July 31, 2005
Science Journal: Definition of infinity expands for scientistsBy Sharon Begley, The Wall Street Journal At the Hotel Infinity, managers never have a problem with overbooking. If you arrive with a reservation and find that the hotel's infinite number of rooms (named 1, 2, 3 and so on, forever) are all occupied, the manager simply moves the guest in Room 1 to Room 2, the guest in Room 2 to Room 3, and on and on until every guest has a room and you get Room 1. In an "infinite set" such as the rooms at the Hotel, whatever you thought was the highest-numbered member of that set isn't. The next time you're in town, you have an infinite number of friends in tow, and you try the Hotel Infinity again. The manager is happy to accommodate a party of infinity even though his infinite rooms are, again, full. Knowing that your friends have an odd aversion to even numbers, he moves the guest in Room 1 to Room 2, the guest in Room 2 to Room 4, the guest in Room 3 to Room 6, etc. You and your friends get the odd-numbered rooms, of which there are, conveniently, an infinite number. If thinking of infinities makes your head spin, you're in good company. Georg Cantor, the early-20th-century mathematician who did more than anyone to explore infinities, suffered a nervous breakdown and repeated bouts of depression. In the 1930s, some fed-up mathematicians even argued that infinities should be banned from mathematics. Today, however, infinities aren't just a central part of mathematics. More surprising, says cosmologist John Barrow of the University of Cambridge, England, in his charming new tome, "The Infinite Book," scientists who study the real world are having to take infinities seriously, too. Not long ago, if the solution to an equation included an infinity, alarms went off. In particle physics, for instance, "the appearance of an infinite answer was always taken as a warning that you had made a wrong turn," Prof. Barrow says. So physicists performed a sleight-of-hand, subtracting the infinite part of the answer and leaving the finite part. The finite part produced by this "renormalization" was always in "spectacularly good agreement with experiments," he says, but "there was always a deep uneasiness" over erasing infinities so blithely. Might physicists, blinded by their abhorrence of infinities, have been erasing a deep truth of nature? Suspecting just that, some scientists now see infinities "as an essential part of the physical description of the universe," says Prof. Barrow. For instance, Einstein's equations say the universe began in, and will end with, an infinity of density and temperature, something long regarded as a sign that his theory breaks down at the beginning and end of time. But in a 2004 paper, Prof. Barrow calculated that Einstein's equations allow a point of infinite pressure to arise throughout the expanding universe at some time in the future. In additon to coming around to the view that infinities might be real, rather than signs of a problem with Einstein's and other theories, some cosmologists suspect that infinities at the beginning and end of time "have quite different structures," Prof. Barrow writes. Just as at the hotel, not all infinities are equal. And that is making the weird math of different-size infinities suddenly relevant in the physical world, too. To mathematicians, "equal" means you can match the elements in one set to the elements in another, one to one, with nothing left over. For instance, there is an infinite number of integers: 1, 2, 3, 4 ... . There is also an infinite number of squares: 1, 4, 9, 16 ... . You can match every integer with a square (1 with 1, 2 with 4, and so on), so the two sets are equal, as long as you never stop matching. But wait: Every square also belongs to the set of integers. That suggests that the set of integers is larger, since it contains all the squares and then some. Surely there are more integers than squares, right? Actually, no. Before his breakdown, Cantor asserted that if the elements in one infinite set match up one to one with the counting numbers, then those infinities are of equal size. The infinity of squares and the infinity of integers (and the infinity of even numbers) are therefore equal, even though the infinity of integers is denser. Decimals, however, are different, mathematicians say. There is an infinite number of them, too, but this infinity is larger than the infinity of integers or squares. Even in the tiny space between zero and 1, there's an infinite number of decimals with no certainty as to what comes next. What comes after .1, for example? Is it .11 or .2? Just as mathematicians found a distinction among infinities, so scientists trying to fathom the physical world may need to distinguish among infinities. In his study of infinities, Prof. Barrow noticed that a universe like ours that seems infinite in size, extending without bound, presents curious ethical dilemmas. An infinite universe must have infinite amounts of good and evil, he writes. Nothing we do, or fail to do, can change that, for adding a bit of good to an infinite amount of good still leaves infinite good, and subtracting a bit of evil from an infinite amount of evil still leaves infinite evil. "What is the status of good and evil," he wonders, "when all possible outcomes actually arise somewhere" ... or sometime? Small wonder infinity drove Cantor mad. Science Journal: Definition of infinity expands for scientists |
July 31, 2005
World Not Ready For Flu PandemicBy DAVID BROWN The Washington Post Health officials say it will take a long time to prepare for what seems inevitable. WASHINGTON -- Public health officials preparing to battle what they view as an inevitable influenza pandemic say the world lacks the medical weapons to fight the disease effectively, and will not have them anytime soon. Public health specialists and manufacturers are working frantically to develop vaccines, drugs, strategies for quarantining and treating the ill, and plans for international cooperation, but these efforts will take years. Meanwhile, the most dangerous strain of influenza to appear in decades -- the H5N1 "bird flu" in Asia -- is showing up in new populations of birds, and occasionally people, almost by the month, global health officials say. If the virus were to start spreading in the next year, the world would have only a relative handful of doses of an experimental vaccine to defend against a disease that, history shows, could potentially kill millions. If the vaccine proved effective and every flu vaccine factory in the world started making it, the first doses would not be ready for four months. By then, the pathogen would probably be on every continent. Theoretically, antiviral drugs could slow an outbreak and buy time. The problem is only one licensed drug, oseltamivir, appears to work against bird flu. At the moment, there is not enough stockpiled for widespread use. Nor is there a plan to deploy the small amount that exists in ways that would have the best chance of slowing the disease. The public, conditioned to believe in the power of modern medicine, has heard little of how poorly prepared the world is to confront a flu pandemic, which is an epidemic that strikes several continents simultaneously and infects a substantial portion of the population. Since the current wave of avian flu began sweeping through poultry in Southeast Asia more than 18 months ago, international and U.S. health authorities have warned of the danger and tried to mobilize. Research on vaccines has accelerated, efforts to build drug supplies are under way, and discussions take place regularly on developing a coordinated global response. The U.S. Department of Health and Human Services will spend $419 million in pandemic planning this year. The National Institutes of Health's influenza research budget has quintupled in the past five years. "The secretary or the chief of staff -- we have a discussion about flu almost every day," said Bruce Gellin, head of HHS's National Vaccine Program Office. This week, a committee is to deliver to HHS Secretary Mike Leavitt an updated plan for confronting a pandemic. Despite these efforts, the world's lack of readiness to meet the threat is huge, experts say. "The only reason nobody's concerned the emperor has no clothes is that he hasn't shown up yet," Harvey V. Fineberg, president of the National Academy of Sciences' Institute of Medicine, said recently of the world's efforts to prepare for pandemic flu. "When he appears, people will see he's naked." Other scientists are sounding the alarm as well. The most outspoken is Michael T. Osterholm, director of the Center for Infectious Disease Research and Policy at the University of Minnesota. In writing and in speeches, Osterholm reminds his audience that after public calamities, the United States usually convenes blue-ribbon commissions to pass judgment. There will be one after a flu pandemic, he thinks. "Right now, the conclusions of that commission would be harsh and sad," he said. In hopes of slowing a pandemic's spread, public health specialists have been debating proposals for unprecedented countermeasures. These could include vaccinating only children, who are statistically most likely to spread the contagion; mandatory closing of schools or office buildings; and imposing "snow day" quarantines on infected families -- prohibiting them from leaving their homes. Other measures would go well beyond conventional boundaries of public health: restricting international travel, closing transit systems or nationalizing supplies of critical medical equipment, such as surgical masks. Osterholm argues such measures would fall far short. He predicts a pandemic would cause widespread shutdowns of factories, transportation and other essential industries. To prepare, he says, authorities should identify and stockpile a list of perhaps 100 crucial products and resources that are essential to keep society functioning until the pandemic recedes and the survivors go back to work. LESS LETHAL, MORE DANGEROUS Since late 2003, 109 people are known to have been infected with the H5N1 virus in Asia. About half -- 55 -- have died. Ironically, for the current H5N1 strain of avian flu to gain "pandemic potential," it will have to become less deadly. Declining lethality is a key sign that the microbe is adapting to human hosts. That is one reason the 34 percent mortality observed in the most recent outbreak -- a cluster of cases in northern Vietnam -worries scientists. Pandemic influenza is not an unusually bad version of the flu that appears each winter. Those outbreaks are caused by flu viruses that have been circulating for decades and change slightly year to year. Pandemics are caused by strains of virus that are highly contagious and to which people have no immunity. Such rare strains arise from the chance scrambling and recombination of an animal flu virus and a human one, resulting in a strain whose molecular identity is wholly new. If H5N1 never becomes easily transmissible in human beings, it will never become a pandemic. If it does become transmissible, the consequences are difficult to imagine. But history provides some clues. The "Spanish flu" in 1918 and 1919 was the biggest and, along with AIDS, the most important infectious disease outbreak of the 20th century. It is on the short list of great disasters in human history. At least 50 million people, and possibly as many as 100 million, died when the world's population was 1.9 billion people, one-third its current size. A LARGE ORDER As the first, small hedge against disaster, the government last fall ordered 2 million doses of H5N1 vaccine from Sanofi Pasteur, one of the country's three flu vaccine makers, even though nobody yet knows whether it works. A half-dozen other countries are working on pandemic vaccines. But making enough to fight an outbreak is a tall order. About 300 million flu shots are made worldwide each year. The vaccine protects against three flu strains. If the global production capacity were directed to make only H5N1 vaccine, the output could be 900 million shots. Unfortunately, virologists are almost certain people will need two doses about a month apart to successfully defend against a wholly new strain such as H5N1. That would cut the theoretical number of recipients worldwide to 450 million.. Can the world produce more flu shots? Not easily. Because nearly all flu vaccine is made by growing the virus in fertilized chicken eggs, special factories and a steady supply of eggs are required. Consequently, a key element of pandemic planning is getting more people to get yearly flu shots, which will give companies a larger market and an incentive to expand. Around the world, flu vaccine production has risen by just onethird in the past decade. New plants in Brazil, South Korea and the Netherlands will boost global production by an additional 25 percent in the near future. In theory, even a modest amount of vaccine might be useful. Fighting disease outbreaks is like fighting fires. You do not have to hose down the whole world to put the fire out, but you do have to hose down the perimeter to keep it from spreading. It might be possible to contain an H5N1 outbreak at its source if the surrounding population were immediately vaccinated. Would the United States, Europe and Japan be willing to donate their precious vaccine supply to mount this long-shot defense? This is perhaps the biggest unanswered question in pandemic flu planning -- and one likely to be answered only at the moment of truth. Officially, it is a possibility. "If it was done in consultation with the WHO (World Health Organization) -- and with other governments that would make contributions, as well -- we would be more likely to consider it," said Gellin at HHS. But observers both in and out of the government said, not for quotation, that they doubt the U.S. government would ever send a significant amount of its vaccine stockpile overseas. A LIMITED HOPE In the absence of vaccine, the only pharmaceutical bulwark against H5N1 is a drug called oseltamivir. It can shorten the illness's duration, and if taken immediately after exposure, it can prevent infection. But the world's supply is limited. Sold as Tamiflu, it is manufactured by one company, Roche, in a laborious, expensive process that takes eight months. Twenty-five countries have ordered oseltamivir to stockpile, and five others have expressed interest, a Roche spokesman, Terence J. Hurley, said recently. The United States has a stockpile, but it is enough to treat less than 1 percent of the population. The government has ordered enough to treat 3 million more people, or about 2 percent total. Would having lots of vaccine or oseltamivir make a difference? In a study published last year, Ira M. Longini Jr. of Emory University ran a mathematical model of what might happen if a pandemic such as the 1957 Asian flu, which was caused by a virus far milder than bird flu, hit the United States. He and his colleagues estimated that with no vaccine or antiviral drugs, there would be 93 million cases and 164,000 deaths. Vaccinating 80 percent of people younger than 19 -- the group most responsible for spreading the virus -- "would reduce the epidemic to just 6 million total cases and 15,000 total deaths in the country." Giving that group eight weeks of oseltamivir would have the same effect, at least temporarily. But it would take the equivalent of 190 million courses of treatment -- more than anyone thinks the country will have in the next few years. Somewhat more realistic is deploying the drug to where the outbreak begins. One researcher, Neil M. Ferguson of Imperial College in London said in an interview that results of his not-yet-published mathematical modeling "are encouraging." But unless antiviral drugs squelch a pandemic at the outset, their ultimate usefulness will be small. Without widespread immunity through vaccination or infection, the virus will move into a population when the drugs run out. World Not Ready For Flu Pandemic |
July 31, 2005
Butterfly unlocks evolution secretBy Julianna Kettlewell BBC News science reporter Why one species branches into two is a question that has haunted evolutionary biologists since Darwin. Given our planet's rich biodiversity, "speciation" clearly happens regularly, but scientists cannot quite pinpoint the driving forces behind it. Now, researchers studying a family of butterflies think they have witnessed a subtle process, which could be forcing a wedge between newly formed species. The team, from Harvard University, US, discovered that closely related species living in the same geographical space displayed unusually distinct wing markings. These wing colours apparently evolved as a sort of "team strip", allowing butterflies to easily identify the species of a potential mate. For me, this is a big discovery just because the system is very beautiful Dr Nikolai Kandul, Harvard University This process, called "reinforcement", prevents closely related species from interbreeding thus driving them further apart genetically and promoting speciation. Although scientists have speculated about this mechanism for years, it has rarely been witnessed in nature. "The phenomenon of reinforcement is one of the very few mechanisms that has natural selection playing a role in speciation," said Harvard co-author Nikolai Kandul. "It might be very widespread but it is hard to find good evidence of it." Geographical isolation For speciation to occur, two branches of the same species must stop breeding with one another for long enough to grow apart genetically. The most obvious way this can happen is through geographical isolation. If a mountain range or river divides a population of animals for hundreds of generations, they might find that if they meet again they are no longer able to breed. But geographical isolation is not enough to explain all speciation. Clearly, organisms do sometimes speciate even if there is no clear river or mountain separating them. The other mechanism that can theoretically divide a species is "reproductive isolation". This occurs when organisms are not separated physically, but "choose" not to breed with each other thereby causing genetic isolation, which amounts to the same thing. Reproductive isolation is much hazier and more difficult to pin down than geographic isolation, which is why biologists are so excited about this family of butterflies. Butterfly clue The Harvard team made the discovery while studying the butterfly genus Agrodiaetus, which has a wide ranging habitat in Asia. The females are brown while the males exhibit a variety of wing colours ranging from silver and blue to brown. Dr Kandul and his colleagues found that if closely related species of Agrodiaetus are geographically separate, they tend to look quite similar. That is to say, they do not display a distinctive "team strip". But if similarly closely related species are living side-by-side, the researchers noticed, they frequently look strikingly different - their "teams" are clearly advertised. This has the effect of discouraging inter-species mating, thus encouraging genetic isolation and species divergence. "This butterfly study presents evidence that the differences in the male's wing colouration is stronger [when the species share a habitat] than [when they do not]," said the speciation expert Axel Meyer, from Konstanz University in Germany. "This pattern would therefore support the interpretation that it was brought about by reinforcement, hence natural selection." The reason evolution favours the emergence of a "team strip" in related species, or sub species, living side-by-side is that hybridisation is not usually a desirable thing. Although many of the Agrodiaetus species are close enough genetically to breed, their hybrid offspring tend to be rather weedy and less likely to thrive. Therefore natural selection will favour ways of distinguishing the species, which is why the clear markings exist. "For me, this is a big discovery just because the system is very beautiful," said Dr Kandul. "As much as we can we are showing that [reinforcement] is the most likely mechanism." Butterfly unlocks evolution secret |
July 26, 2005
