In today's example of kids smarter than you and I, Wired follows the exploits of two teens competing at the International Olympiad in Informatics.
The OEIS Movie is simply a slideshow of one thousand plots from the Online Encyclopedia of Integer Sequences, at two plots per second with sequence-generated music. [more inside]
A Brief History of Mathematics is a BBC series of ten fifteen-minute podcasts by Professor Marcus du Sautoy about the history of mathematics from Newton and Leibniz to Nicolas Bourbaki, the pseudonym of a group of French 20th Century mathematicians. Among those covered by Professor du Sautoy are Euler, Fourier and Poincaré. The podcasts also include short interviews with people such as Brian Eno and Roger Penrose.
The Geometry of the Snail Ball [pdf] - an interesting article (with some DIY advice at the end) about a toy shop curiosity you may have encountered.
Kaggle hosts competitions to glean information from massive data sets, a la the Netflix Prize. Competitors can enter free, while companies with vast stores of impenetrable data pay Kaggle to outsource their difficulties to the world population of freelance data-miners. Kaggle contestants have already developed dozens of chess rating systems which outperform the Elo rating currently in use, and identified genetic markers in HIV associated with a rise in viral load. Right now, you can compete to forecast tourism statistics or predict unknown edges in a social network. Teachers who want to pit their students against each other can host a Kaggle contest free of charge.
If you look around, you'll see that the ratio of 1.618:1 appears in architecture, nature, and artistic works (such as music, previously). Studied by the Greeks, the Golden Ratio is pretty much everywhere and is common accepted as aesthetically pleasing, and now it has been found to exist down into the nanoscale level, as a byproduct of investigating the Heisenberg Uncertainty Principle. We may not be able to nail down both position and speed, but it appears the macro ratio is an echo of the micro one. [more inside]
The evidence that eating a lot of butter will make you better at math is incomplete. The Butter Mind study, to be run from October 20 - November 12, will test the hypothesis that butter improves math performance.
This new Australian tv quiz show is so awkward it's endearing, and Lily's good at maths! [more inside]
Arthur's Classic Novels has 4000 free ebooks, no registration, nicely organized by author and topics: great old Science Fiction magazines l plentiful online education with 650 books for doctors l a vast collection of famous novels l short stories l by women l Buddhist Scriptures, including The Buddhist Bible, a fave of Jack Kerouac l magazines online l stories by Robert Sheckley l The Autobiography of Charles Darwin l huge collection of fairy tales l philosophy l P. G. Wodehouse l vintage technology l Oscar Wilde l Mark Twain l Rudyard Kipling l George MacDonald l the Koran l a collection of eText resource links. About Arthur Wendover. [more inside]
How do you calculate Pi? Build a supercomputer. The Mountains of Pi, a New Yorker profile of the mathematician (sic) the Chudnovsky brothers. Warning: the article is from 1992, and internet is missing its definite article. (Previously)
Music is Math (lots of different variations on the page. Watch this one in full screen and with headphones.)
"Computers can search all possible outcomes of all possible moves in conventional chess and beat even top human players, so Akl wanted to make the computation more difficult." The result? Quantum chess! [via]
1996 BBC documentary of the proof of Fermat's last theorem is now a Google video. John [Lynch] began researching the project, but Wiles was being very elusive. Although John did not know it, the flaw in Wiles's proof had been found, which is why Wiles was in hiding. Eventually the existence of the flaw emerged, and the TV project was abandoned A year or so later, the flaw was fixed... More at SimonSingh.com.
"Michel de Montaigne, whose essays transformed Western consciousness and literature, was not capable of solving basic arithmetic problems. And most other people would not be able to do so either, if not for the invention of decimal notation by an unknown mathematician in India 1500 years ago." The Greatest Mathematical Discovery? (expanded pdf) a paper written for the US Dept. of Energy makes this assertion based in part on the work of Georges Ifrah. [via] [more inside]
Futurama has always been a haven for geek humor, but last week's episode "The Prisoner of Benda" pushed things to the next level. First hinted at in an American Physical Society interview with showrunner David X. Cohen (previously), staff writer and mathematics Ph.D. Ken Keeler devised a novel mathematical proof based on group theory to resolve the logic puzzle spawned by the episode's brain-swapping (but no backsies!) conceit. Curious how it works? Read the proof (in the show or in plain text), then see it in action using this handy chart. Too much math for a lazy Sunday? Then entertain your brain with lengthy clips from the episode -- including two of the funniest moments in the series in the span of two minutes.
