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]
The Nature of Computation - Intellects Vast and Warm and Sympathetic: "I hand you a network or graph, and ask whether there is a path through the network that crosses each edge exactly once, returning to its starting point. (That is, I ask whether there is a 'Eulerian' cycle.) Then I hand you another network, and ask whether there is a path which visits each node exactly once. (That is, I ask whether there is a 'Hamiltonian' cycle.) How hard is it to answer me?" (via) [more inside]
New math theories reveal the nature of numbers [1,2] - "We prove that partition numbers are 'fractal' for every prime. These numbers, in a way we make precise, are self-similar in a shocking way. Our 'zooming' procedure resolves several open conjectures, and it will change how mathematicians study partitions." (/.|via) [more inside]
"Normal" human pregnancies last 40 weeks, right? Well, no; they can vary quite a bit by the mother's race, age, number of previous children, family history of delivering early or late, home state, work habits, and even the fetus' HLA type. So where does that "40 week" thing come from? Oh, dear. So check out this super-nerdy pregnancy statistics website, from an engineer mom who is collecting data from the public (see the raw data and auto-generated graphs, and read the FAQ about the survey, with more cool graphs). Looking for day-by-day probabilities on when that baby's due? This would be your stats table with daily prediction (adjust dates at top of page as needed). Of course, you could always shut up your constantly inquiring relatives and friends another way.
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.
Raft to the Future: An article about the weirdness of physical models of the universe, how that weirdness correlates to the inherent incompleteness of mathematical systems, and how time itself can emerge at the fringes of these incomplete models.