the prosperity of man. This was quasi-theology, the belief that heavenly patterns – mathematical patterns – could be used to model every event in the natural world, in politics, even the body. Macro- and microcosm were scaled reflections of one another, yin and yang in a unifying, salvific mathematical vision. The expensive gadgets, the personnel, the bureaucracy, the debates, the competition – all of this testified to the divinely authoritative power of mathematics. The result, then as now, was overvaluation of mathematical models based on unscientific exaggerations of their utility.
In ancient China it would have been unfair to blame li experts for the pseudoscientific exploitation of their theories. These men had no way to evaluate the scientific merits of assumptions and theories – ‘science’, in a formalised, post-Enlightenment sense, didn’t really exist. But today it is possible to distinguish, albeit roughly, science from pseudoscience, astronomy from astrology. Hypothetical theories, whether those of economists or conspiracists, aren’t inherently pseudoscientific. Conspiracy theories can be diverting – even instructive – flights of fancy. They become pseudoscience only when promoted from fiction to fact without sufficient evidence.
Romer believes that fellow economists know the truth about their discipline, but don’t want to admit it. ‘If you get people to lower their shield, they’ll tell you it’s a big game they’re playing,’ he told me. ‘They’ll say: “Paul, you may be right, but this makes us look really bad, and it’s going to make it hard for us to recruit young people.”’
Demanding more honesty seems reasonable, but it presumes that economists understand the tenuous relationship between mathematical models and scientific legitimacy. In fact, many assume the connection is obvious – just as in ancient China, the connection between li and the world was taken for granted. When reflecting in 1999 on what makes economics more scientific than the other social sciences, the Harvard economist Richard B Freeman explained that economics ‘attracts stronger students than [political science or sociology], and our courses are more mathematically demanding’. In Lives of the Laureates (2004), Robert E Lucas Jr writes rhapsodically about the importance of mathematics: ‘Economic theory is mathematical analysis. Everything else is just pictures and talk.’ Lucas’s veneration of mathematics leads him to adopt a method that can only be described as a subversion of empirical science:
The construction of theoretical models is our way to bring order to the way we think about the world, but the process necessarily involves ignoring some evidence or alternative theories – setting them aside. That can be hard to do – facts are facts – and sometimes my unconscious mind carries out the abstraction for me: I simply fail to see some of the data or some alternative theory.
Even for those who agree with Romer, conflict of interest still poses a problem. Why would skeptical astronomers question the emperor’s faith in their models? In a phone conversation, Daniel Hausman, a philosopher of economics at the University of Wisconsin, put it bluntly: ‘If you reject the power of theory, you demote economists from their thrones. They don’t want to become like sociologists.’
George F DeMartino, an economist and an ethicist at the University of Denver, frames the issue in economic terms. ‘The interest of the profession is in pursuing its analysis in a language that’s inaccessible to laypeople and even some economists,’ he explained to me. ‘What we’ve done is monopolise this kind of expertise, and we of all people know how that gives us power.’
Every economist I interviewed agreed that conflicts of interest were highly problematic for the scientific integrity of their field – but only tenured ones were willing to go on the record. ‘In economics and finance, if I’m trying to decide whether I’m going to write something favourable or unfavourable to bankers, well, if it’s favourable that might get me a dinner in Manhattan with movers and shakers,’ Pfleiderer said to me. ‘I’ve written articles that wouldn’t curry favour with bankers but I did that when I had tenure.’
When mathematical theory is the ultimate arbiter of truth, it becomes difficult to see the difference between science and pseudoscience
Then there’s the additional problem of sunk-cost bias. If you’ve invested in an armillary sphere, it’s painful to admit that it doesn’t perform as advertised. When confronted with their profession’s lack of predictive accuracy, some economists find it difficult to admit the truth. Easier, instead, to double down, like the economist John H Cochrane at the University of Chicago. The problem isn’t too much mathematics, he writes in response to Krugman’s 2009 post-Great-Recession mea culpa for the field, but rather ‘that we don’t have enough math’. Astrology doesn’t work, sure, but only because the armillary sphere isn’t big enough and the equations aren’t good enough.
If overhauling economics depended solely on economists, then mathiness, conflict of interest and sunk-cost bias could easily prove insurmountable. Fortunately, non-experts also participate in the market for economic theory. If people remain enchanted by PhDs and Nobel Prizes awarded for the production of complicated mathematical theories, those theories will remain valuable. If they become disenchanted, the value will drop.
Economists who rationalise their discipline’s value can be convincing, especially with prestige and mathiness on their side. But there’s no reason to keep believing them. The pejorative verb ‘rationalise’ itself warns of mathiness, reminding us that we often deceive each other by making prior convictions, biases and ideological positions look ‘rational’, a word that confuses truth with mathematical reasoning. To be rational is, simply, to think in ratios, like the ratios that govern the geometry of the stars. Yet when mathematical theory is the ultimate arbiter of truth, it becomes difficult to see the difference between science and pseudoscience. The result is people like the judge in Evangeline Adams’s trial, or the Son of Heaven in ancient China, who trust the mathematical exactitude of theories without considering their performance – that is, who confuse math with science, rationality with reality.
There is no longer any excuse for making the same mistake with economic theory. For more than a century, the public has been warned, and the way forward is clear. It’s time to stop wasting our money and recognise the high priests for what they really are: gifted social scientists who excel at producing mathematical explanations of economies, but who fail, like astrologers before them, at prophecy.
Geneticists tell us that somewhere between 1 and 5 percent of the genome of modern Europeans and Asians consists of DNA inherited from Neanderthals, our prehistoric cousins.
At Vanderbilt University, John Anthony Capra, an evolutionary genomics professor, has been combining high-powered computation and a medical records databank to learn what a Neanderthal heritage — even a fractional one — might mean for people today.
We spoke for two hours when Dr. Capra, 35, recently passed through New York City. An edited and condensed version of the conversation follows.
Q. Let’s begin with an indiscreet question. How did contemporary people come to have Neanderthal DNA on their genomes?
A. We hypothesize that roughly 50,000 years ago, when the ancestors of modern humans migrated out of Africa and into Eurasia, they encountered Neanderthals. Matings must have occurred then. And later.
One reason we deduce this is because the descendants of those who remained in Africa — present day Africans — don’t have Neanderthal DNA.
What does that mean for people who have it?
At my lab, we’ve been doing genetic testing on the blood samples of 28,000 patients at Vanderbilt and eight other medical centers across the country. Computers help us pinpoint where on the human genome this Neanderthal DNA is, and we run that against information from the patients’ anonymized medical records. We’re looking for associations.
What we’ve been finding is that Neanderthal DNA has a subtle influence on risk for disease. It affects our immune system and how we respond to different immune challenges. It affects our skin. You’re slightly more prone to a condition where you can get scaly lesions after extreme sun exposure. There’s an increased risk for blood clots and tobacco addiction.
To our surprise, it appears that some Neanderthal DNA can increase the risk for depression; however, there are other Neanderthal bits that decrease the risk. Roughly 1 to 2 percent of one’s risk for depression is determined by Neanderthal DNA. It all depends on where on the genome it’s located.
Was there ever an upside to having Neanderthal DNA?
It probably helped our ancestors survive in prehistoric Europe. When humans migrated into Eurasia, they encountered unfamiliar hazards and pathogens. By mating with Neanderthals, they gave their offspring needed defenses and immunities.
That trait for blood clotting helped wounds close up quickly. In the modern world, however, this trait means greater risk for stroke and pregnancy complications. What helped us then doesn’t necessarily now.
Did you say earlier that Neanderthal DNA increases susceptibility to nicotine addiction?
Yes. Neanderthal DNA can mean you’re more likely to get hooked on nicotine, even though there were no tobacco plants in archaic Europe.
We think this might be because there’s a bit of Neanderthal DNA right next to a human gene that’s a neurotransmitter implicated in a generalized risk for addiction. In this case and probably others, we think the Neanderthal bits on the genome may serve as switches that turn human genes on or off.
Aside from the Neanderthals, do we know if our ancestors mated with other hominids?
We think they did. Sometimes when we’re examining genomes, we can see the genetic afterimages of hominids who haven’t even been identified yet.
A few years ago, the Swedish geneticist Svante Paabo received an unusual fossilized bone fragment from Siberia. He extracted the DNA, sequenced it and realized it was neither human nor Neanderthal. What Paabo found was a previously unknown hominid he named Denisovan, after the cave where it had been discovered. It turned out that Denisovan DNA can be found on the genomes of modern Southeast Asians and New Guineans.
Have you long been interested in genetics?
Growing up, I was very interested in history, but I also loved computers. I ended up majoring in computer science at college and going to graduate school in it; however, during my first year in graduate school, I realized I wasn’t very motivated by the problems that computer scientists worked on.
Fortunately, around that time — the early 2000s — it was becoming clear that people with computational skills could have a big impact in biology and genetics. The human genome had just been mapped. What an accomplishment! We now had the code to what makes you, you, and me, me. I wanted to be part of that kind of work.
So I switched over to biology. And it was there that I heard about a new field where you used computation and genetics research to look back in time — evolutionary genomics.
There may be no written records from prehistory, but genomes are a living record. If we can find ways to read them, we can discover things we couldn’t know any other way.
Not long ago, the two top editors of The New England Journal of Medicine published an editorial questioning “data sharing,” a common practice where scientists recycle raw data other researchers have collected for their own studies. They labeled some of the recycling researchers, “data parasites.” How did you feel when you read that?
I was upset. The data sets we used were not originally collected to specifically study Neanderthal DNA in modern humans. Thousands of patients at Vanderbilt consented to have their blood and their medical records deposited in a “biobank” to find genetic diseases.
Three years ago, when I set up my lab at Vanderbilt, I saw the potential of the biobank for studying both genetic diseases and human evolution. I wrote special computer programs so that we could mine existing data for these purposes.
That’s not being a “parasite.” That’s moving knowledge forward. I suspect that most of the patients who contributed their information are pleased to see it used in a wider way.
What has been the response to your Neanderthal research since you published it last year in the journal Science?
Some of it’s very touching. People are interested in learning about where they came from. Some of it is a little silly. “I have a lot of hair on my legs — is that from Neanderthals?”
But I received racist inquiries, too. I got calls from all over the world from people who thought that since Africans didn’t interbreed with Neanderthals, this somehow justified their ideas of white superiority.
It was illogical. Actually, Neanderthal DNA is mostly bad for us — though that didn’t bother them.
As you do your studies, do you ever wonder about what the lives of the Neanderthals were like?
It’s hard not to. Genetics has taught us a tremendous amount about that, and there’s a lot of evidence that they were much more human than apelike.
They’ve gotten a bad rap. We tend to think of them as dumb and brutish. There’s no reason to believe that. Maybe those of us of European heritage should be thinking, “Let’s improve their standing in the popular imagination. They’re our ancestors, too.’”
- December 20, 2016
- University of Washington
- Researchers present a mathematical model that explores whether “publication bias” — the tendency of journals to publish mostly positive experimental results — influences how scientists canonize facts.
Arguing in a Boston courtroom in 1770, John Adams famously pronounced, “Facts are stubborn things,” which cannot be altered by “our wishes, our inclinations or the dictates of our passion.”
But facts, however stubborn, must pass through the trials of human perception before being acknowledged — or “canonized” — as facts. Given this, some may be forgiven for looking at passionate debates over the color of a dress and wondering if facts are up to the challenge.
Carl Bergstrom believes facts stand a fighting chance, especially if science has their back. A professor of biology at the University of Washington, he has used mathematical modeling to investigate the practice of science, and how science could be shaped by the biases and incentives inherent to human institutions.
“Science is a process of revealing facts through experimentation,” said Bergstrom. “But science is also a human endeavor, built on human institutions. Scientists seek status and respond to incentives just like anyone else does. So it is worth asking — with precise, answerable questions — if, when and how these incentives affect the practice of science.”
In an article published Dec. 20 in the journal eLife, Bergstrom and co-authors present a mathematical model that explores whether “publication bias” — the tendency of journals to publish mostly positive experimental results — influences how scientists canonize facts. Their results offer a warning that sharing positive results comes with the risk that a false claim could be canonized as fact. But their findings also offer hope by suggesting that simple changes to publication practices can minimize the risk of false canonization.