Software Patents Don't ComputeBy Ben Klemens No clear boundary between math and software exists In 1997 the U.S. Patent and Trademark Office granted Amazon.com a patent for "one-click shopping"—a system that lets customers make purchases without having to go through an online checkout. The patent started a fierce debate in both the business and the technical press. Critics felt the Amazon.com patent was the poster child for everything that was wrong with software patents, charging that such patents allowed obvious applications of existing technology to be wrapped up in intellectual property monopolies. The Amazon.com patent is no fluke. Consider the following recently issued patents: Method and system for solving linear systems (U.S. Patent No. 6078938). Cosine algorithm for relatively small angles (No. 6434582). Method of efficient gradient computation (No. 5886908). Methods and systems for computing singular value decompositions of matrices and low rank approximations of matrices (No. 6807536). The arcane details of these patents are not relevant. What is relevant is that these patents are for purely mathematical algorithms, and for centuries prior to the 1990s, mathematics was not patentable. So how did these patents come to be granted? By U.S. law, scientific principles may not be patented. Electromagnetism, the theory of relativity, and a menagerie of quantum particles were all discovered after the inception of the U.S. Patent and Trademark Office, now based in Alexandria, Va. Yet none of these discoveries could have received patents, because until the early 1990s it was universally agreed that mathematical algorithms were in the category of scientific principles that could not be owned by an individual. What has changed is that mathematics has become increasingly reliant on machines. Abstract algorithms that involve inverting large matrices or calculating hundreds of coefficients in a sequence are routine today and of only limited use without physical computers to execute them. Conversely, devices such as video drivers, network interface cards, and robot arms depend on algorithms for their operation. Because of the machine-intensiveness of modern mathematics and the math-intensiveness of modern machines, the line between mathematical algorithms and machinery is increasingly blurred. This blurring is a problem, because without a clear line delimiting what is patentable and what is not, creative entrepreneurs will eventually be able to claim sole ownership of abstract mathematical discoveries. But how do we draw a line that would ensure that mathematical algorithms are not patentable while innovative machines are? THE EASIEST LINE TO DRAW would be simply to say that if an invention is physical, then it should be patentable, and if it is abstract, then it should not be. But what do we do with inventions that involve both the physical and the abstract? For example, the case of Diamond v. Diehr involved a rubber-curing machine that relied on a significant amount of software to control the machine's timing. The U.S. Supreme Court ruled in 1981 that the patent was for industrial equipment, not an abstract algorithm, and thus the overall patent—software plus machine—was valid. But the court left a key question hanging: how much physical invention is necessary before the overall device is patentable? If all of the inventiveness is in the algorithm, which is then applied in a trivial manner to a simple machine, is the overall patent okay? In a long series of rulings, culminating in 1994 with In re Alappat and In re Lowry, the U.S. Court of Appeals for the Federal Circuit ruled that an uninventive physical component added to an inventive abstract component makes the whole patentable. In other words, "a new algorithm to calculate Fourier transforms" is not patentable, but "a stock PC on which is programmed a new algorithm to calculate Fourier transforms" has enough of a physical component to be patentable. Further, the court ruled that since a computer is so integral to a computational algorithm, patent examiners are obliged to assume that one exists. If an application is for "a pure computational algorithm," then the examiner must read it as if the words "a computer on which is programmed" had been prepended to the description of the algorithm. This is the bottom of the slippery slope: there is no longer any meaningful barrier to the patenting of abstract algorithms. The use of any inventive mathematical algorithm that requires more calculation than can be reasonably done by hand is now patentable. ANOTHER APPROACH MIGHT BE to distinguish between the pure mathematical algorithm, which should not be patentable, and its application to real-world problems, which should be. For example, the case of Gottschalk v. Benson concerned the patentability of a program to convert between binary-coded decimal and plain old binary. Evidently, this was too close to unapplied pure math; the Supreme Court struck down the patent in 1972, because "the patent would wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself." In contrast, State Street Bank and Trust Co. v. Signature Financial Group Inc. was a suit over alleged infringement of State Street's patented system for doing the bookkeeping for a suite of mutual funds. The system did not push around physical objects, but the Court of Appeals for the Federal Circuit ruled that the share prices and other numbers it derived still have a real, tangible effect and may therefore be considered to be a valid subject for a patent. So this attempt to distinguish the patentable from the unpatentable is too unreliable. TO FIND OUT WHY all these distinctions fail, we turn to one of the founders of computer science, Alan Turing. In 1936, Turing described a theoretical computer that is effectively equivalent to every computer in existence today. His design included an infinitely long tape and read/write head, which did different things depending on the data on the tape and the machine's state. Because different states cause the machine to do different things, his contraption is often called a state machine. A modern PC is equivalent to Turing's tape and head—a physical device that can store data and execute various operations. The programs that instruct the computer's operation generate the states that dictate how it will operate: they make up the impermanent information that guides the computer, but they do not change its fundamental design or composition. Because almost all modern programming languages encompass the ability to turn a computer into a state machine, they are all, at a deep level, equivalent—a program written in one such language can be directly translated to any other language, such as from Perl to C++ or from Microsoft Visual Basic to Lisp. So all software is essentially made of the same stuff. In 1936, Alonzo Church proved that that stuff is mathematics. Church created lambda calculus, a formal means of writing mathematical expressions and also a tool that can be used to program a state machine. That is, any program written in a language such as C is a trivial translation of a set of purely mathematical lambda-calculus expressions. So where is the line drawn between software and mathematical expression? Based on Church's and Turing's work, there is none. Any legal attempt to force a wedge between pure math and software will fail because the two are one and the same. A patent on a program is a patent on a mathematical expression, regardless of whether it is expressed in C, Lisp, or lambda calculus. BUT WHILE DEMOLISHING the distinction between software and math, Turing and Church's work offers a natural division between patentable machinery and unpatentable mathematics—exactly what we have been looking for. Let the devices that implement state machines—physical objects such as computers—be patentable, and the states to which they are set—information such as programs and data—remain unpatentable. The distinction meets the goal of ensuring that pure mathematics is not patentable while letting those who design faster and better computing devices patent their inventions. The distinction is clear, and it offers no slippery slope down which the courts could slide. An innovative field-programmable gate array (FPGA) is a state machine and so would fall on the patentable side of this fence, while code loaded onto the FPGA would be an unpatentable state to which the state machine has been set. A Java machine constructed on an application-specific integrated circuit (ASIC) would be a state machine, but a Java machine existing only in software running on a general-purpose central processing unit would be a state. A robot arm would be a state machine, but its device driver would be a state. The courts failed to review the mathematics literature and as a result made several vain attempts to reinvent the wheel. Software and lambda calculus are in the same equivalence class, which means any law that allows software to be patentable allows the patenting of the evaluation of certain mathematical expressions. But, fundamentally, if we are to disallow the patenting of pure scientific and mathematical discoveries to foster basic research and innovation, the only way to do so is to disallow the patenting of the states to which state machines may be set—that is, to abolish software patents. Editor's Note: This is the first of two articles on software patents. This article focuses on how the U.S. patent system attempts to draw a dividing line between patentable machines and unpatentable mathematics—and why the system is failing. Next month's article will discuss the economic and legal impact of software patents and a proposed solution. ABOUT THE AUTHOR Ben Klemens has a Ph.D. in social sciences from California State Polytechnic University, in Pasadena. He is currently a guest scholar at The Brookings Institution, Washington, D.C. His book Math You Can't Use: Patents, Copyright, and Software is to be published by the Brookings Institution Press. Software Patents Don't Compute |
July 26, 2005
I Think, Therefore I Am — SortaThe belief system of a virtual mind by MARGARET WERTHEIM Dateline: An unnamed Iraqi village. Locale: Hospital reception room. Décor: Tattered, rundown, rudimentary. The captain's mission: To obtain information about the local medical facilities. On the computer screen in front of me, an animated Army captain is attempting to speak with an Iraqi hospital receptionist. This is a fictional scenario in a state-of-the-art military training game. On the other side of the virtual room, the receptionist listens politely as the captain explains that he has come with supplies and he would like to speak to the hospital director. The receptionist seems to hesitate, but then responds that he will be happy to assist. As a piece of animated action, the scene above is not likely to quicken the pulse of any gamer, but for the U.S. military it offers a glimpse into the future. The characters here are not mouthing a pre-assigned script, they are literally making decisions about what to do and say. Far more than mere cartoons, these virtual people have each been endowed with a virtual mind complete with its own internal "desires" and "goals." Technically known as "agents," they are driven by a revolutionary software system known as PsychSim that enables programmers to simulate the cognitive faculties of human minds. Dr. Stacy Marsella, a leading agent researcher and one of the primary architects of PyschSim, declares that agents actually "think for themselves." Indeed, the ultimate goal of agent research is to create autonomous self-determining minds capable of a full spectrum of human behavior. A small, dark-haired man with a doctorate in artificial intelligence, Marsella is a project leader at USC's Information Sciences Institute in Marina del Rey, one of the world's top centers for agent research. Sitting in his office overlooking the marina, Marsella effervesces with visionary zeal about the potential for what he calls "virtual humans" and dreams openly about agents that can interact with real humans as cognitive and emotional equals. Outside in the marina, actual yachts bob on actual waves beneath a slate-gray sky; inside, I begin to feel that I am being pulled into the Matrix. With PsychSim, Marsella explains, programmers can create agents that "can reason about themselves and about other agents and make decisions about how to respond based on what they believe the other agents are doing." Marsella sees a future in which we will increasingly interact with these ersatz people – at first they will just do mundane tasks such as answering phones to take orders for pizza, or responding to simple queries, but eventually they will be capable of vastly complex interactions. Last year, Marsella and his colleague Dr. David Pynadath developed an agent-based game in which parents of childhood cancer patients engage in virtual counseling sessions with a virtual therapist. The game, called Carmen's Bright Ideas, was pilot-tested at six hospitals nationwide, including Children's Hospital of Los Angeles. Another group Marsella is working with at the ISI's sister organization, the Institute for Creative Technologies, is beginning to work on agent-driven games that could help people suffering from phobias and Post-Traumatic Stress Disorder. Marsella and his colleagues believe they will someday be able to simulate not only a vast range of social interactions but a panoply of personality types and psychologies. In effect, they are attempting to create virtual cyborgs — beings without bodies yet endowed with minds, thoughts and even feelings of their own. But what does it mean to talk about a virtual mind? What, indeed, is a mind of any variety? On his computer Marsella brings up a graphic labeled "Theories of Mind." It's absurdly simple in execution, childish almost, yet it characterizes a profound philosophical argument about what it means to be a thinking being. The focus of the graphic is a purple smiley face with a large thought bubble emanating out of its head. As Marsella explains, the thought bubble renders the agent's mind. Within this bubble are several other smiley faces, each of which has its own thought bubble coming out of its head, each in turn containing other smiley-face agents. The point here, Marsella says, is that "each agent has encoded within it a model both of itself and of the other agents within the system." It has, as it were, a mental image of each member of its community; it "knows" that it exists and it "knows" that its colleagues exist. Crucially, its mental model includes a conception of what it thinks the other agents are thinking. Thus, says Marsella, an agent can make judgments about what they believe any other one will do: "Fred has a model of Alice. So Fred can reason about Alice and how Alice thinks about him. Therefore, if he does some action, what will she think and how will she react. Based on what he thinks she will do, he can make a decision about what he will do. These guys aren't just looking up tables to see what to do next, they are doing little simulations in their heads." While Marsella has been explaining his philosophy of the virtual mind, his PsychSim co-creator has been sitting quietly across the table and looking on with bemused silence. Pynadath, who speaks with the measured tones of a classical scientist, is an expert on multi-agent interactions. He too was trained in the field of artificial intelligence, but he comes from the more technical end of that spectrum. After all this talk about simulated psyches, Pynadath seems to feel a need to inject a bit of "hard" science into the discussion. "From an AI point of view," he notes, "we are using software techniques developed for non-human situations, for example with the robot rovers on Mars." The difference is that whereas most simulation software so far has been used for modeling physical interactions, PsychSim models social interactions. As Pynadath notes, simulation software has become very good at modeling the interactions between molecules of gas and grains of sand, but modeling relations between human beings requires an understanding of social and psychological dynamics. Until very recently, artificial-intelligence researchers believed that modeling the mind was simply a matter of simulating rational cognition, an activity that was seen to be epitomized by strategical games such as chess and go — but over the past decade, computer scientists have come to understand that a virtual mind needs a virtual psychology. To "think" requires not just an ability to carry through a chain of logical inferences; it also requires a mental environment, or psychic context, in which such rationalizations can be given meaning. Having heard the theory of virtual minds, I was eager to see one in action. Marsella handed me over to Mei Si, a 28-year-old Chinese graduate student in USC's Department of Computer Science. "We try to recruit students who have training in psychology as well as in computing," Marsella told me as we headed to her office. Si already has a master's degree in psych. In a windowless room she shares with another graduate student from China — ocean views are clearly reserved for the upper tiers of the hierarchy — Si turned on her computer and scrolled through what seemed like an endless piece of software. She wanted to show me the chunk of code defining the mind of the aforementioned hospital receptionist. It is an extremely minimal agent, she tells me; unlike some of its confreres, it has no desires and only two specified "goals." "The most important goal that agents have is to behave like a human," Si remarked as she pointed out where various mental parameters are defined in the arcane text. For the hospital receptionist, whose only function is to impart basic information, the primary goal is to act according to social norms; the second goal is to be liked. Si showed me where in the relevant lines of code she had defined variables labeled "norm" and "being likeable." Each variable is assigned a value in the range from 0 through 1 and the higher its value, the greater the urgency the agent has to satisfy this goal. Aside from being liked and acting normal, other goals that agents might have are to be polite, to maintain safety within the game's setting, or just to give an appropriate response within the course of a conversation. Si's research is specifically focused on implementing the dynamics of agents' conversations. While humans take this for granted as a trivial task, maintaining a coherent flow of dialogue is a major challenge for artificial-intelligence researchers. To date, computer-generated conversation has been notoriously nonlinear. Si explained the complexities involving even the most banal exchange: An agent needs to "know," for example, "'If you ask me a question, should I respond, and what kind of response should I give?' They need to know what sort of responses are appropriate, when to say 'thank you,' or if that's not appropriate, and perhaps instead I should just look surprised." In Si's work the first goal is merely to keep the conversation going. Agents can talk amongst themselves as part of a pre-defined scenario within a game environment, but by far the most significant conversations they will have are with the human players. From the agents' point of view, Pynadath told me, "a human is regarded as just another agent," albeit one about whom the agent probably has a rather elaborate mental picture. In the smiley-face model above, the human agent would be represented by a much longer list of attributes than other virtual agents. I wondered what agents think about us. How does a virtual mind view one that is instantiated in flesh and blood? "From a structural point of view," Pynadath said, "the human is no different than any other agent." But since we are the ones to whom these virtual minds must primarily respond, our behavior is critical to their behavior. Given this, Pynadath noted that an agent may well have a "different attitude" to humans than to its virtual colleagues. In particular, "it is likely to think that the human is less predictable." At present, most of the ISI's agent research is being funded by the military. The Iraqi hospital scene is one small part of an elaborate learning game produced for the Army that teaches soldiers headed for the Middle East to speak "strategically useful" Arabic. One of the military's other goals is to use agent software to simulate large-scale command structures. In theory, says Marsella, these simulations can be as large as you like. Indeed, an agent may stand in for an individual person, but it may also represent a group. Marsella and Pynadath have been developing agent software that enables them to simulate the social dynamics of entire cities. And the armed forces are not the only ones invested in the potential of large-scale social modeling — it's also of interest to those charged with maintaining homeland security. Marsella and Pynadath are currently working with other USC researchers to develop a project that would model the dynamics of a large international port such as Los Angeles's, a labyrinthine system involving many different agencies. With nearly 500 ships entering the L.A. port every month, it is not possible to search every vessel, let alone every container. Decisions must be made about which ones warrant closer scrutiny, and the various agencies are not particularly good at sharing information or coordinating their efforts. "One of the goals of the project," says Marsella, "is to help them to understand how cooperation and information-sharing can be enhanced, so that they can make better decisions about which ships and which containers to inspect." The project is still in its infancy, and it may be years before there will be any concrete suggestions about how to improve port efficiency. But in the long run, if Marsella and Pynadath can get their model to accurately emulate the real situation, such simulations may save time, money and even lives. As I listened to this talk about simulating the vast morass of the L.A. port, with its daily traffic of ships and cargo from all over the world, its cast of sea captains and smugglers and customs officials, I found myself looking out to the boats beyond the ISI window. Maybe, I thought, Matrix-like, all this is merely a simulation in some giant piece of software installed on some alien computer in a faraway galaxy, and we humans are just virtual agents reflecting within our virtual selves software models of one another. In one form or another, the idea of the simulacra has haunted and enchanted Western culture since at least the time of Plato's cave. Are we finally at a point where we might realize this surreal fantasy by creating a true virtual reality complete with sentient minds? As I considered this science-fiction scenario, I wondered out loud if Marsella and Pynadath ever feel as if they are playing gods. I didn't really expect an answer; I had meant the question rhetorically. Yet without missing a beat, both men answered in the affirmative. "Yes," they said almost in unison. Then in a tone at once excited and wistful, Marsella added, "It's a rather eerie feeling." I Think, Therefore I Am — Sorta |
