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Javier E

Opinion | A.I. Is Harder Than You Think - The New York Times - 1 views

  • The limitations of Google Duplex are not just a result of its being announced prematurely and with too much fanfare; they are also a vivid reminder that genuine A.I. is far beyond the field’s current capabilities, even at a company with perhaps the largest collection of A.I. researchers in the world, vast amounts of computing power and enormous quantities of data.
  • The crux of the problem is that the field of artificial intelligence has not come to grips with the infinite complexity of language. Just as you can make infinitely many arithmetic equations by combining a few mathematical symbols and following a small set of rules, you can make infinitely many sentences by combining a modest set of words and a modest set of rules.
  • A genuine, human-level A.I. will need to be able to cope with all of those possible sentences, not just a small fragment of them.
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  • No matter how much data you have and how many patterns you discern, your data will never match the creativity of human beings or the fluidity of the real world. The universe of possible sentences is too complex. There is no end to the variety of life — or to the ways in which we can talk about that variety.
  • Once upon a time, before the fashionable rise of machine learning and “big data,” A.I. researchers tried to understand how complex knowledge could be encoded and processed in computers. This project, known as knowledge engineering, aimed not to create programs that would detect statistical patterns in huge data sets but to formalize, in a system of rules, the fundamental elements of human understanding, so that those rules could be applied in computer programs.
  • That job proved difficult and was never finished. But “difficult and unfinished” doesn’t mean misguided. A.I. researchers need to return to that project sooner rather than later, ideally enlisting the help of cognitive psychologists who study the question of how human cognition manages to be endlessly flexible.
Javier E

What Does Quantum Physics Actually Tell Us About the World? - The New York Times - 2 views

  • The physics of atoms and their ever-smaller constituents and cousins is, as Adam Becker reminds us more than once in his new book, “What Is Real?,” “the most successful theory in all of science.” Its predictions are stunningly accurate, and its power to grasp the unseen ultramicroscopic world has brought us modern marvels.
  • But there is a problem: Quantum theory is, in a profound way, weird. It defies our common-sense intuition about what things are and what they can do.
  • Indeed, Heisenberg said that quantum particles “are not as real; they form a world of potentialities or possibilities rather than one of things or facts.”
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  • Before he died, Richard Feynman, who understood quantum theory as well as anyone, said, “I still get nervous with it...I cannot define the real problem, therefore I suspect there’s no real problem, but I’m not sure there’s no real problem.” The problem is not with using the theory — making calculations, applying it to engineering tasks — but in understanding what it means. What does it tell us about the world?
  • From one point of view, quantum physics is just a set of formalisms, a useful tool kit. Want to make better lasers or transistors or television sets? The Schrödinger equation is your friend. The trouble starts only when you step back and ask whether the entities implied by the equation can really exist. Then you encounter problems that can be described in several familiar ways:
  • Wave-particle duality. Everything there is — all matter and energy, all known forces — behaves sometimes like waves, smooth and continuous, and sometimes like particles, rat-a-tat-tat. Electricity flows through wires, like a fluid, or flies through a vacuum as a volley of individual electrons. Can it be both things at once?
  • The uncertainty principle. Werner Heisenberg famously discovered that when you measure the position (let’s say) of an electron as precisely as you can, you find yourself more and more in the dark about its momentum. And vice versa. You can pin down one or the other but not both.
  • The measurement problem. Most of quantum mechanics deals with probabilities rather than certainties. A particle has a probability of appearing in a certain place. An unstable atom has a probability of decaying at a certain instant. But when a physicist goes into the laboratory and performs an experiment, there is a definite outcome. The act of measurement — observation, by someone or something — becomes an inextricable part of the theory
  • The strange implication is that the reality of the quantum world remains amorphous or indefinite until scientists start measuring
  • Other interpretations rely on “hidden variables” to account for quantities presumed to exist behind the curtain.
  • This is disturbing to philosophers as well as physicists. It led Einstein to say in 1952, “The theory reminds me a little of the system of delusions of an exceedingly intelligent paranoiac.”
  • “Figuring out what quantum physics is saying about the world has been hard,” Becker says, and this understatement motivates his book, a thorough, illuminating exploration of the most consequential controversy raging in modern science.
  • In a way, the Copenhagen is an anti-interpretation. “It is wrong to think that the task of physics is to find out how nature is,” Bohr said. “Physics concerns what we can say about nature.”
  • Nothing is definite in Bohr’s quantum world until someone observes it. Physics can help us order experience but should not be expected to provide a complete picture of reality. The popular four-word summary of the Copenhagen interpretation is: “Shut up and calculate!”
  • Becker sides with the worriers. He leads us through an impressive account of the rise of competing interpretations, grounding them in the human stories
  • He makes a convincing case that it’s wrong to imagine the Copenhagen interpretation as a single official or even coherent statement. It is, he suggests, a “strange assemblage of claims.
  • An American physicist, David Bohm, devised a radical alternative at midcentury, visualizing “pilot waves” that guide every particle, an attempt to eliminate the wave-particle duality.
  • Competing approaches to quantum foundations are called “interpretations,” and nowadays there are many. The first and still possibly foremost of these is the so-called Copenhagen interpretation.
  • Perhaps the most popular lately — certainly the most talked about — is the “many-worlds interpretation”: Every quantum event is a fork in the road, and one way to escape the difficulties is to imagine, mathematically speaking, that each fork creates a new universe
  • if you think the many-worlds idea is easily dismissed, plenty of physicists will beg to differ. They will tell you that it could explain, for example, why quantum computers (which admittedly don’t yet quite exist) could be so powerful: They would delegate the work to their alter egos in other universes.
  • When scientists search for meaning in quantum physics, they may be straying into a no-man’s-land between philosophy and religion. But they can’t help themselves. They’re only human.
  • If you were to watch me by day, you would see me sitting at my desk solving Schrödinger’s equation...exactly like my colleagues,” says Sir Anthony Leggett, a Nobel Prize winner and pioneer in superfluidity. “But occasionally at night, when the full moon is bright, I do what in the physics community is the intellectual equivalent of turning into a werewolf: I question whether quantum mechanics is the complete and ultimate truth about the physical universe.”
Javier E

