August 31, 2004
Mad about MathsPreeti Mudliar SEVENTEEN-year-old Vaidehi Thatte is at a loss to make non-mathematical brains comprehend the level of mathematics that she is comfortable solving. So you venture a guess, "IIT"? "No", Thatte timidly replies, "Much higher than that, what I adore solving is Abstract Algebra." Back from the first ever Math Olympiad organised by Infosys' Ramanujan Maths Club in Chennai, Thatte who stood second in the 15-18 age group is as modest as they come. Says the Std XII student of SP College, "My achievements have only been possible because of my parents and Professors M Prakash, Dr V Solapurkar and K Barve, of Bhaskaracharya Pratishthan. It is their guidance and encouragement that has made it possible for me to scale such heights." About the Olympiad, Thatte says, "I was felicitated by Narayan Murthy, but what I enjoyed the most was the talk by the Dean of Florida University's Mathematics department." Thatte started out very young as a mathematician. Passing the Ganit Pradnya Pravinya in Std V and subsequently in Std VII, fuelled her desire to excel in the field of mathematics. Says the maths loving girl, who scored a whopping 91 per cent in her SSC exams, "I would love to pursue a research career in Mathematics and I intend studying at Princeton University for the same." Her immediate aim however, is to represent India at the International Maths Olympiad for which she diligently attends all the National Maths Camps. Thatte's interests though are not limited to mathematics alone. She says, "I love music. I can play the synthesiser and am training in Indian classical music. Drawing is another thing that I really enjoy." Having received Rs 5,000 as prize money, does Vaidehi intend spending it on clothes and movies? She very sweetly replies, "No, I want to buy some more books on maths." Mad about Maths |
August 31, 2004
Young man invents mathematics gameA student said on Monday that he had invented a new Mathematical Game - Problematical Probability Game (PPG) - and appealed to the Government and stakeholders to support him in ensuring that mathematics was given a new phase in the form of a game to ensure easy learning. Mr Samuel Innusah, a former student of the Prestea Senior Secondary Technical School in the Western Region, told the Ghana News Agency that the Ministry of Education Youth and Sports and the Institute of Statistical, Social and Economic Research (ISSER), University of Ghana, had viewed his project. He said the Ministry of Environment and Science (MES) had also acknowledged the fact that the Game was a quality piece that involved flexible scientific methods of calculations. Mr Innusah noted that mathematics, which had become a "no go" area for many, could be studied through the simple but scientific Game in a more relaxed atmosphere without the slightest knowledge of the player that he or she was learning something new. The Game, which could be played by a maximum of four persons at a time, enabled students to explain the term probability in a given situation, distinguish between even and odd numbers as well as the term "Even". He said students who played the game would also develop the idea that the sum of two odd numbers was always an even number. Mr Innusah, however, said his invention would not be useful to students if it were not supported to reach the target audience. "My problem now is how to introduce this invention to other people. Though I have the skill and knowledge to invent other things, I have no funds to ensure that others benefit from it." He stated that though the GES was ready to assist him further his education to the tertiary level by awarding him a scholarship, they had been slow in their support to ensure that his project was utilised by students to eradicate fear of mathematics. Mr Innusah urged students who had other talents to come out and exhibit them since they could be useful for future use. Young man invents mathematics game |
August 30, 2004
Fuzzy LogicQuickstudy by Russell Kay DEFINITION: Fuzzy logic is an extension of classic Boolean logic designed to work with imprecise or vague data. Where classical reasoning requires yes and no values, fuzzy logic can handle concepts such as "maybe," "nearly" and "very." AUGUST 30, 2004 (COMPUTERWORLD) - The digital computing world is built on a structure of Boolean logic applied to binary values -- one or zero, yes or no, in or out. But this powerful structure is a gross oversimplification of the real world, where many shades of gray exist between black and white. In everyday life, we use quasimetric notions that are clearly related to numerical concepts or values but lack precision or demarcation. What time is it? If I'm a server time-stamping thousands of files, digital certificates or transactions, I need very fine distinctions. But if I'm asking a co-worker what time it is, do I really care that it's 11:49:54 a.m. Eastern Daylight Time? Or do I just want to know if it's time for lunch yet? Or take the weather. If it's 90 degrees Fahrenheit on a July day, that's hot for Massachusetts but mild for Arizona. A total of several inches of rain that month might constitute a drought in Massachusetts but a welcome relief from one in Arizona. Get Fuzzy The real world simply doesn't map well to binary distinctions, and numerical precision is often unhelpful in making qualitative statements. Fuzzy logic gives us a way to deal with such situations. In fuzzy systems, values are indicated by a number (called a truth value) in the range from 0 to 1, where 0.0 represents absolute falseness and 1.0 represents absolute truth. While this range evokes the idea of probability, fuzzy logic and fuzzy sets operate quite differently from probability. If I tell you that my height is 5 ft. 6 in. (or 168 cm), you may have to think a bit before deciding whether you consider me short or not short (i.e., tall). Moreover, you might reckon me short for a man but tall for a woman. So let's make the statement "Russell is short," and give that a truth value of 0.70. If 0.70 represented a probability value, we would read it as "There is a 70% chance that Russell is short," meaning that we still believe that Russell is either short or not short, and we have a 70% chance of knowing which group he belongs to. But fuzzy terminology really translates to "Russell's degree of membership in the set of short people is 0.70," by which we mean that if we take all the (fuzzy set of) short people and line them up, Russell is positioned 70% of the way to the shortest. In conversation, we would say Russell is "kind of" short and recognize that there is no definite demarcation between short and tall. We can state this mathematically as mSHORT(Russell) = 0.70, where m is the membership function. Fuzzy Logic |
August 30, 2004
Turn Search Into Findby Nathaniel Palmer Statistical analysis algorithms measure word frequency, placement and grouping, as well as the distance between words in a document. This approach requires some form of preliminary training, which might take the form of a basic taxonomy, defined by a human expert. The breadth and validity of the structure and subsequent classification rules can be automated by applying a training set of documents in the design process. In the statistical analysis approach, subsets of documents are identified manually and presented to the software as "exemplary" to a given topic or node of the taxonomy. The provided sample content is analyzed and from this the taxonomy is further refined and the rules of classification established. These rules are then used to automate the analysis of new documents and their classification into the taxonomy. This approach is also referred to as "machine learning." The Bayesian probability approach attempts a concept-based analysis by learning the probabilities of words being related in a given category. The Bayesian algorithm sorts documents by examining the electronic patterns contained in the text or content contained therein. Bayesian probability uses statistical models from words in training sets and uses pattern analysis to assign the probability of correlation. This is one of the more common methods applied to building categories and taxonomy structures. An example of Bayesian probability would be that if a given document contains the words "apples" and "oranges" it is more than likely this document is about fruit, which leads to the assumption that other fruit nouns such as "grapes" or "tangerines" will occur. Neural networks create a matrix of computational nodes. These nodes track and compare topic similarity. A neural network utilizes artificial intelligence to build an interconnected system of processing elements, each with a limited number of inputs and outputs. Rather than being programmed, these systems learn to recognize patterns. Neural networks are an information processing technique based on the way biological nervous systems, such as the brain, process information. Composed of a large number of highly interconnected processing elements, a neural network system uses the technique of learning by example to resolve problems. The neural network is trained for a specific application, such as data classification or pattern recognition. Support vector machine algorithms are derived from statistical learning theory (and thus similarly require manually training with example documents), which calculate the maximum "separation" in multiple dimensions of one document from another. Each document (or any collection of words and phrases that together have meaning) is represented as a vector. The direction of the vector is determined by the words (dimension) it spans. The magnitude of the vector is determined by how many times each word occurs in the document (distance traveled in each dimension). As this iterative method continually analyses documents, it separates them into either the "relevant" or the "irrelevant" space. By repeating the process, it categorizes those documents that are "relevant" into like categories, but more importantly learns how they are different from other categories. Semantic analysis and clustering supports both taxonomy creation and content categorization. Documents are clustered or grouped depending on meaning of words using thesauri, custom dictionaries (for example, a dictionary of abbreviations), parts-of-speech analyzers, rule-based and probabilistic grammar, recognition of idioms, verb chain recognition and noun phrase identifiers (for example, "business unit manager"). Clustering is a technique for partitioning words and documents into subsets of similar words and documents based on the identification of common elements between them. Linguistic software also analyzes the structure of sentences, identifying the subject, verb and objects. The sentence structure analysis is applied to extract the meaning. Stemming (reducing a word to its root) also helps linguistic or semantic clustering. Turn Search Into Find |
August 30, 2004
POSTAGE STAMP ON PANINIThe Department of Posts has released a postage stamp today in commemoration of India's Heritage in Grammar and Mathematics which was influenced by the accomplishments of Panini, one of the greatest grammarians of all time whose work revolutionised the use of language not only in India but also in the rest of the world. The stamp is in the denomination of Rs. 5. Panini, whose lifetime was believed to be between 520 BC and 460 BC, was born in Shalatula, a town near Taxilla on the Indus river in the present-day North-West Province in Pakistan. Though the dates given for Panini's birth range from the seventh to fourth century BC, it is believed he was born about 520 BC. Panini's brilliant account of the structure of the Sanskrit language seeks to provide a complete, maximally concise and theoretically consistent analysis. It unfolds a theory of human language where the infinite language is generated by finite grammar which modern linguistic acknowledges as the complete, generative grammar of any language yet written. Panini gives formal production rules and definitions to describe Sanskrit grammar. There are four major components of his grammar (I) Astadhyayi or Astaka (ii) Sivasutras, (iii) Dhatupatha and (iv) Ganapatha. Today, Panini's grammar has been compared to Euclid's geometry and his constructions can be seen as comparable to modern definitions of a mathematical function. Panini's rules are said to be perfect-that is, they perfectly describe the Sanskrit morphology, and are regarded as so clear that computer scientists have made use of them to teach computers to understand Sanskrit. Panini uses metarules, transformations and recursion in such sophistication that his grammar has the computing power equivalent to a Turing machine. In this sense Panini may be considered the father of computing machines. POSTAGE STAMP ON PANINI |
August 30, 2004
Model method adds up to better treatment for cancer sufferersHELEN PUTTICK, Health Correspondent WILL the cancer come back? That is the fear survivors of the disease can face for the rest of their lives. Now, in an alliance between the hospital ward and the classroom, mathematicians at Dundee University are helping to solve this question for future generations of patients. They have modelled virtual tumours which grow like the real thing, predicting where and how far malignant cells are likely to spread in the body. Created using laboratory data on cancerous cells, the models are intended to help surgeons decide how much tissue to remove when they cut out cancerous lumps from part of the body, such as the breast. They can also help judge how successful chemotherapy or radiotherapy is likely to be for a patient and to assess where the cancer is likely to spread to. The team is working with Ninewells Hospital in Dundee to refine their models using data from scans of patients. Professor Mark Chaplain, a mathematical biologist who has worked on the project since 1987, said leaving just a few cancerous cells behind in the body meant the illness could return, and their virtual tumours could help to reduce this risk. He said: "Cancer is a complex and difficult disease to treat. At the moment, surgeons and medics do not necessarily make what I would say are quantifiable predictions. "We know that if you have a solid lump in your breast it is going to get bigger. The surgeons might say with their expertise that it might get twice as big, but they are not able to give patients detailed information. Mathematics has the potential to give accurate predictions of how fast things grow and where cancer can spread." Model method adds up to better treatment for cancer sufferers |
August 30, 2004
