The auction Web site known as eBay has become a vast marketplace, bringing together buyers and sellers of all sorts of goods. It has also become a handy laboratory for testing ideas in economics about markets and prices.In general, auctions ought to serve as an efficient mechanism for setting prices. Consequently, you would expect that similar items would fetch similar prices.It turns out that on eBay, comparable items may sell for different prices, depending on such factors as whether the sale occurred on a weekend and whether a picture accompanied the item description.These insights come fro...

"Absolute continuity of motion is not comprehensible to the human mind. Laws of motion of any kind become comprehensible to man only when he examines arbitrarily selected elements of that motion; but at the same time, a large proportion of human error comes from the arbitrary division of continuous motion into discontinuous elements."This striking (and perhaps cryptic) passage contrasting the continuous and the discrete starts off the 11th book of the epochal novel War and Peace by Leo Nikolayevich Tolstoy (1828–1920). Tolstoy's tale concerns the tribulations of a group of Russian aristocrats ...

Business firms range in size from boutiques operated by individuals to huge multinational corporations employing thousands. You would expect that there are fewer large businesses than small ones. In economics, however, it's useful to characterize the size distribution of firms more precisely than that. Within an industry, for example, the firm size distribution would indicate the degree of industrial concentration—a quantity that might be of interest in setting antitrust policy.To determine the firm size distribution in the United States, Robert L. Axtell of the Brookings Institution in Washin...

Ladybugs are among the most familiar of beetles. More than 4,000 species are found throughout the world, ranging in size from 4 to 18 millimeters. Also known as lady beetles or ladybirds, these insects (coccinellids) have rounded bodies and bright red, orange, or yellow wing covers, which usually bear an array of contrasting black spots or other markings.Different species generally exhibit distinctive, recognizable patterns. Spot patterns are most common, but some species have stripes or a combination of spots and stripes. In every case, the patterns are symmetric. The position, size, and colo...

Ladybugs are among the most familiar of beetles. More than 4,000 species are found throughout the world, ranging in size from 4 to 18 millimeters. Also known as lady beetles or ladybirds, these insects (coccinellids) have rounded bodies and bright red, orange, or yellow wing covers, which usually bear an array of contrasting black spots or other markings.Different species generally exhibit distinctive, recognizable patterns. Spot patterns are most common, but some species have stripes or a combination of spots and stripes. In every case, the patterns are symmetric. The position, size, and colo...

In the sport of orienteering, a competitor uses a detailed map (and perhaps a compass) to navigate his or her way across varied terrain following a course drawn on the map. Selecting the best available route, each participant races from one marker to the next in the required sequence. The winner is the person who completes the course in the shortest time.Even in recreational orienteering, participants typically start off at staggered times. In that way, each person (or group) navigates the course individually and obtains no help from others on the course. In practice, however, competitors some...

To accompany the telling of a story or recounting of a fable, men of the Chokwe people in south-central Africa traditionally made sand drawings, called sona, to illustrate the tale. These highly stylized geometric illustrations also served as memory aids.The storyteller would clean and smooth the ground, then use his fingertips to press into the sand a rectangular grid of equidistant dots. As he talked, he would trace a winding line among the dots. More often than not, he would draw the line in one continuous motion to create a closed loop. A line could intersect itself but could not be traced...

You're confined to a single lane as you drive along a narrow, winding road. The car in front of you suddenly slows, then just as inexplicably accelerates a short time later, only to slow again. As you keep adjusting to the leading car's erratic speed changes, you sometimes find a clump of vehicles closely tailing you and, at other times, only a few vehicles in sight.From a physicist's point of view, traffic flow can be regarded as a "many-body system of strongly interacting bodies." Various studies have revealed that such systems can show wavelike behavior and abrupt transitions from one state...

You're confined to a single lane as you drive along a narrow, winding road. The car in front of you suddenly slows, then just as inexplicably accelerates a short time later, only to slow again. As you keep adjusting to the leading car's erratic speed changes, you sometimes find a clump of vehicles closely tailing you and, at other times, only a few vehicles in sight.From a physicist's point of view, traffic flow can be regarded as a "many-body system of strongly interacting bodies." Various studies have revealed that such systems can show wavelike behavior and abrupt transitions from one state...

Music publishing was a thriving trade during the latter part of the 18th century in Europe. Publishers vied with one another to print the works of the latest "hot" composer. Many of them looked for novel ways to entice new customers into their music shops.One such ploy was to publish systems that would allow any amateur to compose music without having to know the techniques or rules of composition. The London music publisher Welcker, for example, issued a "Tabular System whereby the Art of Composing Minuets is made so easy that any person, without the least Knowledge of Musick, may compose ten...

Music publishing was a thriving trade during the latter part of the 18th century in Europe. Publishers vied with one another to print the works of the latest "hot" composer. Many of them looked for novel ways to entice new customers into their music shops.One such ploy was to publish systems that would allow any amateur to compose music without having to know the techniques or rules of composition. The London music publisher Welcker, for example, issued a "Tabular System whereby the Art of Composing Minuets is made so easy that any person, without the least Knowledge of Musick, may compose ten...

The simple mathematical concept of a pursuit curve can serve as the starting point for creating wonderfully intricate artistic designs.Pursuit curves can arise in a variety of situations. Suppose, for instance, that four bugs are at the corners of a square. They start to crawl clockwise at a constant rate, each moving toward its neighbor. At any instant, they mark the corners of a square. As the bugs get closer to the original square's center, the new square they define rotates and diminishes in size. In reaching the center, each bug travels on a logarithmic spiral with a length equal to the s...

The simple mathematical concept of a pursuit curve can serve as the starting point for creating wonderfully intricate artistic designs.Pursuit curves can arise in a variety of situations. Suppose, for instance, that four bugs are at the corners of a square. They start to crawl clockwise at a constant rate, each moving toward its neighbor. At any instant, they mark the corners of a square. As the bugs get closer to the original square's center, the new square they define rotates and diminishes in size. In reaching the center, each bug travels on a logarithmic spiral with a length equal to the s...

The simple mathematical concept of a pursuit curve can serve as the starting point for creating wonderfully intricate artistic designs.Pursuit curves can arise in a variety of situations. Suppose, for instance, that four bugs are at the corners of a square. They start to crawl clockwise at a constant rate, each moving toward its neighbor. At any instant, they mark the corners of a square. As the bugs get closer to the original square's center, the new square they define rotates and diminishes in size. In reaching the center, each bug travels on a logarithmic spiral with a length equal to the s...