Opinion | Even Physicists Don't Understand Quantum Mechanics - The New York Times - 2 views

  • “I think I can safely say that nobody really understands quantum mechanics,” observed the physicist and Nobel laureate Richard Feynman.
  • What’s surprising is that physicists seem to be O.K. with not understanding the most important theory they have.
  • Scientists can use quantum mechanics with perfect confidence. But it’s a black box. We can set up a physical situation, and make predictions about what will happen next that are verified to spectacular accuracy. What we don’t do is claim to understand quantum mechanics
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  • There are two problems. One is that quantum mechanics, as it is enshrined in textbooks, seems to require separate rules for how quantum objects behave when we’re not looking at them, and how they behave when they are being observed
  • Why are observations special? What counts as an “observation,” anyway? When exactly does it happen? Does it need to be performed by a person? Is consciousness somehow involved in the basic rules of reality?
  • Together these questions are known as the “measurement problem” of quantum theory.
  • The other problem is that we don’t agree on what it is that quantum theory actually describes, even when we’re not performing measurements.
  • We describe a quantum object such as an electron in terms of a “wave function,” which collects the superposition of all the possible measurement outcomes into a single mathematical object
  • But what is the wave function? Is it a complete and comprehensive representation of the world? Or do we need additional physical quantities to fully capture reality, as Albert Einstein and others suspected? Or does the wave function have no direct connection with reality at all, merely characterizing our personal ignorance about what we will eventually measure in our experiments?
  • For years, the leading journal in physics had an explicit policy that papers on the foundations of quantum mechanics were to be rejected out of hand
sandrine_h

Darwin's Influence on Modern Thought - Scientific American - 0 views

  • Great minds shape the thinking of successive historical periods. Luther and Calvin inspired the Reformation; Locke, Leibniz, Voltaire and Rousseau, the Enlightenment. Modern thought is most dependent on the influence of Charles Darwin
  • one needs schooling in the physicist’s style of thought and mathematical techniques to appreciate Einstein’s contributions in their fullness. Indeed, this limitation is true for all the extraordinary theories of modern physics, which have had little impact on the way the average person apprehends the world.
  • The situation differs dramatically with regard to concepts in biology.
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  • Many biological ideas proposed during the past 150 years stood in stark conflict with what everybody assumed to be true. The acceptance of these ideas required an ideological revolution. And no biologist has been responsible for more—and for more drastic—modifications of the average person’s worldview than Charles Darwin
  • . Evolutionary biology, in contrast with physics and chemistry, is a historical science—the evolutionist attempts to explain events and processes that have already taken place. Laws and experiments are inappropriate techniques for the explication of such events and processes. Instead one constructs a historical narrative, consisting of a tentative reconstruction of the particular scenario that led to the events one is trying to explain.
  • The discovery of natural selection, by Darwin and Alfred Russel Wallace, must itself be counted as an extraordinary philosophical advance
  • The concept of natural selection had remarkable power for explaining directional and adaptive changes. Its nature is simplicity itself. It is not a force like the forces described in the laws of physics; its mechanism is simply the elimination of inferior individuals
  • A diverse population is a necessity for the proper working of natural selection
  • Because of the importance of variation, natural selection should be considered a two-step process: the production of abundant variation is followed by the elimination of inferior individuals
  • By adopting natural selection, Darwin settled the several-thousandyear- old argument among philosophers over chance or necessity. Change on the earth is the result of both, the first step being dominated by randomness, the second by necessity
  • Another aspect of the new philosophy of biology concerns the role of laws. Laws give way to concepts in Darwinism. In the physical sciences, as a rule, theories are based on laws; for example, the laws of motion led to the theory of gravitation. In evolutionary biology, however, theories are largely based on concepts such as competition, female choice, selection, succession and dominance. These biological concepts, and the theories based on them, cannot be reduced to the laws and theories of the physical sciences
  • Despite the initial resistance by physicists and philosophers, the role of contingency and chance in natural processes is now almost universally acknowledged. Many biologists and philosophers deny the existence of universal laws in biology and suggest that all regularities be stated in probabilistic terms, as nearly all so-called biological laws have exceptions. Philosopher of science Karl Popper’s famous test of falsification therefore cannot be applied in these cases.
  • To borrow Darwin’s phrase, there is grandeur in this view of life. New modes of thinking have been, and are being, evolved. Almost every component in modern man’s belief system is somehow affected by Darwinian principles
Javier E