Amazing educator celebrates 50 years of math instructionBy Crissanka Christadoss Christoph Neugebauer writes on the chalkboard in neat cursive and lectures with a clear and obviously German accent. He pauses for a moment to comment on the quality of Purdue chalk, which he thinks is poor. Soft laughter is heard from the class and he goes right back to lecturing. For half a century Neugebauer, professor of math, has walked into classrooms and taught graduate-level math with nothing but chalk. He has aged physically, but his lectures and teaching style are the same. Last week Neugebauer celebrated his 50th teaching anniversary. Actually, it was a surprise celebration. His daughter, Jacqueline Klinker, resident of Crawfordsville, Ind., held a surprise party in his office last Monday. Before the surprise party took place, Klinker said, "If he'd known I planned this, he'd kill me." Neugebauer doesn't think celebrating his 50th year teaching is a big deal; for him it's just another year at Purdue. He started working at Purdue in 1954 when there wasn't even a Math building and the math department was housed in the Recitation building. Neugebauer remembers a time when Purdue was considered small. Of the many changes Neugebauer has seen over the years, the most significant he has seen in students is they are better prepared for math. However, he'd prefer smaller classes and more faculty because he feels more like an actor performing in front of large lecture halls than a teacher. Though he has taught generations of students he doesn't seem to think he has done anything profound. "He thinks (celebrating his 50th teaching anniversary) is stupid. He doesn't think he accomplished anything special or great,"said Klinker. Many of Neugebauer's colleagues and former students consider him to be an excellent professor and mathematician. Marvin Bittinger, professor emeritus of math at Indiana University Purdue University Indianapolis, took a graduate course from Neugebauer in 1968, the same graduate course Neugebauer teaches to this day, MA 544, "Real Analysis and Measure Theory." Bittinger is a math educator and author of over 160 mathematical textbooks. He recently wrote a memoir about his journey through mathematics and one section in the memoir describes people who have inspired him. Neugebauer is one of those people. For Bittinger, he was a role model on how well a lecture should be given. "He was straightforward and serious about what he was doing," he said. In his memoir Bittinger describes Neugebauer coming into class every day without any notes and wearing the same outfit - a sports coat and button down shirt - and giving eloquent lectures. His colleagues praise his clear lecturing style and profound knowledge but they are also in awe of his excitement for mathematics. Rodrigo Banuelos, professor of math, has lived right next to and worked with Neugebauer for the past 15 years. Banuelos said Neugebauer's door is always open to talk or discuss anything, and he's truly remarkable because he shares his excitement for mathematics with colleagues and students. His daughter said she could always find mathematical notes with numbers and symbols around the house while she was growing up. Klinker still finds these notes when she goes to visit him at home. There isn't any profound meaning for why he enjoys teaching and researching. Neugebauer said he has been intrigued by math since he was a boy. He was born in 1927 in Dessau, Germany. At the age of 15 he was drafted into the German air force, Luftwaffe, as a helper. Neugebauer described being a helper as someone who does all the dirty work such as cleaning weapons and manning telephones. After he left the air force, he immigrated to the United States with his family in 1947. Coming to a different country didn't seem to faze Neugebauer at all. "When you're young and energetic, nothing really matters," he said. He received his undergraduate education from the University of Dayton and his Ph.D. from the University of Ohio. In the 1950s many universities were afraid to hire foreigners but Neugebauer found Purdue was one university unafraid of hiring him. Since then he hasn't found a reason to leave. Neugebauer's consistent lectures and love for math will go on until he decides to stop. "If I can't do the job the way I think it should be done, then I'll go." Amazing educator celebrates 50 years of math instruction |
August 30, 2004
'A giant of the last century'By KEVIN HOWE The man who made computers work was recalled as "a giant of the last century" at the Naval Postgraduate School in Monterey during a conference last week celebrating 50 years of computer use on campus. Richard Hamming, author of more than 75 books and papers on mathematics and education, taught at the school from 1976 until his death in 1998, noted Don Brutzman, head of the MOVES (Modeling Virtual Environments and Simulation) Institute at the Navy school. The winner of many honors in the fields of mathematics and computer science, Hamming was the first recipient of an award named after him for his work. Hamming developed the crucial Hamming codes, which allow computers to correct their own errors while running programs rather than shutting themselves down. The codes are part of every computer software program today. Brutzman described a man of genius with a self-effacing sense of humor and a challenging educational philosophy. Hamming began his career at Los Alamos National Laboratories as the Manhattan Project developed the first atomic bomb, and described himself as "a janitor of science" studying at the feet of masters. Of that project, Hamming would say that "no two histories of the time are consistent." His job there was to run the first computers, and on the eve of the first atomic explosion, he wondered if his calculations meant that a nuclear explosion would not detonate earth's atmosphere and wipe out life on the planet. Hamming, Brutzman said, was brimming with tidbits for his students and colleagues about learning and science: • "The purpose of computing is insight, not numbers," Hamming would say in response to arguments in favor of scientific fact because "the computer says so." • "It's better to do the right problem in the wrong way than the wrong problem in the right way." • "Mathematics is the language of clear thinking," and "math is an interesting intellectual sport." • "A good theoretician can account for almost any result produced, right or wrong." • "If you don't work on important problems, it's not likely you'll do important work." Once asked why his doctoral thesis ran only 27 pages, Hamming replied, "There was a lot less to know in 1942." Hamming, Brutzman said, "placed a premium, not on the right answer, but on how you thought about the problem." He would challenge his students by asking those in class to raise their hands if they wanted to do important work or if they were working on something important, and then ask those who hadn't raised their hands, "Why not?" 'A giant of the last century' |
August 29, 2004
Number Devil makes math entertainingGannett News Service If you think math is boring, "The Number Devil," a new software adventure, may be just the ticket. The software presents a mathematical adventure that explores sometimes-challenging concepts such as infinite numbers, prime numbers, fractions, decimals, powers and square roots. It introduces mathematical oddities including triangular numbers, Fibonacci Numbers, Pascal's Triangle and Euler's formula. Robert, a boy who thinks "mathematics is child abuse," narrates the story. His opinion about math changes after he is visited in his dreams for 10 nights by the Number Devil, a mouthy charismatic character. Each night, the Number Devil introduces math concepts in clever and unusual ways. For example, to explain permutations, the Number Devil shifts Robert's whining classmates around to show the different possibilities. Players end each night by exploring a related math game. Number Devil makes math entertaining |
August 29, 2004
DNA could help fight spam e-mailU.S. biologists have devised an anti-spam filter based on the way scientists analyse genetic sequences. Computational biologists at IBM's TJ Watson Research Center said the formula automatically learns patterns of spam vocabulary and has proved to be 96.5-percent efficient. In tests, the filter only misidentified one message in 6,000 as spam, BBC News Online reported. The IBM scientists said they started to develop the formula only about a year ago. They named it Chung-Kwei, after a Feng Shui character who usually is shown carrying a bat and also holds a sword behind him. He is an important figure for those involved in business and who have expensive goods that need protection, they explained. The computer formula was developed originally to help determine the properties of a protein. Now, instead of looking at strings of protein, Chung-Kwei can identify strings of character sequences that appear in spam, but never in non-spam mail. The scientists said they were helped by the large volume of spam they receive. DNA could help fight spam e-mail |
August 28, 2004
There is a place in markets for 'financial scientists'By CHET CURRIER One of the grandest ambitions of the world's great minds is to unlock the mysteries of the financial markets. Fame and acclaim surely await the mathematician-physicist- economist who can strip away our silly superstitions and lay bare the true inner workings of a mechanism like the stock market. This luminary also will earn the thanks of countless people struggling to manage their money amid the current, primitive state of market knowledge. "The financial markets aren't mysterious, but rather physical systems that ought to be examined scientifically and engineered rationally," says a Wall Street Journal summary of the views of one leading light in this campaign, Yale University mathematician Benoit Mandelbrot. Academic inquiry into the principles of investing has already borne some noteworthy fruit. It gave us the idea of market efficiency and the index fund. The efficient market hypothesis, or EMH, says in effect that market prices at any given time already reflect all relevant information that can be known or suspected. Index funds are based on the premise that low-cost portfolios set up to mirror the performance of a market index hold a natural edge over the average higher-cost managed fund. You need not be a believer in index funds to benefit from their ascendancy. The indexers, with roughly a one-sixth share of the stock-fund business, bring intense, relentless competition to bear on active managers, pressing them to keep their performance up and their costs down. Indexers have been around for 30 years. The question is, why hasn't the advance of financial science made many more great strides since then? One obvious obstacle is the human factor in markets. Other sciences may rest on reasonably reliable truths: Ice floats in water, rolling friction is less than sliding friction. In the stock market, alas, higher corporate profits mean higher stock prices only when investors decide it should be so. There is a place in markets for 'financial scientists' |
August 27, 2004
Pi in the skyBy Ariel Rubinstein "Heshbon lehorim" ("Arithmetic for Parents: A Book for Adults on Mathematics for Children") by Ron Aharoni, Schocken, 165 pages, NIS 75. Once a year, Israelis wake up in the morning, open their newspapers, read reports about surveys comparing the level of knowledge in mathematics of our genius children with that of children from countries, which we more or less respect, and discover to our horror that we are slipping badly. Israeli kids, we sadly conclude, are just not all they are cracked up to be. Since the level of knowledge in mathematics is customarily linked with intellectual prowess in general, the myth of Jewish genius suffers a massive blow. Since mathematics is customarily considered the "queen" of the sciences, serious doubts are raised as to whether the Jewish People of Zion can truly build a Temple of Academia and Science to which the nations of the world will flock. And since the quality of our human resources and technological progress are vital for the maintenance of our edge over those nations that are bent on destroying us, our very survival is threatened. Pi in the sky |
August 27, 2004
Studying math equals coolnessBy Kate Jensen As a teacher of Math 101, I've been asked my fair share of questions. Nothing compares, however, to the glowing feeling I get when students scrunch their faces in distaste, shoot up their hands, and ask the achingly familiar question: "But when are we ever going to use this?" It's a common misperception that non-math majors cannot benefit from the study of math. To remedy this and answer my students' questions forevermore, here's a list gleaned from years of math class experience. Ladies and gentlemen, with no further ado I'd like to present the Top 10 Practical Applications of Math to Your Life. 10. Party conversation — Can't think of what to say during awkward party time silences? Imagine interspersing your keg stands with some philosophical conversations about imaginary numbers or enthralling the crowd with a cheerful tale of Lebesgue integration. Nothing says "life of the party" like a good grasp of the modern conventions of mathematics. 9. Sexual appeal — Let's face it, nearly everyone out there is looking for a way to make themselves more attractive. Traditionally, people have relied on nonsensical methods such as "personal hygiene" and "grooming" to improve their attractiveness quotient, but the real key to irresistibility is rolling off obscure mathematical facts with ease. It's like a foreign language: No one understands, but all the chicks (and guys, for that matter) seem to dig it. |
August 27, 2004
Math or psychology: Figuring out investingBy Chet Currier One of the grandest ambitions of the world's great minds is to unlock the mysteries of the financial markets. Fame and acclaim surely await the mathematician-physicist-economist who can strip away our silly superstitions and lay bare the true inner workings of a mechanism like the stock market. This luminary also will earn the thanks of countless people struggling to manage their money amid the present, primitive state of market knowledge. "The financial markets aren't mysterious, but rather physical systems that ought to be examined scientifically and engineered rationally," says a Wall Street Journal summary of the views of one leading light in this campaign, Yale University mathematician Benoit B. Mandelbrot. Suppose we discover that stocks beginning with the letters A-M outperform those starting with N-Z, and find a solid, plausible reason why they do that. Investors will quickly adjust stock prices to account for the disparity, and in so doing neutralize it. For all the stumbling blocks in its path, academic research has made itself a real and potent presence in today's markets. It is embodied in such firms as Dimensional Fund Advisers in Santa Monica, Calif., which manages $55 billion using an approach that, in its own words, "applies academic research to the practical world of investing." Not everybody is so enthusiastic. "Academics are stock market technician/chartists whose fields of study are prices, markets and market price histories, not corporate nitty-gritty and the underlying characteristics of securities," says Martin Whitman, chairman of money manager Third Avenue Management LLC in New York. "That does not seem to have much to do with what Third Avenue is, and what Third Avenue is trying to do," Whitman wrote in a recent shareholder report. Whatever you or I think of it, the march of science into the markets has only just begun. There's so much folk wisdom to be challenged, so many blank spaces still to be filled in. Plus, for those motivated by more than intellectual curiosity, there may also be a lot of money to be made. Maybe someday the art of investing can be turned into a science, maybe it can't. Either way we stand to learn a lot. Math or psychology: Figuring out investing |