These issues have become particularly relevant over the past decade, as prominent articles have questioned the reproducibility of scientific experiments — a hallmark of validity for discoveries made using the scientific method. But neither Bergstrom nor most of the scientists engaged in these debates are questioning the validity of heavily studied and thoroughly demonstrated scientific truths, such as evolution, anthropogenic climate change or the general safety of vaccination.
“We’re modeling the chances of ‘false canonization’ of facts on lower levels of the scientific method,” said Bergstrom. “Evolution happens, and explains the diversity of life. Climate change is real. But we wanted to model if publication bias increases the risk of false canonization at the lowest levels of fact acquisition.”
Bergstrom cites a historical example of false canonization in science that lies close to our hearts — or specifically, below them. Biologists once postulated that bacteria caused stomach ulcers. But in the 1950s, gastroenterologist E.D. Palmer reported evidence that bacteria could not survive in the human gut.
“These findings, supported by the efficacy of antacids, supported the alternative ‘chemical theory of ulcer development,’ which was subsequently canonized,” said Bergstrom. “The problem was that Palmer was using experimental protocols that would not have detected Helicobacter pylori, the bacteria that we know today causes ulcers. It took about a half century to correct this falsehood.”
While the idea of false canonization itself may cause dyspepsia, Bergstrom and his team — lead author Silas Nissen of the Niels Bohr Institute in Denmark and co-authors Kevin Gross of North Carolina State University and UW undergraduate student Tali Magidson — set out to model the risks of false canonization given the fact that scientists have incentives to publish only their best, positive results. The so-called “negative results,” which show no clear, definitive conclusions or simply do not affirm a hypothesis, are much less likely to be published in peer-reviewed journals.
“The net effect of publication bias is that negative results are less likely to be seen, read and processed by scientific peers,” said Bergstrom. “Is this misleading the canonization process?”
For their model, Bergstrom’s team incorporated variables such as the rates of error in experiments, how much evidence is needed to canonize a claim as fact and the frequency with which negative results are published. Their mathematical model showed that the lower the publication rate is for negative results, the higher the risk for false canonization. And according to their model, one possible solution — raising the bar for canonization — didn’t help alleviate this risk.
“It turns out that requiring more evidence before canonizing a claim as fact did not help,” said Bergstrom. “Instead, our model showed that you need to publish more negative results — at least more than we probably are now.”
Since most negative results live out their obscurity in the pages of laboratory notebooks, it is difficult to quantify the ratio that are published. But clinical trials, which must be registered with the U.S. Food and Drug Administration before they begin, offer a window into how often negative results make it into the peer-reviewed literature. A 2008 analysis of 74 clinical trials for antidepressant drugs showed that scarcely more than 10 percent of negative results were published, compared to over 90 percent for positive results.
“Negative results are probably published at different rates in other fields of science,” said Bergstrom. “And new options today, such as self-publishing papers online and the rise of journals that accept some negative results, may affect this. But in general, we need to share negative results more than we are doing today.”
Their model also indicated that negative results had the biggest impact as a claim approached the point of canonization. That finding may offer scientists an easy way to prevent false canonization.
“By more closely scrutinizing claims as they achieve broader acceptance, we could identify false claims and keep them from being canonized,” said Bergstrom.
To Bergstrom, the model raises valid questions about how scientists choose to publish and share their findings — both positive and negative. He hopes that their findings pave the way for more detailed exploration of bias in scientific institutions, including the effects of funding sources and the different effects of incentives on different fields of science. But he believes a cultural shift is needed to avoid the risks of publication bias.
“As a community, we tend to say, ‘Damn it, this didn’t work, and I’m not going to write it up,'” said Bergstrom. “But I’d like scientists to reconsider that tendency, because science is only efficient if we publish a reasonable fraction of our negative findings.”
- Silas Boye Nissen, Tali Magidson, Kevin Gross, Carl T Bergstrom. Publication bias and the canonization of false facts. eLife, 2016; 5 DOI: 10.7554/eLife.21451
- August 24, 2016
- Penn State
- One size does not always fit all, especially when it comes to global climate models, according to climate researchers who caution users of climate model projections to take into account the increased uncertainties in assessing local climate scenarios.
One size does not always fit all, especially when it comes to global climate models, according to Penn State climate researchers.
“The impacts of climate change rightfully concern policy makers and stakeholders who need to make decisions about how to cope with a changing climate,” said Fuqing Zhang, professor of meteorology and director, Center for Advanced Data Assimilation and Predictability Techniques, Penn State. “They often rely upon climate model projections at regional and local scales in their decision making.”
Zhang and Michael Mann, Distinguished professor of atmospheric science and director, Earth System Science Center, were concerned that the direct use of climate model output at local or even regional scales could produce inaccurate information. They focused on two key climate variables, temperature and precipitation.
They found that projections of temperature changes with global climate models became increasingly uncertain at scales below roughly 600 horizontal miles, a distance equivalent to the combined widths of Pennsylvania, Ohio and Indiana. While climate models might provide useful information about the overall warming expected for, say, the Midwest, predicting the difference between the warming of Indianapolis and Pittsburgh might prove futile.
Regional changes in precipitation were even more challenging to predict, with estimates becoming highly uncertain at scales below roughly 1200 miles, equivalent to the combined width of all the states from the Atlantic Ocean through New Jersey across Nebraska. The difference between changing rainfall totals in Philadelphia and Omaha due to global warming, for example, would be difficult to assess. The researchers report the results of their study in the August issue of Advances in Atmospheric Sciences.
“Policy makers and stakeholders use information from these models to inform their decisions,” said Mann. “It is crucial they understand the limitation in the information the model projections can provide at local scales.”
Climate models provide useful predictions of the overall warming of the globe and the largest-scale shifts in patterns of rainfall and drought, but are considerably more hard pressed to predict, for example, whether New York City will become wetter or drier, or to deal with the effects of mountain ranges like the Rocky Mountains on regional weather patterns.
“Climate models can meaningfully project the overall global increase in warmth, rises in sea level and very large-scale changes in rainfall patterns,” said Zhang. “But they are uncertain about the potential significant ramifications on society in any specific location.”
The researchers believe that further research may lead to a reduction in the uncertainties. They caution users of climate model projections to take into account the increased uncertainties in assessing local climate scenarios.
“Uncertainty is hardly a reason for inaction,” said Mann. “Moreover, uncertainty can cut both ways, and we must be cognizant of the possibility that impacts in many regions could be considerably greater and more costly than climate model projections suggest.”
Aldana’s paper, “Discovering Discovery: Chich’en Itza, the Dresden Codex Venus Table and 10th Century Mayan Astronomical Innovation,” in the Journal of Astronomy in Culture, blends the study of Mayan hieroglyphics (epigraphy), archaeology and astronomy to present a new interpretation of the Venus Table, which tracks the observable phases of the second planet from the Sun. Using this multidisciplinary approach, he said, a new reading of the table demonstrates that the mathematical correction of their “Venus calendar” — a sophisticated innovation — was likely developed at the city of Chich’en Itza during the Terminal Classic period (AD 800-1000). What’s more, the calculations may have been done under the patronage of K’ak’ U Pakal K’awiil, one of the city’s most prominent historical figures.
“This is the part that I find to be most rewarding, that when we get in here, we’re looking at the work of an individual Mayan, and we could call him or her a scientist, an astronomer,” Aldana said. “This person, who’s witnessing events at this one city during this very specific period of time, created, through their own creativity, this mathematical innovation.”
The Venus Table
Scholars have long known that the Preface to the Venus Table, Page 24 of the Dresden Codex, contained what Aldana called a “mathematical subtlety” in its hieroglyphic text. They even knew what it was for: to serve as a correction for Venus’s irregular cycle, which is 583.92 days. “So that means if you do anything on a calendar that’s based on days as a basic unit, there is going to be an error that accrues,” Aldana explained. It’s the same principle used for Leap Years in the Gregorian calendar. Scholars figured out the math for the Venus Table’s leap in the 1930s, Aldana said, “but the question is, what does it mean? Did they discover it way back in the 1st century BC? Did they discover it in the 16th? When did they discover it and what did it mean to them? And that’s where I come in.”
Unraveling the mystery demanded Aldana employ a unique set of skills. The first involved epigraphy, and it led to an important development: In poring over the Table’s hieroglyphics, he came to realize that a key verb, k’al, had a different meaning than traditionally interpreted. Used throughout the Table, k’al means “to enclose” and, in Aldana’s reading, had a historical and cosmological purpose.
That breakthrough led him to question the assumptions of what the Mayan scribe who authored the text was doing in the Table. Archaeologists and other scholars could see its observations of Venus were accurate, but insisted it was based in numerology. “They [the Maya] knew it was wrong, but the numerology was more important. And that’s what scholars have been saying for the last 70 years,” Aldana said.
“So what I’m saying is, let’s step back and make a different assumption,” he continued. “Let’s assume that they had historical records and they were keeping historical records of astronomical events and they were consulting them in the future — exactly what the Greeks did and the Egyptians and everybody else. That’s what they did. They kept these over a long period of time and then they found patterns within them. The history of Western astronomy is based entirely on this premise.”
To test his new assumption, Aldana turned to another Mayan archaeological site, Copán in Honduras. The former city-state has its own record of Venus, which matched as a historical record the observations in the Dresden Codex. “Now we’re just saying, let’s take these as historical records rather than numerology,” he said. “And when you do that, when you see it as historical record, it changes the interpretation.”
Putting the pieces together
The final piece of the puzzle was what Aldana, whose undergraduate degree was in mechanical engineering, calls “the machinery,” or how the pieces fit together. Scholars know the Mayans had accurate observations of Venus, and Aldana could see that they were historical, not numerological. The question was, Why? One hint lay more than 500 years in the future: Nicolaus Copernicus.
The great Polish astronomer stumbled into the heliocentric universe while trying to figure out the predictions for future dates of Easter, a challenging feat that requires good mathematical models. That’s what Aldana saw in the Venus Table. “They’re using Venus not just to strictly chart when it was going to appear, but they were using it for their ritual cycles,” he explained. “They had ritual activities when the whole city would come together and they would do certain events based on the observation of Venus. And that has to have a degree of accuracy, but it doesn’t have to have overwhelming accuracy. When you change that perspective of, ‘What are you putting these cycles together for?’ that’s the third component.”
Putting those pieces together, Aldana found there was a unique period of time during the occupation of Chichen’Itza when an ancient astronomer in the temple that was used to observe Venus would have seen the progressions of the planet and discovered it was a viable way to correct the calendar and to set their ritual events.
“If you say it’s just numerology that this date corresponds to; it’s not based on anything you can see. And if you say, ‘We’re just going to manipulate them [the corrections written] until they give us the most accurate trajectory,’ you’re not confining that whole thing in any historical time,” he said. “If, on the other hand, you say, ‘This is based on a historical record,’ that’s going to nail down the range of possibilities. And if you say that they were correcting it for a certain kind of purpose, then all of a sudden you have a very small window of when this discovery could have occurred.”
A Mayan achievement
By reinterpreting the work, Aldana said it puts the Venus Table into cultural context. It was an achievement of Mayan science, and not a numerological oddity. We might never know exactly who made that discovery, he noted, but recasting it as a historical work of science returns it to the Mayans.
“I don’t have a name for this person, but I have a name for the person who is probably one of the authority figures at the time,” Aldana said. “It’s the kind of thing where you know who the pope was, but you don’t know Copernicus’s name. You know the pope was giving him this charge, but the person who did it? You don’t know his or her name.”
Physicists update predator-prey model for more clues on how bacteria evade attack from killer cells
- April 29, 2016
- IOP Publishing
- Studying the way that solitary hunters such as tigers, bears or sea turtles chase down their prey turns out to be very useful in understanding the interaction between individual white blood cells and colonies of bacteria. Researchers have created a numerical model that explores this behavior in more detail.
Studying the way that solitary hunters such as tigers, bears or sea turtles chase down their prey turns out to be very useful in understanding the interaction between individual white blood cells and colonies of bacteria. Reporting their results in the Journal of Physics A: Mathematical and Theoretical, researchers in Europe have created a numerical model that explores this behaviour in more detail.