July 24, 2005
Ecce Homology
This physically interactive new-media work visualizes genetic data as calligraphic forms. A novel computer-vision interface allows multiple participants, through their movement in the installation space, to select genes from the human genome for visualizing the Basic Local Alignment Search Tool (BLAST), a primary algorithm in comparative genomics. Art and Science For both ethical and technical reasons, the function of each gene in the human genome cannot currently be ascertained directly from the human genome itself. Usually, in order to determine the function of a gene, scientists must rely on comparisons between our genes/genome and those of other organisms. BLAST allows researchers to compare DNA or protein sequences of unknown identity, function, and structure with "knowns" from validated databases, providing a measure of similarity or homology among sequences. BLAST analyses are conducted worldwide via web servers supported by major genome sequencing consortia in Europe, Japan, and North America, as well as in local laboratories on individual computers. Every day, an average of 100,000 unique BLAST runs from 70,000 unique IP addresses are conducted on the US National Center for Biotechnology Information's web servers. BLAST is arguably the most widely used data-mining tool in history. Yet, despite its ubiquity, BLAST is a "black-box" process that is not well understood, even by researchers in the biological sciences. For Ecce Homology, intermediate information about the progress of BLAST is revealed by an animation of the intermediate products of the algorithm as it operates on genomic data in real time overlaid on the calligraphic forms. This revelation of the operation of a normally invisible process is at the core of the installation's aesthetic experience. Transformed into an experience that proceeds at the scale of human-perceived time, BLAST is the engine and subject of this interactive installation. We believe that an artistic, holistic visualization of genomic data coupled with an esthetically engaging interactive experience of genomics-based biology can encourage the general public to engage the subject critically. Additionally, Ecce Homology's novel calligraphic visualization of multi-dimensional genomic data is an example of art-science research that explores the possibility that artistic or aesthetic approaches can nurture discovery in the sciences. Unprecedented amounts of genomic data are generated daily. To capitalize on this wealth of data, new tools must be developed. The need to build knowledge from data, or to find patterns within vast datasets, is driving development and application of interdisciplinary and alternative approaches. Ecce Homology is one such approach. Its outcomes are both hybrid process and product. Goals To contribute simultaneously to the realms of science and art while retaining discipline-specific rigor. To investigate the nature of interdisciplinary collaboration. To foster awareness of tools that generate meaning and knowledge in science, particularly genomics. And to explore how artistic practice and aesthetic experience can nurture scientific discovery. Innovation Technical innovations include development of a novel calligraphic gene visualization incorporating multidimensional data and deployment of a new Java-based middle-ware framework: Kolo (and its associated scripting language Nebesko) developed at the UCLA Hypermedia Studio. As users move in the installation space, hand-position information generated by the computer-vision module is forwarded to the pattern-matching module and the graphics modules that render user movement. When the pattern-matching module detects a match between a user-drawn form and a gene character, a BLAST run is triggered. As it runs, the BLAST module sends intermediate progress to the graphics modules for rendering. Finally, a separate state-management module manages the overall state of the installation. Vision As the next era in the life sciences becomes increasingly dominated by interdisciplinary and discovery-based inquiry, Ecce Homology exemplifies an integrated art-science practice that goes beyond models of influence and convergence to explore the deep structures of science and technology in search of their expressive potentials and cultural relevance. Though it is driven by aesthetics, Ecce Homology suggests a new form of scientific visualization that may one day contribute to comparative genomics. If the arts can nurture discovery in the sciences, it is possible that the process can bring about a new paradigm for our relationship to nature, one in which human creativity is the avenue for our rapprochement with nature. Ecce Homology |
July 23, 2005
Brain scientists offer insight into visionWhen you see a flower, neurons deep inside your brain respond to the flower's color, shape and distance from your eyes, somehow working together to create the flower's image in your mind. (I-Newswire) - The question for neuroscientists is, how do they do that? It is known that neurons in the brain are clustered together according to their ability to detect different properties--such as the vertical edge of an object or the horizontal edge, or whether the object is being seen by the left eye or the right. Recently, neuroscientists at the Picower Center for Learning and Memory at MIT explored how these neuron clusters overlap to communicate visual information. They reported their findings in the July 21 issue of Neuron. The evidence suggests that multitasking may be fundamental to the way the brain works. "Since every part of the cortex has neurons that are involved in multiple tasks, there is every reason to think that this is a deep principle of brain organization," said Mriganka Sur, the Sherman Fairchild Professor of Neuroscience and head of MIT's Department of Brain and Cognitive Sciences. In the visual cortex, neighboring neurons detect objects in neighboring regions of space, creating an image or map of the visual scene. Neurons are clustered according to their ability to detect different properties, but they need to overlap so each combination of features can be represented by the cortex. If the clusters did not overlap with each other the correct way, then we would have "blind spots" for certain feature combinations. For example, in certain regions of the visual scene we might detect vertical edges with only the left eye, or horizontal edges with only the right eye. A Finnish mathematician tackled this problem in 1982, when he came up with mathematical formulas that showed how the clusters could pull off this overlapping feat. This study by Sur, postdoctoral associate Hongbo Yu, graduate student Brandon J. Farley, and visiting scientist Dezhe Z. Jin tests the predictions of mathematician Teuvo Kohonen. It does so by factoring in a quirky aspect of some species' cortical map: It's distorted. In some species' brains, a square region of the visual image is represented by a square region of the cortex. But in other species, the visual cortex is distorted, causing a square region in the visual image to be represented by a rectangular region of cortex. The Neuron study shows that the distortion in the mapping of the visual scene onto the cortex has an influence on clustering that Kohonen's formulas predicted. The shape of the clusters of neurons representing similar orientations and eyes also are distorted in such a way that each feature combination can still be detected in each part of space. What's more, the visual cortex's solution to accommodating several parameters probably holds true for other brain regions. Take hearing, for instance. "Hearing, like seeing, has multiple parameters: location of a sound in space, frequency and relative activation of the two ears," Farley said. "Maybe mapping multiple dimensions this way is a general strategy the brain uses when it faces this problem." This work was supported by the National Institutes of Health. Patti Richards MIT News Office Brain scientists offer insight into vision |
July 23, 2005
THE HOLY GRAIL!world wide enquiries jam web site of Nigerian professor who discovered secrets of the universe By Sola Fanawopo Access to the web site of the Nigerian-born, United States-based, Nobel Prize nominee, Professor Gabriel Audu Oyibo, (http://www.geocities.com/igala1) has been jammed throughout last weekend, because several people are trying to log on to the web site to read about his latest discovery, 'God Almighty Grand Unified Theorem' (GAGUT). Several attempts by our correspondent to log on to the site were unsuccessful. An apology boldly displayed on the site greets a visitor. It goes thus: "Sorry, this site is temporarily unavailable! The web site you are trying to access has exceeded its allocated data transfer." Other attempts to access the site through several other search engines such as yahoo, MSN and Google, did not yield the expected result. To underscore the extent of the impact of his work in the Western world, the German Armed Forces, through its Nuclear Bomb Research, is now seriously understudying his works. On a famous German book web site, abebooks.de, the German Federal Armed Forces is offering and promoting one of Oyibo's works, "Highlights of the Grand Unified Field Theorem", at EURO10.00. Also at DESY, the library of the German Nuclear Bomb Research, Oyibo's "Grand Unified Field Theorem: The Discovery of the Theory of Everything and the Fundamental Building Block of Quantum Theory", is listed. In the US, Oyibo's books are mostly reserved in reference sections in major libraries including those in Stanford, Harvard and several top universities in Europe. The quest for more public information about his works is also going at an alarming pace. The New York station of Public Broadcasting Service, PBS, has asked him to join the station in producing a documentary on his findings. According to a release from the New York-based OFAPPIT Institute of Technology, which is the research-based organisation that Oyibo set up as "the official home" of his GAGUT discoveries, "this documentary is expected to be a multi-part series on the discovery." The institute is also embarking on a fundraising drive to collaborate with the PBS in producing the documentary. The drive targets corporations, foundations and individuals' contributions. At Harvard and the Massachusetts Institute of Technology, (MIT) another leading technology and science school in the US, graduate students and some teachers embarked on an aggressive petition drive to make the school authorities invite Oyibo to deliver a public lecture at the school. According to the MIT petition, "We feel that a lecture and discussion about the scientific and social implications of this theory would be beneficial to our school by broadening our academic and social awareness." But crucial to Oyibo's passion is the need to educate Africans about the discovery that he commendably and boldly named after The Almighty God – the God Almighty's Grand Unified Theorem or GAGUT Oyibo insists that the focus of his work is God. "He sent the revelation...and a revelation comes for a reason." He referred to Isaac Newton, a minister of the Church of England in his days, who got a revelation. Oyibo submitted that it was Newton's spiritual basis that helped his scientific findings. Said Oyibo: "The message to Newton was to elevate the Europeans through the revelation on how the planets move. He was referring to the universal gravitational law, which governs the motion of the planets and stars." According to Oyibo, Newton got the formula through a revelation he could not explain – he got a solution without an equation. But 100 years later, Professor Poisson, a French mathematician, supplied the equation. Oyibo then observed that "all knowledge comes from God, in some cases it is acknowledged, others don't." Moving on to Albert Einstein who credited the creation of the world to the Big Bang, Oyibo noted that his discovery was sent to deliver the Jews. "Then the Jewish people were living in ghettos in Europe, undergoing hard times, when there were signs in some public places that 'dogs and Jews' were not welcome. They even put the dogs first," Oyibo explained with a tinge of distaste. It was under those circumstances that Einstein discovered the theory of relativity. That changed the fate of the Jews, as that discovery led to the first atomic bomb in the US, to where several Jews then moved, following Einstein's settling down at Princeton University. Oyibo is now staking out the claim that GAGUT is the father of relativity and "if relativity lifted the Jews, GAGUT is also sent by God to liberate and lift black people." Who is Oyibo? Professor Gabriel Audu Oyibo is a Kogi State, Nigerian-born, mathematical physicist, resident in the United States of America and currently making waves around the world with his GAGUT Theorem – more like the Holy Grail, the theory of everything, holding the entire secrets of the universe. Oyibo's work has advanced Einstein's Relativity and answered questions that the science icon tried to address, regarding the origins of the universe but could not answer, before he died. With the professor's findings he hopes that with the right funding, even incurable diseases such as AIDS, cancer, Parkinson's syndrome and Alzeimer's disease, would be curable within three years. Based on the GAGUT formula, cells in the affected human body would be "re-tuned" rather than killed. Viruses that attack the body's T-cells are not living organisms and therefore cannot be killed. They merely utilise energy from the T-cells to multiply themselves. Professor Oyibo's discovery will merely help doctors re-tune the cells instead of killing them, providing a permanent cure. Gabriel Oyibo, who obtained a Ph.D. in Aeronautics and Mathematics from Rensseler Polytechnic Institute, Troy, New York, has been nominated for the Nobel Prize, thrice now. THE HOLY GRAIL! |
July 23, 2005
PROFESSOR OYIBO'S GAGUT THEORY |
July 23, 2005
The universal question is still elusiveBy MERVYN DYKES Einstein's famous theory of relativity was hailed as the end of a great deal of scientific effort, but it is barely the beginning, really. Professor Gerry Gilmore, who delivered the annual Unesco New Zealand science lecture in Palmerston North last night said the great mathematician raised questions about the universe that in turn stimulated thinking about the very nature of reality. "We are still a long way from knowing what there is to explain, let alone understanding it," he said. "But this is the field in which I work and it is what is exciting young people today. "They are coming out of our schools saying they want to know about reality. They want to know what is real." Timaru-born Professor Gilmore is the Professor of Experimental Philosophy and deputy director of the Institute of Astronomy at the University of Cambridge. He is visiting New Zealand for the lecture series in the Year of Physics which marks 100 years since Einstein proposed his special theory of relativity. The title of his lecture, delivered at the Spiers Centre, was The Origin and Future of the Universe. In it he explored the nature of dark matter and the even more mysterious dark energy which together make up 95 percent of the universe. In pre-Copernician times the prevailing view of the universe placed man and the Earth at the centre of things, he said, but since then everything had turned around. The picture that had emerged was that man and the Earth were insignificant and that the universe in which the Milky Way galaxy spun was but one of many. All that was known and understood made up only 5 percent of reality. Dark matter accounted for another 25 percent and dark energy about 70 percent. The galaxy revolved around its core at such speed that its stars would fly off into space were it not for the dark matter and dark energy holding them together. They were not really dark, he said, but transparent and he described the galaxy as being like a fried egg. The visible elements were the yoke and the other "stuff" was represented by the white. "We live in a small sub-set of the universe where our imagination is limited by four dimensions (time being the fourth) when we now know there are 11 dimensions," he said. "At the moment we cannot even begin to explain them - and that is what is so exciting." * Professor Gilmore will feature in a coming Science Page article. The universal question is still elusive |
July 23, 2005
U.S. Team Survives Hurricane to Place 2nd in International Mathematical OlympiadSource: Mathematical Association of America MERIDA, Mexico, July 19 /PRNewswire/ -- The 2005 International Mathematical Olympiad (IMO), 46th in the annual series of mathematical competitions for high school-age students, announced the medal winners today. At this year's IMO, 513 of the best young mathematicians from 93 countries, making it the largest IMO ever, competed in solving 6 problems posed in a grueling nine-hour test administered over two days (July 13 and 14). The competition which poses six math questions, each worth a total of 7 points, would challenge even the finest professional mathematician. The U.S. finished 2nd overall with a total of 213 points out of a possible 252 points. China came in 1st with 235 points, Russia was 3rd with 212, Iran placed 4th with 201 points and Korea placed 5th with 200. Upon word of their victory, Steve Dunbar, Director of the American Mathematics Competitions for the Mathematical Association of America, exclaimed, "This is an extraordinarily strong performance by the U.S. team, since this is the first time that these six team members have represented the U.S. at the International Mathematical Olympiad. Congratulations to Team Leader Zuming Feng and Deputy Leader Melanie Wood for preparing the team and presenting their solutions to the judges."