August 27, 2004
Constructivist mathematicsBy E. E. Escultura, Ph.D. MY introduction of constructivist mathematics has generated much discussion in the news group MathForg.net (for the interested reader surf: mathforge.net and click: Constructivist Principles . . . under Number Theory; there is advanced discussion there). Therefore, I am writing this article in response. Constructivist mathematics is an advance over Hilbert's introduction of formalist mathematics a century ago. Recognizing the ambiguity of human thought being inaccessible to others and, therefore, cannot be studied collectively and axiomatized, Hilbert studied symbols instead as the subject matter of mathematics. This makes mathematics a language. This is what the real number system is from the formalist perspective. However, the perspective of number theory has not changed. A real number is still seen as symbol for some concept of thought. When one says 1 and 0.99 . . . represent the same concept in his mind, who can dispute it? Others cannot see it that way, using the axioms, the reason there is extensive but unresolved debate in SciMath and MathForge.net on the question of whether 1 = 0.99 . . . , that is, whether 1 and 0.99 . . . represent the same concept in one's mind. To the formalist, they don't. A real number is well-defined if it is constructible, that is, its digits are known or there is an algorithm for computing or determining every digit. Since any physical process is finite, only a finite number of digits and real numbers can be computed. Then most of the irrationals are ill-defined. However, the irrational number pi is well-defined as the sum of a specific infinite series so that any digit can be computed by calculating suitable number of terms of the series. So is the nth root of a prime p as shown in the previous article. A normal number is also well-defined: each digit is chosen at random from the basic integers. The probability that it is periodic is 0. The natural ordering of the new real numbers (lexicographic ordering) says, 0.99 . . . < 1. Therefore, the dark number d* = 1 – 0.99 . . . is well-defined. Its nonstandard decimal numeral is posted in Mathforge.net. It is positive, unique, less than any real number, old or new, and the well-defined counterpart of the ill-defined infinitesimal. Clearly, the new real numbers are finite, unbounded, enriched by at least d*, free from contradiction and adequate for all scientific and practical purposes. Constructivist mathematics |
August 27, 2004
The infinite biological computerby Peter Jorgensen As explained in a previous article, the concept of infinity should probably be perceived differently when talking about theory and talking about facts. Theoretically, or at least mathematically, infinity is easy to grasp. It doesn't take a PhD in anything to accept that it will always be possible add one more number to any other number – or likewise to place a number (fraction) between any two other numbers. Once we agree with this argument, we are also conscious that infinity exists. There is still a problem as to fully understanding the consequences, however. We can't really put the theory into practical use or come close to comprehend that the universe is a never ending "thingy". "When an electrical impulse traveling along the nerve reaches the axon, the neurotransmitter is released and travels across the synapse, either prompting or inhibiting continued electrical impulses along the nerve." Not quite unlike those bits and computer switches. However, the big difference is in the infinite combinations possible when using variations of chemicals and even gases instead of the computer's limited "on/off" mechanical elements. That breakthrough mentioned above would of course mean that our computers need to operate a little more like our brains. Instead of only reaching conclusions by "yes and no" – it should be feasible to introduce some kind of in-between. Whether it will be through gases and chemistry or differentiating the currents into "yes, there's power, but only a little" – I really don't know, but it's a thought worth some research. Well, I can imagine scientists somewhere have already been thinking along these lines. It's just strange that all we get is faster CPUs when the whole dilemma might involve taking an alternative approach. The infinite biological computer |
August 27, 2004
DNA could help fight spam e-mailU.S. biologists have devised an anti-spam filter based on the way scientists analyse genetic sequences. Computational biologists at IBM's TJ Watson Research Center said the formula automatically learns patterns of spam vocabulary and has proved to be 96.5-percent efficient. In tests, the filter only misidentified one message in 6,000 as spam, BBC News Online reported. The IBM scientists said they started to develop the formula only about a year ago. They named it Chung-Kwei, after a Feng Shui character who usually is shown carrying a bat and also holds a sword behind him. He is an important figure for those involved in business and who have expensive goods that need protection, they explained. The computer formula was developed originally to help determine the properties of a protein. Now, instead of looking at strings of protein, Chung-Kwei can identify strings of character sequences that appear in spam, but never in non-spam mail. The scientists said they were helped by the large volume of spam they receive. DNA could help fight spam e-mail |
August 26, 2004
Tycoon takes stock, ADEs to fortune with chipper dayBy Brett Arends It was another day, another $5 million for Hub tycoon Landon Clay yesterday. Clay, 77, added that much to his growing personal fortune when shares in a Massachusetts high-tech company he chairs skyrocketed following record results. ADE, which makes equipment for computer chip manufacturers, zoomed $3.26 or more than a fifth on the New York Stock Exchange to $18.71 after nearly tripling its earnings. Clay, long-serving chairman, is the company's largest personal investor. His stake, helped by yesterday's pop, is valued at $33 million. Not that he needs the money. The former Eaton Vance chairman has cashed in $266 million worth of stock in the Boston-based mutual fund giant in the past 12 months. Clay, a math enthusiast, has been using some of his fortune to endow bodies promoting mathematics and science. They include the Clay Mathematics Institute in Cambridge. Most notably, though, he offered seven $1 million prizes for anyone who could solve seven mathematical puzzles, ranging from ``The Navier-Stokes Equations'' to ``P vs NP.'' The prizes, announced at the College de France in Paris four years ago, stimulated attention around the world but have yet to be claimed. But a spokeswoman at the Clay Institute says: ``There's a lot of excitement over Grigori Perelman's work on the Poincare Conjecture.'' If Perelman is so smart, why didn't he buy ADE stock two years ago, when it was at $2.50? Tycoon takes stock, ADEs to fortune with chipper day |
August 26, 2004
Six degrees of separation and super nodesPeter Cochrane COMMENTARY--The past year has seen the resurgence of the "six degrees of separation" theory. Journalists across the planet have variously trumpeted the "amazing" fact that any two individuals are separated by no more than six acquaintances. The reality, though, is there's absolutely nothing amazing about it. Interesting? Sure. Mind boggling? Never. It is simple to understand at a basic level but gets rapidly more complex as we delve deeper. To get a picture of the mechanisms at work, let's look at a few unusual populations. First, take the case of a Pacific island some 500 years ago with a stable population of around 3,000 people who had arrived by canoe several generations back and since that time had no outside contact. Such societies were highly interdependent and tightly bonded and thus everyone could know everyone else--everyone was connected by a single handshake, or one degree of separation. Second, consider a much bigger (hypothetical) island with a population of 100 million in an evenly distributed society where everyone knows on average around 300 people. The worst-case population connectivity is again defined by 300n, where "n" is the degree of separation. So the question is what value of "n" will span the population? You will not be amazed to see that 3003= 27 million, which is more than a quarter of the island's population, whilst 3004= 8.1 billion, which is 81 times greater than required for full connectivity. We might therefore conclude that today's worldwide population of six billion could be spanned by just four handshakes. This would be the case if the population were evenly distributed. If not, then the degree of separation is bigger. Before we had national and international travel, and of course telecommunications, none of this was quite so obvious or indeed quite so true. Today we have nearly one billion people with access to a telephone, mobile phone and the Internet, plus millions of regular and irregular travelers. So it is feasible that four degrees of separation has been established within this community and five (or six) might be the number when we include a further five billion disenfranchised people outside the modern world. As far as I can tell, the first recorded thinking on the "six degrees of separation" theory started in Budapest around 1929. That's when Frigyes Karinthy wrote a short story entitled "Chains" in which he postulated that one billion people had only five degrees of separation. He was not a mathematician, scientist or engineer but a poet and writer, so where the number five came from remains unclear. Later, in 1967, the sociologist Stanley Milgram conducted the first recorded experiments on social connectivity using post cards in the United States. Despite the crudity of the experiment, and the tardiness of the participants, he recorded a median number of 5.5 degrees of separation. Round up and we see the start of "six degrees of separation." More recently computer simulations, mathematical studies and Internet experiments--plus observations on biological brains and organisms--have served to confirm further the apparently universal separation number. The most revealing discovery related to this theory has been that of the "super node." It seems very few networks offer even or homogenous structures. They are almost always clustered assemblies that concentrate around a smallish number of super nodes. For us such a node might be a manager who knows thousands of people, or an ISP that links directly to an international hub, which in turn connects to all the major cities on the planet. When connecting to others via a super node, the degree of separation is four. If we count our connections to others via a "standard" node--say, our manager's manager or an ISP without the direct international link--then we quickly move up to six. Now here is the fun part: it turns out these super node-based networks are incredibly resilient. Should a node or super node fail or become damaged, the rerouting is super efficient. In most cases, such a failure will see little or no change in the degree of separation. This is a primary reason that Internet failures, brain damage and other biological malfunctions can often be overcome. It is also why companies can often achieve great success despite pockets of disastrous management. I have been witnessing all of the above on the net for over a decade. My practice is to delete contact information from those people who do not reply to my e-mail, or who are so tardy to be ineffective. I also delete web pages and hyperlinks if I don't use them often. It really works. With well over 1,000 e-mail addresses of proactive people and even more websites, reference papers and documents on my laptop, I am now super efficient compared to 10 years ago. So have I become a super node? I have no idea. Apart from the flood of e-mails generated by this column, I still only process around 50 messages a day--although I do find myself linking up people, and thousands visit my home page without contacting me. The tragedy is those who could be super nodes but choose not to be and instead become rapidly isolated. Seems to me on the net we are separated by three or four degrees, while across the planet its closer to five or six. Six degrees of separation and super nodes |
August 25, 2004
Why spam will revolutionize techRupert Goodwins COMMENTARY--It is hard to find a good word to say for spam. Incoherent, unpleasant and unwanted, it slimes through cyberspace on the backs of zombies and oozes into our inbox with the stench of month-old haddock. Yet far from fatally clogging up our information arteries, spam may provide the impetus for a true revolution in information technology--one we've been expecting for more than fifty years. All the problems caused by the stuff can be solved if we can answer one simple question: what is spam? You and I know within a second of opening a piece of e-mail whether it's spam or not--but computers are terribly bad at replicating the task. All spam-filters suffer from two problems, the false negative and the false positive. We can--we do--put up with the false negatives, the spam written cleverly enough to bypass whichever tests are flavor of the month. False positives, when a real e-mail is junked before we read it, are potentially ruinous. Unless filters are absolutely sure, they err on the side of slackness. They are never absolutely sure: some always gets through. And, because spam works on the law of averages, as long as some gets through, the spammers will ramp up the rate to make sure that enough hits to make the sums work. The pressure on our systems is immense. By now, the whole business resembles a planet wide reverse Turing test. Instead of human arbiters deciding whether their interlocutor is man or machine, uncountable thousands of filtering robots anxiously scan gigabytes of chatter to fish out the spawn of their evil cousins. It turns out that the only way to be sure whether something is spam is to look at it like a human, with all our knowledge of context, language, meaning and intent. In short, you must be truly intelligent to do the job. Suddenly, the mildly moribund field of AI has a real job to do: saving the world. Evidence of this can be found as far afield as the University of Melbourne, where programmers Matthew Sullivan and Guy Di Mattina, together with mathematics lecturer Dr Kevin Gates, have stapled a Support Vector Machine to an e-mail firewall to get a claimed rate of 90 e-mails a second with one error every 25,000 messages. Support Vector Machines are fearsome mathematical constructs that have only just escaped from the lab. As far as I can make out, they seek non-linear hyperplanes in Hilbert space using Lagrangian transforms: Check http://www.kernel-machines.org/ if you don't believe me. Why spam will revolutionize tech |