Using mathematical expressions, the group can examine the dynamics of a single predator hunting a herd of prey. The routine splits the hunter’s motion into a diffusive part and a ballistic part, which represent the search for prey and then the direct chase that follows.
“We would expect this to be a fairly good approximation for many animals,” explained Ralf Metzler, who led the work and is based at the University of Potsdam in Germany.
To further improve its analysis, the group, which includes scientists from the National Institute of Chemistry in Slovenia, and Sorbonne University in France, has incorporated volume effects into the latest version of its model. The addition means that prey can now inadvertently get in each other’s way and endanger their survival by blocking potential escape routes.
Thanks to this update, the team can study not just animal behaviour, but also gain greater insight into the way that killer cells such as macrophages (large white blood cells patrolling the body) attack colonies of bacteria.
One of the key parameters determining the life expectancy of the prey is the so-called ‘sighting range’ — the distance at which the prey is able to spot the predator. Examining this in more detail, the researchers found that the hunter profits more from the poor eyesight of the prey than from the strength of its own vision.
Long tradition with a new dimension
The analysis of predator-prey systems has a long tradition in statistical physics and today offers many opportunities for cooperative research, particularly in fields such as biology, biochemistry and movement ecology.
“With the ever more detailed experimental study of systems ranging from molecular processes in living biological cells to the motion patterns of animal herds and humans, the need for cross-fertilisation between the life sciences and the quantitative mathematical approaches of the physical sciences has reached a new dimension,” Metzler comments.
To help support this cross-fertilisation, he heads up a new section of the Journal of Physics A: Mathematical and Theoretical that is dedicated to biological modelling and examines the use of numerical techniques to study problems in the interdisciplinary field connecting biology, biochemistry and physics.
- Maria Schwarzl, Aljaz Godec, Gleb Oshanin, Ralf Metzler. A single predator charging a herd of prey: effects of self volume and predator–prey decision-making. Journal of Physics A: Mathematical and Theoretical, 2016; 49 (22): 225601 DOI: 10.1088/1751-8113/49/22/225601
Sistema computacional desenvolvido por pesquisadores da USP e da Unicamp estabelece regras de racionamento de suprimento hídrico em períodos de seca
Pesquisadores da Escola Politécnica da Universidade de São Paulo (Poli-USP) e da Faculdade de Engenharia Civil, Arquitetura e Urbanismo da Universidade Estadual de Campinas (FEC-Unicamp) desenvolveram novos modelos matemáticos e computacionais voltados a otimizar a gestão e a operação de sistemas complexos de suprimento hídrico e de energia elétrica, como os existentes no Brasil.
Os modelos, que começaram a ser desenvolvidos no início dos anos 2000, foram aprimorados por meio do Projeto Temático “HidroRisco: Tecnologias de gestão de riscos aplicadas a sistemas de suprimento hídrico e de energia elétrica”, realizado com apoio da Fapesp.
“A ideia é que os modelos matemáticos e computacionais que desenvolvemos possam auxiliar os gestores dos sistemas de distribuição e abastecimento de água e energia elétrica na tomada de decisões que têm enormes impactos sociais e econômicos, como a de decretar racionamento”, disse Paulo Sérgio Franco Barbosa, professor da FEC-Unicamp e coordenador do projeto, à Agência Fapesp.
De acordo com Barbosa, muitas das tecnologias utilizadas hoje nos setores hídrico e energético no Brasil para gerir a oferta e a demanda e os riscos de desabastecimento de água e energia em situações de eventos climáticos extremos, como estiagem severa, foram desenvolvidas na década de 1970, quando as cidades brasileiras eram menores e o País não dispunha de um sistema hídrico e hidroenergético tão complexo como o atual.
Por essas razões, segundo ele, esses sistemas de gestão apresentam falhas como não levar em conta a conexão entre as diferentes bacias e não estimar a ocorrência de eventos climáticos mais extremos do que os que já aconteceram no passado ao planejar a operação de um sistema de reservatórios e distribuição de água.
“Houve falha no dimensionamento da capacidade de abastecimento de água do reservatório Cantareira, por exemplo, porque não se imaginou que aconteceria uma seca pior do que a que atingiu a bacia em 1953, considerado o ano mais seco da história do reservatório antes de 2014”, afirmou Barbosa.
A fim de aprimorar esses sistemas de gestão de risco existentes hoje, os pesquisadores desenvolveram novos modelos matemáticos e computacionais que simulam a operação de um sistema de suprimento hídrico ou de energia de forma integrada e em diferentes cenários de aumento de oferta e demanda de água.
“Por meio de algumas técnicas estatísticas e computacionais, os modelos que desenvolvemos são capazes de fazer simulações melhores e proteger mais um sistema de suprimento hídrico ou de energia elétrica contra riscos climáticos”, disse Barbosa.
Um dos modelos desenvolvidos pelos pesquisadores em colaboração com colegas da University of California em Los Angeles, nos Estados Unidos, é a plataforma de modelagem de otimização e simulação de sistemas de suprimento hídrico Sisagua.
A plataforma computacional integra e representa todas as fontes de abastecimento de um sistema de reservatórios e distribuição de água de cidades de grande porte, como São Paulo, incluindo os reservatórios, canais, dutos, estações de tratamento e de bombeamento.
“O Sisagua possibilita planejar a operação, estudar a capacidade de suprimento e avaliar alternativas de expansão ou de diminuição do fornecimento de um sistema de abastecimento de água de forma integrada”, apontou Barbosa.
Um dos diferenciais do modelo computacional, segundo o pesquisador, é estabelecer regras de racionamento de um sistema de reservatórios e distribuição de água de grande porte em períodos de seca, como o que São Paulo passou em 2014, de modo a minimizar os danos à população e à economia causados por um eventual racionamento.
Quando um dos reservatórios do sistema atinge um volume abaixo dos níveis normais e próximo do volume mínimo de operação, o modelo computacional indica um primeiro estágio de racionamento, reduzindo a oferta da água armazenada em 10%, por exemplo.
Se a crise de abastecimento do reservatório prolongar, o modelo matemático indica alternativas para minimizar a intensidade do racionamento distribuindo o corte de água de forma mais uniforme ao longo do período de escassez de água e entre os outros reservatórios do sistema.
“O Sisagua possui uma inteligência computacional que indica onde e quando cortar o fornecimento de água de um sistema de abastecimento hídrico, de modo a minimizar os danos no sistema e para a população e a economia de uma cidade”, afirmou Barbosa.
Os pesquisadores aplicaram o Sisagua para simular a operação e a gestão do sistema de distribuição de água da região metropolitana de São Paulo, que abastece cerca de 18 milhões de pessoas e é considerado um dos maiores do mundo, com vazão média de 67 metros cúbicos por segundo (m³/s).
O sistema de distribuição de água paulista é composto por oito subsistemas de abastecimento, sendo o maior deles o Cantareira, que fornece água para 5,3 milhões de pessoas, com vazão média de 33 m³/s.
A fim de avaliar a capacidade de suprimento do Cantareira em um cenário de escassez de água e, ao mesmo tempo, de aumento da demanda pelo recurso natural, os pesquisadores realizaram uma simulação de planejamento do uso do subsistema em um período de dez anos utilizando o Sisagua.
Para isso, eles usaram dados de vazões afluentes (de entrada de água) do Cantareira entre 1950 e 1960, fornecidos pela Companhia de Saneamento Básico do Estado de São Paulo (Sabesp).
“Essa período de tempo foi escolhido como base para as projeções do Sisagua porque registrou secas severas, quando as afluências ficaram significativamente abaixo das médias por quatro anos seguidos, entre 1952 e 1956”, explicou Barbosa.
A partir dos dados de vazão afluente desse série histórica, o modelo matemático e computacional analisou cenários com demanda variável de água do Cantareira entre 30 e 40 m³/s.
Algumas das constatações do modelo foram que o Cantareira é capaz de atender uma demanda de até 34 m³/s em um cenário de escassez de água como ocorreu entre 1950 a 1960 com um risco insignificante de desabastecimento. Acima desse valor a escassez e, consequentemente, o risco de racionamento de água no reservatório aumenta exponencialmente.
Para que o Cantareira possa atender uma demanda de 38 m³/s em um período de escassez de água, o modelo indicou que seria preciso começar a racionar a água do reservatório 40 meses (3 anos e 4 meses) antes que o nível da bacia atingisse o ponto crítico, abaixo do volume normal e próximo do limite mínimo de operação.
Dessa forma, seria possível atender entre 85% e 90% da demanda de água do reservatório no período de seca até que ele recuperasse seu volume ideal, evitando um racionamento mais grave do que aconteceria caso fosse mantido o nível pleno de abastecimento do reservatório.
“Quanto antes for feito o racionamento de água de um sistema de abastecimento hídrico melhor o prejuízo é distribuído ao longo do tempo”, disse Barbosa. “A população pode se preparar melhor para um racionamento de 15% de água durante um período de dois anos, por exemplo, do que um corte de 40% em apenas dois meses”, comparou.
Em outro estudo, os pesquisadores usaram o Sisagua para avaliar a capacidade de os subsistemas Cantareira, Guarapiranga, Alto Tietê e Alto Cotia atenderem as atuais demandas de água em um cenário de escassez do recurso natural.
Para isso, eles também utilizaram dados de vazões afluentes dos quatro subsistemas no período de 1950 a 1960.
Os resultados das análises feitas pelo método matemático e computacional indicaram que o subsistema de Cotia atingiu um limite crítico de racionamento diversas vezes durante o período simulado de dez anos.
Em contrapartida, o subsistema Alto Tietê ficou com volume de água acima de sua meta frequentemente.
Com base nessas constatações, os pesquisadores sugerem novas interligações para transferência entre esses quatro subsistemas de abastecimento.
Parte da demanda de água do subsistema de Cotia poderia ser fornecida pelos subsistemas de Guarapiranga e Cantareira. Por outro lado, esses dois subsistemas também poderiam receber água do subsistema Alto Tietê, indicaram as projeções do Sisagua.
“A transferência de água entre os subsistemas proporcionaria maior flexibilidade e resultaria em uma melhor distribuição, eficiência e confiabilidade do sistema de abastecimento hídrico da região metropolitana de São Paulo”, avaliou Barbosa.
De acordo com o pesquisador, as projeções feitas pelo Sisagua também indicaram a necessidade de investimentos em novas fontes de abastecimento de água para a região metropolitana de São Paulo.
Segundo ele, as principais bacias que abastecem São Paulo sofrem de problemas como a concentração urbana.
Em torno da bacia do Alto Tietê, por exemplo, que ocupa apenas 2,7% do território paulista, está concentrada quase 50% da população do Estado de São Paulo, superando em cinco vezes a densidade demográfica de países como Japão, Coréia e Holanda.
Já as bacias de Piracicaba, Paraíba do Sul, Sorocaba e Baixada Santista – que representam 20% da área de São Paulo – concentram 73% da população paulista, com densidade demográfica superior ao de países como Japão, Holanda e Reino Unido, apontam os pesquisadores.
“Será inevitável pensar em outras fontes de abastecimento de água para a região metropolitana de São Paulo, como o sistema Juquiá, no interior do estado, que tem água de excelente quantidade e em grandes volumes”, disse Barbosa.
“Em razão da distância, essa obra será cara e tem sido postergada. Mas, agora, não dá mais para adiá-la”, afirmou.
Além de São Paulo, o Sisagua também foi utilizado para modelar os sistemas de suprimento hídrico de Los Angeles, nos Estados Unidos, e Taiwan.
O artigo “Planning and operation of large-scale water distribution systems with preemptive priorities”, (doi: 10.1061/(ASCE)0733-9496(2008)134:3(247)), de Barros e outros, pode ser lido por assinantes do Journal of Water Resources Planning and Managementem ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9496%282008%29134%3A3%28247%29.
Then there is water.
Water may be the most important item in our lives, our economy and our landscape about which we know the least. We not only don’t tabulate our water use every hour or every day, we don’t do it every month, or even every year.
The official analysis of water use in the United States is done every five years. It takes a tiny team of people four years to collect, tabulate and release the data. In November 2014, the United States Geological Survey issued its most current comprehensive analysis of United States water use — for the year 2010.
The 2010 report runs 64 pages of small type, reporting water use in each state by quality and quantity, by source, and by whether it’s used on farms, in factories or in homes.
