The visual image is inherently ambiguous: an image of a person on the retina would be the same size for a dwarf seen from up close or a giant viewed from a distance. Perception is partly a matter of using certain assumptions about the world to resolve such ambiguities. We can use illusions to uncover what the brain’s hidden rules and assumptions are. In this column, we consider illusions of shading.
In illustration a, the disks are ambiguous; you can see either the top row as convex spheres or “eggs,” lit from the left, and the bottom row as cavities--or vice versa. This observation reveals that the visual centers in the brain have a built-in supposition that a single light source illuminates the entire image, which makes sense given that we evolved on a planet with one sun. By consciously shifting the light source from left to right, you can make the eggs and cavities switch places.
[More]The visual image is inherently ambiguous: an image of a person on the retina would be the same size for a dwarf seen from up close or a giant viewed from a distance. Perception is partly a matter of using certain assumptions about the world to resolve such ambiguities. We can use illusions to uncover what the brain’s hidden rules and assumptions are. In this column, we consider illusions of shading.
In illustration a, the disks are ambiguous; you can see either the top row as convex spheres or “eggs,” lit from the left, and the bottom row as cavities--or vice versa. This observation reveals that the visual centers in the brain have a built-in supposition that a single light source illuminates the entire image, which makes sense given that we evolved on a planet with one sun. By consciously shifting the light source from left to right, you can make the eggs and cavities switch places.
[More]Editor's Note: Thist story was originally published in the May 1998 edition of Scientific American. We are posting it in light of recent news involving Lehman Brothers and Merrill Lynch.
Months before El Niño– driven storms battered the Pacific Coast of the U.S., the financial world was making its own preparations for aberrant weather. Beginning last year, an investor could buy or sell a contract whose value depended entirely on fluctuations in temperature or accumulations of rain, hail or snow.
[More]Editor's Note: Thist story was originally published in the May 1998 edition of Scientific American. We are posting it in light of recent news involving Lehman Brothers and Merrill Lynch.
Months before El Niño– driven storms battered the Pacific Coast of the U.S., the financial world was making its own preparations for aberrant weather. Beginning last year, an investor could buy or sell a contract whose value depended entirely on fluctuations in temperature or accumulations of rain, hail or snow.
[More]GAMING THE VOTE: WHY ELECTIONS AREN’T FAIR (AND WHAT WE CAN DO ABOUT IT)by William Poundstone. Hill and Wang, 2008
[More]GAMING THE VOTE: WHY ELECTIONS AREN’T FAIR (AND WHAT WE CAN DO ABOUT IT)by William Poundstone. Hill and Wang, 2008
[More]If you ever swim or paddle upstream, you will notice two things. First, a river's speed varies a lot. Second, those variations should cause you to pull harder when you hit rapidly flowing water. If you don't, you will simply make no progress. This puzzle replaces your muscles with a motor, but still asks you to figure out how to trade off energy for time. [More]
If you ever swim or paddle upstream, you will notice two things. First, a river's speed varies a lot. Second, those variations should cause you to pull harder when you hit rapidly flowing water. If you don't, you will simply make no progress. This puzzle replaces your muscles with a motor, but still asks you to figure out how to trade off energy for time. [More]
Have you ever gone to the phone to call a friend only to have your friend ring you first? What are the odds of that? Not high, to be sure, but the sum of all probabilities equals one. Given enough opportunities, outlier anomalies--even seeming miracles--will occasionally happen.
Let us define a miracle as an event with million-to-one odds of occurring (intuitively, that seems rare enough to earn the moniker). Let us also assign a number of one bit per second to the data that flow into our senses as we go about our day and assume that we are awake for 12 hours a day. We get 43,200 bits of data a day, or 1.296 million a month. Even assuming that 99.999 percent of these bits are totally meaningless (and so we filter them out or forget them entirely), that still leaves 1.3 “miracles” a month, or 15.5 miracles a year.
[More]Have you ever gone to the phone to call a friend only to have your friend ring you first? What are the odds of that? Not high, to be sure, but the sum of all probabilities equals one. Given enough opportunities, outlier anomalies--even seeming miracles--will occasionally happen.
Let us define a miracle as an event with million-to-one odds of occurring (intuitively, that seems rare enough to earn the moniker). Let us also assign a number of one bit per second to the data that flow into our senses as we go about our day and assume that we are awake for 12 hours a day. We get 43,200 bits of data a day, or 1.296 million a month. Even assuming that 99.999 percent of these bits are totally meaningless (and so we filter them out or forget them entirely), that still leaves 1.3 “miracles” a month, or 15.5 miracles a year.
[More]It's fourth and goal, and your team is down by three points with seconds left in the game. Do you kick a field goal and try to eke out the win in overtime, or do you go for the touchdown to seal the deal? That was Baltimore Ravens coach Brian Billick's dilemma last December in a game against the 0-13 Miami Dolphins.