August 25, 2004
Insect micro robot army unleashedNick Farrell FICTION IS BECOMING fact as Aussie boffins work on a plan which was first mooted by Jurassic Park author Michael Crichton. In the penny dreadful Prey, Crichton describes scientists developing swarms of microscopic robots that used their collective intelligence to set about killing their creators. Now it seems that the Australian government's Defence Science and Technology Organisation think this is a wizard idea and is working on computer software recreating swarm behaviour for use on the battlefield. The big idea is to develop swarms of small robots that can carry out missions in environments too dangerous for humans. According to AFP, the scientists are using insect swarms as a template because they showed great versatility and adaptability in nature despite the fact that on their own insects are a little dim. The scientists are replicating swarm behaviour using algorithms to develop an intelligent and communicating network. However the boffins are laughing off the idea that they may end up creating a monster killing machine and claiming that fears about artificial intelligence are overstated. Mind you I don't think that the bloke who got bitten on the Karzi by the giant lizard in Jurassic Park laughed much. Insect micro robot army unleashed |
August 25, 2004
Crude Oil Falls After U.S. Reports Gasoline Supply Is UnchangedAug. 25 (Bloomberg) -- Crude oil futures fell for a fourth session, led by gasoline, after an Energy Department report showed that U.S. supplies of the fuel were unchanged last week. Gasoline inventories were at 205.7 million barrels. Fourteen analysts surveyed by Bloomberg expected a decline of 2.25 million barrels, according to the median of forecasts. Crude oil supplies fell 1.7 million barrels to 291.3 million in the week ended Aug. 20, the department said. ``You should have had a 2 million barrel draw in gasoline at this time of year,'' said Ed Silliere, vice president of risk management at Energy Merchant LLC in New York, which markets wholesale gasoline and heating oil. ``The crude number wasn't big enough to send us higher.'' A Fibonacci graph of the move in oil futures from lows in July pointed to $45 as a support level for oil, said Bill O'Grady, director of fundamental futures research at A.G. Edwards & Sons Inc. in St. Louis. The decline in prices accelerated after falling below $45. The next support level is $42, O'Grady said. Fibonacci analysis, named for the 13th century mathematician, helps traders determine whether gains or losses will continue. ``There is major, major support between $41 and $42,'' O'Grady said. ``I'm agnostic about technicals but when the fundamentals aren't giving a clear signal, you have to use them.'' Crude Oil Falls After U.S. Reports Gasoline Supply Is Unchanged |
August 24, 2004
Tweaking the Math to Make Happier Medical MarriagesBy SARA ROBINSON Earlier this month, a federal district court dismissed an antitrust challenge to the Residency Match, the program that assigns medical students to residency positions. The plaintiffs say they will continue their legal efforts, but whatever the outcome, the case has already captured the attention of mathematical economists, who are wrestling with a question at the heart of it: By making it difficult for students to negotiate the terms of employment, does the match program enable hospitals to underpay residents? The solution was a matching process, which evolved into what was shown to be a classic mathematical recipe, the so-called stable marriage algorithm. Given equal numbers of boys and girls, each with a list of preferences, the algorithm pairs them so that the relationships are likely to last. The algorithm, frequently taught in math, computer science and economics courses, has proved powerful in real life. Variants are used for assigning clinical psychologists to internships, and students to slots at New York City public high schools. The marriage algorithm was devised in 1962 by the mathematicians Dr. David Gale, now a professor emeritus at the University of California, Berkeley, and Dr. Lloyd Shapley, an emeritus professor at the University of California at Los Angeles. But it was not until 20 years later that Dr. Alvin E. Roth, a professor of economics and business at Harvard, observed that it was essentially the same as the one used in the match. It works like this: Each boy ranks all the girls in order of his preference, and each girl does the same. Then, each boy asks his first choice for a date. Each girl with one or more offers dates her favorite and says "no" to the rest. In the next round, the boys who were rejected move on to their second-choice girl. The girls again date their favorites, possibly throwing over their date from the earlier round for someone better. Continuing in this way, the mathematicians showed, the dating frenzy eventually subsides into a stable situation where each girl has only one boy, and there is no boy and girl who prefer each other to the people they are dating. That is, every time a boy does not get his first choice, he has no hope of getting anything better. Each of the girls he prefers is paired with someone she prefers to him. The same is true for a girl. In the match, the students are the boys, and the residency positions are the girls. Each year, after interviews, students and hospitals rank one another in secret preference lists. A computer program then automatically plays out the rounds of dating, producing a match participants must accept. Tweaking the Math to Make Happier Medical Marriages |
August 24, 2004
Mathematician argues markets more dangerous than investors knowBy Warren Boroson, Daily Record A key message of Benoit Mandelbrot's book "The (Mis)behavior of Markets" (Basic Books, 2004, co-written by Richard L. Hudson), is that investment markets in general and the stock market in particular are riskier and more dangerous than people know. Investors should therefore be more cautious. Mandelbrot, 80, is a mathematician at Yale and the creator of "fractal" geometry, which focuses on the regularities in various irregular systems, from wind tunnels to coastlines. If mathematicians received Nobel Prizes, he probably would be first in line. His book is difficult. Sometimes I had trouble understanding him, especially when he is writing about fractals and not about investing, which is much too often. But he is not afraid to argue that the emperor has no clothes, that most of the leading financial theories accepted today are - if not exactly hogwash - badly flawed. Indeed, the last sentence in his book is: "Like the weather, markets are turbulent. We must learn to recognize that, and better cope." Mathematician argues markets more dangerous than investors know |
August 24, 2004
Math concepts may be limited by languageGeoff Koch (KRT) - A rose by any other name may smell as sweet. But when it comes to accurately counting the flowers in that bouquet, the numbers' names matter. The isolated Piraha tribe in Brazil has no words in its vocabulary for numbers greater than two. Columbia University's Peter Gordon explored how this truncated "one, two, many ... " system of counting affected the Piraha's ability to make judgments about numbers. Gordon asked the Piraha study participants to do a series of matching and counting exercises using clusters of batteries and other everyday objects. The participants responded with high accuracy as long as the clusters contained no more than two or three objects. However, for tasks that involved larger quantities, such as comparing pictures of three vs. four fish, performance quickly deteriorated. In an article published online last week in Science, Gordon writes that his study makes a "unique case for strong linguistic determinism" – the idea that thought is influenced and even constrained by language. Math concepts may be limited by language |
August 26, 2004
Encryption gets a boostFlorence Olsen Cryptographic technology, unlike other information technologies, has been rather stodgy and secretive. But a few years ago, National Institute of Standards and Technology officials re-energized cryptography by holding a global competition and inviting cryptographers to submit their best encryption algorithms. From those submissions, NIST experts selected a fast and tough-to-break algorithm to be the federal government's most advanced encryption standard. They bestowed a modest name, Advanced Encryption Standard (AES), on the speedy new algorithm, and cryptography suddenly got new legs. Just as AES has helped make encryption commonplace, elliptic curve cryptography (ECC) has popularized public-key systems. Such systems generate and distribute the cryptographic keys used in encrypting or digitally signing documents, for example. And like AES, ECC works considerably faster than older technologies. Last October, the National Security Agency signed a $25 million deal with Certicom to license 26 patents related to ECC. Since then, NSA officials have been using ECC and AES to modernize many of the federal government's public-key systems. A growing number of companies offer cryptographic products and services. Security experts say a rise in security incidents and new regulations and laws such as the Federal Information Security Management Act have created an expanding market for new cryptographic products. Some of the well-known and newer companies in the market are Certicom, Entrust Inc., Ingrian Networks Inc., PGP, RSA Security Inc., SSH Communications Security Corp. and VeriSign Inc. Cryptography is not yet as integrated into networks and applications as security officials would like it to be, Roback said. But it still provides security protections that no other information technology can. "If you want to protect the contents of e-mail across the Internet," he said, "we don't have any means other than something cryptographic to hide the content." Encryption gets a boost |
August 24, 2004
Hi honey, I'm virtually home aloneBy Jennifer Dudley FEELING lonesome? Mobile telephone no longer ringing? Why not SMS your Virtual Girlfriend? Australian mobile telephone users may be able to buy and woo virtual dates this year after the release of a Virtual Girlfriend game for 3G mobile telephones. But lonely or curious men should not expect an easy time of it - this 3D beauty uses artificial intelligence technology to replicate human behaviour and responses. In short, she expects attention and regular gifts and will ignore you if she doesn't get her way. Virtual Girlfriend was developed by Hong-Kong-based company Artificial Life and will allow subscribers to interact with a slight, three-dimensional brunette. Each girlfriend will follow a daily and weekly schedule, which evolves over time, and sees her visit her virtual home, workplace or bar, and go shopping with virtual friends. Real-life boyfriends can also send their virtual partners SMS or MMS messages or chat to them. But to keep their companions happy, subscribers will have to send their girlfriends virtual gifts that cost a lot of money and allow them to progress further in the game and unlock new levels. "The Virtual Girlfriend is a lot of fun to play and the game sets new and high standards for future 3G mobile games," Artificial Life CEO Eberhard Schoeneburg said. Hi honey, I'm virtually home alone |
August 23, 2004
Nevada researcher re-ignites mammal reproduction debateOne of the most debated hypotheses in evolutionary biology received new support today, thanks to a study by a scientist at the University of Nevada, Reno. Elissa Cameron, a mammal ecologist in the Department of Natural Resources and Environmental Science, has helped to disprove critics of a scientific theory developed in 1973. At that time, ecologist Bob Trivers and mathematician Dan Willard said that large healthy mammals produce more male offspring when living in good conditions, such as areas where there is an ample food supply. Conversely, female mammals living in less desirable conditions would tend to have female offspring. According to Cameron, the hypothesis demonstrated the idea that having more male offspring leads to greater evolutionary success for mammal parents, if living conditions support larger populations. Should conditions be less desirable, having female offspring would be a better investment for mammal parents. "Male zebras can father more than a hundred offspring in a lifetime, whereas female zebras are constrained to minimal reproductive rates--about one a year," Cameron said. "Sons, therefore, offer higher breeding rates to zebra parents, while female offspring are a lower-risk investment. "Therefore, if the animal's living conditions aren't suitable, giving birth to a female would better ensure the animal's genetic success in the long term. Daughters of less healthy mothers would out-reproduce sons in poorer conditions because males that are unsuccessful in having mates have few offspring while most females breed throughout their lifetime." Nevada researcher re-ignites mammal reproduction debate |
August 23, 2004
Khatami Inaugurates Hamedan's Avicenna MuseumMullah President inaugurated a museum dedicated to Avicenna in Hamedan on Saturday. The museum is housed in a building dating back to the Qajar Dynasty and occupies a one-hectare piece of land. Mullah visited different parts of the museum accompanied by Minister of Culture and Islamic Guidance Ahmad Masjed Jamei, Director-General of the Cultural Heritage and Tourism Organization Hossein Mar'ashi, and the city's governor-general and representative of the Valiyat-e Faqih (religious jurisprudent) Hojjatoleslaam Qiyaaseddin Mohammadi. Khatami also visited the museum library, which contains different books on and by the great Iranian philosopher, mathematician and physician Avicenna. Khatami arrived in Hamedan early today along with his to attend the First International Conference on Avicenna at his mausoleum. The event coincides with Avicenna's birthday, which is also known in Iran as "Physician Day". Khatami Inaugurates Hamedan's Avicenna Museum |
August 23, 2004
Big Computers For Big ScienceA visiting neutron scattering scientist at ORNL sends data from her experiment to a San Diego supercomputer for analysis. The calculation results are sent to Argonne National Laboratory, where they are turned into "pictures." These visualizations are sent to a collaborating scientist's workstation at North Carolina State University, one of the core universities of UT-Battelle, which manages ORNL for DOE. To make their discoveries, scientists must interact with supercomputers to generate, examine, and archive huge datasets. To turn data into insight, this interaction must occur on human time scales, not over days or weeks, but over minutes. Big science requires big computers that are not just scaled-up desktop personal computers. Big computers are fundamentally different from PCs in their ability to model enormous systems, generate immense volumes of data, and, as a payoff, solve uniquely difficult scientific problems. To put this difference in perspective, next-generation science datasets will approach or exceed a petabyte in size. If one of today's desktop PCs had a disk able to hold a petabyte-sized file, the PC would require over three years to read the file. The Center for Computational Sciences at ORNL has been tasked by DOE to develop the next generation of scientific networks to address the challenges of large science applications. The techniques developed in Oak Ridge will eventually filter out into the high end of the business world. Just as yesterday's scientific supercomputers have become today's central business and engineering computers, the same transfer will result in this network, called the DOE UltraScience Net, becoming the core of tomorrow's commercial networks. Big Computers For Big Science |