It doesn’t take four years to get five years of data. All we get every five years is one year of data.
The data system is ridiculously primitive. It was an embarrassment even two decades ago. The vast gaps — we start out missing 80 percent of the picture — mean that from one side of the continent to the other, we’re making decisions blindly.
In just the past 27 months, there have been a string of high-profile water crises — poisoned water in Flint, Mich.; polluted water in Toledo, Ohio, and Charleston, W. Va.; the continued drying of the Colorado River basin — that have undermined confidence in our ability to manage water.
In the time it took to compile the 2010 report, Texas endured a four-year drought. California settled into what has become a five-year drought. The most authoritative water-use data from across the West couldn’t be less helpful: It’s from the year before the droughts began.
In the last year of the Obama presidency, the administration has decided to grab hold of this country’s water problems, water policy and water innovation. Next Tuesday, the White House is hosting a Water Summit, where it promises to unveil new ideas to galvanize the sleepy world of water.
The question White House officials are asking is simple: What could the federal government do that wouldn’t cost much but that would change how we think about water?
The best and simplest answer: Fix water data.
More than any other single step, modernizing water data would unleash an era of water innovation unlike anything in a century.
We have a brilliant model for what water data could be: the Energy Information Administration, which has every imaginable data point about energy use — solar, wind, biodiesel, the state of the heating oil market during the winter we’re living through right now — all available, free, to anyone. It’s not just authoritative, it’s indispensable. Congress created the agency in the wake of the 1970s energy crisis, when it became clear we didn’t have the information about energy use necessary to make good public policy.
That’s exactly the state of water — we’ve got crises percolating all over, but lack the data necessary to make smart policy decisions.
Congress and President Obama should pass updated legislation creating inside the United States Geological Survey a vigorous water data agency with the explicit charge to gather and quickly release water data of every kind — what utilities provide, what fracking companies and strawberry growers use, what comes from rivers and reservoirs, the state of aquifers.
Good information does three things.
First, it creates the demand for more good information. Once you know what you can know, you want to know more.
Second, good data changes behavior. The real-time miles-per-gallon gauges in our cars are a great example. Who doesn’t want to edge the M.P.G. number a little higher? Any company, community or family that starts measuring how much water it uses immediately sees ways to use less.
Finally, data ignites innovation. Who imagined that when most everyone started carrying a smartphone, we’d have instant, nationwide traffic data? The phones make the traffic data possible, and they also deliver it to us.
The truth is, we don’t have any idea what detailed water use data for the United States will reveal. But we can be certain it will create an era of water transformation. If we had monthly data on three big water users — power plants, farmers and water utilities — we’d instantly see which communities use water well, and which ones don’t.
We’d see whether tomato farmers in California or Florida do a better job. We’d have the information to make smart decisions about conservation, about innovation and about investing in new kinds of water systems.
Water’s biggest problem, in this country and around the world, is its invisibility. You don’t tackle problems that are out of sight. We need a new relationship with water, and that has to start with understanding it.
SCIENTIFIC METHOD 10:23 AM MAR 7, 2016
What are you trying to say
— Stephen Ziliak, Roosevelt University economics professor
How many statisticians does it take to ensure at least a 50 percent chance of a disagreement about p-values? According to a tongue-in-cheek assessment by statistician George Cobb of Mount Holyoke College, the answer is two … or one. So it’s no surprise that when the American Statistical Association gathered 26 experts to develop a consensus statement on statistical significance and p-values, the discussion quickly became heated.
It may sound crazy to get indignant over a scientific term that few lay people have even heard of, but the consequences matter. The misuse of the p-value can drive bad science (there was no disagreement over that), and the consensus project was spurred by a growing worry that in some scientific fields, p-values have become a litmus test for deciding which studies are worthy of publication. As a result, research that produces p-values that surpass an arbitrary threshold are more likely to be published, while studies with greater or equal scientific importance may remain in the file drawer, unseen by the scientific community.
The results can be devastating, said Donald Berry, a biostatistician at the University of Texas MD Anderson Cancer Center. “Patients with serious diseases have been harmed,” he wrote in a commentary published today. “Researchers have chased wild geese, finding too often that statistically significant conclusions could not be reproduced.” Faulty statistical conclusions, he added, have real economic consequences.
“The p-value was never intended to be a substitute for scientific reasoning,” the ASA’s executive director, Ron Wasserstein, said in a press release. On that point, the consensus committee members agreed, but statisticians have deep philosophical differences1 about the proper way to approach inference and statistics, and “this was taken as a battleground for those different views,” said Steven Goodman, co-director of the Meta-Research Innovation Center at Stanford. Much of the dispute centered around technical arguments over frequentist versus Bayesian methods and possible alternatives or supplements to p-values. “There were huge differences, including profoundly different views about the core problems and practices in need of reform,” Goodman said. “People were apoplectic over it.”
The group debated and discussed the issues for more than a year before finally producing a statement they could all sign. They released that consensus statement on Monday, along with 20 additional commentariesfrom members of the committee. The ASA statement is intended to address the misuse of p-values and promote a better understanding of them among researchers and science writers, and it marks the first time the association has taken an official position on a matter of statistical practice. The statement outlines some fundamental principles regarding p-values.
Among the committee’s tasks: Selecting a definition of the p-value that nonstatisticians could understand. They eventually settled on this: “Informally, a p-value is the probability under a specified statistical model that a statistical summary of the data (for example, the sample mean difference between two compared groups) would be equal to or more extreme than its observed value.” That definition is about as clear as mud (I stand by my conclusion that even scientists can’t easily explain p-values), but the rest of the statement and the ideas it presents are far more accessible.
One of the most important messages is that the p-value cannot tell you if your hypothesis is correct. Instead, it’s the probability of your data given your hypothesis. That sounds tantalizingly similar to “the probability of your hypothesis given your data,” but they’re not the same thing, said Stephen Senn, a biostatistician at the Luxembourg Institute of Health. To understand why, consider this example. “Is the pope Catholic? The answer is yes,” said Senn. “Is a Catholic the pope? The answer is probably not. If you change the order, the statement doesn’t survive.”
A common misconception among nonstatisticians is that p-values can tell you the probability that a result occurred by chance. This interpretation is dead wrong, but you see it again and again and again and again. The p-value only tells you something about the probability of seeing your results given a particular hypothetical explanation — it cannot tell you the probability that the results are true or whether they’re due to random chance. The ASA statement’s Principle No. 2: “P-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.”
Nor can a p-value tell you the size of an effect, the strength of the evidence or the importance of a result. Yet despite all these limitations, p-values are often used as a way to separate true findings from spurious ones, and that creates perverse incentives. When the goal shifts from seeking the truth to obtaining a p-value that clears an arbitrary threshold (0.05 or less is considered “statistically significant” in many fields), researchers tend to fish around in their data and keep trying different analyses until they find something with the right p-value, as you can see for yourself in a p-hacking tool we built last year.
Indeed, many of the ASA committee’s members argue in their commentaries that the problem isn’t p-values, just the way they’re used — “failing to adjust them for cherry picking, multiple testing, post-data subgroups and other biasing selection effects,” as Deborah Mayo, a philosopher of statistics at Virginia Tech, puts it. When p-values are treated as a way to sort results into bins labeled significant or not significant, the vast efforts to collect and analyze data are degraded into mere labels, said Kenneth Rothman, an epidemiologist at Boston University.
The 20 commentaries published with the ASA statement present a range of ideas about where to go from here. Some committee members argued that there should be a move to rely more on other measures, such as confidence intervals or Bayesian analyses. Others felt that switching to something else would only shift the problem around. “The solution is not to reform p-values or to replace them with some other statistical summary or threshold,” wrote Columbia University statistician Andrew Gelman, “but rather to move toward a greater acceptance of uncertainty and embracing of variation.”
If there’s one takeaway from the ASA statement, it’s that p-values are not badges of truth and p < 0.05 is not a line that separates real results from false ones. They’re simply one piece of a puzzle that should be considered in the context of other evidence.
This story began with a haiku from one of the p-value document’s companion responses; let’s end it with a limerick by University of Michigan biostatistician Roderick Little.
In statistics, one rule did we cherish:
P point oh five we publish, else perish!
Said Val Johnson, “that’s out of date, Our studies don’t replicate
P point oh oh five, then null is rubbish!”
CORRECTION (March 7, 11:05 a.m.): An earlier version of this article misstated the university where Deborah Mayo is a professor. She teaches at Virginia Tech, not the University of Pennsylvania.
- Even the Supreme Court has weighed in, unanimously ruling in 2011 that statistical significance does not automatically equate to scientific or policy importance. ^
Christie Aschwanden is FiveThirtyEight’s lead writer for science.
We create words to label people, places, actions, thoughts, and more so we can express ourselves meaningfully to others. Do humans’ shared cognitive abilities and dependence on languages naturally provide a universal means of organizing certain concepts? Or do environment and culture influence each language uniquely?
Using a new methodology that measures how closely words’ meanings are related within and between languages, an international team of researchers has revealed that for many universal concepts, the world’s languages feature a common structure of semantic relatedness.
“Before this work, little was known about how to measure [a culture’s sense of] the semantic nearness between concepts,” says co-author and Santa Fe Institute Professor Tanmoy Bhattacharya. “For example, are the concepts of sun and moon close to each other, as they are both bright blobs in the sky? How about sand and sea, as they occur close by? Which of these pairs is the closer? How do we know?”
Translation, the mapping of relative word meanings across languages, would provide clues. But examining the problem with scientific rigor called for an empirical means to denote the degree of semantic relatedness between concepts.
To get reliable answers, Bhattacharya needed to fully quantify a comparative method that is commonly used to infer linguistic history qualitatively. (He and collaborators had previously developed this quantitative method to study changes in sounds of words as languages evolve.)
“Translation uncovers a disagreement between two languages on how concepts are grouped under a single word,” says co-author and Santa Fe Institute and Oxford researcher Hyejin Youn. “Spanish, for example, groups ‘fire’ and ‘passion’ under ‘incendio,’ whereas Swahili groups ‘fire’ with ‘anger’ (but not ‘passion’).”
To quantify the problem, the researchers chose a few basic concepts that we see in nature (sun, moon, mountain, fire, and so on). Each concept was translated from English into 81 diverse languages, then back into English. Based on these translations, a weighted network was created. The structure of the network was used to compare languages’ ways of partitioning concepts.
The team found that the translated concepts consistently formed three theme clusters in a network, densely connected within themselves and weakly to one another: water, solid natural materials, and earth and sky.
“For the first time, we now have a method to quantify how universal these relations are,” says Bhattacharya. “What is universal – and what is not – about how we group clusters of meanings teaches us a lot about psycholinguistics, the conceptual structures that underlie language use.”
The researchers hope to expand this study’s domain, adding more concepts, then investigating how the universal structure they reveal underlies meaning shift.
Their research was published today in PNAS.
Date: January 21, 2016
- Source: The Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences
Summary: James Joyce, Julio Cortazar, Marcel Proust, Henryk Sienkiewicz and Umberto Eco. Regardless of the language they were working in, some of the world’s greatest writers appear to be, in some respects, constructing fractals. Statistical analysis, however, revealed something even more intriguing. The composition of works from within a particular genre was characterized by the exceptional dynamics of a cascading (avalanche) narrative structure.
James Joyce, Julio Cortazar, Marcel Proust, Henryk Sienkiewicz and Umberto Eco. Regardless of the language they were working in, some of the world’s greatest writers appear to be, in some respects, constructing fractals. Statistical analysis carried out at the Institute of Nuclear Physics of the Polish Academy of Sciences, however, revealed something even more intriguing. The composition of works from within a particular genre was characterized by the exceptional dynamics of a cascading (avalanche) narrative structure. This type of narrative turns out to be multifractal. That is, fractals of fractals are created.
As far as many bookworms are concerned, advanced equations and graphs are the last things which would hold their interest, but there’s no escape from the math. Physicists from the Institute of Nuclear Physics of the Polish Academy of Sciences (IFJ PAN) in Cracow, Poland, performed a detailed statistical analysis of more than one hundred famous works of world literature, written in several languages and representing various literary genres. The books, tested for revealing correlations in variations of sentence length, proved to be governed by the dynamics of a cascade. This means that the construction of these books is in fact a fractal. In the case of several works their mathematical complexity proved to be exceptional, comparable to the structure of complex mathematical objects considered to be multifractal. Interestingly, in the analyzed pool of all the works, one genre turned out to be exceptionally multifractal in nature.