Farewell to Kenneth Arrow, a Gentle Genius of Economics - WSJ - 0 views

  • Is there a voting system that can be relied on to distill the will of a group of people? Arrow’s impossibility theorem regarding voting and combining preferences put him in the rarefied group of economists with theorems named after them.
  • Drawing upon mathematical logic, it shows that there is no possible voting scheme that can consistently and sensibly reflect the preferences of a set of individuals with diverse views
  • Any scheme that could ever be invented will be at risk of perverse outcomes, where, for example, the choice between options A and B is affected by the presence or absence of option C; or where a vote switch by one person toward option A makes it less likely to prevail.
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  • it also explained why committees have so much trouble coming to consistent conclusions and why, with an increasingly polarized electorate, democracy can become increasingly dysfunctional.
  • until Kenneth drew on the techniques of topology (that is, the study of geometric properties and spatial relations), no one had ever been able to establish precise conditions under which there would be prices that would clear all markets, or under which one could assume that the market outcome was optimal
  • in the early 1950s, he clarified the very specific conditions under which market outcomes were for the best and, of equal importance, the far more general conditions under which public interventions in markets had the potential to make things better.
Javier E

The Story Behind the SAT Overhaul - NYTimes.com - 2 views

  • “When you cover too many topics,” Coleman said, “the assessments designed to measure those standards are inevitably superficial.” He pointed to research showing that more students entering college weren’t prepared and were forced into “remediation programs from which they never escape.” In math, for example, if you examined data from top-performing countries, you found an approach that emphasized “far fewer topics, far deeper,” the opposite of the curriculums he found in the United States, which he described as “a mile wide and an inch deep.”
  • The lessons he brought with him from thinking about the Common Core were evident — that American education needed to be more focused and less superficial, and that it should be possible to test the success of the newly defined standards through an exam that reflected the material being taught in the classroom.
  • she and her team had extensive conversations with students, teachers, parents, counselors, admissions officers and college instructors, asking each group to tell them in detail what they wanted from the test. What they arrived at above all was that a test should reflect the most important skills that were imparted by the best teachers
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  • for example, a good instructor would teach Martin Luther King Jr.’s “I Have a Dream” speech by encouraging a conversation that involved analyzing the text and identifying the evidence, both factual and rhetorical, that makes it persuasive. “The opposite of what we’d want is a classroom where a teacher might ask only: ‘What was the year the speech was given? Where was it given?’ ”
  • in the past, assembling the SAT focused on making sure the questions performed on technical grounds, meaning: Were they appropriately easy or difficult among a wide range of students, and were they free of bias when tested across ethnic, racial and religious subgroups? The goal was “maximizing differentiation” among kids, which meant finding items that were answered correctly by those students who were expected to get them right and incorrectly by the weaker students. A simple way of achieving this, Coleman said, was to test the kind of obscure vocabulary words for which the SAT was famous
  • In redesigning the test, the College Board shifted its emphasis. It prioritized content, measuring each question against a set of specifications that reflect the kind of reading and math that students would encounter in college and their work lives. Schmeiser and others then spent much of early last year watching students as they answered a set of 20 or so problems, discussing the questions with the students afterward. “The predictive validity is going to come out the same,” she said of the redesigned test. “But in the new test, we have much more control over the content and skills that are being measured.”
  • Evidence-based reading and writing, he said, will replace the current sections on reading and writing. It will use as its source materials pieces of writing — from science articles to historical documents to literature excerpts — which research suggests are important for educated Americans to know and understand deeply. “The Declaration of Independence, the Constitution, the Bill of Rights and the Federalist Papers,” Coleman said, “have managed to inspire an enduring great conversation about freedom, justice, human dignity in this country and the world” — therefore every SAT will contain a passage from either a founding document or from a text (like Lincoln’s Gettysburg Address) that is part of the “great global conversation” the founding documents inspired.
  • The idea is that the test will emphasize words students should be encountering, like “synthesis,” which can have several meanings depending on their context. Instead of encouraging students to memorize flashcards, the test should promote the idea that they must read widely throughout their high-school years.
  • The Barbara Jordan vocabulary question would have a follow-up — “How do you know your answer is correct?” — to which students would respond by identifying lines in the passage that supported their answer.
  • . No longer will it be good enough to focus on tricks and trying to eliminate answer choices. We are not interested in students just picking an answer, but justifying their answers.”
  • the essay portion of the test will also be reformulated so that it will always be the same, some version of: “As you read the passage in front of you, consider how the author uses evidence such as facts or examples; reasoning to develop ideas and to connect claims and evidence; and stylistic or persuasive elements to add power to the ideas expressed. Write an essay in which you explain how the author builds an argument to persuade an audience.”
  • The math section, too, will be predicated on research that shows that there are “a few areas of math that are a prerequisite for a wide range of college courses” and careers. Coleman conceded that some might treat the news that they were shifting away from more obscure math problems to these fewer fundamental skills as a dumbing-down the test, but he was adamant that this was not the case. He explained that there will be three areas of focus: problem solving and data analysis, which will include ratios and percentages and other mathematical reasoning used to solve problems in the real world; the “heart of algebra,” which will test how well students can work with linear equations (“a powerful set of tools that echo throughout many fields of study”); and what will be called the “passport to advanced math,” which will focus on the student’s familiarity with complex equations and their applications in science and social science.
  • “Sometimes in the past, there’s been a feeling that tests were measuring some sort of ineffable entity such as intelligence, whatever that might mean. Or ability, whatever that might mean. What this is is a clear message that good hard work is going to pay off and achievement is going to pay off. This is one of the most significant developments that I have seen in the 40-plus years that I’ve been working in admissions in higher education.”
  • The idea of creating a transparent test and then providing a free website that any student could use — not to learn gimmicks but to get a better grounding and additional practice in the core knowledge that would be tested — was appealing to Coleman.
  • (The College Board won’t pay Khan Academy.) They talked about a hypothetical test-prep experience in which students would log on to a personal dashboard, indicate that they wanted to prepare for the SAT and then work through a series of preliminary questions to demonstrate their initial skill level and identify the gaps in their knowledge. Khan said he could foresee a way to estimate the amount of time it would take to achieve certain benchmarks. “It might go something like, ‘O.K., we think you’ll be able to get to this level within the next month and this level within the next two months if you put in 30 minutes a day,’ ” he said. And he saw no reason the site couldn’t predict for anyone, anywhere the score he or she might hope to achieve with a commitment to a prescribed amount of work.
Javier E