August 22, 2004
The PhotogramThe ancients observed the patterns of light and shade caused by the sun and, more vividly, the dancing shadows made by their fires on cave walls. Well over two thousand years ago, the images that were produced by small holes in the shutters covering a window were noticed and described, both in China and Greece. From this phenomenon came the camera, originally a darkened room (camera obscura), later as a portable device which artists could use as an aid to sketching. The first known automatic recording of an image from such a camera took place only two hundred years ago, in research prompted by the Industrial Revolution. Earlier in the eighteenth century several European scientists had discovered and investigated the darkening by light of silver compounds. Thomas Wedgwood, son of Josiah Wedgwood who founded the great pottery company, took up an investigation in the hope that it might provide a way of decorating pottery. He enlisted the help of one of the greatest English scientists of the time, Humphrey Davy and together they produced negative images from drawings, objects and the projected image of a solar microscope on silver nitrate soaked paper and leather. They published their results in 1802, but were unable either to produce positive images or to fix their images to prevent fading when exposed to light. Their efforts can easily be reproduced today. A friend of mine has a pale coloured chamois leather carefully folded in a black plastic bag. Over ten years ago he soaked it in silver nitrate solution, exposed it in contact with a negative until the dark brown image was clearly visible, then washed and dried it in subdued light. Kept in the dark and only taken out for short periods, avoiding bright light, its image has hardly faded. While William Henry Fox Talbot, an English mathematician and scientist was drawing using the camera lucida (a portable development of the camera obscura) on a tour of Italy in the early 1830's he was sufficiently frustrated by his results to decide to engage in the scientific study of photography. Shortly after he was producing prints by placing leaves, flowers, lace and other translucent or opaque materials on 'salted paper' and exposing these to light. The Photogram |
August 21, 2004
Computers Can Argue, Researcher ClaimsBy Mike Martin In "2001: A Space Odyssey," astronaut Dave Bowman has a problem with a computer named HAL. "Open the pod bay doors, HAL." "I'm sorry Dave, I'm afraid I can't do that." "What's the problem?" "I think you know what the problem is just as well as I do." "What are you talking about, HAL?" "This mission is too important for me to allow you to jeopardize it." "HAL, I won't argue with you anymore! Open the doors!" Feisty Computers But can computers really argue? British researcher Nick Jennings says "yes." And that's not all. Jennings claims computers can evaluate the most successful strategy for conflict resolution, including reformulating their actions, or evading confrontation. And like HAL -- who is certain his human masters are about to disconnect him -- computer agents only argue as a last resort, Jennings maintains. Negotiation Station Jennings -- a computer science professor at the University of Southampton -- assesses the effectiveness of so-called "argumentation-based negotiation" (ABN) for computer agents in a recently published paper. Agents are computer systems to which an operator can delegate tasks. Considered autonomous in comparison to programs that depend on every keystroke, agents are increasingly used in a wide range of industrial and commercial domains, including robotics, e-commerce, computer games and information retrieval. In systems with more than one agent, where "autonomous entities pursue their own goals, conflict is inevitable," Jennings explained. Negotiation among the agents is the best way to "resolve these problems," he added. To resolve conflicts through negotiation, computers need artificial intelligence programs, which are "increasingly being used on the Internet, in our homes, and in the workplace," Jennings told NewsFactor. "To improve their performance, we need to ensure they have the ability to overcome real-world problems, such as conflict," he stressed. "I am very much in agreement with Prof. Jennings on the importance and the promise of agent technology," said Agentis chief technology officer David Kinny, who with Jennings and Michael Wooldridge co-authored the landmark "Gaia" paper on agent-oriented analysis and design. "Negotiation techniques are crucial in open-agent systems," said Kinny, "where agents representing different individuals or organizations interact -- as well as in any systems where agents have conflicting goals or information." One Easy Piece? A crucial aspect of agents is their potential in e-commerce, Kinny said. "As worldwide markets become more complex and timeframes narrow, companies are keen to automate parts of their activities," Kinny explained. "We are aiming to design programs that can mirror and occasionally improve human decision making." But negotiation, Kinny said, "is just one piece of that puzzle." Producing useful artificial agents, he told NewsFactor, "demands the automation of a broad range of decision-making behaviors, not only those concerned with reaching agreements or solving conflicts." Despite this caveat, Kinny said Jennings' work on agent-based negotiation "appears to be a significant addition to our understanding of how to automate the sorts of complex behaviors that -- until now -- have been exhibited only by people." Computers Can Argue, Researcher Claims |
August 20, 2004
The power of collective intelligenceShyamal Majumdar / New Delhi August 20, 2004 Company chief executives might hate this fascinatingly well-crafted book. For, it raises one fundamental question: why do companies rely so much on the judgment of one person—namely the CEO? Despite genuflections to decentralisation, it is no secret that most fail to tap the insights of their employees, suppliers, and others by using well-designed decision markets for everything—from forecasting demand to deciding which products to create. One reason: such an approach might limit CEOs' ability to justify their huge compensation packages! A Delhi-based chief executive told me the other day that this is "literature in a hurry written by a journalist eager to meet his deadline. " But before dismissing the book, CEOs would do well to remember that its author is no ideologue. Financial journalist James Surowiecki doesn't shy from evidence that counters his theory. Still, he musters ample proof that the payoff from heeding collective intelligence (the wisdom of crowds) is greater than many of us imagine. In The Wisdom of Crowds, the New Yorker staff writer provocatively argues that, in many circumstances, the group collectively reaches better decisions—and solves problems more efficiently—than the smartest man or woman alone. Consider the examples given by Surowiecki in support of his arguments for exploiting the power of a large number of independent minds in solving big problems. Linux, the open-source operating system created by Finnish programmer Linus Torvalds in 1991 but effectively owned by no one, is now the major rival to Microsoft's Windows. Independent computer programmers from around the world contribute to improving the operating system, and solving the problems that intrigue them, although Torvalds and his peers keep a tight rein on what changes are acceptable. When a problem arises with the way Linux works, it only gets fixed if someone, on his own, offers a good solution. There are no bosses ordering people around, no organisational charts dictating people's responsibilities. Instead, people work on what they are interested in and ignore the rest. This seems like—in fact, it is—a rather haphazard way to solve the problems. After all, if thousands of programmers are spending their time trying to come up with a solution that only a few of them are going to find, that's many hours wasted that could be spent doing something else. But as Surowiecki has shown so far at least, Linux's seeming wastefulness is a kind of strength, which has made it the single most important challenger to Microsoft. Or, take the case of the disappearance of USS Scorpion, a submarine on its way to Newport News. The US Navy had a general idea where the submarine sank, but it was an area 20 miles wide and many thousands of feet deep. Naval officer John Craven hit upon a solution. He gathered a group of diverse experts and asked for their best guesses on why the submarine ran into trouble, its speed as it fell to the ocean floor, the slant of its descent, and so on. Craven took all the speculations, ran them through a sophisticated mathematical formula, and ended up with the team's overall guesstimate. The Navy found the ship 220 yards from where Craven's group had predicted it would be, yet not one individual had picked that spot. "The final estimate was a genuinely collective judgment that the group as a whole had made," says Surowiecki. "It was also a genuinely brilliant judgment." The capital markets provide the classic examples of Surowiecki's thesis: Even if they are sometimes prone to bouts of enthusiasm or depression, they are an amazing social and economic institution for communicating all kinds of data and knowledge through price changes. The more pervasive the financial markets, the more investors will find and fund profitable ideas and, at the same time, flee from failed management strategies. Of course, the crowd can go spectacularly wrong, as some of the best parts of this book reveal. For instance, the stock market, with its decentralised structure, can go horribly wrong with speculation at times spiralling out of control. The reasons are many: Investors sometimes herd, preferring the safety of the company of others to make independent decisions. They give too much credence to recent high-profile news while underestimating the importance of longer-lasting trends or less dramatic events, in the same way that people worry about being killed in a plane crash while not paying attention to their high cholesterol. Surowiecki doesn't wish away these imperfections. He merely discusses an interesting theory, gives arguments both for and against it, and leaves the judgement to "the wisdom of crowds." The book begins with an interesting anecdote about the popular TV game show "Who wants to be a Millionaire" (remember "Kaun Banega Crorepati?"). The show's gimmick was that if a contestant got stumped by a question, he could pursue three avenues of assistance. First, he could have two of the four multiple-choice answers removed. Second, he could call a person whom, before the show, he had singled out as one of the smartest people he knew. And third, he could poll the studio audience, which would immediately cast its votes by computer. Conventional wisdom says that the "smartest" people would be able to do much better than the crowd of people with nothing better to do on a weekday afternoon than sit in a TV studio. The actual result, however, was an eye-opener: while the "experts" got the right answer 65 per cent of the time, the crowd picked the right answer 91 per cent of the time. Sometimes, "literature in a hurry" can indeed leave a long-lasting impression. The power of collective intelligence |
August 20, 2004
Deciphering crop circlesThere is no denying the mystery of authentic crop circle designs. Their geometric and mathematical perfection do not occur naturally in nature. Science-fiction/fantasy filmmaker M. Night Shyamalan's movie "Signs" cuts straight to the chase. Crop circles are made by aliens who are warning us about . . . something. "The look of crop circles - their strangeness, their sense of mystery and the bizarreness of the designs - is the first thing that attracts people to crop circles. Always," said Steve Canada, who is described as the most prolific book writer on crop circles in the world. Not bad, when you consider he didn't even think much about crop circles until 1990. A few years later, Canada, who lives in California, took an early retirement from his career in social work to devote his life full time to the study and interpretation of crop circles. "Everybody has a different idea of what crop circles mean. And people always believe what they need to believe," said Canada, who will be in Tucson tomorrow to discuss his research. All the designs have always been built on mathematical principles. Just about everybody can agree on that. They are mathematical pictographs - messages in the "language" of mathematics. Once again Canada calls up names of respected scientists. Albert Einstein often said discovering the world of numbers freed him from the more confining world of words. But for many folks, the language of math might as well be the language of Mars, no matter how simply the most basic communications in algebra and calculus are explained. But Canada is convinced crop circles are pictorial representations of a more abstract mathematical language that makes our languages of written words (using the same small collection of letters) seem as primitive as the cave drawings from our own ancient history. All the designs have always been built on mathematical principles. Just about everybody can agree on that. They are mathematical pictographs - messages in the "language" of mathematics. Once again Canada calls up names of respected scientists. Albert Einstein often said discovering the world of numbers freed him from the more confining world of words. But for many folks, the language of math might as well be the language of Mars, no matter how simply the most basic communications in algebra and calculus are explained. But Canada is convinced crop circles are pictorial representations of a more abstract mathematical language that makes our languages of written words (using the same small collection of letters) seem as primitive as the cave drawings from our own ancient history. But what is known for sure is that crop circles do exist. And it's known that the crop circles in England make the British government nervous. At least those particular crop circles, which are astonishingly elaborate with their three-dimensional designs of crops bent over at several different heights. They could not possibly have been made by cynical lads with ropes and boards working in the dark of the night. "Whatever is making the crop circles, the British government considers that to be a foreign force invading their country. And the British army can't stop them," Canada said. "Several years ago the British army was ordered to figure out how to make a crop circle. "So far they haven't able to do it." Whatever is making the crop circles doesn't have any trouble making more. There are no numbers - but they are out there. While most of us spend our working days earning a living, Steve Canada is out there on our behalf with his computer software that pinpoints all manner of exact locations on Earth and in space, juggling the numbers, looking for patterns that will reveal the truth. Deciphering crop circles |