Members and competitions results of this year's team are:
Brian Lawrence, Perfect Paper, Gold Medalist
Attends Montgomery Blair High School, Silver Spring, Maryland
Eric Price, 41 points, Gold Medalist
Graduated from Thomas Jefferson High School of Science and Technology,
Alexandria, Virginia
Thomas Mildorf, 39 Points, Gold Medalist
Graduated from Thomas Jefferson High School of Science and Technology,
Alexandria, Virginia
Robert Cordwell, 36 points, Gold Medalist
Graduated from Manzano High School, Albuquerque, New Mexico
Sherry Gong, 28 points, Silver Medalist
Attends Phillips Exeter Academy in Exeter, New Hampshire
Hyun Soo Kim, 27 points, Silver Medalist
Graduated from the Academy for Advancement of Science and Technology,
River Edge, New Jersey
The U.S. Team is sponsored by the Mathematical Association of America (http://www.maa.org) with support by other mathematical societies, the University of Nebraska and the Akamai Foundation. Transportation is provided through a grant from the Army Research Office. Additional contributions come from 19 organizations and companies in the mathematical sciences. The team is chosen through a four-stage process of mathematics testing by the MAA's American Mathematics Competitions Program.
Contact: Steven R. Dunbar, Director
MAA American Mathematics Competitions
U.S. Team Survives Hurricane to Place 2nd in International Mathematical Olympiad
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July 19, 2005
Between Series, an Actress Became a Superstar (in Math)By KENNETH CHANG On her Web site, Danica McKellar, the actress best known as Winnie Cooper on the television series "The Wonder Years," takes on questions that require more than a moment's thought to answer. "If it takes Sam six minutes to wash a car by himself," one fan asked recently, "and it takes Brian eight minutes to wash a car by himself, how long will it take them to wash a car together?" "This is a 'rates' problem," Ms. McKellar wrote in reply. "The key is to think about each of their 'car washing rates' and not the 'time' it takes them." Ms. McKellar, now a semiregular on "The West Wing" playing a White House speechwriter, Elsie Snuffin, is probably the only person on prime-time television who moonlights as a cyberspace math tutor. Her mathematics knowledge extends well beyond calculus. As a math major at the University of California, Los Angeles, she also took more esoteric classes, the ones with names like "complex analysis" and "real analysis," and she pondered making a career move to professional mathematician. "I love that stuff," Ms. McKellar said last month during a visit to Manhattan after a play-reading in the Hamptons. Her conversation was peppered with terminology like "epsilons" and "limsups" (pronounced "lim soups"). "I love continuous functions and proving if functions are continuous or not," she said. She may also be the only actress, now or ever, to prove a new mathematical theorem, one that bears her name. Certainly, she is the only theorem prover who appears wearing black lingerie in the July issue of Stuff magazine. Even in that interview, she mentioned math. Ms. McKellar was 13 when "The Wonder Years" started in 1988 and when it ended five years later, she took a respite from acting to attend U.C.L.A. She expected that she would resume acting when she graduated, and she expected that she would major in film. In her freshman year, though, she found that she missed the structured logic that she had enjoyed in high school math, and she started taking math classes at U.C.L.A. "I felt my brain was getting mushy," she said. To her surprise, she excelled. Later, she was surprised by her surprise, because she had done well in math classes from elementary school through high school. But she had never considered studying math or science in college. "It wasn't like I thought about it and thought, 'No, I can't do that,' " she recalled. "It just never occurred to me." Next, she took the more complicated complex analysis course. The professor, Lincoln Chayes, invited her to enroll even though she had not taken all of the prerequisites. And then she had another class, real analysis, also taught by Professor Chayes. She quizzed him with enough questions that he offered her and another student, Brandy Winn, the opportunity to tackle some original research, the first time he had given a research project to undergraduates. For a simple model of magnetism, Professor Chayes thought that they might be able to prove a property that would indicate when the magnetic field would line up in a certain direction. Professor Chayes tutored the two women for months on the background knowledge they would need. Then the students spent months more, up to 12 hours a day, working on the proof. "I thought that the two were really, really first rate," Professor Chayes said. Sometimes, they spent days on an approach before finding an obvious flaw. Other times, they thought they had finished, before Professor Chayes would find an error or oversight. And, finally, Professor Chayes found no more gaps. A paper with an imposing title - "Percolation and Gibbs States Multiplicity for Ferromagnetic Ashkin-Teller Models on Z²" - appeared in a British mathematical physics journal, and Ms. McKellar presented the findings at a statistical mechanics conference at Rutgers, the only undergraduate to speak. Today, the proof is known as the Chayes-McKellar-Winn theorem. Ms. McKellar had toyed with the idea of going to graduate school. "She certainly had the capability and talent to do that," Professor Chayes said. But by then, she had decided to return to acting. The academic world, she said, was too isolating and lonely. Professor Chayes said he was not disappointed. "I think disappointed is too strong," he said. "I would have been even happier if she were doing what she is doing now coupled with a career in mathematics." Since graduating in 1998 with highest honors, Ms. McKellar has reappeared on television, in her recurring role on "The West Wing," and as a guest star on shows like "NYPD Blue" and "Navy: NCIS." Her voice has been heard in the cartoons "King of the Hill" and "Justice League." She has also written and directed a couple of short films. The other member of the math proof team did continue in math. Ms. Winn, now Dr. Winn, completed her Ph.D. in mathematics at the University of Chicago this year. At U.C.L.A, Dr. Winn had decided to major in math before even meeting Ms. McKellar. But she said she had not expected to continue in the field beyond her bachelor's degree. "Pretty much because of Lincoln and Danica, I did go on," Dr. Winn said. Ms. McKellar remains enthusiastic about math. She even managed to combine math and acting for one role, in a production of "Proof," the Pulitzer-winning play by David Auburn, in her hometown, San Diego. She played the main character, a young woman who claims to have solved a complicated mathematical proof. "I don't think there is any other time in my life when I knew that this role was supposed to be for me," she said. At an audition, the casting director asked about what she knew of math. Ms. McKellar said she was co-author of a mathematics proof. "She went into a five-minute explanation," said Sam Woodhouse, the artistic director of the San Diego Repertory Theater. "Which was a stunning and mystifying five minutes." Ms. McKellar said she hoped to be a role model for future mathematicians, especially middle school girls. She testified to a Congressional subcommittee in 2000 about how to draw more women into science and math. She has just signed on as spokeswoman for the Math-a-Thon at St. Jude Children's Research Hospital in Memphis, where children work through a book of math problems, and their friends and family pledge money to the hospital for each problem that is solved. For several years, Ms. McKellar has also been answering math questions at danicamckellar.com, under the "mathematics" link. It helps her maintain some of her skills, although she sometimes needs to consult old notes and textbooks. "I have all of them since the seventh grade, except for my ninth-grade geometry book," she said, "which my sister used when she was in ninth grade, and she sold it at the book sale when you sell your books back. "I was like, 'You sold my book?' She's like, 'Yeah.' 'But that was mine.' She's like, 'Oh, oops.' I have every other book." To the person asking about the time it would take to wash a car, Ms. McKellar worked through the calculation of how long it would take if Brian and Sam worked together. The answer: a little less than three and a half minutes. "Yes, I think they should work together," she wrote. "It gets done much more quickly that way." Between Series, an Actress Became a Superstar (in Math) |
July 14, 2005
Floating ideasMarc Abrahams Almost nothing is more romantic than a mathematical theorem - if that theorem is stuffed into a bottle and cast adrift during a perilous sea voyage in wartime, and if the person who wrote it is one of the world's top mathematicians. Shizuo Kakutani, who died last August, threw many such bottles into the ocean more than 60 years ago. Their fate is a complete mystery. Kakutani went on to become a legendary mathematician. Like most famous mathematicians, his fame is mostly among those in his profession. Indirectly, though, the public is almost aware of Kakutani, for two reasons. The movie and book A Beautiful Mind was about the mathematician John Nash. Nash's most famous concept, the Nash equilibrium, is based on the Kakutani fixed-point theorem. And Kakutani's daughter, Michiko, is the most influential book reviewer at the New York Times. The story of Kakutani's bottled theorems has only just now been told outside the tight circles of those who really, truly, deeply understand the nature of, well, circles. Stanley Eigen, a mathematics professor at Northeastern University in Boston, wrote an appreciation of his longtime collaborator and friend. He published it in the Annals of Improbable Research. Eigen explains: "At the start of world war two, Kakutani was a visiting professor at the Institute for Advanced Study in Princeton. With the outbreak of war he was given the option of staying at the institute or returning to Japan. He chose to return. "So he was put on a Swedish ship which sailed across the Atlantic, down around the Cape, and up to Madagascar, or thereabouts, where he and other Japanese were traded for Americans on a ship from Japan. "The trip across the Atlantic was long and hard. What, you may wonder, did Kakutani do? He proved theorems. Every day, he sat on deck and worked on his mathematics. Every night, he took his latest theorem, put it in a bottle and threw it overboard. Each one contained the instruction that if found it should be sent to the institute in Princeton. To this day, not a single letter has been received." Is there much chance of finding them? No one knows. There is precious little scholarship about messages found in bottles. Robert Kraske's too-slim book The Twelve Million Dollar Note: Strange But True Tales of Messages Found in Seagoing Bottles. The messages-in-bottles collection at the Turks and Caicos National Museum. The rubber-ducks-and-other-things-that-wash-up-on-beaches research of Seattle-based oceanographer Curtis Ebbesmeyer. These, our greatest chronicler/gatherers, have so far disappointed us in the case of Kakutani. · Marc Abrahams is editor of the bimonthly magazine Annals of Improbable Research (www.improbable.com), and organiser of the Ig Nobel Prize Floating ideas |
July 14, 2005
Art by numbersBy Mary Voelz Chandler, Rocky Mountain News The relationship between art and science is a long and treasured one, reflected in the timeless appeal of proportional theories such as the Golden Mean and the Fibonacci series of numbers. And although exhibitions occasionally go on view here involving artists who use those principles in their work, the 2005 CU Special Year in Art and Mathematics inspired a series of shows that stress the links between the natural and aesthetic worlds. "Mathematics is a field that is more restricted," said Carla Farsi, an artist who teaches topics ranging from art and math to calculus for the mathematics department of the University of Colorado. "Some ideas are the same, they just come out in different languages." Farsi, who joined the CU faculty in 1991, also is an active member of Core New Art Space and chairwoman of the committee that set up exhibitions that began in 2004 to mark the Year in Art and Math. Support came from educational and art institutions in the area, as well as from an $18,000 grant from the Colorado Council on the Arts. At the heart, though, was a conference last month at CU that tied the two disciplines together - just as past events had addressed issues such as "math and weather." Farsi said about 70 people attended the 2005 conference, which included a program by area artists Charles Wooldridge and Dismas Rotta, who have a show of related paintings and sculpture - "Contrast+ive" - on view through Friday at Studio Aiello in Denver. The gallery's owners, Monica and Tyler Aiello, helped jury the series' centerpiece show and offered it its first venue: "Intersection" ran briefly at Studio Aiello, then in late June moved to the UMC Art Gallery in Boulder (UMC's Kristi Graham also was a juror). On view there through Aug. 5, "Intersection" involves work that interprets mathematical principles through visual means. Brandon Borchert, for instance, is represented by two paintings in which he uses his random "power ball" drawing system to choose imagery to include in the work. Angela Forster's digital prints record the wave activity in water generated by moth wings. Sue Simon, perhaps the doyenne of the genre in this region and an artist with a background in scientific notation and illustration, is represented by paintings that address string theory and the mathematical universe. And Chris Weller presents an untitled grid of shifting circles that, according to his artist statement, "represents a collaboration between the world of random numbers, stochastic processes and the algorithms, constraints and designs I impose on all of that chaos." Sculpture is part of the show, too, including Allen Linder's marble and bronze depictions of cell division and Benjamin Storch's forged metal views of a space knot and a piece titled Minimal Moebius. • Also organized as part of the CU program is a small show on view through Aug. 12 at Naropa Institute's Lincoln Gallery. "WomenMenArtMath," with work by 11 artists mainly from Boulder and Denver, moves beyond purely art and math to look at gender issues as well. Pieces range from Simon's painting Point of View, with its panels referencing DNA, to Naropa's visual arts chairwoman Sue Hammond West's Power and Roots, which combines mathematical tables with visual elements. Naropa's Lincoln Gallery is on the school's Arapahoe Campus, 2130 Arapahoe Ave., Boulder. Information: 303-245-4637. • Along with exhibitions organized as part of the Year in Art and Mathematics, two others with related work emerged independently. The first instance is a revelation, exhibitions organized by CU Art Museum's Lisa Tamiris Becker that feature work by three women who studied art at CU in the 1960s or 1970s and have built solid reputations teaching and making art outside the region: Suzanne Anker's "The Genetic Gaze," Barbara Takenaga's "Micro/Macro" and Marlene Tseng Yu's "Forces of Nature: Oversize Paintings." Tseng Yu's mammoth works on canvas depict, in an abstracted fashion, natural phenomena such as an avalanche and a glacier in radiant colors, in itself a nod to earth science. But Anker and Takenaga hone in on more specific scientific subjects. Along with wall works that track the human genome, Anker also sculpts representations of different stages of human life (Cubist Baby, First Fetus) and, in a major work, two tables with objects that derive from life forms, mixed with chunks of pyrite, or fool's gold. Her 2004 installation, "Origins and Futures II," ties the building blocks of life with the false promise of riches inherent in that particular mineral. And Takenaga brings the galaxy alive with paint on board pieces that combine patterning and almost obsessive attention to detail with explosions, whorls and what seems like a million exploding stars. It's a summer sleeper of a show, through July 22, with work that makes rediscovering a trio of alumnae a visual adventure. The CU Art Museum is in the Sibell Wolle Fine Arts Building at CU. Information: 303-492-8300. • Meanwhile, Jeanne Shoaff, of the Fort Collins Museum of Contemporary Art, organized "Convergence of Art and Science" because "I was interested in the topic, and it seems to be a big area of crossover right now." She selected a dozen artists to exhibit from the 50 that responded to a small call for entry. Along with a series of experiments in growth and human behavior by David Melrose, the exhibition includes digital images by Susan Kaprov of genetic fruit and vegetable hybrids notable for their color, handkerchiefs printed and beaded with virus arrays (the beautiful but unnerving Viral Warfare?, by Jennifer Smith), and a new version of wax sculptures by Gary Voss that resemble fleshy deposits and surgical sites, as seen through containers of frosty ABS plastic. Shoaff also invited Daniel E. Goods to participate in the show, with a projection piece about locating planets and stars in a busy sky. Goods, an advanced concepts architect with NASA's Jet Propulsion Labs in California (think a form of artist-in-residence), will speak about his work at 3 p.m. on Aug. 13, the show's closing day. Art by numbers |