Op-Ed Contributor - Scientifically Tested Tests - NYTimes.com - 2 views

  • we should come up with assessments that truly measure the qualities of well-educated children: the ability to understand what they read; an interest in using books to gain knowledge; the capacity to know when a problem calls for mathematics and quantification; the agility to move from concrete examples to abstract principles and back again; the ability to think about a situation in several different ways; and a dynamic working knowledge of the society in which they live.
  • In recent years, psychologists have found ways to measure things as subtle as the forces that govern our moral choices and the thought processes that underlie unconscious stereotyping. And many promising techniques already used by child development experts could provide a starting point for improving school assessments.
caelengrubb

The Economics of Bitcoin - Econlib - 0 views

  • Bitcoin is an ingenious peer-to-peer “virtual” or “digital currency” that challenges the way economists have traditionally thought about money.
  • My conclusion is that, in principle, nothing stands in the way of the whole world embracing Bitcoin or some other digital currency. Yet I predict that, even with the alternative of Bitcoin, people would resort to gold if only governments got out of the way.
  • According to its official website: “Bitcoin uses peer-to-peer technology to operate with no central authority; managing transactions and the issuing of bitcoins is carried out collectively by the network.”
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  • To fully understand how Bitcoin operates, one would need to learn the subtleties of public-key cryptography.
  • In the real world, when people want to buy something using Bitcoin, they transfer their ownership of a certain number of bitcoins to other people, in exchange for goods and services.
  • This transfer is effected by the network of computers performing computations and thereby changing the “public key” to which the “sold” bitcoins are assigned.
  • The encryption involved in Bitcoin concerns the identification of the legitimate owner of a particular bitcoin.
  • Without delving into the mathematics, suffice it to say: There is a way that the legitimate owner of a bitcoin can publicly demonstrate to the computers in the network that he or she really is the owner of that bitcoin.
  • Only someone with the possession of the “private key” will be able to produce a valid “signature” that convinces the computers in the network to update the public ledger to reflect the transfer of the bitcoin to another party.
  • When Bitcoin was first implemented in early 2009, computers in the network—dubbed “miners”—received 50 new bitcoins when performing the computations necessary to add a “block” of transactions to the public ledger.
  • In principle, the developers of Bitcoin could have released all 21 million units of the currency immediately with the software.
  • With the current arrangement—where the “mining” operations needed to keep the system running simultaneously yield new bitcoins to the machines performing the calculations—there is an incentive for owners to devote their machines’ processing power to the network.
  • Here, the danger is that the issuing institution—once it had gotten the world to accept its notes or electronic deposits as money—would face an irresistible temptation to issue massive quantities.6
  • Bitcoin has no such vulnerability. No external technological or physical event could cause Bitcoin inflation, and since no one is in charge of Bitcoin, there is no one tempted to inflate “from within.”
  • Some critics argue that Bitcoin’s fixed quantity would imply constant price deflation. Although this is true, everyone will have seen this coming with more than a century’s notice, and so long-term contracts would have been designed accordingly.
  • Whether to call Bitcoin a “fiat” currency depends on the definition. If “fiat” means a currency that is not legally redeemable in some other commodity, then yes, Bitcoin is a fiat currency. But if “fiat” means a currency relying on government fiat to define what will count as legal money, then Bitcoin is not.
  • Bitcoin is an ingenious concept that challenges the way economists have traditionally thought about money. Its inbuilt scarcity provides an assurance of purchasing power arguably safer than any other system yet conceived.
  • We need to let the decentralized market test tell us what is the best money, or monies.
caelengrubb