August 20, 2004
Fraud claims by Chavez critics rejectedBy DUDLEY ALTHAUS CARACAS, VENEZUELA - International observers overseeing an audit of Venezuelan President Hugo Chavez's victory in this week's recall referendum concluded Thursday that the opposition's key fraud allegation was baseless. In pressing their claims, opposition leaders argued that a computer program used Sunday in the electronic voting process had limited the number of anti-Chavez votes, automatically switching those above the cap to votes in favor of the president. As evidence, the opposition pointed to hundreds of cases in which different voting machines in the same precincts recorded the exact or nearly exact number of anti-Chavez votes. But a computerized review Thursday of the electronic ballots cast nationwide found that parallel vote totals appeared both for and against Chavez in more than 700 of 12,000 polling stations. The review, conducted by experts from the Atlanta-based Carter Center and the Organization of American States, found exact or nearly matching anti-Chavez vote totals on different machines in 402 stations. But the study also found nearly identical tallies in favor of Chavez in 311 voting places. While seemingly suspicious, the incidence of parallel counts fell within the range of mathematical probability, a Carter Center official said. "The main point here is that it affects both sides," said Jennifer McCoy of the Carter Center, the organization headed by former President Jimmy Carter that observes elections worldwide. "That indicates a random mathematical effect." The Carter Center and the OAS are supervising an audit by the government-controlled National Electoral Council of 359 voting machines from 150 precincts. Auditors are matching the electronic votes cast on each machine with paper receipts, which were then deposited in ballot boxes. The conclusions of the audit are expected to be announced today. But barring any unexpected further evidence presented by the opposition, McCoy said foreign observers don't expect the outcome of the referendum to change. "This is it," McCoy said. "We're trying to give the Venezuelan people the most information possible, so they can draw their own conclusions about the process." Opposition leaders had demanded a review of Sunday's vote almost immediately after the referendum results were announced Monday. On Wednesday, however, they announced they would not recognize the conclusions of the audit, because it was incapable of discovering cyber fraud. Both Carter and Cesar Gaviria, secretary-general of the Organization of American States, have said that the referendum was clean. Fraud claims by Chavez critics rejected |
August 19, 2004
Mathematicians know him by nameSARA ROBINSON, New York Times Shizuo Kakutani, a mathematician known for fundamental tools that have come to bear his name and that are used in disparate fields including economics, died Tuesday in New Haven, Conn. He was 92 and lived in Hamden, Conn. A native of Japan and a professor at Yale for 33 years, Kakutani was known to mathematicians for his influential work in the fields of ergodic theory, functional analysis and Brownian motion, as it relates to probability theory. To economists, he was known for a mathematical tool used to prove theorems about social systems. In a discipline famous for people who work in isolation, Kakutani was remarkable for his gregariousness. Most of his research was done in collaboration with others, and groups of active researchers tended to form around him. "He didn't like to travel far, so people would come to him," said Jal Choksi, an emeritus professor at McGill University in Montreal and a member of Kakutani's circle. The tool he developed, known as the Kakutani fixed-point theorem, was a key step in the original proof of the existence of Nash equilibria, the theorem for which John Forbes Nash received his Nobel Prize. Kakutani's theorem is also used to prove a famous 1954 theorem by the economists Kenneth Arrow and Gerard Debreu, which says that there are prices for goods that balance supply and demand in a complex economy. Both economists also won Nobel Prizes, partly for this work. In the mathematical specialty ergodic theory, a fundamental tool is called the Kakutani skyscraper. Used to describe a random process, like coin flipping, for example, the skyscraper is a way of organizing the process into a picture, with levels that look like the floors of an office tower. This picture makes it easier to understand the properties of the process. In the case of coin flipping, tossing the coin corresponds to ascending one floor in the skyscraper. Mathematicians know him by name |
August 19, 2004
The Accoona French-American Women's World Chess ChampionshipIt's Almira vs Irina in New York |
August 18, 2004
Defence develops smart birds of preyChris Jenkins SWARMS of networked, smart pilotless planes could become part of Australia's defence arsenal if work by from Defence's peak research body is successful. The Adelaide-based Defence Science and Technology Organisation (DSTO) has begun research on a "collective intelligence" for unmanned aerial vehicles (UAVs), using advanced maths to model different scenarios. Groups of small, inexpensive UAVs could be put to work in a variety of missions, including reconnaissance, work in hazardous environments and to carry weapons. "Each agent in the network has its own function while there is an over-arching utility function for the whole system," DSTO mathematician Alex Ryan said. "It is vital that the agents don't work at cross purposes, and they must each be able to react to unexpected circumstances." The project was "working on the edge of chaos", he said. "There's a fine line between systems that are too ordered and stagnate or systems that are too chaotic and collapse into total disorder." UAVs have become a hot topic within Defence, with the government in April announcing a $1 billion program to acquire the US-made Global Hawk aircraft. However, Mr Ryan said groups of smaller less expensive aircraft could be a more cost effective option than large expensive vehicles such as the Global Hawk. The DSTO established a program in December to investigate the use of robots on the battlefield, predicting that various kinds of unmanned vehicles would be part of Australia's mainstream defences within 10 years. One issue that needed to be resolved was the amount of human support each unmanned vehicle required, Mr Ryan said. "At present, each unmanned aircraft needs a support crew of about 30 people," he said. Defence develops smart birds of prey |
August 18, 2004
Mathematical model for the vibratoWith her PhD defended at the Public University of Navarre, telecommunications engineer Ixone Arroabarren has analysed the vibrato, one of the most important tools of classical singers The study applies both to the teaching of singing in music as well as to the medical treatment of voice pathologies. It has put forward a mathematical model for the production of the voice that can be used both in the medical study/detection of pathologies of the vocal chords and speech as well as the teaching of the art of singing. This PhD has been developed within the framework of the research project awarded by CEIN as the best Project for the Transference of Research Result. This model of vibrato production has permitted relating the most important acoustic characteristics - fundamental frequency, timbre and volume, with the most relevant elements in voice production at the level of acoustics, glottal source and response of the vocal tract. In this way we have demonstrated that the features of both elements do not show substantial changes during vibrato, only the fundamental frequency of the glottal excitation varying. All this enables two models of signal production of the vibrato to be put forward. A Non-Interactive Model of Vibrato Production, has enabled relating the most important acoustic characteristics – variations in fundamental frequency, timbre and volume, with and Response of Vocal Tract elements in voice production. With this it has been shown that variations in fundamental frequency generated in the Glottal Source are the cause of the variations in timbre and volume, dependant on both elements of voice production. Besides, there is an Interactive Model of Vibrato Production, which enables us to state that the variations in amplitude and frequency of the harmonics of the acoustic signal can be used to obtain more information about the mechanisms of voice production. Moreover, this model admits the inclusion of additional effects, such as synchronic variations of the Response of the Vocal Tract, which may be related to similar effects identified by other authors through physiological studies. Mathematical model for the vibrato |
August 18, 2004
Cryptography break threatens digital signaturesAlun Williams Researchers in the field of cryptography have been successfully breaking the hash functions that are used to secure the privacy of electronic communications, threatening the integrity of digital signatures, according to a report on Slashdot. Details from the Crypto 2004 conference indicate that one Antoine Joux has broken the hash function used within the SHA-0 algorithm, and there are rumours that somebody is about to announce a partial break of the SHA-1, which is one of most popular cryptographic hash functions (CHF). As well as potentially undermining secure email web connections, such breakthroughs threaten the integrity of digital signatures. The importance of such electronic signatures, for securely underpinning online commerce in the future, can hardly be overstated. The mathematically-based security schemes are the basis for providing any fully-trusted communications. According to the W3C, in an XML Digital Signatures Activity statement: 'Digital signatures provide integrity, signature assurance and non-repudiatability over Web data. Such features are especially important for documents that represent commitments such as contracts, price lists, and manifests. This capability is critical for a variety of electronic commerce applications, including payment tools.' The real impact of these apparent breakthroughs will be measured in the coming weeks or months, as other computer scientists get to grips with the announcements. So called 'one way' hash functions are useful in taking a variable sized input (ie. message content) and producing a finite result, which can then be used within algorithms to both encrypt and then decrypt communications. There results are not reversible, in that the output should not give a predictable guide to their original input. In such a way a 'public key' can be applied to a message encrypted with a 'private key' to reproduce - via mathematical manipulation - the original content of a message. Cryptography break threatens digital signatures |
August 17, 2004
Amplified Intelligence: Machines as Brain BoostersAstrobiology Magazine (AM): The IMHC research agenda broadly seems to cover robotics, cognition and simulations. Are there parts of machine intelligence that your research institute doesn't cover today, but that you see as growth areas? Ken Ford (KF): Don't forget that second letter is 'H'. Although a lot of our research could be categorized as AI, and five of our researchers are AAAI (American Association for Artificial Intelligence) Fellows, IHMC is not a traditional machine intelligence laboratory. The focus and theme of our research is what has become known as human-centered computing which, in a nutshell, is about fitting technology to people instead of fitting people to technology. The human is part of the system, and it is the performance of the whole system, including the human, that we are interested in. This requires that machines should be designed to fit us physically, cognitively, and perhaps even socially. We think of AI as meaning "Amplified Intelligence." The interesting thing is that many traditional AI technologies in fact are being used in just this way. We like to refer to it as building cognitive prostheses, computational systems that leverage and extend human intellectual capacities, just as eyeglasses are a kind of ocular prosthesis. Building cognitive prostheses is fundamentally different from AI's traditional Turing Test ambitions -- it doesn't set out to imitate human abilities, but to extend them. And yet (unlike, say, the ambition of developing artificial insects) it keeps human thought at the center of our science. The "prostheses" metaphor emphasizes the importance of designing systems that fit human beings. I am now typing on a computer that I regard as my cognitive prosthesis, if I lost it I would be lost but unfortunately it doesn't fit me very well. It knows almost nothing about humans, whereas I have to know quite a lot about it. I also had to adapt myself to use it, for example to type on its keyboard: again, fitting humans to machines, rather than machines to humans. The design and fit of these computational prostheses requires a broader interdisciplinary range than has traditionally been associated with AI work, including computer scientists, cognitive scientists, physicians, social scientists of various stripes, and even some philosophers. Current active research areas at IHMC include: adjustable autonomy, advanced interfaces and displays, biologically-inspired robotics, cognitive work analysis, communication and collaboration, computer-mediated learning systems, expertise studies, human strength and endurance amplifying devices, intelligent data understanding, knowledge modeling and sharing, knowledge representation, natural language processing, software agents, work practice simulation. As you can see, this covers more than traditional AI, which is itself now a huge subject, and no single institution could be expected to encompass all of it. Amplified Intelligence: Machines as Brain Boosters |
August 16, 2004