The 300th issue of This Week's Finds in Mathematical Physics will be the last. It is not an exaggeration to say that when John Baez started publishing TWF in 1993, he invented the science blog, and an (academic) generation has now grown up reading his thoughts on higher category theory, zeta functions, quantum gravity, crazy pictures of roots of polynomials, science fiction, and everything else that can loosely be called either "mathematical" or "physics." Baez continues to blog actively at n-category cafe and the associated nLab (an intriguingly fermented commune of mathematicians, physicists, and philosophers.) He is now starting a new blog, Azimuth, "centered around the theme of what scientists can do to help save the planet."
Learn how to operate the world's first fully electronic digital computer in this helpful instructional video. No, not ENIAC - the Atanasoff Berry Computer. Here's an operator's manual. More information about the reconstruction.
Interested in teaching yourself some statistics? Here is an excellent online and interactive statistics textbook developed at UC Berkeley, and also used at CUNY, UCSC, SJSU, and Bard. Here is the syllabus for the course at Berkeley. And here are some insightful reflections from the professor on developing Berkeley's first fully approved online course.
Bruce and Katharine Cornwell are primarily known for a series of remarkable animated films on the subject of geometry. Created on the Tektronics 4051 Graphics Terminal, they are brilliant short films, tracing geometric shapes to intriguing music, including the memorable 'Bach meets Third Steam Jazz' musical score in ‘Congruent Triangles.’
It has applications in Economics, Biology, Pharmaceuticals, and is rooted in State Space Modeling, which with Kalman Filtering (paper, breakdown [warning: long]) was used in the Apollo program. Dynamic Linear Models are gaining in popularity. There exists an R package, and both a short doc and a really great (read: worth buying) book (sorry, not a download, but here's chapter 2) by Giovanni Petris, Sonia Petrone, and Patrizia Campagnoli with its own little website.
Math Is No Match for Locust Swarms. "Mathematicians have now figured out the dynamics that drive locusts across the landscape, devastating everything underfoot — and the math says people will never be able to predict where the little buggers will go. The new analysis, reported in an upcoming issue of Physical Review E, suggests that random factors accumulate and influence how swarming locusts collectively decide to change course. “These swarms are driven by intrinsic dynamics,” says team member Iain Couzin, a biologist at Princeton University. “In all practical terms, predicting when a swarm is going to change direction is going to be impossible." More information here.
Editors of the pop-culture magazine Wired provided the title "iPhone 4’s ‘Retina’ Display Claims Are False Marketing" to a highly critical article about the new iPhone's high-resolution "Retina" display, so-called as the human eye cannot resolve individual pixels when viewing it. A technician who worked on the Hubble telescope disagreed with the Wired editors' choice of rhetoric in very strong technical terms and issued less stringent disagreement with Raymond Soneira, the writer of the piece. Neuroscientist and photographer Bryan Jones published his own highly readable technical analysis of the display's pixel arrangement, that helped him decide whether Apple's claims were truthful or not.
The great[pdf] Russian mathematican Vladimir Igorevich Arnol'd, foremost modern practitioner of classical mechanics, influential teacher, namesake of a minor planet, and semi-nude cross-country skier has died.
"Gary Foshee, a collector and designer of puzzles from Issaquah near Seattle walked to the lectern to present his talk. It consisted of the following three sentences: "I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"" [more inside]
Plus magazine has compiled all their articles on mathematics and the arts into one handy-dandy page full of highly enjoyable articles ranging from limericks and screeching violins to the restoration of frescoes.
Dan Meyer is a high school math teacher with a clever idea: make math about the real world. On his blog, he writes about classroom management, the real skills of teaching, labels, information design, and assessment.
Since its first printing in 1964, Abramowitz and Stegun's Handbook of Mathematical Functions has been a standard (and public domain) reference manual for special functions and applied mathematics. This week, NIST released its successor, the Digital Library of Mathematical Functions, online to the public.
If politicians were mathematicians. "I would like to suggest two systems for parliamentary votes, one that would weaken the party system but without killing it off entirely, and one that would protect large minorities. Neither has the slightest chance of being adopted, because they are both too complicated to be taken seriously. But mathematicians wouldn’t find them complicated at all — hence the title of this post." Fields medalist Tim Gowers messes around with political axioms.
