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21. Chaos and Reductionism

21. Chaos and Reductionism
Related:  Complexity

On Early Warning Signs At a closed meeting held in Boston in October 2009, the room was packed with high-flyers in foreign policy and finance: Henry Kissinger, Paul Volcker, Andy Haldane, and Joseph Stiglitz, among others, as well as representatives of sovereign wealth funds, pensions, and endowments worth more than a trillion dollars—a significant slice of the world’s wealth. The session opened with the following telling question: “Have the last couple of years shown that our traditional finance/risk models are irretrievably broken and that models and approaches from other fields (for example, ecology) may offer a better understanding of the interconnectedness and fragility of complex financial systems?” Science is a creative human enterprise. Discoveries are made in the context of our creations: our models and hypotheses about how the world works. Examples of catastrophic and systemic changes have been gathering in a variety of fields, typically in specialized contexts with little cross-connection.

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Rio inaugura escola sem salas, turmas ou séries O Rio de Janeiro começa, nas próximas semanas, a experimentar um novo tipo de escola. Nada de séries, salas de aula com carteiras enfileiradas e crianças ordenadamente caminhando pelo espaço comum. A aposta para dar a 180 crianças e jovens da Rocinha uma educação mais alinhada com o século 21 é o Gente, acrônimo para Ginásio Experimental de Novas Tecnologias, na escola Municipal André Urani. O espaço, que acaba de ser totalmente reformulado para comportar a nova proposta, perdeu paredes, lousas, mesas individuais e professores tradicionais e ganhou grandes salões, tablets, “famílias”, times e mentores. Não houve pré-seleção. Os alunos que farão parte dessa nova metodologia já são os matriculados na escola antes da reforma. Essa avaliação, que ocorre assim que eles chegarem ao Gente, pretende fazer um raio-x do estado da aprendizagem de cada um, tanto do ponto de vista do conteúdo tradicional quanto das habilidades não cognitivas, como comunicação, senso crítico, autoria.

Math Isn't Just Computation. So Why Is That All We Teach? - Education A reader named Monika Hardy recently noticed that I harp a lot on the importance of math when blogging about education. (Guilty as charged.) So, she sent me an excellent talk from the recent TEDGlobal event from this summer. The speaker is Conrad Wolfram, brother of Stephen Wolfram, the polyglot behind the applications Mathematica and Wolfram|Alpha, who runs the firm Wolfram Research. His idea: Math is made up of four parts, and our schools are only teaching one of them. The elements of math, according to Wolfram are: posing questions, translating real world problems into mathematical language, performing computation, and translating mathematical answers into real world solutions. Computers should be doing those calculations. What about the processes needed to solve mathematical problems? Check out the video, it's really good stuff—at least, I think so.

Holism Holism: Holism as an idea or philosophical concept is diametrically opposed to atomism. Where the atomist believes that any whole can be broken down or analyzed into its separate parts and the relationships between them, the holist maintains that the whole is primary and often greater than the sum of its parts. The atomist divides things up in order to know them better; the holist looks at things or systems in aggregate and argues that we can know more about them viewed as such, and better understand their nature and their purpose. The early Greek atomism of Leucippus and Democritus (fifth century B.C.) was a forerunner of classical physics. In the seventeenth century, at the same time that classical physics gave renewed emphasis to atomism and reductionism, Spinoza developed a holistic philosophy reminiscent of Parmenides. Hegel, too, had mystical visions of the unity of all things, on which he based his own holistic philosophy of nature and the state.

The War on Kids (2009 THE WAR ON KIDS is a 95 minute documentary that shows how American public schools continue to become more dangerously authoritarian. In addition to failing in their mission to educate effectively, they erode the country's democratic foundation and often resemble prisons. School children are interviewed as are high school teachers and administrators, as well as prison security guards, plus renowned educators and authors including: Henry Giroux: Author of Stealing Innocence Corporate Culture's War on Children Mike A. Music in the film is performed by The Chumps, Tommy Gardner, John S. THE WAR ON KIDS is directed by Cevin Soling who won the NYIIFVF award for "best educational film" in 2009.

Body updated version is published in Mathematical Intelligencer, Vol. 23, No. 2, pp. 17-28, Spring 2001. David W. Henderson Department of Mathematics, Cornell University, Ithaca, NY, USA, dwh2@cornell.edu Daina Taimiða Department of Mathematics, Cornell University, dtaimina@math.cornell.edu For God's sake, please give it up.  Wolfgang Bolyai urging his son János Bolyai to give up work on hyperbolic geometry. In June of 1997, Daina was in a workshop watching the leader of the workshop, David, helping the participants study ideas of hyperbolic geometry using a paper and tape surface in much the same way that one can study ideas of spherical geometry by using the surface of a physical ball. But, Wait! Constructions of Hyperbolic Planes We will describe three different isometric constructions of the hyperbolic plane (or approximations to the hyperbolic plane) as surfaces in 3-space. 1. This is the paper and tape surface that David learned from William Thruston. Figure 1. 2. Figure 2. Figure 3. 3. 1.

NetLogo Home Page NetLogo is a multi-agent programmable modeling environment. It is used by many tens of thousands of students, teachers and researchers worldwide. It also powers HubNet participatory simulations. What can you do with NetLogo? Join mailing lists here. Download NetLogo Go to NetLogo Web NetLogo comes with a large library of sample models. 8 Studies Demonstrating the Power of Simplicity Psychological research on cognitive fluency shows why easy to understand = more profitable, more pleasurable, more intelligent and safer. Which of these would you say sounds like the more dangerous food additive: Hnegripitrom or Magnalroxate? The majority of people say Hnegripitrom sounds more dangerous. It turns out that the word ‘Magnalroxate’ is easier to think about than ‘Hnegripitrom’, probably because it’s more pronounceable, and people equate simplicity with safety (actually both words are made up). This is one example of psychological research on meta-cognition: thoughts about other thoughts. Here are 8 of my favourite studies on cognitive fluency, showing just how much can be explained by the feeling that something is easy to think about (or otherwise). 1. Many of us did it in school: tried to impress teachers with fancy language and convoluted sentences, assuming it would make us look clever. So if you want to be perceived as more intelligent (and who doesn’t?) 2. 3. 4. 5. 6. 7.

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