The real datings of the New Testament events are rediscovered.United Kingdom, Douglas, Isle of Man (PRWEB) August 16, 2004 -- The real datings of the New Testament events are rediscovered. The first thing we learn about the temporal localization of the events described in the Gospels is that they took place around the beginning of the New Era, which is supposed to have started 2000 years ago. The roundness and the greatness of this figure are truly a great comfort. All of this knowledge is usually acquired at an early enough age to accept it without questioning later on. We do know that the science confirms the dates and the locations, though. Or does it? A. T. Fomenko, the eminent mathematician, suggests that the Nativity and the Crucifixion can be dated to the XI century AD, and offers bulletproof scientific evidence to support the theory. This sounds a little bit less preposterous once we remember that the modern BC/AD datings were introduced in the XVI-XVII century, and it obviously took them some time to attain global renown. Some extracts from "History: Fiction or Science", which was published in English recently and may well be regarded as the most explosive tractate on history ever written – but every theory it contains, no matter how unorthodox, is backed by solid scientific data: "The Catholic Church has been claiming the "very house" that Virgin Mary had lived in and where "Archangel Gabriel appeared before her" to have been located in the Italian town of Loreto since the XIII century, which means that the Catholic version transfers a part of evangelical events to Italy." "Seeck in his "History of the Ancient World's Decline" wrote that "we have no intention… of picturing his [Christ's – A. F. earthly destiny… all the issues of the origins of Christianity are so complex that we are glad to have the opportunity and the right to leave them well alone". A convenient stance, and one that has got absolutely nothing to do with science." Two quotes from the eminent archaeologist Schwegler offered by Fomenko himself: "This is where the tragedy begins for the believer whose primary need is to know the place on Earth where his Saviour had lived and suffered. But it is the location of the place of his (Christ's) death, that remains covered in impenetrable darkness, if we're to think in archaeological categories." "Apparently, there is no possibility of determining the location of the cities of Nazareth and Capernaum, as well as that of Golgotha etc., on the territory of modern Palestine." Learn more at http://history.mithec.com The real datings of the New Testament events are rediscovered. |
August 15, 2004
Just perfect… or perfectly mad?WALTER PETRYSHYN led a life of American dreams. He soared above his beginnings as a Ukrainian immigrant to become a professor of mathematics at Rutgers University in New Jersey. He lived in a townhouse with his beloved wife Arcadia, a painter and critic of international renown. He wrote a textbook for Cambridge University Press and discovered after publication that it contained an error. His editors didn't mind - they said the error was small, the book was great and selling well, and that correction slips could be sent out. But Petryshyn was upset. It disturbed him that his mistake would be enshrined in print and feared that it would turn him into a laughing stock in an academic community that prizes precision above all else. He descended into paranoia and depression, a spiral whose whirling ended on 6 May 1996, when Petryshyn clubbed his wife to death with a claw hammer. Petryshyn was found "not guilty" on the grounds of insanity, and kept in hospital. It was, said his long-standing colleague, the noted mathematician Felix Browder, "as if his perfectionism drove him to insanity". Gordon Flett, professor of psychology at York University in Toronto, would agree. One of the world's experts on perfectionism, Flett does not subscribe to the fashionable idea that it is a covetable trait that turns its possessor into a high-achieving success. Instead, he believes extreme perfectionism wrecks lives, is a substantial risk factor for depression, anorexia and suicide, and should be classed as a mental disorder. "When perfectionism impairs the ability to function in the workplace, or at home, or is causing distress to either the person or the people around them, then it's a disorder," Flett says. "Often these people aren't aware they have it, nor of the impact it has on others." His analysis lies on one side of an absorbing and timely debate within psychology about whether perfectionist tendencies can ever be a good thing. One camp argues that some forms can be beneficial, or "adaptive". The pernicious form is termed "maladaptive". Flett makes no secret of his disdain for this point of view: "I'd like to ask them what's adaptive about this (the Petryshyn) case. He ended up killing his wife because he made some mistake in a textbook." Just perfect… or perfectly mad? |
August 15, 2004
Don't sell at the last minuteBy Tony Jackson Why is it that people persist in buying shares whose future is, let us say, a trifle murky? If that sounds a patronising question, it is not so intended. My summer reading has included a lively book entitled A mathematician plays the market, by John Allen Paulos. The author, a US maths professor who knows a great deal about the stock market, tells how he bought WorldCom all the way down from $47 a share to under $5 - it then went bankrupt - and muses over what the blazes he thought he was up to. Much of the answer, of course, is psychological. We tend to get stuck with particular numbers - in Paulos's case, the price he first bought at, so that each lower price seemed an opportunity. We embrace arguments that support our position and ignore those that don't. And we hate losses more than we like gains, so we take bigger risks to avoid the former than to secure the latter. But all that only applies if you owned the stock in the first place. What about the people who buy it only after it has hit the slide? Some of those are the perennial market punters: those - often employed on the fringes of stockbroking - who have a touching faith that they are smarter and better-informed than the next guy. Such sheep in wolves' clothing are always with us. But I still think there is a message here about the wider market. Paulos observes that in earlier days, he invested his money prudently in indexed funds. It was only when the bubble came along that he abandoned principles which he knew perfectly well all along. Don't sell at the last minute |
August 14, 2004
Math Olympiad in AthensIvars Peterson The Olympic games in ancient Greece were part of a major religious festival honoring the god Zeus. Every 4 years, men from every corner of the Greek world gathered for several days of celebrations, athletic contests, and ceremonies. The term olympiad refers to the 4-year interval between Olympic games by which time was reckoned in ancient Greece. Inevitably, the games attracted vendors, traders, sculptors, poets, writers, and others—all presenting varied wares to sell to or entertain the many spectators. The Olympic games were not the only athletic contests in ancient Greece. The Pythian games took place at Delphi every 4 years, 2 years after the Olympic games. These games had started off as music contests in honor of the god Apollo, but by 582 B.C., they also included athletic events. The festivities lasted 6 to 8 days and featured various cultural activities. Musicians and actors competed to be the best in playing the flute, singing, or reciting tragedy. In that spirit, modern-day Olympic Games have included a variety of cultural events. This year, as Athens prepared for the latest edition of the Olympic Games, the Hellenic Mathematical Society hosted the 45th International Mathematical Olympiad (IMO), July 6–18. Held annually since 1959, the IMO brings together teams of high school students from around the world to compete in solving extremely challenging math problems. This year's competition in Athens featured six-student teams from 85 countries. Over the course of 2 days, the competing students had 9 hours to solve six problems. In the final team standings, China took first place, followed by the United States and Russia. It was the best U.S. showing since 1994. The IMO also awarded 45 gold medals to the students who managed to "correctly and elegantly" solve all six problems. Overall, the U.S. team earned five gold medals and one silver medal. Oleg Golberg of Bedford, Mass., earned a gold medal and 40 out of 42 possible points, obtaining the best score on the U.S. team. The other gold-medal winners were Tiankai Liu of Saratoga, Calif., (38 points), Aaron Pixton of Vestal, N.Y., (37 points), Alison Miller of Niskayuna, N.Y., (33 points), and Tony Zhang of Arcadia, Calif., (33 points). Miller was the first female gold-medal winner for a team from the U.S. Matt Ince of Arnold, Mo., earned 31 points and a silver medal. Interestingly, Tiankai was a member of the 2001 U.S. IMO team. That team's efforts are vividly described in Steve Olson's book Count Down. He also participated in the 2002 IMO. Tiankai has a Web site at http://www.oocities.org/buniakowski/. How would you do at the IMO? You can find a list of questions (and solutions) featured at these competitions since 1959 at http://www.kalva.demon.co.uk/imo.html. Math Olympiad in Athens |
August 14, 2004
iTunes wireless music streaming crackedApple's wireless streaming technology for iTunes has been cracked to allow it support non-Apple software platforms. Norwegian computer programmer Jon Johansen released a program called JusteForte that defeats the encryption used on Apple's Airport Express on Thursday. Johansen was made famous in 1999 for breaking the encryption used in software called CSS that prevented DVD copying. Airport Express is a small base station that wirelessly connects a computer to the internet or to a local network. It also has an audio socket that can be used to link a computer to a conventional stereo or pair of speakers. This allows music stored digitally to be played remotely. Until now, however, this feature has only been compatible with Apple computers and an add-on for Apple's iTunes audio software called AirTunes. Encryption algorithms Johansen figured out the secret encryption key used to secure the wireless link between a computer and an Airport Express base station and lock other systems out. His program, JusteForte, uses this key to send MP4 digital audio files from a Windows computer to an Airport Express base station. Johansen has also published the encryption key online, opening the way others to design software that can access the base stations. He says Airport Express uses a combination of two encryption algorithms AES and RSA. But precisely how Johansen succeeded in cracking the key is unclear. Cryptographic algorithms encode information by jumbling it up using mathematical formulas and a key consisting of a string of characters. Both algorithms have stood up to extensive testing, so Johansen is likely to have found a weakness in the way these algorithms are implemented rather than the algorithms themselves. "There are lots of ways to break an encryption system," says Bruce Schneier, a renowned cryptography expert. "The lesson is that it's hard to do." Software update Schneier told New Scientist Apple could change the key Airport Express uses via a software update, but that Johansen would probably be able to obtain the new key using the same undisclosed method. Schneier also defends Johansen's actions explaining that he is it is important to test the security of any system. "It's interesting science," he says. "He does it because that's how you learn and we are more secure because he does it." iTunes wireless music streaming cracked |
August 14, 2004
How bacteria fight antibioticsBy Cathy Holding Researchers report in two separate papers in Science this week on novel methods used by bacteria to avoid being killed by antibiotics. In one study, scientists at the Rockefeller University report that the bacterial cells known as persisters, which tolerate but do not become resistant to antibiotics, preexist in a population and that their random switching between normal and slow-growing persister states enables them to escape antibiotic killing. And in an accompanying paper, Stanford University researchers demonstrate that certain antibiotics trigger the SOS response in bacteria, resulting in shutdown of DNA replication and transient dormancy, enabling survival of the antibiotic sensitive bacteria. The SOS response prevents damaged DNA from being copied at cell division, said Christine Miller, lead author of the Stanford study. "It's common throughout the whole plant, animal, bacterial world," she said. Nathalie Balaban's group at the Rockefeller cultured single bacterial cells and monitored the effect on them and their progeny in the presence and absence of antibiotics. "It's a technique that's based on Steve Quake's microfluidic devices, and we just adapted it for this experiment," Balaban said. They found that the slow-growing persisters flip into normal growth mode and back again in a stochastic fashion and therefore escape antibiotic killing. The authors write that even before antibiotic treatment, persisters could be clearly distinguished from the normal cells by their reduced growth rate. The group mathematically modeled the switching from a normal to a persister state and vice versa. "We have described it is as stochastic, but we don't know a specific mechanism [to account for the switch]," Balaban said. How bacteria fight antibiotics |
August 13, 2004
Elkies Wins Ford Math AwardALAN J. TABAK Professor of Mathematics Noam D. Elkies will be awarded the Lester R. Ford Award today by the Mathematical Association of America (MAA), the world's largest organization dedicated to collegiate mathematics education. The Lester R. Ford Award—named after a former editor of American Mathematical Monthly and president of the MAA—was created in 1964 to recognize authors of articles in the magazine that demonstrated expository excellence, according to an MAA press release. MAA officials could not be reached for comment at the Summer MathFest in Providence, R.I., where the award will be given. Elkies' paper examined a series of numbers discovered by influential 18th century mathematician Leonhard Euler. "The rational numbers 1/8, 1/32, 1/96, 5/1536...that occur on the right-hand sides of these formulas are remarkably ubiquitous in mathematics and the mathematical sciences: they pop up in contexts ranging from power series for trig functions, to black-body radiation in physics, to abstruse mathematical disciplines such as K-theory and homotopy groups," Elkies wrote in an e-mail. Elkies' paper consisted of three parts. The first was the presentation of a recent proof of Euler's formulas that Elkies said was not yet well-known in the mathematical community. The second, Elkies wrote, was "a combinatorial problem involving 'up-down permutations' such as 2 < 6 > 1 < 9 > 7 < 8 > 3 < 5 > 4 < 10—the number of ways to distribute the numbers 1 through 10 to make this work is 50521, same as the numerator of the 10th Euler formula." Elkies added that the third aspect of his paper examined "the integrals of 'odd Fourier series' (series that among other things describe physical phenomena such as the sound waves produced by the clarinet—indeed this part of mathematics is sometimes known as 'harmonic analysis'!)." Elkies wrote that he considered one-third of his paper to be original work. "The first two [parts of the paper] constitute the 'expository' part of my paper: the mathematics was known before, and my contribution was only to write about them in a manner that the readers of this journal (typically at or above the level of math majors at an average American college) would find comprehensible and appealing," Elkies wrote. "The third is also 'research,' in that this connection of Fourier series with up-down permutations and the Euler formulas was not known before." "As noted in the citation, the paper is a model of clear exposition showing unexpected and interesting relations between different, seemingly unrelated areas of mathematics," the MAA wrote in its press release. Elkies wrote in an e-mail that he is in California and will not be at the Summer MathFest to collect his certificate and $500 prize money. "It is an unexpected honor and pleasure to have my first Monthly paper recognized by the Lester R. Ford Award," Elkies wrote in an acceptance response that will be included in the prize booklet distributed today. Up to five Lester R. Ford Awards are given each year. The other winners this year included Ruediger Thiele from the Karl-Sudhoff Institute at the University of Leipzig, R. Michael Range from the State University of New York-Albany, and Charles Livingston from Indiana University. —Staff writer Alan J. Tabak can be reached at tabak@fas.harvard.edu. Elkies Wins Ford Math Award |