Investment - Econlib - 0 views

  • nvestment is one of the most important variables in economics.
  • Its surges and collapses are still a primary cause of recessions.
  • By investment, economists mean the production of goods that will be used to produce other goods. This definition differs from the popular usage, wherein decisions to purchase stocks (see stock market) or bonds are thought of as investment.
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  • Investment is usually the result of forgoing consumption. In a purely agrarian society, early humans had to choose how much grain to eat after the harvest and how much to save for future planting. The latter was investment.
  • In a more modern society, we allocate our productive capacity to producing pure consumer goods such as hamburgers and hot dogs, and investment goods such as semiconductor foundries. If we create one dollar worth of hamburgers today, then our gross national product is higher by one dollar.
  • Investment need not always take the form of a privately owned physical product. The most common example of nonphysical investment is investment in human capital.
  • In an economy that is closed to the outside world, investment can come only from the forgone consumption—the saving—of private individuals, private firms, or government.
  • In an open economy, however, investment can surge at the same time that a nation’s saving is low because a country can borrow the resources necessary to invest from neighboring countries.
  • That economists have a fairly strong understanding of firms’ investment behavior makes sense. A firm that maximizes its profits must address investment using the framework discussed in this article.
  • This method of financing investment has been very important in the United States. The industrial base of the United States in the nineteenth century—railroads, factories, and so on—was built on foreign finance, especially from Britain. More recently, the United States has repeatedly posted significant investment growth and very low savings.
  • Investment fluctuates a lot because the fundamentals that drive investment—output prices, interest rates, and taxes—also fluctuate. But economists do not fully understand fluctuations in investment. Indeed, the sharp swings in investment that occur might require an extension to the Jorgenson theory.
  • In Jorgenson’s user cost model, firms will purchase a machine if the extra revenue the machine generates is a smidgen more than its cost.
  • The general conclusion is that there is a gain to waiting if there is uncertainty and if the installation of the machine entails sunk costs, that is, costs that cannot be recovered once spent.
  • Although quantifying this gain exactly is a highly mathematical exercise, the reasoning is straightforward. That would explain why firms typically want to invest only in projects that have a high expected profit.
  • The fact of irreversibility might explain the large fluctuations in investment that we observe.
  • The theory of investment dates back to the giants of economics. irving fisher, arthur cecil pigou, and alfred marshall all made contributions; as did john maynard keynes, whose Marshallian user cost theory is a central feature in his General Theory.
  • Consumer behavior is harder to study than firms’ behavior. Market forces that drive irrational people out of the marketplace are much weaker than market forces that drive bad companies from the market.
  • Because the saving response of consumers must be known if one is to fully understand the impact of any investment policy, and because saving behavior is so poorly understood, much work remains to be done.
kaylynfreeman

Opinion | How Fear Distorts Our Thinking About the Coronavirus - The New York Times - 0 views

  • When it comes to making decisions that involve risks, we humans can be irrational in quite systematic ways — a fact that the psychologists Amos Tversky and Daniel Kahneman famously demonstrated with the help of a hypothetical situation, eerily apropos of today’s coronavirus epidemic, that has come to be known as the Asian disease problem.
  • This is irrational because the two questions don’t differ mathematically. In both cases, choosing the first option means accepting the certainty that 200 people live, and choosing the second means embracing a one-third chance that all could be saved with an accompanying two-thirds chance that all will die. Yet in our minds, Professors Tversky and Kahneman explained, losses loom larger than gains, and so when the options are framed in terms of deaths rather than cures, we’ll accept more risks to try to avoid deaths.
  • Our decision making is bad enough when the disease is hypothetical. But when the disease is real — when we see actual death tolls climbing daily, as we do with the coronavirus — another factor besides our sensitivity to losses comes into play: fear.
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  • The brain states we call emotions exist for one reason: to help us decide what to do next. They reflect our mind’s predictions for what’s likely to happen in the world and therefore serve as an efficient way to prepare us for it. But when the emotions we feel aren’t correctly calibrated for the threat or when we’re making judgments in domains where we have little knowledge or relevant information, our feelings become more likely to lead us astray.
ilanaprincilus06

Best COVID-19 Vaccination Strategies, According To Mathematicians : Shots - Health News... - 1 views

  • Only a vaccine will save America from the COVID -19 pandemic. At least that's the opinion of nearly all public health officials.
  • But there's another group that plays a less obvious but still crucial role in making sure vaccines do what they're intended: mathematicians.
  • How best to use that limited supply is a question mathematicians can help answer.
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  • They can help with decisions about who gets the vaccine first when supplies are limited.
  • "One of those is how much is the virus spreading as the vaccine is being rolled out? And another factor is. How fast is the vaccine being rolled out?"
  • It's also important to know how effective a vaccine is at preventing disease, how long protection lasts, and whether it not only prevents someone from getting sick but also from transmitting COVID-19.
  • Larremore says to end a pandemic, it generally makes sense to vaccinate those most capable of spreading disease.
  • But even if a mathematical model suggests the most effective path, it doesn't provide all the answers public health officials need.
  • Right now, modelers are trying to help public health officials decide if it makes sense to use a single dose of the Moderna and Pfizer vaccine to extend the limited supply, even though the vaccine has only really been tested using a two-dose regimen
caelengrubb

I'm So Totally Over Newton's Laws of Motion | WIRED - 0 views

  • We don't need to be stuck with the traditions of the past if we want students to understand physics.
  • Newton's First Law: An object in motion stays in motion unless acted on by a force. An object at rest, stays at rest unless acted on by a force.Newton's Second Law: The magnitude of an object's acceleration is proportional to the net force and inversely proportional to the mass of the object.Newton's Third Law: For every force there is an equal and opposite force. (I've already complained about the way most books talk about this one)
  • Newton's First Law Is Really About Aristotle
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  • Remember that before Galileo and Newton, people looked to Aristotle for ideas about physics
  • Yes, it's true that Aristotle wasn't a scientist since he didn't really do any experiments. However, that didn't stop him from become a huge influence on the way people think about physics
  • Do I think that we should ban Newton's Laws? No. There is still a place to talk about the historical development of the interaction between forces and matter and Newton played a large role here (but so did Aristotle and Galileo
  • Let's write down Newton's Second Law in its common form as an equation:Although this is a very useful model, it doesn't always work. If you take a proton moving at half the speed of light and push on it with a force, you cannot use this to find the new velocity of the proton---but it's still a great model. So, maybe we shouldn't call it a Law.
  • Science is all about models. If there is one thing I've tried to be consistent about---it's that we build models in science. These models could be conceptual, physical, or mathematical
  • Since Newton's ideas are Laws, does that mean that they are true? No---there is no truth in science, there are just models. Some models work better than others, and some models are wrong but still useful
  • Just because most physics textbooks (but not all) have been very explicit about Newton's Laws of Motion, this doesn't mean that is the best way for students to learn.
pier-paolo