Fractals are self-similar mathematical objects: when we begin to expand one fragment or another, what eventually emerges is a structure that resembles the original object. Typical fractals, especially those widely known as the Sierpinski triangle and the Mandelbrot set, are monofractals, meaning that the pace of enlargement in any place of a fractal is the same, linear: if they at some point were rescaled x number of times to reveal a structure similar to the original, the same increase in another place would also reveal a similar structure.
Multifractals are more highly advanced mathematical structures: fractals of fractals. They arise from fractals ‘interwoven’ with each other in an appropriate manner and in appropriate proportions. Multifractals are not simply the sum of fractals and cannot be divided to return back to their original components, because the way they weave is fractal in nature. The result is that in order to see a structure similar to the original, different portions of a multifractal need to expand at different rates. A multifractal is therefore non-linear in nature.
“Analyses on multiple scales, carried out using fractals, allow us to neatly grasp information on correlations among data at various levels of complexity of tested systems. As a result, they point to the hierarchical organization of phenomena and structures found in nature. So we can expect natural language, which represents a major evolutionary leap of the natural world, to show such correlations as well. Their existence in literary works, however, had not yet been convincingly documented. Meanwhile, it turned out that when you look at these works from the proper perspective, these correlations appear to be not only common, but in some works they take on a particularly sophisticated mathematical complexity,” says Prof. Stanislaw Drozdz (IFJ PAN, Cracow University of Technology).
The study involved 113 literary works written in English, French, German, Italian, Polish, Russian and Spanish by such famous figures as Honore de Balzac, Arthur Conan Doyle, Julio Cortazar, Charles Dickens, Fyodor Dostoevsky, Alexandre Dumas, Umberto Eco, George Elliot, Victor Hugo, James Joyce, Thomas Mann, Marcel Proust, Wladyslaw Reymont, William Shakespeare, Henryk Sienkiewicz, JRR Tolkien, Leo Tolstoy and Virginia Woolf, among others. The selected works were no less than 5,000 sentences long, in order to ensure statistical reliability.
To convert the texts to numerical sequences, sentence length was measured by the number of words (an alternative method of counting characters in the sentence turned out to have no major impact on the conclusions). The dependences were then searched for in the data — beginning with the simplest, i.e. linear. This is the posited question: if a sentence of a given length is x times longer than the sentences of different lengths, is the same aspect ratio preserved when looking at sentences respectively longer or shorter?
“All of the examined works showed self-similarity in terms of organization of the lengths of sentences. Some were more expressive — here The Ambassadors by Henry James stood out — while others to far less of an extreme, as in the case of the French seventeenth-century romance Artamene ou le Grand Cyrus. However, correlations were evident, and therefore these texts were the construction of a fractal,” comments Dr. Pawel Oswiecimka (IFJ PAN), who also noted that fractality of a literary text will in practice never be as perfect as in the world of mathematics. It is possible to magnify mathematical fractals up to infinity, while the number of sentences in each book is finite, and at a certain stage of scaling there will always be a cut-off in the form of the end of the dataset.
Things took a particularly interesting turn when physicists from the IFJ PAN began tracking non-linear dependence, which in most of the studied works was present to a slight or moderate degree. However, more than a dozen works revealed a very clear multifractal structure, and almost all of these proved to be representative of one genre, that of stream of consciousness. The only exception was the Bible, specifically the Old Testament, which has so far never been associated with this literary genre.
“The absolute record in terms of multifractality turned out to be Finnegan’s Wake by James Joyce. The results of our analysis of this text are virtually indistinguishable from ideal, purely mathematical multifractals,” says Prof. Drozdz.
The most multifractal works also included A Heartbreaking Work of Staggering Genius by Dave Eggers, Rayuela by Julio Cortazar, The US Trilogy by John Dos Passos, The Waves by Virginia Woolf, 2666 by Roberto Bolano, and Joyce’s Ulysses. At the same time a lot of works usually regarded as stream of consciousness turned out to show little correlation to multifractality, as it was hardly noticeable in books such as Atlas Shrugged by Ayn Rand and A la recherche du temps perdu by Marcel Proust.
“It is not entirely clear whether stream of consciousness writing actually reveals the deeper qualities of our consciousness, or rather the imagination of the writers. It is hardly surprising that ascribing a work to a particular genre is, for whatever reason, sometimes subjective. We see, moreover, the possibility of an interesting application of our methodology: it may someday help in a more objective assignment of books to one genre or another,” notes Prof. Drozdz.
Multifractal analyses of literary texts carried out by the IFJ PAN have been published in Information Sciences, a journal of computer science. The publication has undergone rigorous verification: given the interdisciplinary nature of the subject, editors immediately appointed up to six reviewers.
- Stanisław Drożdż, Paweł Oświȩcimka, Andrzej Kulig, Jarosław Kwapień, Katarzyna Bazarnik, Iwona Grabska-Gradzińska, Jan Rybicki, Marek Stanuszek. Quantifying origin and character of long-range correlations in narrative texts. Information Sciences, 2016; 331: 32 DOI: 10.1016/j.ins.2015.10.023
If I asked you what most defines Donald Trump supporters, what would you say? They’re white? They’re poor? They’re uneducated?
You’d be wrong.
That’s right, Trump’s electoral strength—and his staying power—have been buoyed, above all, by Americans with authoritarian inclinations. And because of the prevalence of authoritarians in the American electorate, among Democrats as well as Republicans, it’s very possible that Trump’s fan base will continue to grow.
My finding is the result of a national poll I conducted in the last five days of December under the auspices of the University of Massachusetts, Amherst, sampling 1,800 registered voters across the country and the political spectrum. Running a standard statistical analysis, I found that education, income, gender, age, ideology and religiosity had no significant bearing on a Republican voter’s preferred candidate. Only two of the variables I looked at were statistically significant: authoritarianism, followed by fear of terrorism, though the former was far more significant than the latter.
Authoritarianism is not a new, untested concept in the American electorate. Since the rise of Nazi Germany, it has been one of the most widely studied ideas in social science. While its causes are still debated, the political behavior of authoritarians is not. Authoritarians obey. They rally to and follow strong leaders. And they respond aggressively to outsiders, especially when they feel threatened. From pledging to “make America great again” by building a wall on the border to promising to close mosques and ban Muslims from visiting the United States, Trump is playing directly to authoritarian inclinations.
Not all authoritarians are Republicans by any means; in national surveys since 1992, many authoritarians have also self-identified as independents and Democrats. And in the 2008 Democratic primary, the political scientist Marc Hetherington found that authoritarianism mattered more than income, ideology, gender, age and education in predicting whether voters preferred Hillary Clinton over Barack Obama. But Hetherington has also found, based on 14 years of polling, that authoritarians have steadily moved from the Democratic to the Republican Party over time. He hypothesizes that the trend began decades ago, as Democrats embraced civil rights, gay rights, employment protections and other political positions valuing freedom and equality. In my poll results, authoritarianism was not a statistically significant factor in the Democratic primary race, at least not so far, but it does appear to be playing an important role on the Republican side. Indeed, 49 percent of likely Republican primary voters I surveyed score in the top quarter of the authoritarian scale—more than twice as many as Democratic voters.
Political pollsters have missed this key component of Trump’s support because they simply don’t include questions about authoritarianism in their polls. In addition to the typical battery of demographic, horse race, thermometer-scale and policy questions, my poll asked a set of four simple survey questions that political scientists have employed since 1992 to measure inclination toward authoritarianism. These questions pertain to child-rearing: whether it is more important for the voter to have a child who is respectful or independent; obedient or self-reliant; well-behaved or considerate; and well-mannered or curious. Respondents who pick the first option in each of these questions are strongly authoritarian.
Based on these questions, Trump was the only candidate—Republican or Democrat—whose support among authoritarians was statistically significant.
So what does this mean for the election? It doesn’t just help us understand what motivates Trump’s backers—it suggests that his support isn’t capped. In a statistical analysis of the polling results, I found that Trump has already captured 43 percent of Republican primary voters who are strong authoritarians, and 37 percent of Republican authoritarians overall. A majority of Republican authoritarians in my poll also strongly supported Trump’s proposals to deport 11 million illegal immigrants, prohibit Muslims from entering the United States, shutter mosques and establish a nationwide database that track Muslims.
And in a general election, Trump’s strongman rhetoric will surely appeal to some of the 39 percent of independents in my poll who identify as authoritarians and the 17 percent of self-identified Democrats who are strong authoritarians.
What’s more, the number of Americans worried about the threat of terrorism is growing. In 2011, Hetherington published research finding that non-authoritarians respond to the perception of threat by behaving more like authoritarians. More fear and more threats—of the kind we’ve seen recently in the San Bernardino and Paris terrorist attacks—mean more voters are susceptible to Trump’s message about protecting Americans. In my survey, 52 percent of those voters expressing the most fear that another terrorist attack will occur in the United States in the next 12 months were non-authoritarians—ripe targets for Trump’s message.
Take activated authoritarians from across the partisan spectrum and the growing cadre of threatened non-authoritarians, then add them to the base of Republican general election voters, and the potential electoral path to a Trump presidency becomes clearer.
So, those who say a Trump presidency “can’t happen here” should check their conventional wisdom at the door. The candidate has confounded conventional expectations this primary season because those expectations are based on an oversimplified caricature of the electorate in general and his supporters in particular. Conditions are ripe for an authoritarian leader to emerge. Trump is seizing the opportunity. And the institutions—from the Republican Party to the press—that are supposed to guard against what James Madison called “the infection of violent passions” among the people have either been cowed by Trump’s bluster or are asleep on the job.
It is time for those who would appeal to our better angels to take his insurgency seriously and stop dismissing his supporters as a small band of the dispossessed. Trump support is firmly rooted in American authoritarianism and, once awakened, it is a force to be reckoned with. That means it’s also time for political pollsters to take authoritarianism seriously and begin measuring it in their polls.
11 de dezembro de 2015
José Tadeu Arantes | Agência FAPESP – O computador quântico poderá deixar de ser um sonho e se tornar realidade nos próximos 10 anos. A expectativa é que isso traga uma drástica redução no tempo de processamento, já que algoritmos quânticos oferecem soluções mais eficientes para certas tarefas computacionais do que quaisquer algoritmos clássicos correspondentes.
Até agora, acreditava-se que a chave da computação quântica eram as correlações entre dois ou mais sistemas. Exemplo de correlação quântica é o processo de “emaranhamento”, que ocorre quando pares ou grupos de partículas são gerados ou interagem de tal maneira que o estado quântico de cada partícula não pode ser descrito independentemente, já que depende do conjunto (Para mais informações veja agencia.fapesp.br/20553/).
Um estudo recente mostrou, no entanto, que mesmo um sistema quântico isolado, ou seja, sem correlações com outros sistemas, é suficiente para implementar um algoritmo quântico mais rápido do que o seu análogo clássico. Artigo descrevendo o estudo foi publicado no início de outubro deste ano na revista Scientific Reports, do grupo Nature: Computational speed-up with a single qudit.
O trabalho, ao mesmo tempo teórico e experimental, partiu de uma ideia apresentada pelo físico Mehmet Zafer Gedik, da Sabanci Üniversitesi, de Istambul, Turquia. E foi realizado mediante colaboração entre pesquisadores turcos e brasileiros. Felipe Fernandes Fanchini, da Faculdade de Ciências da Universidade Estadual Paulista (Unesp), no campus de Bauru, é um dos signatários do artigo. Sua participação no estudo se deu no âmbito do projeto Controle quântico em sistemas dissipativos, apoiado pela FAPESP.
“Este trabalho traz uma importante contribuição para o debate sobre qual é o recurso responsável pelo poder de processamento superior dos computadores quânticos”, disse Fanchini à Agência FAPESP.
