Can you ever be reasonably sure that something is random, in the same sense you can be reasonably sure something is not random (for example, because it consists of endless nines)? Even if a sequence looked random, how could you ever rule out the possibility that it had a hidden deterministic pattern? And what exactly do we mean by “random,” anyway?
Computers are providing solutions to math problems that we can't check - "A computer has solved the longstanding Erdős discrepancy problem! Trouble is, we have no idea what it's talking about — because the solution, which is as long as all of Wikipedia's pages combined, is far too voluminous for us puny humans to confirm." (via; previously ;)
Based on the Wheat and Chessboard problem, the Chess Board Clock is "a binary clock counting down 2 to the 63rd power in hundredths of a second". The first few squares go by super fast (a non-seizure mode is available) while the last square won't be reached for over 2 billion years. [via mefi projects]
Arthur C. Clarke, Benoit Mandelbrot, Stephen Hawking, David Gilmour and many more trip the fuck out about Fractals, the Colors of Infinity.
Polyhedra and the Media - On the new polyhedra of Schein and Gayed, and mathematical journalism.
Finite time blowup for an averaged three-dimensional Navier-Stokes equation - "[Terence Tao] has shown that in an alternative abstract universe closely related to the one described by the Navier-Stokes equations, it is possible for a body of fluid to form a sort of computer, which can build a self-replicating fluid robot that, like the Cat in the Hat, keeps transferring its energy to smaller and smaller copies of itself until the fluid 'blows up.' " [1,2,3] (previously)
The Teaching of Arithmetic: The Story of an experiment. In the fall of 1929 I made up my mind to try the experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite - my new Three R's. And by reciting I did not mean giving back, verbatim, the words of the teacher or of the textbook. I meant speaking the English language. I picked out five rooms - three third grades, one combining the third and fourth grades, and one fifth grade. I asked the teachers if they would be willing to try the experiment.
Discovering Free Will (Part II, Part III) - a nice discussion of the Conway-Kochen "Free Will Theorem". [more inside]
Network Theory Overview - "The idea: nature and the world of human technology are full of networks! People like to draw diagrams of networks. Mathematical physicists know that in principle these diagrams can be understood using category theory. But why should physicists have all the fun? This is the century of understanding living systems and adapting to life on a finite planet. Math isn't the main thing we need, but it's got to be part of the solution... so one thing we should do is develop a unified and powerful theory of networks." (via ;)
You Should Always Get the Bigger Pizza (SL NPR blog post w/interactive graph)
Astroblast and Overstepping Artifacts are music videos by the project Musicians with Guns, which take the viewer through detailed tours of some beauty. Relax and enjoy.
Each month, the Notices of the American Math Society runs a column called "What is...." which aims to explain an advanced mathematical concept in two pages, at a level accessible to a good undergrad math major. Armin Straub, a postdoc at Illinois, has collected them all in one place. [more inside]
Reaction-diffusion reactions used to design housewares, puzzles, and more. If you want to experiment yourself, you might get some ideas from the demos at WebGL Playground or you might use this brief intro as a jumping-off point.
Geogebra is an interactive geometry tool which started as a free clone of Geometer's Sketchpad, but is now also an algebra, statistics and calculus tool. It is available for download for Windows, Mac, Linux, iOS and Android, or as a web app. [more inside]
Visual Patterns. Here are the first few steps. What's the equation?
Open warfare erupts in the world of mathematical biology, as Lior Pachter of UC-Berkeley writes three blog posts attacking two papers in Nature Bioscience, accusing one of them of being "dishonest and fraudulent": The Network Nonsense of Albert-Laszlo Barabasi, The Network Nonsense of Manolo Kellis, and Why I Read the Network Nonsense Papers. Kellis (MIT) and his co-authors respond (.pdf.)
The Hierarchy of Hexagons. School geometry seems to me one of the most lifeless topics in all of mathematics. And the worst of all? The hierarchy of quadrilaterals.
What would happen if a cue ball struck a rack of 15 perfectly round, frictionless billiard balls, exactly head-on?
How a Math Genius Hacked OkCupid to Find True Love
“I think that what I did is just a slightly more algorithmic, large-scale, and machine-learning-based version of what everyone does on the site,” McKinlay says. Everyone tries to create an optimal profile—he just had the data to engineer one.[more inside]
M.I.T. professor Max Tegmark explores the possibility that math does not just describe the universe, but makes the universe.
1 + 2 + 3 + 4 + 5 ... = -1/12 -- Numberphile explains a counter-intuitive summation of an infinite series. [more inside]
"The IPython Notebook is a web-based interactive computational environment where you can combine code execution, text, mathematics, plots and rich media into a single document". It can be installed faily easily with anaconda or on Amazon EC2. Various interesting notebooks are to be found at the official Notebook Viewer site Another collection of interesting notebooks on many topics. [more inside]
It's a bit late for the holiday, but math(s) comedian Helen Arney sings about her Christmas wish -- the largest known Mersenne Prime, Mersenne 48. [more inside]
According to statistician Aki Vehtari of Aalto University in Finland, there is diminished 20% chance that today, December 25th, is your birthday. There is a 5% higher likelihood than chance that your birthday is actually February 14th. [more inside]
Charan Langton (blog) hosts Complex To Real: which "...offers tutorials I have written on various topics in analog and digital communications that will help you cut through this complexity." [more inside]
531 of the most interesting articles on Wikipedia covering everything from the linguistic (self-contradicting words in English) to the philosophical (The Ultimate 747 Gambit); from the only German military landing in the Americas (Weather Station Kurt) to the world's only Bigfoot Trap; to oddities both geometric (Gömböc ) and mathematical (Tupper's self-referential formula); great lists of various things (Bible errata, unsolved problems, camouflage patterns, blurred spots on Google Maps, lost art, the last monarchs of the Americas) to things that will make great band names (Orbiting Frog Otolith). [prev, shorter lists]
Watching one of the exciting snow-bound football games yesterday, the thought may have occurred to you: If I was a coach, would I go for it on this 4th down? This bot from the New York Times will tell you, and maybe even add a little attitude to the answer, which is usually much more aggressive than NFL coaches.