Logic and Neutrality - The New York Times - 0 views

  • an idea many philosophers and logicians have about the function of logic in our cognitive life, our inquiries and debates
  • It isn’t a player. Rather, it’s an umpire, a neutral arbitrator between opposing theories, imposing some basic rules on all sides in a dispute. The picture is that logic has no substantive conten
  • The idea that logic is uninformative strikes me as deeply mistaken,
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  • when we extend our knowledge by deducing logical consequences of what we already know. If you know that either Mary or Mark did the murder (only they had access to the crime scene at the right time), and then Mary produces a rock-solid alibi, so you know she didn’t do it, you can deduce that Mark did it
  • Logic also helps us recognize our mistakes, when our beliefs turn out to contain inconsistencies. If I believe that no politicians are honest, and that John is a politician, and that he is honest, at least one of those three beliefs must be false, although logic doesn’t tell me which one.
  • The power of logic becomes increasingly clear when we chain together such elementary steps into longer and longer chains of reasoning, and the idea of logic as uninformative becomes correspondingly less and less plausible. Mathematics provides the most striking examples, since all its theorems are ultimately derived from a few simple axioms by chains of logical reasoning
  • The conception of logic as a neutral umpire of debate also fails to withstand scrutiny, for similar reasons. Principles of logic can themselves be debated,
  • one principle of standard logic is the law of excluded middle, which says that something either is the case, or it isn’t. Either it’s raining, or it’s not.
  • Whichever side is right, logical theories are players in these debates, not neutral umpires.
caelengrubb

How Galileo Changed Your Life - Biography - 0 views

  • Galileo’s contributions to the fields of astronomy, physics, mathematics, and philosophy have led many to call him the father of modern science.
  • But his controversial theories, which impacted how we see and understand the solar system and our place within it, led to serious conflict with the Catholic Church and the long-time suppression of his achievements
  • Galileo developed one of the first telescopesGalileo didn’t invent the telescope — it was invented by Dutch eyeglass makers — but he made significant improvements to it.
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  • His innovations brought him both professional and financial success. He was given a lifetime tenure position at the University of Padua, where he had been teaching for several years, at double his salary.
  • And he received a contract to produce his telescopes for a group of Venetian merchants, eager to use them as a navigational tool.
  • He helped created modern astronomyGalileo turned his new, high-powered telescope to the sky. In early 1610, he made the first in a remarkable series of discoveries.
  • While the scientific doctrine of the day held that space was perfect, unchanging environments created by God, Galileo’s telescope helped change that view
  • His studies and drawings showed the Moon had a rough, uneven surface that was pockmarked in some places, and was actually an imperfect sphere
  • He was also one of the first people to observe the phenomena known as sunspots, thanks to his telescope which allowed him to view the sun for extended periods of time without damaging the eye.
  • Galileo helped prove that the Earth revolved around the sunIn 1610, Galileo published his new findings in the book Sidereus Nuncius, or Starry Messenger, which was an instant success
  • The following year, the Church banned all works that supported Copernicus’ theories and forbade Galileo from publicly discussing his works.
  • Kepler’s experiments had led him to support the idea that the planets, Earth included, revolved around the sun. This heliocentric theory, as well as the idea of Earth’s daily rotational turning, had been developed by Polish astronomer Nicolaus Copernicus half a century earlier
  • Their belief that the Sun, and not the Earth, was the gravitational center of the universe, upended almost 2,000 years of scientific thinking, dating back to theories about the fixed, unchanging universe put forth by the Greek philosopher and scientist Aristotle.
  • Galileo had been testing Aristotle’s theories for years, including an experiment in the late 16th century in which he dropped two items of different masses from the Leaning Tower of Pisa, disproving Aristotle’s belief that objects would fall at differing speeds based on their weight (Newton later improved upon this work).
  • Galileo paid a high price for his contributionsBut challenging the Aristotelian or Ptolemaic theories about the Earth’s role in the universe was dangerous stuff.
  • Geocentrism was, in part, a theoretical underpinning of the Roman Catholic Church. Galileo’s work brought him to the attention of Church authorities, and in 1615, he was called before the Roman Inquisition, accused of heresy for beliefs which contradicted Catholic scripture.
  • He became close with a number of other leading scientists, including Johannes Kepler. A German astronomer and mathematician, Kepler’s work helped lay the foundations for the later discoveries of Isaac Newton and others.
  • In 1632, after the election of a new pope who he considered more liberal, he published another book, Dialogue on the Two Chief World Systems, Ptolemaic and Copernican, which argued both sides of the scientific (and religious) debate but fell squarely on the side of Copernicus’ heliocentrism.
  • Galileo was once again summoned to Rome. In 1633, following a trial, he was found guilty of suspected heresy, forced to recant his views and sentenced to house arrest until his death in 1642.
  • It took nearly 200 years after Galileo’s death for the Catholic Church to drop its opposition to heliocentrism.
  • In 1992, after a decade-long process and 359 years after his heresy conviction, Pope John Paul II formally expressed the Church’s regret over Galileo’s treatment.
caelengrubb