July 14, 2005
Professor Lets Her Fingers Do the TalkingBy MICHELLE YORK ITHACA, N.Y. - Some people looking at the crocheted objects on Daina Taimina's kitchen table would see funky modern art. Others would see advanced geometry. The curvy creations, made of yarn, are actually both. And they are helping two very different groups - artists and mathematicians - learn more about each other. Increasingly, they are also making a quirky celebrity out of the woman who created them. "The forms are amazing," said Binnie B. Fry, the gallery director of the Eleven Eleven Sculpture Space, an art gallery in Washington, where Dr. Taimina's creations are part of a summer exhibition called "Not the Knitting You Know." Dr. Taimina, a math researcher at Cornell University, started crocheting the objects so her students could visualize something called hyperbolic space, which is an advanced geometric shape with constant negative curvature. Say what? Well, balls and oranges, for example, have constant positive curvature. A flat table has zero curvature. And some things, like ruffled lettuce leaves, sea slugs and cancer cells, have negative curvatures. This is not some abstract - or frightening - math lesson. Hyperbolic space is useful to many professionals - engineers, architects and landscapers, among others. So Dr. Taimina expected some attention for her yarn work, especially from math students destined for those professions. But her work has recently drawn interest from crocheting enthusiasts. Math professors have been teaching about hyperbolic space for decades, but did not think it was possible to create an exact physical model. In the 1970's, some educators, including Dr. Taimina's husband, David Henderson, a math professor at Cornell, created hyperbolic models, but the first ones, made from paper and cellophane tape, were too fragile to be of much use. Though she did not realize it at the time, Dr. Taimina was a good candidate to create a better model. As a precocious child in her native Latvia, she tried her elementary school teacher's patience. When her fellow second graders did not understand a math lesson, she recalled, she would jump up and yell, "I can't stand these idiots," prompting her teacher to send notes home. By high school she had settled down, and was most impressed by a teacher who was known to keep his advanced students laughing and engaged. When she became an educator, she decided that no student, regardless of aptitude level, would feel out of place in her classroom. One way she assured that was by using everyday objects to explain theories. (She was known for peering so intently at the oranges at her local grocery to see if she could find perfectly round ones to use in her geometry class that she scared the clerks.) But it was her crocheting hobby that would prove really useful and make her something of a star - at least to knitters and math lovers. In 1997, while on a camping trip with her husband, she started crocheting a simple chain, believing that it might yield a hyperbolic model that could be handled without losing its original shape. She added stitches in a precise formula, keeping the yarn tight and the stitches small. After many flicks of her crocheting needle, out came a model. One professor who had taught hyperbolic space for years saw one and said, "Oh, so that's how they look," Dr. Taimina recalled in an interview at her home here, not far from the Cornell campus. A year after she created the models, she and her husband gave a talk about them to mathematicians at a workshop at Cornell. "The second day, everyone had gone to Jo-Ann fabrics, and had yarn and crochet hooks," said Dr. Taimina. "And these are math professors." The crossover to the art world began last year. An official of the Institute for Figuring, an educational organization based in Los Angeles, spotted an article about Dr. Taimina's models in New Scientist magazine and invited her and her husband to California to speak about them. An audience that included artists and movie producers was there. "They told us this helps with their imagination," Dr. Henderson said. In February, the two spoke in New York City. To their surprise, the talk, at the Kitchen, a performance space in Chelsea, sold out. Some enthusiasts asked if they were going on tour. Gwen Blakley Kinsler, the director of the Crochet Guild of America, believes Dr. Taimina's objects will be of interest to free-form crocheters. "It's always nice to be validated," she said. "People think only grannies do this and it's just doilies." She plans to publish an article about Dr. Taimina and her hyperbolic creations in Crochet Fantasy magazine later this year. That would be interesting notoriety for someone who, as a child, was told by her teachers not to waste time in art classes. As an adult, when terrified artists started showing up in her math classes to fulfill their degree requirements, she signed up for a watercolor class, thinking, "Then I will know how they feel." Now when students tell her they simply cannot understand math, she pulls out one of her paintings and says, "I learned that in three months." Then she might pull out one of her crochet models. Professor Lets Her Fingers Do the Talking See also Those crafty scientists |
July 14, 2005
Where maths meets biologyUniversities take note: systems biology is the field of the future and you could host a centre to train PhD students. Linda Nordling reports Universities wanting to stay at the top of their game need to keep abreast of which disciplines are hot, and which are not. So when a couple of research councils announce they want to set up a handful of doctoral training centres in a brand new field of biology, universities will sit up and listen. The Engineering and Physical Sciences Research Council (EPSRC) and the Biotechnology and Biological Sciences Research Council (BBSRC) are funding new centres in systems biology. By this time next year, a handful of institutions could be recruiting their first cohorts of PhD students in this exciting new field of research. Systems biology is, roughly speaking, where traditional biology meets mathematics and computing. It uses mathematical models and high-power computing to understand how cells make up organs, or how organs make up organisms. The ultimate aim is to move from lab-based - or "wet" - biology to predictive biology, in which experiments can be carried out by computer. The transition has been made possible by the rapid growth in computer processing power, making hugely complex data sets, such as genetic code, manageable. Systems biology requires scientists capable of bridging the divide between mathematics and biology. The centres will produce such people, and it is hoped that many of them will continue their research at UK institutions. The BBSRC has already sponsored systems biology research centres at Imperial College and the universities of Manchester and Newcastle. At least three more will be set up by 2007-08, the BBSRC says. The scope of the doctoral training centres will be wide, as you would expect from a discipline in which new ground is being broken all the time. Students will be drawn from a variety of backgrounds and, to give them the breadth of knowledge they will require to tackle interdisciplinary research questions, up to a quarter of the PhD will be made up of taught elements. The centre competition is open to all UK universities, but they should demonstrate an imaginative approach to PhD training in their applications. The funding will support around 10 new PhD students a year for three years, although the scheme could be extended for another two years. The funding will cover student stipends (in 2006-07, a minimum of £12,300 a year), as well as costs related to teaching, conference attendance, travel and research. Grants will also cover management costs incurred by hosting centres. As with the research centres, competition for the doctoral training centres will be fierce. Universities interested in hosting one should write to Dr Gavin Salisbury at the EPSRC (g.t.salisbury@epsrc.ac.uk), to make sure their application is suitable. Only applications given the thumbs up by Salisbury will be accepted. The deadline is September 28 and results are expected by Christmas. · Linda Nordling is news editor of Research Fortnight Where maths meets biology |
July 14, 2005
A numbers gameBy Heather Holmes The way to teach local kids math is to teach them how to read The state's new math TAKS test consists of 60 word problems, and it's not the numbers that are puzzling students. According to area teachers, students aren't getting lost in the multiplication process, but rather, in the text of the questions that make math applicable to real life. Johnny might be able to figure out the equation, but he struggles when he has to apply it to compounding annual interest or figuring how many rose bushes to plant in a 10-foot garden. Some experts say that Johnny's trouble may result from his misunderstanding of words such as "annual." According to the Intercultural Development Research Association, one in seven students in the United States learned English as a second language. Jose Rodriguez, education associate at IDRA, echoed many lecturers at last week's International Mathematics and Education Conference when he told teachers to speak more slowly and carefully explain terms that are easily confused with other words, such as median and medium. Math teachers often must also become reading teachers to help their students succeed. Rodriguez encouraged teachers to connect with their students, saying that kids bring knowledge into the classroom and teachers need to build on that. "I had to learn 'cholo' (gangsta) as my third language," joked Rodriguez, who speaks Spanish and English. In her address at the conference, Miriam Leiva, president of TODOS: Mathematics for ALL, told about 300 teachers and administrators that she has watched her students successfully complete a math equation but trip up when the same equation was written as a word problem. "They couldn't get through a sentence," she said. TODOS is a national organization designed to support and assist educators in teaching mathematics, particularly to Hispanic and Latino students. Leiva explained that the old ways of teaching math did not produce great math and science minds. Many of the great mathematicians and scientists are from other countries, she said citing New York Times columnist and author of The World is Flat, Thomas Friedman. He points out in his book that the proportion of foreign-born Ph.D.s in the American science and engineering labor force has risen to 38 percent while federal funding for mathematical science research has declined 37 percent in the last 35 years. According to a 2003 Trends in International Mathematics and Science study, 15-year-old students in the United States scored below the average international math score and were outperformed by 23 of 38 countries in math. Scores are even worse for Texas children, who rank below the national level in state standardized tests and college entrance exams. While 2003 SAT scores in math reached a 36-year high nationwide, Texans saw only a one-point increase and outscored only four states, according to College Board, which operates the SAT, the nation's leading college entrance exam. "If we have one weakness of students who enter UTSA it's in mathematics," said Guy Bailey, UTSA provost and vice president for academic affairs. "You can't be an accountant or biologist without it." Hispanic and African-American students generally score lower on standardized tests than white students. Experts often cite economic disadvantages and language barriers to explain the lower marks. In 2005, 88 percent of white sixth graders passed the math portion of the TAKS test; 70 percent of Hispanics and 64 percent of black students did the same. Only 35 percent of students labeled "limited English proficient" met the passing standard. Students can take the TAKS test three times in Spanish, but must pass it in English to graduate high school. "Mathematics really is a determining factor with our kids," said Jose Franco, a professor at the University of California, Berkeley, who serves on the board of TODOS. "If they're not taking accelerated math and science classes, it's difficult for them to get into our four-year universities." Hispanics are disproportionately underrepresented in Texas universities, accounting for 25 percent of higher-education students but 40 percent of those who are of college age, according to the 2000 census. The mathematics conference last week aimed to show teachers how to teach math to students for whom English is a second language. However, many teachers at the conference credited lack of funding, parental uninvolvement, and unmotivated kids for low test scores. The biggest complaint of teachers seemed to be a scarcity time with their students, saying that 45 minutes a day is too short of a class period. Funding shortfalls have also left a dearth of teachers and therefore prompted larger class sizes, meaning teachers have less individual time with each student. A recent study by the Center on Education Policy showed that two-thirds of the nation's poorest school districts will receive less money for the next school year. Spending under the Department of Education's Title I program, which benefits children in high poverty areas, is increasing by 3.2 percent, but the growing number of poor children outpaces the funding increase. Yet local teachers are accustomed to "making do." As they left the conference last week, teachers expressed the hope that they are returning to their classrooms better math teachers, and apparently better reading teachers, too. A numbers game |
July 10, 2005
Researchers explore whether parrot has concept of zero Special to World Science Researchers are exploring whether a parrot has developed a numerical concept that mathematicians failed to grasp for centuries: Oddly, it seems he may have achieved the feat during a temper tantrum, the scientists say. Although zero is an obvious notion to most of us, it wasn't to people long ago. Scholars say it came into widespread use in the West only in the 1600s; India had it about a millennium earlier. Yet Alex, a 28-year-old Grey parrot, recently began—unprompted—using the word "none" to describe an absence of quantity, according to researchers at Brandeis University in Waltham, Mass. Alex thus possesses a "zero-like concept," wrote the scientists. Years earlier, Alex had been taught another meaning of "none," as a lack of information, they added. But his feat was to extend the concept to a context involving numbers, during a test of his counting skills. The researchers, Irene Pepperberg and Jesse Gordon, described the findings in the May issue of The Journal of Comparative Psychology, a research journal. Alex's apparent insight into nothingness doesn't necessarily extend to other arithmetical talents, the researchers noted: the researchers found these to lag in some respects behind those of young human children. The scientists also said it will take further study to determine whether Alex—who has been the subject of intelligence and communication tests throughout his life—really understands zero. Zero and none "are not identical," Pepperberg wrote in a recent email. But since Alex never learned "zero," the researchers said, it's impressive that he started using a word he knew to denote something like it: an absence of a quantity. Also unclear, though, was whether by "none" he meant no colors, no objects or something else. "We just started yet another series of experiments to see if he can easily be trained to understand that 'none' can be used for true zero," Pepperberg said via email. It looks like he can, she added, but it's "far too early to make serious claims." Chimps and possibly squirrel monkeys show some understanding of zero, but only after training, the researchers said. So Alex's feat is the first time this has been documented in a bird, "and the first time it occurred spontaneously," Pepperberg said via email. But the achievement didn't come without a few bumps. The story began when researchers started testing Alex to see whether he understood small numbers, between one and six. Zero wasn't expected of him. The researchers would lay out an array of objects of different colors and sizes, and asked questions such as "what color four?"