A generating function is a way to keep track of a lot of related numbers all at once... The study of generating functions is an art and a science known as 'generatingfunctionology,' and its bible is free for all to download. [more inside]
Every number from 1 to 9,999 has a special meaning. (much mathematical terminology, scrolling)
Robert Hodgin's Magnetic sculptures: "These forms are created with cylinder magnets, spherical magnets, and ball bearings. Magnetism is the only thing holding the forms together. They are fairly fragile and picking them up will likely crush them. All of the forms I created were variations of the 12 sided dodecahedron. This particular platonic solid seems to be the form the magnets are happiest with." [via]
Mathematics Illuminated is a set of thirteen surveys in varied topics in mathematics, nicely produced with video, text, and interactive Flash gadgets for each of the topics.
"Crazy as it sounds, over the next several weeks I’m going to try to do something close to that. I’ll be writing about the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject — but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it." Mathematics in the pages of the New York Times! [more inside]
"Take a little bad psychology, add a dash of bad philosophy and ethics, and liberal quantities of bad logic, and any economist can prove that the demand curve for a commodity is negatively inclined." MIT economist Andrew Lo and string theorist turned asset manager Mark Mueller on the "physics envy" that plagues economics, and how to stop worrying and love uncertainty.
Trigonometric Delights. This book is neither a textbook of trigonometry—of which there are many—nor a comprehensive history of the subject, of which there is almost none. It is an attempt to present selected topics in trigonometry from a historic point of view and to show their relevance to other sciences. It grew out of my love affair with the subject, but also out of my frustration at the way it is being taught in our colleges.
Sure, big numbers are fine. But infinity (in the set theoretic sense) is where the fun really starts. Developed almost entirely by one man in the late 19th century, set theory now forms the foundation of modern mathematics. Cantor showed that not all infinite sets are the same size. Notably, while there are just as many integers as rational numbers, there are more real numbers than integers. These results, along with others that soon followed like the axiom of choice, led to several fascinating consequences: [more inside]
Everyone knows about the Six Degrees of Kevin Bacon, right? Pursuant to this authoritative source I learned of Erdos numbers, which are fascinating in their own right, but not nearly as much as Erdos-Bacon numbers. Sir Alec Guiness does surprisingly well with a 3. Bacon does not. [more inside]
There's always been hyperbole in fashion; but fashion became truly hyperbolic this week when mathematican William Thurston, winner of a 1982 Fields Medal for his revolutionary re-envisioning of low-dimensional topology and geometry, teamed up with designer Dai Fujiwara (of the house of Issey Miyake) to produce a Paris runway show based on the fundamental geometries of 3-dimensional spaces. Thurston and Fujiwara briefly interviewed. Thurston's famous essay "Proof and Progress in Mathematics" concerns, among other things, Thurston's belief that the production of mathematical understanding can be carried out by means other than the writing down of formal proofs (though fashion shows are not specifically mentioned.) Previously in wearable non-Euclidean geometry: Daina Taimina's hyperbolic skirt.
Uncoiling the spiral: Maths and hallucinations So common are these geometric hallucinations, that in the last century scientists began asking themselves if they couldn't tell us something fundamental about how our brains are wired up. And it seems that they can. (via MAPS)
Early elementary school teachers in the United States are almost exclusively female (>90%), and we provide evidence that these female teachers’ anxieties relate to girls’ math achievement via girls’ beliefs about who is good at math. A study (abstract and full-text [pdf]) by the University of Chicago Department of Psychology and Committee on Education found a link between math anxiety in elementary school teachers and their female students' math abilities. [more inside]
From 1980 - 1988, a science education series called 3-2-1 Contact ran on PBS. Produced by Children's Television Workshop, the series was geared toward an older audience than other popular CTW offerings Sesame Street and The Electric Company, and focused on teaching kids about science, math and the world around them. [more inside]
Nontransitive dice are sets of dice (A, B, C, etc.) with counterintuitive properties: die A beats die B and die B beats die C, but die C beats die A. [more inside]
The Sexaholics of Truthteller Planet - yes, it's one of those rotten logic problems, one of many that can be found at Tanya Khovanova’s Math Guide to the MIT Mystery Hunt.