August 12, 2004
Interview with Bruce Schneier, Counterpane Internet SecurityBruce Schneier, founder and CTO of Counterpane Internet Security, is one of the world's foremost security experts and author of the influential books Applied Cryptography, Secrets & Lies and Beyond Fear. His free monthly newsletter, Crypto-Gram, has over 100,000 readers. Interviewed by Glyn Moody, he discusses the lack of accountability of software companies, security through diversity, and why he would rather re-write Windows than TCP/IP. Q. You've said that Applied Cryptography described a "mathematical utopia" of algorithms and protocols: what was the attraction of that utopia for you? A. Cryptographic security comes from mathematics, not from people and not from machines. Mathematical security is available to everyone, both the weak and the powerful alike, and gives ordinary people a very powerful tool to protect their privacy. That's the cryptographic ideal of security. Q. To what extent is the Internet and its global linking of computers together to blame for the destruction of that utopia? A. They're entirely to blame, although "blame" is not really the right word. Cryptography worked well in the era of radios and telegraphs, where the threat was eavesdropping and mathematical cryptography could protect absolutely. But in the world of computers and networks, the threats are more complex and involve software and system vulnerabilities. Cryptography is much less able to provide security in this new world; that's the cryptographic reality of security. Interview with Bruce Schneier, Counterpane Internet Security |
August 12, 2004
Israeli mathematical formula recognized as crucial milestone in development of InternetAug. 12 - If Robert Kahn is the "Father of the Internet," two Israeli professors just may be its favorite uncles. The Institute of Electrical and Electronics Engineers (IEEE) - the leading standards association for the computer and electronics industry - recently proclaimed the pioneering work of Israelis Jacob Ziv and Abraham Lempel to be an "IEEE Milestone in Electrical Engineering and Computing." The Lempel-Ziv Data Compression Algorithm - a mathematical formula developed by the duo in 1977 - became the basis for maximizing compression and transmission of information between computers. It has contributed significantly to making the Internet a global communications medium. Ziv of the Technion's Faculty of Electrical Engineering received the 1995 Marconi International Fellowship, one of the world's most prestigious engineering honors. He is also a laureate of his country's most significant award -the Israel Prize, as well as the IEEE Richard W. Hamming Medal. Lempel is a past recipient of the Golden Jubilee Award for Technological Innovation from the IEEE Information Theory Society. Israeli mathematical formula recognized as crucial milestone in development of Internet |
August 5, 2004
A point of inspirationDavid McKie On platform one at Derby railway station there's a modest plaque which claims this as the spot where Joseph Paxton conceived the idea for the Crystal Palace. Paxton was not in motion when his moment of breakthrough occurred, merely waiting on the station for a train to London; but the spectacle of high-velocity trains rushing past may have stimulated his powers of imagination. A recent TV programme movingly recreated the moment when Stephen Hawking climbed off a train to chalk on the platform of Cambridge station a diagram of his brand new conception of how life began; though some claim that this version is an embroidery of the truth. Karl Sabbagh's recent book on the Riemann hypothesis, described as the greatest unsolved problem in mathematics, discusses a proof produced by a mathematician called Louis de Branges, a key step of which came to him on a railway platform at Gif-sur-Yvelle. Nor is the humble bus to be excluded. The French mathematician Henri Poincaré, Sabbagh tells us in the same book, described in a lecture how, having spent restless nights trying to prove the non-existence of Fuschian functions, suddenly thought of the answer as he put his foot on the step of a bus taking him to Coutances. A point of inspiration |
Augusy 5, 2004
Shining named perfect scary movieStanley Kubrick's The Shining, starring Jack Nicholson, has been named the perfect scary film, according to a new mathematical formula. The secret of making a scary movie has been calculated by university experts. Scientists have worked out an equation to prove why thrillers like Psycho and the Blair Witch Project are so successful at terrifying audiences. The formula combines elements of suspense, realism and gore, plus shock value, to measure how scary a film is. Researchers spent two weeks watching horror films like The Exorcist, The Texas Chainsaw Massacre, and Silence of the Lambs in pursuit of the formula. The model focuses on three major areas: suspense, realism and gore. Shining named perfect scary movie |
August 5, 2004
Scientists find links between brain circuitry, math abilityBy GEOFF KOCH DALLAS, Texas - Put two piles of coins on a table, one with two pennies and the other with nine. It's a snap to tell where the profit is. Next, compare piles of two and three pennies. Even for a monkey, it's still a quick calculation. Do it again, but this time compare stacks of 16 and 17 coins. Chances are, your selection process slows down. These math tendencies may come from a common set of nerve cell circuits seen in many species, new research suggests. Mathematical intuition may be as much a product of hardwiring as of hard work. Scientists have known for years that young children and animals share the same basic math skills. Researchers suspected that these skills were built on brain circuitry descended from evolutionary ancestors. New ways of peering into heads confirm that the same regions of the brain light up when people and rhesus monkeys judge quantities. "It's not a surprise; more like a relief, actually," says Earl Miller, a neuroscientist at the Massachusetts Institute of Technology. Using scanning technology, Miller and others have found evidence of number-specific circuitry in the brains of people and animals. This same scanning technology, combined with a bit of evolutionary biology, is revealing secrets of the extreme math-elite, and of boys' apparent math advantage over girls. For everyone, genius or otherwise, the brain's processing power is split into two hemispheres. Logical, sequential thinkers often think of themselves as left-brained. Those who are more intuitive and better at synthesizing diverse ideas often tout their right-brained status. It's a rough distinction and there are lots of subtleties that scientists have discovered over the years. For instance, now they know that the left hemisphere is better at perceiving fine details, like individual brush strokes in an impressionist painting. The right hemisphere is better at taking in the big picture. Extreme math-heads are equally good at brush strokes and big-picture processing, O'Boyle reported in a recent issue of the journal Neuropsychology. This suggests lots of interaction and cooperation between hemispheres. Some amount of cooperation between the two sides of the brain happens for everyone. But compared with single-side processing, most people slow down and make more mistakes when using both halves of their head. Math brains, by contrast, work considerably faster and make fewer mistakes when hemispheric handshaking is involved. "The bottom line is that, for spatial reasoning and higher-level tasks, these kids can call on bigger guns than the rest of us," O'Boyle says. Scientists find links between brain circuitry, math ability |
August 4, 2004
Solution to boy genius' problem evades fatherBy Hani M. Bathish and Amira Agarib DUBAI - He can be described as a walking, talking human computer, able to absorb and calculate numbers in the billions and trillions all in his head. And he can calculate the square and cube roots of almost any number, and yet the school system in his native Sudan has branded him as retarded and an autistic. He is 17-year-old Mamoun El Sheikh Haboub A mathematical genius by any standard, his early school days were marked by an unwillingness to sit in class with other children of his own age. He would, instead, go to the higher classes and looking through the window during math lessons he would solve complex math problems written on the blackboard even before the teacher. Mamoun was accepted in a computer course at El Neelein University in Khartoum from April to December 2002 and a report issued by the university states: "We have taught him numerical systems and he has been able to transform numbers from any numerical system to any other numerical system and sometimes he was able to propose new numerical systems. We started teaching him logical mathematics but we have been confronted by his inability to deal with equations or algebra in general despite his knowledge of logarithms and other mathematical skills." Solution to boy genius' problem evades father |
August 2, 2004
Modern Burr PuzzlesEd Pegg Jr. In 1803, the Bestelmeier Toy catalog listed a 6-piece burr puzzle. In 1899, Scientific American introduced a 3-piece burr puzzle by Wilhelm Segerblom. In 1917, US patent 1225760 described a 6-piece burr puzzle. All of these puzzles were slightly difficult to take apart -- interlocking pieces held the puzzle together. Over the next 60 years, millions of similar puzzles were made. Burr designs became so overused that they were considered somewhat trite, as a puzzle type. Modern Burr Puzzles |
August 2, 2004
Fact, Fable, and DarwinBy Rodney Stark I write as neither a creationist nor a Darwinist, but as one who knows what is probably the most disreputable scientific secret of the past century: There is no plausible scientific theory of the origin of species! Darwin himself was not sure he had produced one, and for many decades every competent evolutionary biologist has known that he did not. Although the experts have kept quiet when true believers have sworn in court and before legislative bodies that Darwin's theory is proven beyond any possible doubt, that's not what reputable biologists, including committed Darwinians, have been saying to one another. In keeping with Darwin's views, evolutionists have often explained new species as the result of the accumulation of tiny, favorable random mutations over an immense span of time. But this answer is inconsistent with the fossil record wherein creatures appear "full-blown and raring to go." Consequently, for most of the past century, biologists and geneticists have tried to discover how a huge number of favorable mutations can occur at one time so that a new species would appear without intermediate types. However, as the eminent and committed Darwinist Ernst Mayr explained,The occurrence of genetic monstrosities by mutation...is well substantiated, but they are such evident freaks that these monsters can only be designated as 'hopeless.' They are so utterly unbalanced that they would not have the slightest chance of escaping elimination through selection. Giving a thrush the wings of a falcon does not make it a better flyer....To believe that such a drastic mutation would produce a viable new type, capable of occupying a new adaptive zone, is equivalent to believing in miracles. The word miracle crops up again and again in mathematical assessments of the possibility that even very simple biochemical chains, let alone living organisms, can mutate into being by a process of random trial and error. For generations, Darwinians have regaled their students with the story of the monkey and the typewriter, noting that given an infinite period of time, the monkey sooner or later is bound to produce Macbeth purely by chance, the moral being that infinite time can perform miracles. However, the monkey of random evolution does not have infinite time. The progression from simple to complex life forms on earth took place within a quite limited time. Moreover, when competent mathematicians considered the matter, they quickly calculated that even if the monkey's task were reduced to coming up with only a few lines of Macbeth, let alone Shakespeare's entire play, the probability is far, far beyond mathematical possibility. The odds of creating even the simplest organism at random are even more remote--Fred Hoyle and Chandra Wickramasinghe, celebrated cosmologists, calculated the odds as one in ten to the 40,000th power. (Consider that all atoms in the known universe are estimated to number no more than ten to the 80th power.) In this sense, then, Darwinian theory does rest on truly miraculous assumptions. Fact, Fable, and Darwin |
August 1, 2004
Mind ReadingThe new science of decision making. It's not as rational as you think.By Jerry Adler In the control room next door are Steven Quartz, a Caltech neuroscientist, and Colin Camerer, an economist, who are looking inside my brain to help understand some of the most vexing problems in postmodern society—irrational market bubbles, intractable Third World poverty and loser brothers-in-law who want to borrow $5,000 to open a franchised back-rub parlor. My brain was helping science explain why, despite centuries of progress in economic theory since Adam Smith, actual human beings so often refuse to behave as equations say they should. The new paradigm sweeping the field, under the rubric of "behavioral economics," holds that studying what people actually do is at least as valuable as deriving equations for what they should do. And when you look at human behavior, you discover, as Camerer and his collaborator George Loewenstein of Carnegie Mellon have written, that "the Platonic metaphor of the mind as a charioteer driving twin horses of reason and emotion is on the right track—except that cognition is a smart pony, and emotion a big elephant." The fMRI machine enables researchers in the emerging field of neuro-economics to investigate the interplay of fear, anger, greed and altruism that are activated each time we touch that most intimate of our possessions, our wallets. Mind Reading |