— meaning which color are the objects of which there are four. Alex performed well on this, with no training, for dozens of trials, the researchers recounted. But then he balked. Alex started ignoring questions, or giving wrong answers, seemingly deliberately. He seemed to enjoy the experimenters' frustrated reactions, they said. There was evidence, they added, that his stubbornness stemmed from boredom with the rewards he had been getting for right answers. The researchers found some more interesting toys to give as rewards. After two weeks of obstructionism, Alex grudgingly returned to the game, though he occasionally seemed to lapse back. One of these apparent lapses occurred one day when an experimenter asked Alex "what color three?" Laid out before Alex were sets of two, three and six objects, each set differently colored. Alex insisted on responding: "five." This made no sense given that the answer was supposed to be a color. After several tries the experimenter gave up and said: "OK, Alex, tell me: what color five?" "None," the bird replied. This was correct, in that there was no color that graced exactly five of the objects. The researchers went on to incorporate "none" into future trials, and Alex consistently used the word correctly, they said. "We cannot determine what cognitive process led to this behavior," the researchers wrote. "We suggest only that his action, occurring soon after a period of noncompliance, resulted from a lack of interest in the given task and was a possible attempt to make the procedure more challenging." In the future, the researchers said they want to test Alex for his ability to add and subtract small quantities, including possibly zero. As they investigate whether Alex really understands zero, they will also have to untangle the meanings of "none" and "zero." Merriam-Webster's online dictionary defines zero as follows: "the arithmetical symbol… denoting the absence of all magnitude or quantity," or "the number between the set of all negative numbers and the set of all positive numbers." The entry continues with several more definitions. By contrast, the dictionary defines "none" as not any, not one, nobody, not any such thing or person, no part, or nothing. Of course, these words may well mean different things to the authors of a dictionary, and to a parrot. A related question is the history of both words. "None" seems to be older than "zero." Zero was common in the West only from the 1600s on, though similar concepts appeared earlier in fits and starts, according to J.J. O'Connor of the University of St. Andrews in St. Andrews, Scotland. In pre-zero times, O'Connor wrote in an online essay, some mathematicians tied themselves in knots to solve problems that would have been much easier with a zero. But ancient peoples as a whole probably didn't think of it because they didn't need it: "If ancient peoples solved a problem about how many horses a farmer needed," he wrote, "then the problem was not going to have 0 or –23 as an answer." "None" is considerably older than "zero" in Western cultures. It's related to a neinn—an early medieval Viking word—and is similar to the still older Latin word noenum, meaning "not one," according to the Online Etymology Dictionary. Whatever the etymological roots of Alex's utterances, his performance has its limitations, the researchers said. Several years ago, they tried to teach him to recite a number line by presenting written numerals on their own, without reference to groups of items. Alex performed rather poorly. Schoolchildren, by contrast, can usually learn this fairly easily. Thus Alex's apparent insight into zero doesn't necessarily reflect across-the-board mathematical brilliance. Alex's abilities might parallel those of children "who have trouble learning language and counting skills," the researchers wrote. Researchers explore whether parrot has concept of zero |
July 10, 2005
What Are the Limits of Conventional Computing?Charles Seife At first glance, the ultimate limit of computation seems to be an engineering issue. How much energy can you put in a chip without melting it? How fast can you flip a bit in your silicon memory? How big can you make your computer and still fit it in a room? These questions don't seem terribly profound. In fact, computation is more abstract and fundamental than figuring out the best way to build a computer. This realization came in the mid-1930s, when Princeton mathematicians Alonzo Church and Alan Turing showed--roughly speaking--that any calculation involving bits and bytes can be done on an idealized computer known as a Turing machine. By showing that all classical computers are essentially alike, this discovery enabled scientists and mathematicians to ask fundamental questions about computation without getting bogged down in the minutiae of computer architecture. For example, theorists can now classify computational problems into broad categories. P problems are those, broadly speaking, that can be solved quickly, such as alphabetizing a list of names. NP problems are much tougher to solve but relatively easy to check once you've reached an answer. An example is the traveling salesman problem, finding the shortest possible route through a series of locations. All known algorithms for getting an answer take lots of computing power, and even relatively small versions might be out of reach of any classical computer. Mathematicians have shown that if you could come up with a quick and easy shortcut to solving any one of the hardest type of NP problems, you'd be able to crack them all. In effect, the NP problems would turn into P problems. But it's uncertain whether such a shortcut exists--whether P = NP. Scientists think not, but proving this is one of the great unanswered questions in mathematics. In the 1940s, Bell Labs scientist Claude Shannon showed that bits are not just for computers; they are the fundamental units of describing the information that flows from one object to another. There are physical laws that govern how fast a bit can move from place to place, how much information can be transferred back and forth over a given communications channel, and how much energy it takes to erase a bit from memory. All classical information-processing machines are subject to these laws--and because information seems to be rattling back and forth in our brains, do the laws of information mean that our thoughts are reducible to bits and bytes? Are we merely computers? It's an unsettling thought. But there is a realm beyond the classical computer: the quantum. The probabilistic nature of quantum theory allows atoms and other quantum objects to store information that's not restricted to only the binary 0 or 1 of information theory, but can also be 0 and 1 at the same time. Physicists around the world are building rudimentary quantum computers that exploit this and other quantum effects to do things that are provably impossible for ordinary computers, such as finding a target record in a database with too few queries. But scientists are still trying to figure out what quantum-mechanical properties make quantum computers so powerful and to engineer quantum computers big enough to do something useful. By learning the strange logic of the quantum world and using it to do computing, scientists are delving deep into the laws of the subatomic world. Perhaps something as seemingly mundane as the quest for computing power might lead to a newfound understanding of the quantum realm. What Are the Limits of Conventional Computing? |
July 10, 2005
Algebra AcademyBy KAT ISAACSON/Democrat Staff Writer Math minds get more creative It's called: Yodagon. But the newly created polygon was only made possible through the emergence of the Algebra Academy, a new three-week summer program run by the Woodland Joint Unified School District which allows students to gain hands-on mathematical experience. Classes are held from 8 a.m. through noon at Douglass Middle School. The academy is currently a pilot program, to which the school district invited incoming 7th- and 8th-graders who scored at proficient or advanced levels in math to participate during the summer. Friday concluded the end of the first three-week session, during which students created inflatable polygons, by duct-taping sheets of plastic measuring 10 feet by 10 feet to create large three-dimensional shapes and blowing air into them, making them spacious enough for multiple people to fit inside. "They knew they had a goal ... the kids felt wonderful about accomplishing this," said teacher Glen Lusebrink, who described standing inside the inflatable shapes as equivalent to standing inside "a big can of soup." But while most students worked diligently to create large pentagons, pyramids and cubes, Willie Jenkins, 12, and Cole "Slaw" Souza, 12, were busy creating "Yodagon," a three-dimensional plastic representation of Yoda, the Jedi Master from the Star Wars movies. Grinning, Jenkins and Souza explained "Yodagon" is a polygon, as a polygon is simply defined as "many sides." "Yodagon" includes a plastic head duct-taped to a plastic body, with arms and pointy ears duct-taped on as well. Other classmates joined in to help Jenkins and Souza draw eyes, a nose and a mouth onto "Yodagon," which was able to float when the plastic body, left open on the bottom, was placed over a fan. "When we voted yesterday on what polygons we wanted to make, the kids insisted Yodagon be one of the shapes," said Lusebrink, with a smile. The academy includes instruction on pre-algebra and geometry, using puzzles, games, art and problem-solving to help students understand concepts such as scaling in art, polygons and conversions. Many of the activities rely on conceptual learning, instructing students on how to apply various mathematical concepts to everyday activities, such as art. "In the classroom, there's usually a lot of emphasis on the procedural," explained WJUSD Math and Science Coordinator Kerry Planow, who created the program. "The academy helps students learn to use problem solving and a conceptual approach to balance that. It's about taking it to a higher level." Students also realize the importance of the new academy. "It's a really good experience for kids," said Alexa Andreassen, 13, who attends Lee Middle School. "I'm glad they started this because lots of my friends aren't really doing well in math, and this class has helped bring up their grades." And aside from helping prepare students to do well in geometry and algebra classes and raise their test scores, the academy also serves to help middle school students begin contemplating college. "Research has shown algebra is the gateway to higher education," Planow explained. "Students who do well at math have a better chance of going on to a four-year college." Planow added the program may continue in the fall, at which point the academy will remain open to any and all math students. The academy is also still in need of instructors to help provide classes. Planow explained the position is paid and applicants should be energetic and hold a bachelor's degree, as well as possess a background in math, for example, in business, engineering or science. Anyone interested in becoming an instructor for the academy can contact Kerry Planow at 662-0201 ext. 4350 or kplanow@wjusd.org. Algebra Academy |
July 07, 2005
Fundamental limitation to quantum computersQuantum computers that store information in so-called quantum bits (or qubits) will be confronted with a fundamental limitation. This is the claim made by Dutch theoretical physicists from the Foundation for Fundamental Research on Matter (FOM) and Leiden University in an article recently published in the journal Physical Review Letters. A quantum computer can only function if the information exists for long enough to be processed. The so-called coherence of the qubit ensures that the quantum information remains intact. The researchers have now discovered that the coherence spontaneously disappears over the course of time and with this the stored information as well. This could pose a considerable problem for the development of a quantum computer. A quantum computer makes use of the fact that a quantum mechanical system -an electron, an atom or even a larger system such as a superconducting quantum bit - can simultaneously exist in two states. Normally one of the two states disappears as soon as the system comes into contact with the outside world. The coherence then disappears as a result of the decoherence process and the information in a quantum bit is lost. A quantum bit typically consists of a large number of particles, with an unavoidably large number of possibilities to be influenced by the environment and thus be subjected to decoherence. Jasper van Wezel, Jeroen van den Brink (FOM) and Jan Zaanen, all attached to the Lorentz Institute of Leiden University have now investigated whether it is possible to maintain the coherence in an isolated qubit. Much to their surprise they discovered that the coherence tends to spontaneously disappear, even without external influences. The degredation process is linked to the occurrence of quantum mechanical spontaneous symmetry breaking. In classical physics an equivalent example of this process is spontaneous crystallisation in a solution. At a certain position a crystal is spontaneously formed, as a result of which the fluid structure is broken. According to the researchers' predictions, the coherence in some highly promising concepts for qubits will disappear after about a second. Moreover, the smaller the qubits the faster that process occurs. All of this would seem to pose a fundamental limitation on the development of qubits. Experimental research will now have to demonstrate whether this phenomenon actually occurs.
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July 07, 2005
Brains Not Like Computers, Study FindsBy Michael Schirber, LiveScience Staff Writer As you read this sentence, your brain is processing the letters into words. One popular theory associates this activity with a computer that inputs each bit of data – in this case letters – one after the other. But a new study finds that language comprehension is not broken up into discrete chunks. Indeed, the brain may work in a more continuous, analog fashion – in which the yes-no, on-off, one-zero precision of the digital computer is only gradually achieved. Michael Spivey, a psycholinguist from Cornell University, tracked mouse movements on a computer screen of 42 student volunteers. When the students heard a word, such as "candle," they were instructed to click on one of two images that corresponded to the word. Struggling with ambiguity When presented with images whose names did not sound alike – for instance, candle and jacket – the subjects moved the mouse in a straight line to the correct image. However, when the images had similar names – like candle and candy – the subjects took longer to click. "When there was ambiguity, the participants briefly didn't know which picture was correct and so for several dozen milliseconds, they were in multiple states at once," Spivey said. The evidence for "multiple states" is the fact that the mouse trajectories in the ambiguous cases were no longer straight, but curved. If the brain worked like a computer, one might expect the students to wait until they had processed the whole word before moving. Or perhaps they would make a preliminary guess towards one image, and then correct themselves and change direction. But a curved line seems to indicate that the students started moving the mouse after only processing part of the word. And yet they appear to hedge their bet by staying somewhere in between the two guesses. "The degree of curvature of the trajectory shows how much the other object is competing for their interpretation; the curve shows continuous competition," Spivey said. "[The students] sort of partially heard the word both ways, and their resolution of the ambiguity was gradual rather than discrete." Shades of gray Neurons in the brain may still work like electrical circuits or a computer network, but this activity may not correspond to the black and white clarity of a computer. Spivey and his collaborators are advocating a "biological" model of the brain that allows for shades of gray. "In thinking of cognition as working as a biological organism does," Spivey said, "you do not have to be in one state or another like a computer, but can have values in between – you can be partially in one state and another, and then eventually gravitate to a unique interpretation." This sounds a bit like Schroedinger's Cat – a paradox from quantum physics in which an unfortunate feline can be both dead and alive. So perhaps a quantum computer – whenever one of those finally gets built – will make a better analogy to the human brain.
This study was published online last week in the Proceedings of the National Academy of Sciences.