NFL teams are notoriously hesitant to go for fourth-down attempts, even when the stakes are much lower. Last year, teams attempted an average of 16.7 fourth-down plays during the entire 16-game regular season. The Ravens tied their game with a field goal but lost in overtime.
[More]It's fourth and goal, and your team is down by three points with seconds left in the game. Do you kick a field goal and try to eke out the win in overtime, or do you go for the touchdown to seal the deal? That was Baltimore Ravens coach Brian Billick's dilemma last December in a game against the 0-13 Miami Dolphins.
NFL teams are notoriously hesitant to go for fourth-down attempts, even when the stakes are much lower. Last year, teams attempted an average of 16.7 fourth-down plays during the entire 16-game regular season. The Ravens tied their game with a field goal but lost in overtime.
[More]By the numbers, the Piedmont Highlanders should not have won so many football games. The squad at the Piedmont, Calif., high school was cobbled together from slim pickings--thanks to an 800-person student body that's half the size of the other schools in their division.
But head coach Kurt Bryan and Steve Humphries, the Highlander's offensive coordinator, invented a secret weapon to keep them competitive: the A-11 offense.
[More]By the numbers, the Piedmont Highlanders should not have won so many football games. The squad at the Piedmont, Calif., high school was cobbled together from slim pickings--thanks to an 800-person student body that's half the size of the other schools in their division.
But head coach Kurt Bryan and Steve Humphries, the Highlander's offensive coordinator, invented a secret weapon to keep them competitive: the A-11 offense.
[More]We humans seem to be born with a number line in our head. But a May 30 study in Science suggests it may look less like an evenly segmented ruler and more like a logarithmic slide rule on which the distance between two numbers represents their ratio (when divided) rather than their difference (when subtracted).
The mathematical idea of a number line--a line of numbers placed in order at equal intervals--is a simple yet surprisingly powerful tool, useful for everything from taking measurements to geometry and calculus.
[More]We humans seem to be born with a number line in our head. But a May 30 study in Science suggests it may look less like an evenly segmented ruler and more like a logarithmic slide rule on which the distance between two numbers represents their ratio (when divided) rather than their difference (when subtracted).
The mathematical idea of a number line--a line of numbers placed in order at equal intervals--is a simple yet surprisingly powerful tool, useful for everything from taking measurements to geometry and calculus.
[More]In the ancient society of Machudo, families wanted no more than three kids. Their eldest son had a chance of becoming king, so they would stop having children after they had their first boy. A family that had three children or had a boy was said to be "complete." [More]
In the ancient society of Machudo, families wanted no more than three kids. Their eldest son had a chance of becoming king, so they would stop having children after they had their first boy. A family that had three children or had a boy was said to be "complete." [More]
[The following is an exact transcript of this podcast.]
[More][The following is an exact transcript of this podcast.]
[More]Eating with TensionThe long, thin beaks of shorebirds called phalaropes are no good at sucking up water and any tasty crustaceans within. Instead they rely on the attractive force of liquid known as surface tension to ferry prey upward. The birds first swim in small, fast circles on the surface of the water, creating a vortex that pulls creatures up within their reach. They next peck at the water and then rapidly open and close their beaks. This scissoring motion both pulls and squeezes droplets, about two millimeters in size, and moves them from the tip of their beaks into their mouths. In experiments with mechanical beaks, scientists at the Massachusetts Institute of Technology and the French National Center for Scientific Research find that the droplets do not move well if the water contains oil, detergents and other pollutants that alter water’s surface tension. Draw in the findings from the May 16 Science.
[More]Eating with TensionThe long, thin beaks of shorebirds called phalaropes are no good at sucking up water and any tasty crustaceans within. Instead they rely on the attractive force of liquid known as surface tension to ferry prey upward. The birds first swim in small, fast circles on the surface of the water, creating a vortex that pulls creatures up within their reach. They next peck at the water and then rapidly open and close their beaks. This scissoring motion both pulls and squeezes droplets, about two millimeters in size, and moves them from the tip of their beaks into their mouths. In experiments with mechanical beaks, scientists at the Massachusetts Institute of Technology and the French National Center for Scientific Research find that the droplets do not move well if the water contains oil, detergents and other pollutants that alter water’s surface tension. Draw in the findings from the May 16 Science.
[More]FINALIST YEAR: 1991 [More]
FINALIST YEAR: 1991 [More]
Readers of this column will recall from last month Sir Birnie, the aristocratic landowner whose bequests used geometry to define his heirs' inheritance. When his first great-grandchild, Emma May, came of age, there was again great excitement. The fortunes of the family had risen and his eldest grandchild, Johanna, had been able to buy out the southern neighbor, so the entire property shown in the original map now belonged to the family--although only after the former neighbor to the south had heavily logged his portion. YZ was now clearly marked and the property extended a full kilometer to the east of the intersection and a half-kilometer to the west.