“Partindo da ideia de Gedik, realizamos no Brasil um experimento, utilizando o sistema de ressonância magnética nuclear (RMN) da Universidade de São Paulo (USP) em São Carlos. Houve, então, a colaboração de pesquisadores de três universidades: Sabanci, Unesp e USP. E demonstramos que um circuito quântico dotado de um único sistema físico, com três ou mais níveis de energia, pode determinar a paridade de uma permutação numérica avaliando apenas uma vez a função. Isso é impensável em um protocolo clássico.”
Segundo Fanchini, o que Gedik propôs foi um algoritmo quântico muito simples que, basicamente, determina a paridade de uma sequência. O conceito de paridade é utilizado para informar se uma sequência está em determinada ordem ou não. Por exemplo, se tomarmos os algarismos 1, 2 e 3 e estabelecermos que a sequência 1- 2-3 está em ordem, as sequências 2-3-1 e 3-1-2, resultantes de permutações cíclicas dos algarismos, estarão na mesma ordem.
Isso é fácil de entender se imaginarmos os algarismos dispostos em uma circunferência. Dada a primeira sequência, basta girar uma vez em um sentido para obter a sequência seguinte, e girar mais uma vez para obter a outra. Porém, as sequências 1-3-2, 3-2-1 e 2-1-3 necessitam, para serem criadas, de permutações acíclicas. Então, se convencionarmos que as três primeiras sequências são “pares”, as outras três serão “ímpares”.
“Em termos clássicos, a observação de um único algarismo, ou seja uma única medida, não permite dizer se a sequência é par ou ímpar. Para isso, é preciso realizar ao menos duas observações. O que Gedik demonstrou foi que, em termos quânticos, uma única medida é suficiente para determinar a paridade. Por isso, o algoritmo quântico é mais rápido do que qualquer equivalente clássico. E esse algoritmo pode ser concretizado por meio de uma única partícula. O que significa que sua eficiência não depende de nenhum tipo de correlação quântica”, informou Fanchini.
O algoritmo em pauta não diz qual é a sequência. Mas informa se ela é par ou ímpar. Isso só é possível quando existem três ou mais níveis. Porque, havendo apenas dois níveis, algo do tipo 1-2 ou 2-1, não é possível definir uma sequência par ou ímpar. “Nos últimos tempos, a comunidade voltada para a computação quântica vem explorando um conceito-chave da teoria quântica, que é o conceito de ‘contextualidade’. Como a ‘contextualidade’ também só opera a partir de três ou mais níveis, suspeitamos que ela possa estar por trás da eficácia de nosso algoritmo”, acrescentou o pesquisador.
Conceito de contextulidade
“O conceito de ‘contextualidade’ pode ser melhor entendido comparando-se as ideias de mensuração da física clássica e da física quântica. Na física clássica, supõe-se que a mensuração nada mais faça do que desvelar características previamente possuídas pelo sistema que está sendo medido. Por exemplo, um determinado comprimento ou uma determinada massa. Já na física quântica, o resultado da mensuração não depende apenas da característica que está sendo medida, mas também de como foi organizada a mensuração, e de todas as mensurações anteriores. Ou seja, o resultado depende do contexto do experimento. E a ‘contextualidade’ é a grandeza que descreve esse contexto”, explicou Fanchini.
Na história da física, a “contextualidade” foi reconhecida como uma característica necessária da teoria quântica por meio do famoso Teorema de Bell. Segundo esse teorema, publicado em 1964 pelo físico irlandês John Stewart Bell (1928 – 1990), nenhuma teoria física baseada em variáveis locais pode reproduzir todas as predições da mecânica quântica. Em outras palavras, os fenômenos físicos não podem ser descritos em termos estritamente locais, uma vez que expressam a totalidade.
“É importante frisar que em outro artigo [Contextuality supplies the ‘magic’ for quantum computation] publicado na Nature em junho de 2014, aponta a contextualidade como a possível fonte do poder da computação quântica. Nosso estudo vai no mesmo sentido, apresentando um algoritmo concreto e mais eficiente do que qualquer um jamais imaginável nos moldes clássicos.”
Scalable 3-D silicon chip architecture based on single atom quantum bits provides a blueprint to build operational quantum computers
- October 30, 2015
- University of New South Wales
- Researchers have designed a full-scale architecture for a quantum computer in silicon. The new concept provides a pathway for building an operational quantum computer with error correction.
Australian scientists have designed a 3D silicon chip architecture based on single atom quantum bits, which is compatible with atomic-scale fabrication techniques — providing a blueprint to build a large-scale quantum computer.
Scientists and engineers from the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (CQC2T), headquartered at the University of New South Wales (UNSW), are leading the world in the race to develop a scalable quantum computer in silicon — a material well-understood and favoured by the trillion-dollar computing and microelectronics industry.
Teams led by UNSW researchers have already demonstrated a unique fabrication strategy for realising atomic-scale devices and have developed the world’s most efficient quantum bits in silicon using either the electron or nuclear spins of single phosphorus atoms. Quantum bits — or qubits — are the fundamental data components of quantum computers.
One of the final hurdles to scaling up to an operational quantum computer is the architecture. Here it is necessary to figure out how to precisely control multiple qubits in parallel, across an array of many thousands of qubits, and constantly correct for ‘quantum’ errors in calculations.
Now, the CQC2T collaboration, involving theoretical and experimental researchers from the University of Melbourne and UNSW, has designed such a device. In a study published today in Science Advances, the CQC2T team describes a new silicon architecture, which uses atomic-scale qubits aligned to control lines — which are essentially very narrow wires — inside a 3D design.
“We have demonstrated we can build devices in silicon at the atomic-scale and have been working towards a full-scale architecture where we can perform error correction protocols — providing a practical system that can be scaled up to larger numbers of qubits,” says UNSW Scientia Professor Michelle Simmons, study co-author and Director of the CQC2T.
“The great thing about this work, and architecture, is that it gives us an endpoint. We now know exactly what we need to do in the international race to get there.”
In the team’s conceptual design, they have moved from a one-dimensional array of qubits, positioned along a single line, to a two-dimensional array, positioned on a plane that is far more tolerant to errors. This qubit layer is “sandwiched” in a three-dimensional architecture, between two layers of wires arranged in a grid.
By applying voltages to a sub-set of these wires, multiple qubits can be controlled in parallel, performing a series of operations using far fewer controls. Importantly, with their design, they can perform the 2D surface code error correction protocols in which any computational errors that creep into the calculation can be corrected faster than they occur.
“Our Australian team has developed the world’s best qubits in silicon,” says University of Melbourne Professor Lloyd Hollenberg, Deputy Director of the CQC2T who led the work with colleague Dr Charles Hill. “However, to scale up to a full operational quantum computer we need more than just many of these qubits — we need to be able to control and arrange them in such a way that we can correct errors quantum mechanically.”
“In our work, we’ve developed a blueprint that is unique to our system of qubits in silicon, for building a full-scale quantum computer.”
In their paper, the team proposes a strategy to build the device, which leverages the CQC2T’s internationally unique capability of atomic-scale device fabrication. They have also modelled the required voltages applied to the grid wires, needed to address individual qubits, and make the processor work.
“This architecture gives us the dense packing and parallel operation essential for scaling up the size of the quantum processor,” says Scientia Professor Sven Rogge, Head of the UNSW School of Physics. “Ultimately, the structure is scalable to millions of qubits, required for a full-scale quantum processor.”
In classical computers, data is rendered as binary bits, which are always in one of two states: 0 or 1. However, a qubit can exist in both of these states at once, a condition known as a superposition. A qubit operation exploits this quantum weirdness by allowing many computations to be performed in parallel (a two-qubit system performs the operation on 4 values, a three-qubit system on 8, and so on).
As a result, quantum computers will far exceed today’s most powerful super computers, and offer enormous advantages for a range of complex problems, such as rapidly scouring vast databases, modelling financial markets, optimising huge metropolitan transport networks, and modelling complex biological molecules.
How to build a quantum computer in silicon https://youtu.be/zo1q06F2sbY
Modelos de computador sugerem que leste amazônico, que contém a maior parte da floresta, teria mais estiagens, incêndios e morte de árvores, enquanto o oeste ficaria mais chuvoso.
As mudanças climáticas podem aumentar a frequência tanto de secas quanto de chuvas extremas na Amazônia antes do meio do século, compondo com o desmatamento para causar mortes maciças de árvores, incêndios e emissões de carbono. A conclusão é de uma avaliação de 35 modelos climáticos aplicados à região, feita por pesquisadores dos EUA e do Brasil.
Segundo o estudo, liderado por Philip Duffy, do WHRC (Instituto de Pesquisas de Woods Hole, nos EUA) e da Universidade Stanford, a área afetada por secas extremas no leste amazônico, região que engloba a maior parte da Amazônia, pode triplicar até 2100. Paradoxalmente, a frequência de períodos extremamente chuvosos e a área sujeita a chuvas extremas tende a crescer em toda a região após 2040 – mesmo nos locais onde a precipitação média anual diminuir.
Já o oeste amazônico, em especial o Peru e a Colômbia, deve ter um aumento na precipitação média anual.
A mudança no regime de chuvas é um efeito há muito teorizado do aquecimento global. Com mais energia na atmosfera e mais vapor d’água, resultante da maior evaporação dos oceanos, a tendência é que os extremos climáticos sejam amplificados. As estações chuvosas – na Amazônia, o período de verão no hemisfério sul, chamado pelos moradores da região de “inverno” ficam mais curtas, mas as chuvas caem com mais intensidade.
No entanto, a resposta da floresta essas mudanças tem sido objeto de controvérsias entre os cientistas. Estudos da década de 1990 propuseram que a reação da Amazônia fosse ser uma ampla “savanização”, ou mortandade de grandes árvores, e a transformação de vastas porções da selva numa savana empobrecida.
Outros estudos, porém, apontaram que o calor e o CO2 extra teriam o efeito oposto – o de fazer as árvores crescerem mais e fixarem mais carbono, de modo a compensar eventuais perdas por seca. Na média, portanto, o impacto do aquecimento global sobre a Amazônia seria relativamente pequeno.
Ocorre que a própria Amazônia encarregou-se de dar aos cientistas dicas de como reagiria. Em 2005, 2007 e 2010, a floresta passou por secas históricas. O resultado foi ampla mortalidade de árvores e incêndios em florestas primárias em mais de 85 mil quilômetros quadrados. O grupo de Duffy, também integrado por Paulo Brando, do Ipam (Instituto de Pesquisa Ambiental da Amazônia), aponta que de 1% a 2% do carbono da Amazônia foi lançado na atmosfera em decorrência das secas da década de 2000. Brando e colegas do Ipam também já haviam mostrado que a Amazônia está mais inflamável, provavelmente devido aos efeitos combinados do clima e do desmatamento.
Os pesquisadores simularam o clima futuro da região usando os modelos do chamado projeto CMIP5, usado pelo IPCC (Painel Intergovernamental sobre Mudança Climática) no seu último relatório de avaliação do clima global. Um dos membros do grupo, Chris Field, de Stanford, foi um dos coordenadores do relatório – foi também candidato à presidência do IPCC na eleição realizada na semana passada, perdendo para o coreano Hoesung Lee.
Os modelos de computador foram testados no pior cenário de emissões, o chamado RMP 8.5, no qual se assume que pouca coisa será feita para controlar emissões de gases-estufa.
Eles não apenas captaram bem a influência das temperaturas dos oceanos Atlântico e Pacífico sobre o padrão de chuvas na Amazônia – diferenças entre os dois oceanos explicam por que o leste amazônico ficará mais seco e o oeste, mais úmido –, como também mostraram nas simulações de seca futura uma característica das secas recorde de 2005 e 2010: o extremo norte da Amazônia teve grande aumento de chuvas enquanto o centro e o sul estorricavam.
Segundo os pesquisadores, o estudo pode ser até mesmo conservador, já que só levou em conta as variações de precipitação. “Por exemplo, as chuvas no leste da Amazônia têm uma forte dependência da evapotranspiração, então uma redução na cobertura de árvores poderia reduzir a precipitação”, escreveram Duffy e Brando. “Isso sugere que, se os processos relacionados a mudanças no uso da terra fossem mais bem representados nos modelos do CMIP5, a intensidade das secas poderia ser maior do que a projetada aqui.”
O estudo foi publicado na PNAS, a revista da Academia Nacional de Ciências dos EUA. (Observatório do Clima/ #Envolverde)
* Publicado originalmente no site Observatório do Clima.
