Chess Concept: Running Out of Book

One of the problems with playing against computers is how quickly and how often they change. Grandmasters are used to preparing very deeply for our opponents, researching all of their latest games and looking for weaknesses. Mostly this preparation focuses on openings, the established sequences of moves that start the game and have exotic names like the Sicilian Dragon and the Queen's Indian Defense. We prepare new ideas in these openings, and look for strong new moves ("novelties") with whic...

 Knowledge Work

The growing importance of knowledge as an economic resource reflects the fact that, as economies and production technologies develop, they become ever more complex and specialized, leading to increasing coordination costs. In the language of information economics, the organizational or informational task of coordinating the diverse steps in the productive chain grows, as the number of transactions within and among productive units increases (Joncher, 1983). Logically, the increasingly complex...

 All Failures are the Result of Insufficient Knowledge

Optimism (in the sense that I have advocated) is the theory that all failures—all evils—are due to insufficient knowledge. . . . Problems are inevitable, because our knowledge will always be infinitely far from complete. Some problems are hard, but it is a mistake to confuse hard problems with problems unlikely to be solved. Problems are soluble, and each particular evil is a problem that can be solved. An optimistic civilization is open and not afraid to innovate, and is based on traditi...

 The Magic Circle of Gameplay

In the play-state you experience a protective frame which stands between you and the "real" world and its problems, creating an enchanted zone in which, in the end, you are confident that no harm can come. Although this frame is psychological, interestingly it often has a perceptible physical representation: the proscenium arch of the theater, the railings around the park, the boundary line on the cricket pitch, and so on. But such a frame may also be abstract, such as the rules governing the...

 Teachers Must Put Themselves in the Student's Place

According to Devlin, teachers have a responsibility to learn about kids' interests. "It's not the students' responsibility to put themselves in our place. As teachers, it's our responsibility to put ourselves in the students' place. And if they are in a digital world, where they will invest many hours solving difficult, challenging problems in a video game, it would be criminal if we didn't start where they are and take advantage of the things they want to do. That's the world they live in, t...

 Of All Times in which to Live, You Would Choose Today

I don't think in terms of one year, but I can tell people what I genuinely believe, which is that if we take responsibility in being involved in our own fate if we participate, if we engage, if we speak out, if we work in our communities, if we volunteer, if we see the joy that comes from service to others, then all the problems that we face are solvable despite all the terrible news that you see, despite all the genuine cruelty, pain, and hardship people are experiencing all around the world...

 Mathematical Cue Words

Addition: add, plus, sum, total, altogether, increased by, grew, gained, total of, combined, more than (as in, “3 more than 7 is 10”), put together, in all Subtraction: minus, take away, diff erence, less than, from, remove, subtract, gives away, sells, loses, fewer than, decreased by, diff erence between Multiplication: product, times, doubled (tripled, etc.), some problems give information about one and ask for total amounts (also, when dealing with multiplication of fractions, of us...

 Ways of Being "Good at Math"

It’s a common misconception that someone who’s good at math is someone who can compute quickly and accurately. But mathematics is a broad discipline, and there are many ways to be smart in math. Some students are good at seeing relationships among numbers, quantities, or objects. Others may be creative problem solvers, able to come up with nonroutine ways to approach an unfamiliar problem. Still others may be good at visually representing relationships or problems or translating from one ...

 Political Pragmatism

A reasonable and logical way of doing things or of thinking about problems that is based on dealing with specific situations instead of on ideas and theories. An approach to philosophy, primarily held by American philosophers, which holds that the truth or meaning of a statement is to be measured by its practical (i.e., pragmatic) consequences. William James and John Dewey were pragmatists. Pragmatism in common usage may mean simply a practical approach to problems and affairs. But it’s al...

 Flatland Science: Dimensions

What and where is Flatland? A Square gives us several interesting answers, many of th contradictory. We know that it’s flat, big (but how big?), and very thin, the most important question of all is “how thin?” A lot depends on the answer… A Square himself eliminates the version that’s easiest for three-dimensional readers to understand; a world that’s thin – maybe only a few atoms thick - but nevertheless has some physical height. It would have some sort of solid or semi-solid ...