See image here
[More]Readers of this column will recall from last month Sir Birnie, the aristocratic landowner whose bequests used geometry to define his heirs' inheritance. When his first great-grandchild, Emma May, came of age, there was again great excitement. The fortunes of the family had risen and his eldest grandchild, Johanna, had been able to buy out the southern neighbor, so the entire property shown in the original map now belonged to the family--although only after the former neighbor to the south had heavily logged his portion. YZ was now clearly marked and the property extended a full kilometer to the east of the intersection and a half-kilometer to the west.
See image here
[More]Jane has $3.05 in nickels and quarters. [More]
Jane has $3.05 in nickels and quarters. [More]
Princeton astrophysicist J. Richard Gott discusses some of the realities and speculations of time travel (one human holds the record for time travel--1/48 of a second) as well as how best to evaluate presidential election polling data. Plus, we'll test your knowledge of some recent science in the news. Web sites mentioned on this episode include www.colleyrankings.com, www.snipurl.com/2oorv
Podcast Transcription
[More]Princeton astrophysicist J. Richard Gott discusses some of the realities and speculations of time travel (one human holds the record for time travel--1/48 of a second) as well as how best to evaluate presidential election polling data. Plus, we'll test your knowledge of some recent science in the news. Web sites mentioned on this episode include www.colleyrankings.com, www.snipurl.com/2oorv
Podcast Transcription
[More]FINALIST YEAR: 1993 [More]
FINALIST YEAR: 1993 [More]
Editor's Note: The online puzzles mentioned in the July magazine can be found here.
Millions of people have been perplexed at one time or another by Rubik’s Cube, a fascinating puzzle that took the world by storm in the 1980s. If you somehow missed the puzzle--or the 1980s--the cube is a plastic gizmo that appears to be made up of 27 small cubes, or “cubies,” stacked into a larger cube, three cubies to an edge. Each of the six square faces of the larger cube is colored in one of six eye-catching colors--typically blue, green, orange, red, yellow or white. We said the cube appears to be a stack of cubies, but appearances here are deceptive. An ingenious mechanism, invented in 1974 by a Hungarian teacher named Erno Rubik (and, independently, in 1976 by a Japanese engineer named Terutoshi Ishige), enables any of the six square faces of the large cube to be twisted about the center of that face. Twist the faces in some random sequence five or six times, and you have a cube so scrambled that only an expert--a cubemeister--can restore order. The object of the puzzle is to put an arbitrarily scrambled cube back into its original state, one solid color per face, thereby “solving” the cube.
[More]Editor's Note: The online puzzles mentioned in the July magazine can be found here.
Millions of people have been perplexed at one time or another by Rubik’s Cube, a fascinating puzzle that took the world by storm in the 1980s. If you somehow missed the puzzle--or the 1980s--the cube is a plastic gizmo that appears to be made up of 27 small cubes, or “cubies,” stacked into a larger cube, three cubies to an edge. Each of the six square faces of the larger cube is colored in one of six eye-catching colors--typically blue, green, orange, red, yellow or white. We said the cube appears to be a stack of cubies, but appearances here are deceptive. An ingenious mechanism, invented in 1974 by a Hungarian teacher named Erno Rubik (and, independently, in 1976 by a Japanese engineer named Terutoshi Ishige), enables any of the six square faces of the large cube to be twisted about the center of that face. Twist the faces in some random sequence five or six times, and you have a cube so scrambled that only an expert--a cubemeister--can restore order. The object of the puzzle is to put an arbitrarily scrambled cube back into its original state, one solid color per face, thereby “solving” the cube.
[More]This story is a supplement to the feature "Rubik's Cube Inspired Puzzles Demonstrate Math's "Simple Groups"" which was printed in the July 2008 issue of Scientific American.
Solving the authors’ new puzzles builds on techniques developed for the study of mathematical entities called groups. One essential technique from group theory is specifying a simple, unambiguous system for writing down the elements of the group and how they combine.
[More]This story is a supplement to the feature "Rubik's Cube Inspired Puzzles Demonstrate Math's "Simple Groups"" which was printed in the July 2008 issue of Scientific American.
Solving the authors’ new puzzles builds on techniques developed for the study of mathematical entities called groups. One essential technique from group theory is specifying a simple, unambiguous system for writing down the elements of the group and how they combine.
[More]This story is a supplement to the feature "Rubik's Cube Inspired Puzzles Demonstrate Math's "Simple Groups" which was printed in the July 2008 issue of Scientific American.
M12 Puzzle [More]
This story is a supplement to the feature "Rubik's Cube Inspired Puzzles Demonstrate Math's "Simple Groups" which was printed in the July 2008 issue of Scientific American.
M12 Puzzle [More]
Dear EarthTalk: I want to offer my employees a 401(k) plan that is socially and environmentally responsible. Are there such plans and, if so, where do I look?-- CJ Hughes, Queens, NY
[More]Dear EarthTalk: I want to offer my employees a 401(k) plan that is socially and environmentally responsible. Are there such plans and, if so, where do I look?-- CJ Hughes, Queens, NY
[More]