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July 07, 2005
Poker playing robots? Surely notBeware! There's a new player in town - and he's got a mean poker face. Terry Kirby meets the latest card robots as they prepare to clean up in Vegas They don't wear eyeshades or smoke cigars, and their capacity to bluff is somewhat limited. But a new breed of robotic poker player is sending a shiver of fear through the world of the green baize table. It is a poker game being contested in cyberspace, with the ultimate prize being a share of the mega millions being gambled on online poker sites. After all, when you are sitting around a poker table, you've a pretty good chance of telling if your opponent is a robot; competing online is another matter entirely. Welcome to the strange world of the poker "bot" - bot being short for robot. But what we are talking about here are not supercomputers like Deep Blue, the IBM creation that trounced chess genius Garry Kasparov in 1997, but pirate computer programs, created in secret by players determined to challenge the new hegemony of the online gaming houses, where bots are outlawed. "The online people are very scared about poker bots. The idea that a machine can be used to defeat players online is terrible PR for them,'' says Crispin Nieboer, head of the Poker Channel, a recent addition to the Sky portfolio of niche television channels. But now, the online industry, scared that people will not play online because they have no chance of beating the bots, is fighting back. The existence of a television station devoted entirely to poker is a testament to the current popularity of the game. Poker has moved out of the darkened rooms of backstreet gambling dens and the bright lights of casinos to become both a post-dinner party entertainment for members of the middle classes and something close to an obsession for those addicted to solitary online playing, which has boomed since it was first introduced to the internet in the late 1990s. Only last week, the London-based company Party Gaming, which runs the online site Party Poker, floated on the stock market with a value of £4.6bn - making it bigger than British Airways or Boots, and giving some idea of the vast amount of cash being traded; its profits come by simply taking a commission for hosting games. Poker bots have been in existence for more than a decade, and were originally conceived as computer software to teach people to play and to compete against on their computer at home. As online gaming exploded in popularity, a small number of competitors who were better at writing computer programs than playing poker began to create their own bots to compete on their behalf. When playing online, they sign in manually and then launch their bots to compete against other players. No one knows how many poker bots are out there playing in cyberspace, but the numbers are believed to be substantial. And they never lose concentration or suffer from fatigue. But, says Brian "Catfish" Edwards, an IT administrator and bot creator from Florida, they are not infallible. "Bots are not that good yet, and no one has come up with the perfect program,'' he says. "Poker is not like chess. Poker is about adapting and being flexible, about bluffing and about who is sitting around the table. Humans can keep a database of experience and use that to compete and figure out the strategies of their opponents. Computers are much better at carrying out numerous but routine tasks.'' Edwards claims that he does not use his bot online, but has developed it simply to help him play better. "Most of those who play with bots online compete on low-limit games. A decent player can still defeat a bot by adapting and changing their game - which bots cannot do.'' Another bot designer, Roger Gabriel, a software engineer from California, believes bots will eventually take over. "If computers can play chess, they can play poker," he says. Both men are among six bot operators who have been invited to compete in the first World Series of Poker Robots (WSOPR), which takes place in Las Vegas, starting on 12 July, an event that will be entirely machine vs machine. All software designers or artificial intelligence experts, they have been tempted away from their computer screens by the lure of a $100,000 (£54,0000) first prize and the chance for the winner to challenge, Deep Blue style, the winner of the World Poker Series, which is taking place at the same time. However, all is not quite what it seems. The WSOPR is actually sponsored by Golden Palace, an online casino, whose chief executive, Steven Baker, is frank about the reason for his involvement: "We need to become more knowledgeable about the world of poker robots. We see this as an opportunity to learn more about poker robots and how they are developing. It is in the best interests of online poker rooms to find out.'' Baker's company is busy developing ''counter-bot'' software programs. But he adds: "At the moment there is no definite means of determining whether a player is a bot or not.'' Although many believe that it will be some years before a bot is created that can beat all-comers, it is clear that the online poker companies are feeling jumpy. At Party Gaming, a spokesman says that the company has more than 100 people working on fraud detection, but declined to discuss what it is doing about bots. He adds: "We have an anti-bots policy and we have had a fair degree of success in weeding out bots. But I'm not going to get into details of how many or how we detect them.'' For an expert's view, The Independent turned to Liam Flood, a player for more than 20 years and a former European champion who recently won $250,000 in a televised tournament. He says: "Playing online is a completely different experience to playing around a table: you can't see the dealer, see how people hold their cards or sense moods. Whether you are playing a bot or a human, you have to play completely tight - take no risks, play straight and assume that your opponent always has the best hand, which is not always the case in normal poker. That's the way to beat 'em.'' Flood believes online gaming will survive the challenge of the bots, but adds: "I think they are going to do very well; they will eventually begin to beat the system. You see, a poker player plays with life's experiences behind them and no matter how tightly you play, you will have to take chances at some point. Machines don't do that.'' Poker playing robots? Surely not |
July 07, 2005
Before computers, there were these humans...By Gregory M. Lamb Looked on as drudges, human computers spat out calculations for decades For two centuries they were the blue collar workers of science, mental laborers who could grind out logarithms as efficiently as other factory workers turned out pins. A large percentage of them were women. Though male scientists deemed creative mathematics beyond feminine abilities, they saw women as perfect for this kind of numerical needlework. One even measured computing time in "girl hours": A complex calculation might even require "kilo-girl-hours." In "When Computers Were Human," David Alan Grier tells the tale of these human drudges of mathematical calculation. They came in with the 18th-century Industrial Revolution and quickly disappeared in the mid-20th as electronic computers proved to be faster and, eventually, more reliable. Most of the human computers left no record of their personal lives. They didn't think they were doing anything remarkable as they calculated using ink and paper and, later on, early mechanical computing machines like the Felt & Tarrant Comptometer or the Burroughs Arithometer. One of the earliest human computers was Nicole-Reine Lepaute, the wife of France's royal clockmaker. In the 1750s, teamed with two male colleagues, she did some fancy figuring to predict the return of Halley's Comet in 1758 after a 76-year absence. The team's estimate was off by just over a month. A few computers were innovators. In the early 20th century, Mary Clem, a woman with only a high school education working at the Iowa State Statistical Lab, developed her own system of "zero checks" for detecting errors in calculations. Foreshadowing today's networked computers, human computers learned to divide up complex tasks. They cross-checked and doublechecked to winnow out errors. A supervising computer, called the comparator, checked the work and searched for discrepancies. By 1940, the Mathematical Tables Project, a giant effort funded by the Works Progress Administration, still employed more than 300 human computers, half of them using paper and pencil. But in 1952, IBM began selling its Model 701 electronic computer. By the 1960s, nearly all the number-crunching was being done by machines. Grier has a knack for making elaborate scientific concepts understandable. His opening device, in which he tries to discover why his grandmother told him proudly that she took calculus in college in 1921, lends a human note. Yet even a thorough historian like Grier somehow missed the amazing story of Henrietta Swan Leavitt. Fortunately, George Johnson has filled in the gap in his compelling "Miss Leavitt's Stars." The daughter of a Congregational minister and a graduate of Radcliffe College, Leavitt took a job as a computer at the Harvard University Observatory in the 1880s. Her task was to compare glass photographic plates of the Magellanic Clouds to detect tiny differences in the brightness of the stars. "We know them now as neighboring galaxies, companions to our Milky Way," Johnson writes. "Back then no one was quite sure what they were. Hunched over the plates in an observatory workroom, Miss Leavitt found the pattern that eventually led to the answer. She discovered a way to measure beyond the galaxy and begin to map the universe." A star's brightness might be the function of its magnitude or its distance from earth: Stars that had similar apparent magnitudes could be vastly different distances away. But Leavitt had also noticed that "variable" stars gave off pulses of light and that a star's true brightness could be measured by the speed of its pulses. Brighter stars blinked more slowly. Compare that with the star's apparent brightness, and you could estimate how far away it was. Male astronomers were impressed. "What a variable star 'fiend' Miss Leavitt is - One can't keep up with the roll of the new discoveries," a Princeton astronomer wrote in a letter to her boss. Though she was commended for her good work, Miss Leavitt earned no promotion, no privilege to pursue her own research. She quietly continued computing, remaining single and living the life of a proper Bostonian. Her feelings about her important discovery remain a mystery, Johnson says. She left no journals or letters. Other women computers who did leave written accounts sometimes expressed frustration that they weren't allowed to explore the deeper implications of what they found. Not all human computers were women, of course. Some were men, mostly young and in search of a steady job. The work was temporary; they were mathematical clerks, not scientists. But a few, such as Miss Leavitt, looked up to the stars and made human computing into something much more. • Gregory M. Lamb is on the Monitor staff. Before computers, there were these humans... |
July 07, 2005
Gates vision for the future: tech miraclesBy Raju Chellam , Business Times IN the future, the blind will see, the deaf will hear, and everyone will be free. That will be the gift of the chip, and your brain won't be the same. That's the vision that Microsoft's chairman and chief software architect Bill Gates has. 'Cochlear implants (in the ear) are already being used to treat hearing problems, and medical advances are being made on implants that can help fix eyesight problems,' he told a 7,000-strong audience at a public seminar at Suntec City on Friday. 'These types of technologies will be improved and expanded, especially in areas where they would be correcting deficiencies. We will have those capabilities.' Mr Gates cited author Ray Kurzweil, whom he called 'the best at predicting the future of artificial intelligence,' as believing that links - between humans and computers - would become mainstream in the far future. Dr Kurzweil is an institution in himself. He has received 12 honorary doctorates and honours from three US presidents. His book, The Age of Intelligent Machines, was named Best Computer Science Book of 1990. His bestseller, The Age of Spiritual Machines: When Computers Exceed Human Intelligence, has been published in nine languages. He has been called 'the restless genius' by The Wall Street Journal, 'the ultimate thinking machine' by Forbes, and compared to Thomas Edison by Time. Dr Kurzweil was principal developer of the first omni-font optical character recognition (OCR), the first print-to-speech reading machine for the blind, the first CCD flat-bed scanner, the first text-to-speech synthesizer, and the first commercially marketed, large-vocabulary speech recognition. His website, at KurzweilAI.net, is a leading resource on artificial intelligence. Mr Gates said that advances in technology enable computers to learn to interact with human beings and learn how the human brain works. Microsoft invests over US$6 billion a year on R&D to be able to make the twain - between computer and human - meet, he said. 'The next 10 years would be far more interesting than the past 30 years because technology gains will change at a faster pace - the way people work and live.' Microsoft employs 55,000 people across 85 countries, including about 600 in Singapore. The final question: how soon would it be before computer chips are implanted in the human brain? 'One of the guys that works at Microsoft always says to me 'I'm ready, plug me in,'' Mr Gates said at the seminar. 'I however don't feel quite the same way. I'm happy to have the computer over there and I'm over here.' Gates vision for the future: tech miracles |
July 03, 2005
Lost notes on alchemy by Isaac Newton foundLONDON (Reuters) - A collection of notes by the 17th century English mathematician and physicist Sir Isaac Newton, that scientists thought had been lost forever, have been found. The notes on alchemy were originally discovered after Newton's death in 1727 but were lost after they were sold at auction in July 1936 for 15 pounds ($27). They were found while researchers were cataloguing manuscripts at the Royal Society, Britain's academy of leading scientists. "This is a hugely exciting find for Newton scholars and for historians of science in general," Dr John Young, of London's Imperial College Newton Project, said in a statement on Friday. Newton's celebrated work "Philosophiae Naturalis Principia Mathematica" (or Mathematical Principles of Natural Philosophy) is considered one of the most important works in the history of modern science. In it he formulates the three laws of motion and that of gravity. Some scientists in Newton's time believed alchemy held the secret of how to transform base metals into silver or gold. Newton's notes were written in English in his own handwriting. "It provides vital evidence about the alchemical authors Newton was reading, and the alchemical theories he was investigating in the last decades of the 17th century," Young added. The notes will be on display at the Royal Society's annual Summer Science Exhibition in London which begins on July 4. Lost notes on alchemy by Isaac Newton found |
July 03, 2005
Navigating MathematicsA new course at the high school is asking students to get lost -- and find their way again. Coastal Navigation, a mathematics course that sets sail this fall, shows students how geometry, trigonometry and algebra can aid them on a high seas adventure, or at the very least, a short kayaking trip in Long Island Sound. "It's something different that hopefully the students will enjoy," said Mike Ellis, who teaches descriptive geometry, plane geometry and is swapping out his probability and statistics class for Coastal Navigation. Ellis masterminded the course after taking part in two classes offered at the Mystic Seaport: Introduction to Coastal Navigation and Piloting and Dead-Reckoning, both six-week courses. He took the courses to keep up with his brother-in-law, who owns a local marina and captains a tugboat. "It was just all math ..." he said. "I thought, 'That would fit the type of student who is a hands-on kind of learner. Can we do more than what we normally do with them if it's visual for them?'" Ellis spent a lot of time on the water but didn't know the ins and outs of charting a course, reading maps and using a compass -- just like many of his students. "They have the charts in their boats, but they never knew how to use them," he said. The school system just happened to be overhauling its math curriculum this year, and Ellis, a fifth-year teacher at Waterford, went out on a limb and asked Department Head Sharon Carter what she thought about adjusting the Mystic Seaport course for high school students. She loved it. "Certainly the new shining star in our curriculum is navigation," Carter said. As part of the course, students will spend a day at the Mystic Seaport Planetarium where planetarium lecturer and instructor R.M. "Max" Maxwell, who taught both courses at the seaport, will show students how they can use the stars to find their location on a map. "Once you know where you are, then you can figure out how to get where you're going," Maxwell said. Also a part of the semester-long course, offered to standard-level juniors and seniors, is an actual sailing adventure with Project Oceanology. Near the end of the semester, Ellis will take his students out on a real boat, to test their knowledge of such things as true versus magnetic north, factoring the tide into a course, avoiding hazards and using a nautical chart. "We'll tell the captain of the boat where to steer and how many knots to travel at," Ellis said. According to Ellis, 45 students have already signed up for the class, which the Board of Education recently approved along with two other new math courses: Java and Math Concepts. The Mystic Seaport offers a number of nautical courses, including a 10-week course in celestial navigation and an accredited college program run in conjunction with Williams College. Those interested should contact Suzanne Reardon at suzanne.reardon@mysticseaport.org or call (860) 572-5323. Navigating Mathematics |
July 03, 2005