Recently Emily Graslie, of the fantastic natural history tumblr and youtube series TheBrainScoop, was asked a question about whether she had personally experienced sexism in her field. Her response is fucking amazing.
Inside is her goldmine of awesome female science educators online with channels that focus on Science Technology Engineering and Math. My work day is fucked.[more inside]
Closing in on the twin prime conjecture (Quanta) - "Just months after Zhang announced his result, Maynard has presented an independent proof that pushes the gap down to 600. A new Polymath project is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower." [more inside]
Beijing and Amsterdam-based studio NEXT architects have won first place in a bridge design competition for Meixi Lake near the Changsha capital in Hunan, China. The shape was inspired by the Mobius Strip and Chinese knotting.
"Psychologists Lisa Blackwell, Kali Trzesniewski, and Carol Dweck [found that] convincing students that they could make themselves smarter by hard work led them to work harder and get higher grades. The intervention had the biggest effect for students who started out believing intelligence was genetic."
"He calls this the Tao of Hawkeye. You can’t just have a database around Hawkeye, right? Not if you really want to understand Hawkeye over time. Because Hawkeye isn’t just Hawkeye. He’s also Ronin and Goliath and Clint Barton. Sometimes he’s dead. Oh, and by the way: he started as a villain. Who remembers that? -- Back in the eighties people like Mark Gruenwald and Peter Sanderson guarded Marvel Comics' continuity. These days Peter Olson tries to do the same for a much bigger Marvel using science and math.
The Washington Post reports on a ridiculous mathematics test for first graders administered under New York's Common Core standards initiative. [Common Core previously.]
io9 takes a look at why the number 1729 shows up in so many Futurama episodes. It's mathtastic!
Amaze Your Friends, Solve World Hunger; How to Create Chocolate out of Nothing! [slyt]
Walter Hickey at Business Insider looks at when you should buy a Powerball ticket and whether to take the lump sum or annuity if you win.
This is one example of a phenomenon I noticed throughout this chart: natural rival franchises tend to have similar numbers of goon seasons. This would suggest that goon employment may be (in some instances) localized arms races between rivals, whose cyclical number of goons tends to reflect the other’s in some perverted game of Mutually Assured Terrible Hockey (MATH)... We also have a team like Detroit near the bottom of the list, with only 8.5 goon seasons in their history. Since 1985-86, the Wings have only had 4.5 goon seasons. They’ve only had 2 goon seasons since 1988-89. Coincidentally, they’ve been pretty damned swell at winning hockey games since that time. The Evolution of Goon Culture in the NHL
Revelations in the field of quantum physics have resulted in the discovery of the Amplituhedron, a jewel-like higher dimensional object whose volume elegantly predicts fundamental physical processes that took the brilliant Dr. Richard Feynman hundreds of pages of abstruse mathematics to describe. The theoretical manifold not only enables simple pen-and-paper calculation of physics that would normally require supercomputers to work out, but also challenges basic assumptions about the nature of reality -- forgoing the core concepts of locality and unitarity and suggesting that space and time are merely emergent properties of a timeless, infinitely-sided "master amplituhedron," whose geometry represents the sum total of all physical interactions. More: The 152-page source paper on arXiv [PDF] - Lead author Nima Arkani-Hamed's hour-long lecture at SUSY 2013 - Scans of Arkani-Hamed's handwritten lecture notes - A far more detailed lecture series "Scattering Without Space Time": one, two, three - Arkani-Hamed previously on MeFi - A hot-off-the-presses Wikipedia page (watch this space)
If the NSA is able to break through banks' computer security, does that mean it solved the prime factorization problem? The New York Times reported recently that “the agency has circumvented or cracked much of the encryption, or digital scrambling, that guards global commerce and banking systems.” Since banks' encryption codes rely on the fact that nobody knows how to find the prime factors of really large numbers, it could mean that the NSA has found a way to do that. Or it could mean that the NSA has simply gotten lots of banks to give up their information, or found other ways around their encryption. But if they've cracked this long-standing math problem, might the secret leak? What would be the effects?
The Movie Math Quiz: Can you figure out which movies are being described by these mathematical equations?
Wonkblog has a new advice column called "Dear Dylan" where Dylan Matthews answers the usual advice column staples using game theory, mathematics and charts.
Paperscape is a searchable 2-dimensional visualization of the 800,000+ scientific papers (mostly in physics and math) on the arXiv preprint server.
This is a visualization of Beach Boys vocals inspired by the physics of church bells. Using a mathematical relationship between a the circumference of a circular surface and pitch, I wrote code that draws a circle for each note of the song. (Single Link Vimeo)
You Can't Do Simple Maths Under Pressure (autoplay music)