How Isaac Newton Changed the World | Live Science - 0 views

  • To the probable dismay of some befuddled calculus and physics students the world over, Isaac Newton didn't just live, he grew up and lived long enough to become the single-most influential scientist of the 17th-century.
  • Newton's wide range of discoveries, from his theories of optics to his groundbreaking work on the laws of motion and gravity, formed the basis for modern physics.
  • The true genius of his work, experts think, is how he ultimately took those theories and applied them to the universe at large, explaining the motions of the Sun and planets in a way that had never been done before.
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  • Upon getting bumped on the head by a falling apple, Newton airily dreams up the laws of gravity and the rest, as they say, is history
  • When the black plague closed Cambridge University, where he was a student, for two years starting in 1665, he spent the long months locked up at home studying complex mathematics, physics and optics.
  • It was during this fruitful time that Newton, with the help of a crystal prism, became the first to discover that white light is made up a spectrum of colors
  • He also developed the concept of infinite-series calculus, the kind of scary math studied today by engineering and statistics scholars.
  • By 1666, Newton had even laid the blueprints for his three laws of motion, still recited by physics students everywhere:An object will remain in a state of inertia unless acted upon by force.The relationship between acceleration and applied force is F=ma.For every action there is an equal and opposite reaction.
  • Across the pages of the Principia, Newton breaks down the workings of the solar system into "'simple"' equations, explaining away the nature of planetary orbits and the pull between heavenly bodies.
caelengrubb

8 Things You May Not Know About Galileo - HISTORY - 0 views

  • When he was 16, Galileo enrolled at the University of Pisa to study medicine, at his father’s urging. Instead, though, he became interested in mathematics and shifted his focus to that subjec
  • Galileo left the school in 1585 without earning a degree.
  • Galileo didn’t invent the telescope—Dutch eyeglass maker Hans Lippershey is generally credited with its creation—but he was the first person to use the optical instrument to systematically study the heavens.
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  • In 1609, Galileo learned about the device and developed one of his own, significantly improving its design. That fall, he pointed it at the moon and discovered it had craters and mountains, debunking the common belief that the moon’s surface was smooth.
  • Galileo soon went on to make other findings with his telescope, including that there were four moons orbiting Jupiter and that Venus went through a complete set of phases (indicating the planet traveled around the sun).
  • Galileo had three children with a woman named Marina Gamba, who he never married. In 1613, he placed his two daughters, Virginia, born in 1600, and Livia, born in 1601, in a convent near Florence, where they remained for the rest of their lives, despite their father’s eventual troubles with the Catholic Church
  • Copernicus’ heliocentric theory about the way the universe works challenged the widely accepted belief, espoused by the astronomer Ptolemy in the second century, that put the Earth at the center of the solar system.
  • Galileo received permission from the Church to continue investigating Copernicus’ ideas, as long as he didn’t hold or defend them.
  • As a result, the following year Galileo was ordered to stand trial before the Inquisition in Rome
  • After being found guilty of heresy, Galileo was forced to publicly repent and sentenced to life in prison.
  • Although Galileo was given life behind bars, his sentence soon was changed to house arrest. He lived out his final years at Villa Il Gioiello (“the Jewel”), his home in the town of Arcetri, near Florence
  • In 1979, Pope John Paul II initiated an investigation into the Catholic Church’s condemnation of Galileo.
  • Thirteen years later, and 359 years after Galileo was tried by the Inquisition, the pope officially closed the investigation and issued a formal apology in the case, acknowledging that errors were made by the judges during the trial.
caelengrubb

How Did Language Begin? | Linguistic Society of America - 0 views

  • The question is not how languages gradually developed over time into the languages of the world today. Rather, it is how the human species developed over time so that we - and not our closest relatives, the chimpanzees and bonobos - became capable of using language.
  • Human language can express thoughts on an unlimited number of topics (the weather, the war, the past, the future, mathematics, gossip, fairy tales, how to fix the sink...). It can be used not just to convey information, but to solicit information (questions) and to give orders.
  • Every human language has a vocabulary of tens of thousands of words, built up from several dozen speech sounds
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  • Animal communication systems, in contrast, typically have at most a few dozen distinct calls, and they are used only to communicate immediate issues such as food, danger, threat, or reconciliation. Many of the sorts of meanings conveyed by chimpanzee communication have counterparts in human 'body language'.
  • The basic difficulty with studying the evolution of language is that the evidence is so sparse. Spoken languages don't leave fossils, and fossil skulls only tell us the overall shape and size of hominid brains, not what the brains could do
  • All present-day languages, including those of hunter-gatherer cultures, have lots of words, can be used to talk about anything under the sun, and can express negation. As far back as we have written records of human language - 5000 years or so - things look basically the same.
  • According to current thinking, the changes crucial for language were not just in the size of the brain, but in its character: the kinds of tasks it is suited to do - as it were, the 'software' it comes furnished with.
  • So the properties of human language are unique in the natural world.
  • About the only definitive evidence we have is the shape of the vocal tract (the mouth, tongue, and throat): Until anatomically modern humans, about 100,000 years ago, the shape of hominid vocal tracts didn't permit the modern range of speech sounds. But that doesn't mean that language necessarily began the
  • Some researchers even propose that language began as sign language, then (gradually or suddenly) switched to the vocal modality, leaving modern gesture as a residue.
  • . In an early stage, sounds would have been used to name a wide range of objects and actions in the environment, and individuals would be able to invent new vocabulary items to talk about new things
  • In order to achieve a large vocabulary, an important advance would have been the ability to 'digitize' signals into sequences of discrete speech sounds - consonants and vowels - rather than unstructured calls.
  • These two changes alone would yield a communication system of single signals - better than the chimpanzee system but far from modern language. A next plausible step would be the ability to string together several such 'words' to create a message built out of the meanings of its parts.
  • This has led some researchers to propose that the system of 'protolanguage' is still present in modern human brains, hidden under the modern system except when the latter is impaired or not yet developed.
  • Again, it's very hard to tell. We do know that something important happened in the human line between 100,000 and 50,000 years ago: This is when we start to find cultural artifacts such as art and ritual objects, evidence of what we would call civilization.
  • One tantalizing source of evidence has emerged recently. A mutation in a gene called FOXP2 has been shown to lead to deficits in language as well as in control of the face and mouth. This gene is a slightly altered version of a gene found in apes, and it seems to have achieved its present form between 200,000 and 100,000 years ago.
  • Nevertheless, if we are ever going to learn more about how the human language ability evolved, the most promising evidence will probably come from the human genome, which preserves so much of our species' history. The challenge for the future will be to decode it.
knudsenlu