The calculus of artBy Aviva Lori The first moment of the encounter with Miri Segal's video installation was a bit frightening. Having to enter a dark hall alone, sit on a black armchair, put on earphones and, for 10 minutes, give yourself up to what the artist has conjured generates a feeling of unease. Outside, people waited for their turn to enter the dark space. With a sure hand, Segal activated the instruments and left the hall. The armchair started to revolve. Saying "Stop the armchair, I want to get off" was pointless: There was no one there to talk to. After a few revolutions, at a comfortable pace which is adjusted to the eye of the beholder, the feeling of uneasiness gave way to curiosity and one could be receptive to what was happening on the screen. On the back of the chair, adjacent to the viewer's line of vision, a projector screened Segal's video, which moved across the walls as the chair followed the images. "Place de la bonne heure" is the title of the solo show, which will open next week at the Dvir Gallery in Tel Aviv. Actually, the show is not really opening but reopening; it was already held in April and May, and is being mounted again due to public demand and at the request of several curators from abroad, who expressed a desire to come to Israel especially to view it. The installation is a kind of road movie, accompanied by an original soundtrack by Uri Frost, formerly a member of the rock band Carmela Gross Wagner and, at present, Segal's partner. The journey begins in a square called Place de la bonne heure in Tel Aviv and moves from there, in a rough cut, to the Qalandiyah checkpoint and back again in an endless cycle. Where in Tel Aviv is there a square with such a promising name? Between the Dan Panorama Hotel and Textile House by the sea, the city fathers have created a round public square with handsome vegetation, but the city's residents appear to be unaware of its existence. "A landscape architect told me about the place, and it amazed me," Segal says. "Because to get to the offbeat site you have to climb stairs that are suspended in the air from four directions, and only then are these abandoned spaces exposed. There is a view of the sea from the square, but most of the time it is empty. Only once in a while do you find homeless people there. This square is a metaphor for the aspect of Israeliness that has a distorted conception of the environment, like building such a fertile garden in the air." And the Qalandiyah checkpoint? Segal: "The Qalandiyah checkpoint, which lies on an ancient Roman road, is the opposite of the Place de la bonne heure. It is throbbing with life. Until a year ago there was a vibrantly alive market there, which the Israeli forces evacuated. In the scene I am photographing everything is stuck, the cars are backed up, bumper to bumper, in an endless snarl-up, standing and not moving, only honking hysterically. It looks like the gate to hell. "The connection between the two images draws a geographic comparison between the two squares. Both are places of `togetherness,' which is to a degree fictitious. One is always empty, the other is subject to constant pressure. That, in my view, provides a very particular view of our existence here and of its reflection in the eye of the beholder." Seven times eight Five works by Segal are currently on display in a group exhibition at the Tel Aviv Museum of Art, entitled "Dreaming Art / Dreaming Reality," which is being held to mark the 10th anniversary of the Nathan Gottesdiener Israeli Art Prize, awarded to Segal in 2002. Segal, 39, is a new face in Israeli art. Six years ago, as the holder of a doctorate in mathematics from the Hebrew University of Jerusalem, her career was focused on academia. In the short time since she decided to take up a new profession, she has succeeded in gaining an honorable place in the field of art, both here and overseas. Segal has achieved this without having attended any of the prestigious art schools - in fact, she never studied art systematically - and without rubbing elbows with the teachers who set the tone in the art world and shape public opinion. Miri Segal was born in Haifa to a middle-class family who were part of the Revisionist movement in Zionism (the precursor of today's Likud). "We were a normal family," she says. "Dad is an engineer, Mom is an accountant, and neither of them was involved with art." Her father immigrated to Israel from Romania in the 1950s; her mother is native-born, from a Haredi (ultra-Orthodox) family which goes back seven generations in Safed. "My maternal grandfather was a textile merchant and a cantor. He was a Haredi of the old type and used to ride a mule to Syria and Lebanon to buy fabrics. In my grandparents' house the languages spoken were Hebrew, Yiddish and Arabic. My mother abandoned the faith." Both her parents are professional bridge players - her mother is a member of the Israeli national team - and very right-wing in their politics. "My mother had a brother who was killed in an operation of the Irgun [pre-1948 underground organization]; my father's parents had vineyards and a lot of property in Romania. After the Soviet communist occupation all my family's assets were expropriated and they lived very meagerly. I think those events affected each of them separately." The daughter absorbed her parents' right-wing views. "In my early twenties I underwent an ideological transformation," she recalls. "The more my interest in myself developed, and the more my interest in my surroundings grew, the more my right-wing attitude from home was replaced by a left-wing approach." Segal was not a very good student in high school, beset by problems of concentration and perhaps minor dyslexia, she says. To her father's disappointment, she failed her matriculation exam in mathematics (which she took for three points - the lowest level). "My father was a frustrated mathematician. His dream was to study mathematics, but he studied engineering in Romania. When I was a girl he used to give me riddles in mathematics." Not wanting to reprise her father's career as a frustrated mathematician, Segal decided to fight her dyslexia. She sat for the mathematics exam again, this time at the five-point (highest) level - and passed. In the army she was a flight instructor on a simulator. After completing her service she enrolled at the Hebrew University of Jerusalem, taking psychology and mathematics. "Until I started university it was hard for me to concentrate in mathematics. Maybe it had something to do with the dyslexia, which is felt less over the years, though when I am tired I can still make mistakes in Hebrew, confuse right and left, and not know how much seven times six is - the hardest thing to remember in the multiplication table." She was admitted to the department of mathematics, even though her psychometric score was not brilliant. "At that time almost everyone who wanted was accepted to mathematics, because so few people registered for it," Segal recalls. She eventually completed her doctorate and felt very sure about her choice and about the continuation of her career. "Mathematics interested me very much," she explains. "My doctoral thesis was on a subject that was close to a research group at Caltech, and the university sent me there a few times. My supervisor was Prof. Menachem Magidor, who is now president of the Hebrew University." Invasion of privacy Segal started to paint as a hobby during her student days. She studied drawing and painting in various departments. While doing her M.A. she applied to and was accepted as a student by the Art Teachers College, which was then in Ramat Hasharon, but she lasted only a month there. "It gave the impression of being a place where there was a tremendous invasion of privacy, because in artwork one exposes oneself," Segal explains. "At that stage I wasn't yet ready for that." She immersed herself into the tranquil life of the junior faculty at the university, as a student and a tutorial assistant. "Starting with the M.A., the university paid me a small salary. I had a steady job and a lot of spare time, so I could allow myself to paint. I had a studio in my rented apartment and at the same time I was a volunteer in the unit for social involvement at the university and gave courses in mathematics to gifted children and to children from Yeroham [a southern development town] who needed help." Toward the end of her doctoral studies she went to San Francisco with the man who was then her partner, a professor of mathematics. He went to spend a year at an institute of mathematics; she completed her thesis and enrolled in the San Francisco Art Institute. "It is a private place that charges a very high tuition fee, because in the American art world it's terribly important to have a diploma," she says. "I didn't go there to get a diploma, because I only came for a year. I registered for only two courses, but the school let me audit courses and started to take an interest in my work." During this period, Segal started to suffer from mild "schizophrenia": On the one hand, she dug deep and invested energy and much love in her mathematics thesis, but at the same time, art grabbed her hard and shook her up. "Before I went to San Francisco I had mainly sculpted and painted. Over there we rented a house in the Berkeley area, which belonged to Japanese people who had gone on sabbatical for a year, a wonderful house that was very well kept but a bit shaky. I did one sculpture in their kitchen but I was afraid I was wrecking the kitchen. So I painted a little, but I didn't have room to paint, either." Her dilemma led her to a "cleaner medium" - she started to make video works. "I did most of the work from the car, where I kept all my equipment, and I started to work in video in the school, too. The two happiest years of my life were the first year of studying mathematics - the love of my life - and the year I lived in San Francisco." Fictitious exhibition Returning to Israel in 1998, she submitted her doctoral thesis, but instead of the usual postdoctoral track, Segal decided to devote herself to her second love, art. Before leaving San Francisco she organized a "fictitious exhibition" at the city's Museum of Modern Art. What is a fictitious exhibition? "I came to a decision to make the move to art, but my resume was hopeless. One big blank. It was important for me to enrich it. I decided that I was going to have an exhibition at the Museum of Modern Art, which was notorious for its lack of female artists. I sent invitations to all the VIPs in the city announcing a solo show by Miri Segal to be held at the museum on the floor of the permanent exhibitions. On the back of the invitation was a photograph of the hall where my exhibition was `supposed' to take place. The photo shows paintings by Andy Warhol and Robert Rauschenberg, which are on permanent display there, and in the space between them is supposedly another picture - me in a gilded dress and on the back of the dress a circle is sewn, which is not completely decipherable on the invitation. "I hired a private detective to document the event, because photography is not allowed inside. So, for a few Saturdays I stood in the space between the two pictures, with my face to the wall and my back to the audience, and froze for a few hours every time. On the back of my dress was an oval frame, inside which I was seen standing in the hall, in the space between the two pictures, with my face to the wall and my back to the audience. "The first time a guided tour came by, people asked the guide who I was, and she didn't know what to say. After a while another tour came by with the same guide, and this time she said, `This is what contemporary artists do. They look at paintings and paint themselves looking at paintings.' All kinds of art critics wrote about me in all kinds of papers, even in Germany." Didn't you have qualms about forsaking mathematics? "Serious qualms. It was hard decision, because I really loved mathematics and the decision also had repercussions with respect to my way of life and my income level. But I thought that if I did not try art at that stage, I would never be able to take it up professionally afterward." There was also something else that made her change direction. She was pretty fed up with being referred to as the "meideleh" at mathematics conferences. "It was a nightmare," she recalls. "I attended mathematics conferences from the age of 25. Sometimes there was another woman there, but usually not, and there were 40 middle-aged men in whom sexism wasn't all that rare. The world of art, fortunately, is far more receptive to women, and that was a change that made me utter a big sigh of relief." "Miri was a riveting mathematician," says her former supervisor, Prof. Magidor. "I was very frustrated and disappointed when she decided to leave, one reason being that I wanted to promote an academic career for women. I am very sorry that she left mathematics, at which she could have succeeded wonderfully, but on the other hand the art world benefited." `Dvir took me on' Segal moved to Tel Aviv, where she now lives in a rented apartment in Kikar Hamoshavot, near the old central bus station, an area which until not long ago was colorful and very much alive, populated mainly by foreign workers. Segal captured the neighborhood in one of her works, which she calls "Shfelat stav," (a play on words meaning something like "low autumn"), as an ironic counterpoint to "Ramat Aviv," the upscale city neighborhood whose name means, more or less, "high spring." She held her first exhibition in 1999, at the Dvir Gallery. "After I got back to Israel," she relates, "I approached a few gallery owners and asked them to come to my studio, because it was impossible to explain or document my works or bring them to the galleries - some of them were complex, unfinished installations. Of all the people I contacted, only Dvir [Intrator] came, saw the works, and took me on." "Dvir took me on" is a key phrase in the Israeli art scene. The Dvir Gallery has connections to museum directors, collectors, gallery owners and other people and institutions able to advance those artists the gallery believes in and wants to promote. After her 1999 show, Segal was invited to take part in group exhibitions at the Israel Museum in Jerusalem, the Tel Aviv Museum of Art and several international exhibitions, including a solo show at one of the most coveted art spaces in New York: P.S. 1 Center for Contemporary Art, in Queens, a museum owned by New York's Museum of Modern Art. Afterward she had exhibitions in Lucerne, Munich, and in 2004 at the Lisson Gallery in London, with which Segal has been connected ever since. In 2002, the year in which she received the Gottesdiener Prize, she had a solo exhibition at the Tel Aviv Museum of Art and spent five months working at the art center of the Ecole des Beaux Arts in Nice, France. In two weeks she will return to France, this time to Paris, where she has received a studio and an apartment as part of a scholarship for artists awarded by the government of France. Four years ago Segal started to teach at the Bezalel Academy of Art and Design in Jerusalem, so far on a part-time basis. To help make ends meet she worked as a consultant in mathematics to high-tech firms. However, in the past two years she has been able to make a living from art alone and is trying to integrate the sciences into her work. "The chair in my work at Dvir is a very basic and not very sophisticated example of the integration of technological means into art." In another work of hers, which was shown in a huge hall in the Helena Rubinstein Pavilion of the Tel Aviv Museum of Art in 2000, a small image of the sea was screened on a wall. "All in all, it was very boring," the artist acknowledges. Most of the time nothing happened in the room, and the viewers left after a few seconds. Once in a while, though, without advance preparation, the image would suddenly open up and a huge wave flooded the room reaching almost to the feet of the astonished visitors. The soundtrack was of a laughing woman and the whole room seemed to fill up, awash in water and light. "That was a work that dealt with the potential for contact between the artist and the viewer," Segal notes. "Instead of the viewer opening to the work of art, it opens to the viewer. The whole thing lasted for three seconds, and immediately receded." Where do you see yourself in another 10 years? "Art is a way of existence that has multiple difficulties, but I intend to continue with it. Video is not a picture you hang on the wall, so it is harder to see it and to sell. Works of mine have actually sold well. The collector Doran Sabag bought a video work from me, the Israel Museum bought one, so did other private collectors, whose names I cannot reveal, and in Lucerne all the works I exhibited were sold. In Paris an art space called Maison Rose recently opened and they also bought one of my video works, which will be part of the permanent architecture of the place. "I have not succeeded in getting rich from this. Since I got involved in art, my standard of living has only declined. In the months I spend working on a production such as the exhibition at Dvir, not only do I not earn money, I also underwrite it with my own funds, which can reach NIS 20,000 or NIS 30,000. The game in this market is uncertainty: Your work might sell immediately, but it could take months before it is sold." Are you a bit sorry that you left a more promising career? "To engage in art is a great privilege, which demands a sacrifice of economic security. On the other hand, my art career has been relatively very brief, but I have already had successes, exhibitions in very prestigious places. I feel no regret; on the contrary, I am very happy to be engaged in art - though I sometimes miss mathematics." n The calculus of art |
July 03, 2005
Man said to recite pi to 83,431 digitsTOKYO --A Japanese psychiatric counselor has recited pi to 83,431 decimal places from memory, breaking his own personal best of 54,000 digits and setting an unofficial world record, a media report said Saturday. Akira Haraguchi, 59, had begun his attempt to recall the value of pi -- a mathematical value that has an infinite number of decimal places -- at a public hall in Chiba city, east of Tokyo, on Friday morning and appeared to give up by noon after only reaching 16,000 decimal places, the Tokyo Shimbun said on its Web site. But a determined Haraguchi started anew and had broken his old record on Friday evening, about 11 hours after first sitting down to his task, the paper said. He reached the 80,000-digit mark after midnight early Saturday, according to the paper, which had a photo showing Haraguchi with his eyes closed, his face contorted in concentration. If verified and recognized by the Guinness Book of Records, Haraguchi's feat would beat his own previous best -- currently under review -- of 54,000 digits. The official current record-holder, also Japanese, calculated pi from memory to 42,195 decimal places in 1995. Pi, usually given as an abbreviated 3.14, is the ratio of the circumference to the diameter of a circle. The number has fascinated and confounded mathematicians for centuries. Aided by a supercomputer, a University of Tokyo mathematician set the world record for figuring out pi to 1.24 trillion decimal places in 2002. Researchers say that calculating pi to more than about 1,000 decimal places has not much purpose in math or engineering, though mathematicians have done so to test the accuracy and limits of supercomputers. Man said to recite pi to 83,431 digits |