- August 25, 2015
- University of Warwick
- Targeted punishments could provide a path to international climate change cooperation, new research in game theory has found.
Targeted punishments could provide a path to international climate change cooperation, new research in game theory has found.
Conducted at the University of Warwick, the research suggests that in situations such as climate change, where everyone would be better off if everyone cooperated but it may not be individually advantageous to do so, the use of a strategy called ‘targeted punishment’ could help shift society towards global cooperation.
Despite the name, the ‘targeted punishment’ mechanism can apply to positive or negative incentives. The research argues that the key factor is that these incentives are not necessarily applied to everyone who may seem to deserve them. Rather, rules should be devised according to which only a small number of players are considered responsible at any one time.
The study’s author Dr Samuel Johnson, from the University of Warwick’s Mathematics Institute, explains: “It is well known that some form of punishment, or positive incentives, can help maintain cooperation in situations where almost everyone is already cooperating, such as in a country with very little crime. But when there are only a few people cooperating and many more not doing so punishment can be too dilute to have any effect. In this regard, the international community is a bit like a failed state.”
The paper, published in Royal Society Open Science, shows that in situations of entrenched defection (non-cooperation), there exist strategies of ‘targeted punishment’ available to would-be punishers which can allow them to move a community towards global cooperation.
“The idea,” said Dr Johnson, “is not to punish everyone who is defecting, but rather to devise a rule whereby only a small number of defectors are considered at fault at any one time. For example, if you want to get a group of people to cooperate on something, you might arrange them on an imaginary line and declare that a person is liable to be punished if and only if the person to their left is cooperating while they are not. This way, those people considered at fault will find themselves under a lot more pressure than if responsibility were distributed, and cooperation can build up gradually as each person decides to fall in line when the spotlight reaches them.”
For the case of climate change, the paper suggests that countries should be divided into groups, and these groups placed in some order — ideally, according roughly to their natural tendencies to cooperate. Governments would make commitments (to reduce emissions or leave fossil fuels in the ground, for instance) conditional on the performance of the group before them. This way, any combination of sanctions and positive incentives that other countries might be willing to impose would have a much greater effect.
“In the mathematical model,” said Dr Johnson, “the mechanism works best if the players are somewhat irrational. It seems a reasonable assumption that this might apply to the international community.”
- Samuel Johnson. Escaping the Tragedy of the Commons through Targeted Punishment. Royal Society Open Science, 2015 [link]
“The chemical echo of this century’s CO2 pollutiuon will reverberate for thousands of years,” said the report’s co-author, Hans Joachim Schellnhuber Photograph: Doug Perrine/Design Pics/Corbis
German researchers have demonstrated once again that the best way to limit climate change is to stop burning fossil fuels now.
In a “thought experiment” they tried another option: the future dramatic removal of huge volumes of carbon dioxide from the atmosphere. This would, they concluded, return the atmosphere to the greenhouse gas concentrations that existed for most of human history – but it wouldn’t save the oceans.
That is, the oceans would stay warmer, and more acidic, for thousands of years, and the consequences for marine life could be catastrophic.
The research, published in Nature Climate Change today delivers yet another demonstration that there is so far no feasible “technofix” that would allow humans to go on mining and drilling for coal, oil and gas (known as the “business as usual” scenario), and then geoengineer a solution when climate change becomes calamitous.
Sabine Mathesius (of the Helmholtz Centre for Ocean Research in Kiel and the Potsdam Institute for Climate Impact Research) and colleagues decided to model what could be done with an as-yet-unproven technology called carbon dioxide removal. One example would be to grow huge numbers of trees, burn them, trap the carbon dioxide, compress it and bury it somewhere. Nobody knows if this can be done, but Dr Mathesius and her fellow scientists didn’t worry about that.
They calculated that it might plausibly be possible to remove carbon dioxide from the atmosphere at the rate of 90 billion tons a year. This is twice what is spilled into the air from factory chimneys and motor exhausts right now.
The scientists hypothesised a world that went on burning fossil fuels at an accelerating rate – and then adopted an as-yet-unproven high technology carbon dioxide removal technique.
“Interestingly, it turns out that after ‘business as usual’ until 2150, even taking such enormous amounts of CO2 from the atmosphere wouldn’t help the deep ocean that much – after the acidified water has been transported by large-scale ocean circulation to great depths, it is out of reach for many centuries, no matter how much CO2 is removed from the atmosphere,” said a co-author, Ken Caldeira, who is normally based at the Carnegie Institution in the US.
The oceans cover 70% of the globe. By 2500, ocean surface temperatures would have increased by 5C (41F) and the chemistry of the ocean waters would have shifted towards levels of acidity that would make it difficult for fish and shellfish to flourish. Warmer waters hold less dissolved oxygen. Ocean currents, too, would probably change.
But while change happens in the atmosphere over tens of years, change in the ocean surface takes centuries, and in the deep oceans, millennia. So even if atmospheric temperatures were restored to pre-Industrial Revolution levels, the oceans would continue to experience climatic catastrophe.
“In the deep ocean, the chemical echo of this century’s CO2 pollution will reverberate for thousands of years,” said co-author Hans Joachim Schellnhuber, who directs the Potsdam Institute. “If we do not implement emissions reductions measures in line with the 2C (35.6F) target in time, we will not be able to preserve ocean life as we know it.”
Looking across the frozen sea of Ullsfjord in Norway. Melting Arctic sea ice is one complicating factor in comparing modeled and observed surface temperatures. Photograph: Neale Clark/Robert Harding World Imagery/Corbis
Global climate models aren’t given nearly enough credit for their accurate global temperature change projections. As the 2014 IPCC report showed, observed global surface temperature changes have been within the range of climate model simulations.
Now a new study shows that the models were even more accurate than previously thought. In previous evaluations like the one done by the IPCC, climate model simulations of global surface air temperature were compared to global surface temperature observational records like HadCRUT4. However, over the oceans, HadCRUT4 uses sea surface temperatures rather than air temperatures.
A depiction of how global temperatures calculated from models use air temperatures above the ocean surface (right frame), while observations are based on the water temperature in the top few metres (left frame). Created by Kevin Cowtan.
Thus looking at modeled air temperatures and HadCRUT4 observations isn’t quite an apples-to-apples comparison for the oceans. As it turns out, sea surface temperatures haven’t been warming fast as marine air temperatures, so this comparison introduces a bias that makes the observations look cooler than the model simulations. In reality, the comparisons weren’t quite correct. As lead author Kevin Cowtan told me,
We have highlighted the fact that the planet does not warm uniformly. Air temperatures warm faster than the oceans, air temperatures over land warm faster than global air temperatures. When you put a number on global warming, that number always depends on what you are measuring. And when you do a comparison, you need to ensure you are comparing the same things.
The model projections have generally reported global air temperatures. That’s quite helpful, because we generally live in the air rather than the water. The observations, by mixing air and water temperatures, are expected to slightly underestimate the warming of the atmosphere.
The new study addresses this problem by instead blending the modeled air temperatures over land with the modeled sea surface temperatures to allow for an apples-to-apples comparison. The authors also identified another challenging issue for these model-data comparisons in the Arctic. Over sea ice, surface air temperature measurements are used, but for open ocean, sea surface temperatures are used. As co-author Michael Mann notes, as Arctic sea ice continues to melt away, this is another factor that accurate model-data comparisons must account for.
One key complication that arises is that the observations typically extrapolate land temperatures over sea ice covered regions since the sea surface temperature is not accessible in that case. But the distribution of sea ice changes seasonally, and there is a long-term trend toward decreasing sea ice in many regions. So the observations actually represent a moving target.
A depiction of how as sea ice retreats, some grid cells change from taking air temperatures to taking water temperatures. If the two are not on the same scale, this introduces a bias. Created by Kevin Cowtan.
When accounting for these factors, the study finds that the difference between observed and modeled temperatures since 1975 is smaller than previously believed. The models had projected a 0.226°C per decade global surface air warming trend for 1975–2014 (and 0.212°C per decade over the geographic area covered by the HadCRUT4 record). However, when matching the HadCRUT4 methods for measuring sea surface temperatures, the modeled trend is reduced to 0.196°C per decade. The observed HadCRUT4 trend is 0.170°C per decade.
So when doing an apples-to-apples comparison, the difference between modeled global temperature simulations and observations is 38% smaller than previous estimates. Additionally, as noted in a 2014 paper led by NASA GISS director Gavin Schmidt, less energy from the sun has reached the Earth’s surface than anticipated in these model simulations, both because solar activity declined more than expected, and volcanic activity was higher than expected. Ed Hawkins, another co-author of this study, wrote about this effect.
Combined, the apparent discrepancy between observations and simulations of global temperature over the past 15 years can be partly explained by the way the comparison is done (about a third), by the incorrect radiative forcings (about a third) and the rest is either due to climate variability or because the models are slightly over sensitive on average. But, the room for the latter effect is now much smaller.
Comparison of 84 climate model simulations (using RCP8.5) against HadCRUT4 observations (black), using either air temperatures (red line and shading) or blended temperatures using the HadCRUT4 method (blue line and shading). The upper panel shows anomalies derived from the unmodified climate model results, the lower shows the results adjusted to include the effect of updated forcings from Schmidt et al. (2014).
As Hawkins notes, the remaining discrepancy between modeled and observed temperatures may come down to climate variability; namely the fact that there has been a preponderance of La Niña events over the past decade, which have a short-term cooling influence on global surface temperatures. When there are more La Niñas, we expect temperatures to fall below the average model projection, and when there are more El Niños, we expect temperatures to be above the projection, as may be the case when 2015 breaks the temperature record.
We can’t predict changes in solar activity, volcanic eruptions, or natural ocean cycles ahead of time. If we want to evaluate the accuracy of long-term global warming model projections, we have to account for the difference between the simulated and observed changes in these factors. When the authors of this study did so, they found that climate models have very accurately projected the observed global surface warming trend.
In other words, as I discussed in my book and Denial101x lecture, climate models have proven themselves reliable in predicting long-term global surface temperature changes. In fact, even more reliable than I realized.
Denial101x climate science success stories lecture by Dana Nuccitelli.
There’s a common myth that models are unreliable, often based on apples-to-oranges comparisons, like looking at satellite estimates of temperatures higher in the atmosphere versus modeled surface air temperatures. Or, some contrarians like John Christy will only consider the temperature high in the atmosphere, where satellite estimates are less reliable, and where people don’t live.
This new study has shown that when we do an apples-to-apples comparison, climate models have done a good job projecting the observed temperatures where humans live. And those models predict that unless we take serious and immediate action to reduce human carbon pollution, global warming will continue to accelerate into dangerous territory.
3 junho 2015
Um estudo de uma universidade britânica desenvolveu um novo meio de estimar multidões em protestos ou outros eventos de massa: através da análise de dados geográficos de celulares e Twitter.
Pesquisadores da Warwick University, na Inglaterra, analisaram a geolocalização de celulares e de mensagens no Twitter durante um período de dois meses em Milão, na Itália.
Em dois locais com números de visitantes conhecidos – um estádio de futebol e um aeroporto – a atividade nas redes sociais e nos celulares aumentou e diminuiu de maneira semelhante ao fluxo de pessoas.
A equipe disse que, utilizando esta técnica, pode fazer medições em eventos como protestos.
Outros pesquisadores enfatizaram o fato de que há limitações neste tipo de dados – por exemplo, somente uma parte da população usa smartphones e Twitter e nem todas as áreas em um espaço estão bem servidos de torres telefônicas.
Mas os autores do estudo dizem que os resultados foram “um excelente ponto de partida” para mais estimativas do tipo – com mais precisão – no futuro.
“Estes números são exemplos de calibração nos quais podemos nos basear”, disse o coautor do estudo, Tobias Preis.
“Obviamente seria melhor termos exemplos em outros países, outros ambientes, outros momentos. O comportamento humano não é uniforme em todo o mundo, mas está é uma base muito boa para conseguir estimativas iniciais.”
O estudo, divulgado na publicação científica Royal Society Open Science, é parte de um campo de pesquisa em expansão que explora o que a atividade online pode revelar sobre o comportamento humano e outros fenômenos reais.