The Theory That Explains the Structure of the Internet - The Atlantic - 1 views

  • A paper posted online last month has reignited a debate about one of the oldest, most startling claims in the modern era of network science: the proposition that most complex networks in the real world—from the World Wide Web to interacting proteins in a cell—are “scale-free.” Roughly speaking, that means that a few of their nodes should have many more connections than others, following a mathematical formula called a power law, so that there’s no one scale that characterizes the network.
  • Purely random networks do not obey power laws, so when the early proponents of the scale-free paradigm started seeing power laws in real-world networks in the late 1990s, they viewed them as evidence of a universal organizing principle underlying the formation of these diverse networks. The architecture of scale-freeness, researchers argued, could provide insight into fundamental questions such as how likely a virus is to cause an epidemic, or how easily hackers can disable a network.
  • Amazingly simple and far-reaching natural laws govern the structure and evolution of all the complex networks that surround us,” wrote Barabási (who is now at Northeastern University in Boston) in Linked. He later added: “Uncovering and explaining these laws has been a fascinating roller-coaster ride during which we have learned more about our complex, interconnected world than was known in the last hundred years.”
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  • “These results undermine the universality of scale-free networks and reveal that real-world networks exhibit a rich structural diversity that will likely require new ideas and mechanisms to explain,” wrote the study’s authors, Anna Broido and Aaron Clauset of the University of Colorado at Boulder.
  • Network scientists agree, by and large, that the paper’s analysis is statistically sound. But when it comes to interpreting its findings, the paper seems to be functioning like a Rorschach test, in which both proponents and critics of the scale-free paradigm see what they already believed to be true. Much of the discussion has played out in vigorous Twitter debates.
  • The scale-free paradigm in networks emerged at a historical moment when power laws had taken on an outsize role in statistical physics. In the 1960s and 1970s, they had played a key part in universal laws that underlie phase transitions in a wide range of physical systems, a finding that earned Kenneth Wilson the 1982 Nobel Prize in physics. Soon after, power laws formed the core of two other paradigms that swept across the statistical-physics world: fractals, and a theory about organization in nature called self-organized criticality.
  • From the beginning, though, the scale-free paradigm also attracted pushback. Critics pointed out that preferential attachment is far from the only mechanism that can give rise to power laws, and that networks with the same power law can have very different topologies. Some network scientists and domain experts cast doubt on the scale-freeness of specific networks such as power grids, metabolic networks, and the physical internet.
  • If you were to observe 1,000 falling objects instead of just a rock and a feather, Clauset says, a clear picture would emerge of how both gravity and air resistance work. But his and Broido’s analysis of nearly 1,000 networks has yielded no similar clarity. “It is reasonable to believe a fundamental phenomenon would require less customized detective work” than Barabási is calling for, Clauset wrote on Twitter.
krystalxu

If Philosophy Won't Diversify, Let's Call It What It Really Is - The New York Times - 0 views

  • while the American Philosophical Association has slowly broadened the representation of the world’s philosophical traditions on its programs, progress has been minimal.
  • particularly for those who endorse, implicitly or explicitly, this Eurocentric orientation.
  • There are no comparable differences in how mathematics or physics are practiced in other contemporary cultures.
tongoscar

Understanding the World Through Math | Asia Society - 0 views

  • The body of knowledge and practice known as mathematics is derived from the contributions of thinkers throughout the ages and across the globe. It gives us a way to understand patterns, to quantify relationships, and to predict the future. Math helps us understand the world — and we use the world to understand math.
  • The world is interconnected. Everyday math shows these connections and possibilities.
  • Algebra can explain how quickly water becomes contaminated and how many people in a third-world country drinking that water might become sickened on a yearly basis.
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  • For students to function in a global context, math content needs to help them get to global competence, which is understanding different perspectives and world conditions, recognizing that issues are interconnected across the globe, as well as communicating and acting in appropriate ways.
  • In a similar vein, a study of statistics and probability is key to understanding many of the events of the world, and is usually reserved for students at a higher level of math, if it gets any study in high school at all.
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