Federico Botta, estudante de PhD que liderou a análise, afirmou que a metodologia baseada em celulares tem vantagens importantes sobre outros métodos para estimar o tamanho de multidões – que costumam se basear em observações no local ou em imagens.
“Este método é muito rápido e não depende do julgamento humano. Ele só depende dos dados que vêm dos telefones celulares ou da atividade no Twitter”, disse à BBC.
Margem de erro
Com dois meses de dados de celulares fornecidos pela Telecom Italia, Botta e seus colegas se concentraram no aeroporto de Linate e no estádio de futebol San Siro, em Milão.
Eles compararam o número de pessoas que se sabia estarem naqueles locais a cada momento – baseado em horários de voos e na venda de ingressos para os jogos de futebol – com três tipos de atividade em telefones celulares: o número de chamadas feitas e de mensagens de texto enviadas, a quantidade de internet utilizada e o volume de tuítes feitos.
“O que vimos é que estas atividades realmente tinham um comportamento muito semelhante ao número de pessoas no local”, afirma Botta.
Isso pode não parecer tão surpreendente, mas, especialmente no estádio de futebol, os padrões observados pela equipe eram tão confiáveis que eles conseguiam até fazer previsões.
Houve dez jogos de futebol no período em que o experimento foi feito. Com base nos dados de nove jogos, foi possível estimar quantas pessoas estariam no décimo jogo usando apenas os dados dos celulares.
“Nossa porcentagem absoluta média de erro é cerca de 13%. Isso significa que nossas estimativas e o número real de pessoas têm uma diferença entre si, em valores absolutos, de cerca de 13%”, diz Botta.
De acordo com os pesquisadores, esta margem de erro é boa em comparação com as técnicas tradicionais baseadas em imagens e no julgamento humano.
Eles deram o exemplo do manifestação em Washington, capital americana, conhecida como “Million Man March” (Passeata do milhão, em tradução livre) em 1995, em que mesmo as análises mais criteriosas conseguiram produzir estimativas com 20% de erro – depois que medições iniciais variaram entre 400 mil e dois milhões de pessoas.
Segundo Ed Manley, do Centro para Análise Espacial Avançada do University College London, a técnica tem potencial e as pessoas devem sentir-se “otimistas, mas cautelosas” em relação ao uso de dados de celulares nestas estimativas.
“Temos essas bases de dados enormes e há muito o que pode ser feito com elas… Mas precisamos ter cuidado com o quanto vamos exigir dos dados”, afirmou.
Ele também chama a atenção para o fato de que tais informações não refletem igualitariamente uma população.
“Há vieses importantes aqui. Quem exatamente estamos medindo com essas bases de dados?”, o Twitter, por exemplo, diz Manley, tem uma base de usuários relativamente jovem e de classe alta.
Além destas dificuldades, há o fato de que é preciso escolher com cuidado as atividades que serão medidas, porque as pessoas usam seus telefones de maneira diferente em diferentes lugares – mais chamadas no aeroporto e mais tuítes no futebol, por exemplo.
Outra ressalva importante é o fato de que toda a metodologia de análise defendida por Botta depende do sinal de telefone e internet – que varia muito de lugar para lugar, quando está disponível.
“Se estamos nos baseando nesses dados para saber onde as pessoas estão, o que acontece quando temos um problema com a maneira como os dados são coletados?”, indaga Manley.
⋅ APR 22, 2015
I have always liked to think of myself as a good listener. Whether you are in therapy (or should be), conversing with colleagues, working with customers, embarking on strategic planning, or collaborating on a task, a dose of emotional intelligence – that is, embracing patience and the willingness to listen — is essential.
At the American Mathematical Society, we recently embarked on ambitious strategic planning effort across the organization. On the publishing side we have a number of electronic products, pushing us to consider how we position these products for the next generation of mathematician. We quickly realized that it is easy to be complacent. In our case we have a rich history online, and yet – have we really moved with the times? Does a young mathematician need our products?
We came to a sobering and rather exciting realization: In fact, we do not have a clear idea how mathematicians use online resources to do their research, teaching, hiring, and job hunting. We of course have opinions, but these are not informed by anything other than anecdotal evidence from conversations here and there.
To gain a sense of how mathematicians are using online resources, we embarked on an effort to gather more systematic intelligence embracing a qualitative approach to the research – ethhnography. The concept of ethnographic qualitative research was a new one to me – and it felt right. I quickly felt like I was back in school and a graduate student in ethnography, reading the literature, and thinking through with colleagues how we might apply qualitative research methods to understanding mathematicians’ behavior. It is worth taking a look at two excellent books: Just Enough Research by Erika Hall, and Practical Ethnography: A Guide to Doing Ethnography in the Private Sector by Sam Ladner.
What do we mean by ethnographic research? In essence we are talking about a rich, multi-factorial descriptive approach. While quantitative research uses pre-existing categories in its analysis, qualitative research is open to new ways of categorizing data – in this case, mathematicians’ behavior in using information. The idea is that one observes the subject (“key informant” in technical jargon) in their natural habitat. Imagine you are David Attenborough, exploring an “absolutely marvelous” new species – the mathematician – as they operate in the field. The concept is really quite simple. You just want to understand what your key informants are doing, and preferably why they are doing it. One has to do it in a setting that allows for them to behave naturally – this really requires an interview with one person not a group (because group members may influence each other’s actions).
Perhaps the hardest part is the interview itself. If you are anything like me, you will go charging in saying something along the lines of “look at these great things we are doing. What do you think? Great right?” Well, of course this is plain wrong. While you have a goal going in, perhaps to see how an individual is behaving with respect to a specific product, your questions need to be agnostic in flavor. The idea is to have the key informant do what they normally do, not just say what they think they do – the two things may be quite different. The questions need to be carefully crafted so as not to lead, but to enable gentle probing and discussion as the interview progresses. It is a good idea to record the interview – both in audio form, and ideally with screen capture technology such as Camtasia. When I was involved with this I went out and bought a good, but inexpensive audio recorder.
We decided that rather than approach mathematicians directly, we should work with the library at an academic institution. Libraries are our customers. The remarkable thing about academic libraries is that ethnography is becoming part of the service they provide to their stakeholders at many institutions. We actually began with a remarkable librarian, based at Rice University – Debra Kolah. She is the head of the user experience office at the Fondren Library of Rice University in Texas. She also happens to be the physics, math and statistics librarian at Rice. Debra is remarkable, and has become an expert in ethnographic study of academic user experience. She has multiple projects underway at Rice, working with a range of stakeholders, aiming to foster the activity of the library in the academic community she directly serves. She is a picture of enthusiasm when it comes to serving her community and to gaining insights into the cultural patterns of academic user behavior. Debra was our key to understanding how important it is to work with the library to reach the mathematical community at an institution. The relationship is trusted and symbiotic. This triangle of an institution’s library, academic, and outside entity, such as a society, or publisher, may represent the future of the library.
So the interviews are done – then what? Analysis. You have to try to make sense of all of this material you’ve gathered. First, transcribing audio interviews is no easy task. You have a range of voices and much technical jargon. The best bet is to get one of the many services out there to take the files and do a first pass transcription. They will get most of it right. Perhaps they will write “archive instead of arXiv, but that can be dealt with later. Once you have all this interview text, you need to group it into meaningful categories – what’s called “coding”. The idea is that you try to look at the material with a fresh, unbiased eye, to see what themes emerge from the data. Once these themes are coded, you can then start to think about patterns in the data. Interestingly, qualitative researchers have developed a host of software programs to aid the researcher in doing this. We settled for a relatively simple, web based solution – Dedoose.
With some 62 interviews under our belt, we are beginning to see patterns emerge in the ways that mathematicians behave online. I am not going to reveal our preliminary findings here – I must save that up for when the full results are in – but I am confident that the results will show a number of consistent threads that will help us think through how to better serve our community.
In summary, this experience has been a fascinating one – a new world for me. I have been trained as a scientist. As a scientist, I have ideas about what scientific method is, and what evidence is. I now understand the value of the qualitative approach – hard for a scientist to say. Qualitative research opens a window to descriptive data and analysis. As our markets change, understanding who constitutes our market, and how users behave is more important than ever.
Carry on listening!
- April 27, 2015
- Vienna University of Technology
- The ‘holographic principle,’ the idea that a universe with gravity can be described by a quantum field theory in fewer dimensions, has been used for years as a mathematical tool in strange curved spaces. New results suggest that the holographic principle also holds in flat spaces. Our own universe could in fact be two dimensional and only appear three dimensional — just like a hologram.
At first glance, there is not the slightest doubt: to us, the universe looks three dimensional. But one of the most fruitful theories of theoretical physics in the last two decades is challenging this assumption. The “holographic principle” asserts that a mathematical description of the universe actually requires one fewer dimension than it seems. What we perceive as three dimensional may just be the image of two dimensional processes on a huge cosmic horizon.
Up until now, this principle has only been studied in exotic spaces with negative curvature. This is interesting from a theoretical point of view, but such spaces are quite different from the space in our own universe. Results obtained by scientists at TU Wien (Vienna) now suggest that the holographic principle even holds in a flat spacetime.
The Holographic Principle
Everybody knows holograms from credit cards or banknotes. They are two dimensional, but to us they appear three dimensional. Our universe could behave quite similarly: “In 1997, the physicist Juan Maldacena proposed the idea that there is a correspondence between gravitational theories in curved anti-de-sitter spaces on the one hand and quantum field theories in spaces with one fewer dimension on the other,” says Daniel Grumiller (TU Wien).
Gravitational phenomena are described in a theory with three spatial dimensions, the behaviour of quantum particles is calculated in a theory with just two spatial dimensions — and the results of both calculations can be mapped onto each other. Such a correspondence is quite surprising. It is like finding out that equations from an astronomy textbook can also be used to repair a CD-player. But this method has proven to be very successful. More than ten thousand scientific papers about Maldacena’s “AdS-CFT-correspondence” have been published to date.
Correspondence Even in Flat Spaces
For theoretical physics, this is extremely important, but it does not seem to have much to do with our own universe. Apparently, we do not live in such an anti-de-sitter-space. These spaces have quite peculiar properties. They are negatively curved, any object thrown away on a straight line will eventually return. “Our universe, in contrast, is quite flat — and on astronomic distances, it has positive curvature,” says Daniel Grumiller.
However, Grumiller has suspected for quite some time that a correspondence principle could also hold true for our real universe. To test this hypothesis, gravitational theories have to be constructed, which do not require exotic anti-de-sitter spaces, but live in a flat space. For three years, he and his team at TU Wien (Vienna) have been working on that, in cooperation with the University of Edinburgh, Harvard, IISER Pune, the MIT and the University of Kyoto. Now Grumiller and colleagues from India and Japan have published an article in the journal Physical Review Letters, confirming the validity of the correspondence principle in a flat universe.
Calculated Twice, Same Result
“If quantum gravity in a flat space allows for a holographic description by a standard quantum theory, then there must by physical quantities, which can be calculated in both theories — and the results must agree,” says Grumiller. Especially one key feature of quantum mechanics -quantum entanglement — has to appear in the gravitational theory.
When quantum particles are entangled, they cannot be described individually. They form a single quantum object, even if they are located far apart. There is a measure for the amount of entanglement in a quantum system, called “entropy of entanglement.” Together with Arjun Bagchi, Rudranil Basu and Max Riegler, Daniel Grumiller managed to show that this entropy of entanglement takes the same value in flat quantum gravity and in a low dimension quantum field theory.
“This calculation affirms our assumption that the holographic principle can also be realized in flat spaces. It is evidence for the validity of this correspondence in our universe,” says Max Riegler (TU Wien). “The fact that we can even talk about quantum information and entropy of entanglement in a theory of gravity is astounding in itself, and would hardly have been imaginable only a few years back. That we are now able to use this as a tool to test the validity of the holographic principle, and that this test works out, is quite remarkable,” says Daniel Grumiller.
This however, does not yet prove that we are indeed living in a hologram — but apparently there is growing evidence for the validity of the correspondence principle in our own universe.
- Arjun Bagchi, Rudranil Basu, Daniel Grumiller, Max Riegler. Entanglement Entropy in Galilean Conformal Field Theories and Flat Holography. Physical Review Letters, 2015; 114 (11) DOI: 10.1103/PhysRevLett.114.111602