(By Constable Ichabod Crane (casted by Johnny Depp) in the movie "Sleepy Hollow")
Villainy wears many masks, none of which are more dangerous than virtue.
Friday, December 21, 2007
Wednesday, November 21, 2007
The Matrix - Blue Pill or Red Pill
(Extracted from the initial conversation in the living room between Neo (casted by "Keanu Reeves) and Morpheus (casted by Laurence Fishburne) in the movie "Matrix")
Morpheus: I imagine that right now you're feeling a bit like Alice. Tumbling down the rabbit hole?
Neo: You could say that.
Morpheus: I can see it in your eyes. You have the look of a man who accepts what he sees because he's expecting to wake up. Ironically, this is not far from the truth. Do you believe in fate, Neo?
Neo: No.
Morpheus: Why not?
Neo: 'Cause I don't like the idea that I'm not in control of my life.
Morpheus: I know exactly what you mean. Let me tell you why you're here. You're here because you know something. What you know, you can't explain. But you feel it. You felt it your entire life. That there's something wrong with the world. You don't know what it is, but it's there. Like a splinter in your mind -- driving you mad. It is this feeling that has brought you to me. Do you know what I'm talking about?
Neo: The Matrix?
Morpheus: Do you want to know what it is?
(Neo nods his head.)
Morpheus: The Matrix is everywhere, it is all around us. Even now, in this very room. You can see it when you look out your window, or when you turn on your television. You can feel it when you go to work, or when go to church or when you pay your taxes. It is the world that has been pulled over your eyes to blind you from the truth.
Neo: What truth?
Morpheus: That you are a slave, Neo. Like everyone else, you were born into bondage, born inside a prison that you cannot smell, taste, or touch. A prison for your mind.
(long pause, sighs)
Unfortunately, no one can be told what the Matrix is. You have to see it for yourself. This is your last chance. After this, there is no turning back.
(In his left hand, Morpheus shows a blue pill.)
Morpheus: You take the blue pill and the story ends. You wake in your bed and believe whatever you want to believe.
(a red pill is shown in his other hand)
You take the red pill and you stay in Wonderland and I show you how deep the rabbit-hole goes. (Long pause; Neo begins to reach for the red pill)
Remember -- all I am offering is the truth, nothing more.
(Neo takes the red pill and swallows it with a glass of water)
Morpheus: I imagine that right now you're feeling a bit like Alice. Tumbling down the rabbit hole?
Neo: You could say that.
Morpheus: I can see it in your eyes. You have the look of a man who accepts what he sees because he's expecting to wake up. Ironically, this is not far from the truth. Do you believe in fate, Neo?
Neo: No.
Morpheus: Why not?
Neo: 'Cause I don't like the idea that I'm not in control of my life.
Morpheus: I know exactly what you mean. Let me tell you why you're here. You're here because you know something. What you know, you can't explain. But you feel it. You felt it your entire life. That there's something wrong with the world. You don't know what it is, but it's there. Like a splinter in your mind -- driving you mad. It is this feeling that has brought you to me. Do you know what I'm talking about?
Neo: The Matrix?
Morpheus: Do you want to know what it is?
(Neo nods his head.)
Morpheus: The Matrix is everywhere, it is all around us. Even now, in this very room. You can see it when you look out your window, or when you turn on your television. You can feel it when you go to work, or when go to church or when you pay your taxes. It is the world that has been pulled over your eyes to blind you from the truth.
Neo: What truth?
Morpheus: That you are a slave, Neo. Like everyone else, you were born into bondage, born inside a prison that you cannot smell, taste, or touch. A prison for your mind.
(long pause, sighs)
Unfortunately, no one can be told what the Matrix is. You have to see it for yourself. This is your last chance. After this, there is no turning back.
(In his left hand, Morpheus shows a blue pill.)
Morpheus: You take the blue pill and the story ends. You wake in your bed and believe whatever you want to believe.
(a red pill is shown in his other hand)
You take the red pill and you stay in Wonderland and I show you how deep the rabbit-hole goes. (Long pause; Neo begins to reach for the red pill)
Remember -- all I am offering is the truth, nothing more.
(Neo takes the red pill and swallows it with a glass of water)
Sunday, October 14, 2007
经典对白: 西游记
(By 至尊宝/孙悟空 - 周星驰饰)
曾经有一份至真至诚的爱情放在我面前, 我没有珍惜, 等我失去的时候才后悔莫及, 人世间最痛苦的事莫过于此....
如果上天能够给我一个再来一次的机会, 我会对那个女孩子说三个字: 我爱你.
如果非要在这份爱上加上一个期限, 我希望是.... 一万年.
曾经有一份至真至诚的爱情放在我面前, 我没有珍惜, 等我失去的时候才后悔莫及, 人世间最痛苦的事莫过于此....
如果上天能够给我一个再来一次的机会, 我会对那个女孩子说三个字: 我爱你.
如果非要在这份爱上加上一个期限, 我希望是.... 一万年.
Saturday, September 08, 2007
Wednesday, August 08, 2007
Sunday, July 22, 2007
Point of Law: Hearsay Rule
The Hearsay Rule is an analytic rule of evidence that defines hearsay and provides for both exceptions and exemptions from that rule. Historically, the rule against hearsay is aimed at prohibiting the use of a person's assertion, as equivalent to testimony to the fact asserted, unless the assertor is brought to testify in court on the stand where he may be placed under oath and cross-examined. The theory of the rule against hearsay is that assertions made by human beings are naturally unreliable. It therefore becomes necessary to subject such forms of evidence to “scrutiny or analysis calculated to discover and expose in detail its possible weaknesses, and thus to enable the tribunal to estimate it at no more than its actual value”.
However, some statements are defined as hearsay, but may nevertheless be admissible as evidence in court. These statements relate to exceptions to the general rule on hearsay. Some exceptions to the hearsay rule apply only when the declarant is unavailable for testimony at the trial or hearing.
Hearsay exceptions that apply even where the declarant is available
1. Excited utterances: These are statements relating to startling events or condition made while the declarant was under the stress of excitement caused by the event or condition. An excited utterance does not have to be made at the same time of the startling event. A statement made minutes, hours or even days after the startling event can be excited utterances, so long as the declarant is still under the stress of the startling event.
2. Present sense impressions: These are statements expressing the declarant's impression of a condition existing at the time the statement was made. Unlike an excited utterance, it need not be made in response to a startling event. Instead, it is admissible because it is a condition that the witness would likely have been experiencing at the same time as the declarant, and would instantly be able to corroborate.
3. Declarations of present state of mind: Much like a present-sense impression describes the outside world, declarant's statement to the effect of of his or her emotions will be admissible to prove that the declarant was indeed in that state of mind. This is normally used in cases where the declarant's mental state is at issue. Present-state-of-mind statements are also used as circumstantial evidence of subsequent acts committed by the declarant.
4. Statements made in the course of medical treatment: These are statements made by a patient to a medical professional to help in diagnosis and treatment. Any statements contained therein that attribute fault or causation to an individual will generally not be admissible under this exception, unless it involves a small child as stipulated under the "Tender Years" doctrine.
5. Business records exception: business records created during the ordinary course of business are considered reliable and can usually be brought in under this exception if the proper foundation is laid when the records are introduced into evidence.
6. Guantanamo Bay exception: The military tribunals used to try some Guantanamo Bay prisoners allow any evidence, including hearsay, "if the military judge determines that the evidence would have probative value to a reasonable person".
7. Other exceptions, declarant's availability immaterial: In the United States Federal Rules of Evidence, separate exceptions are made for public records, family records, and records in ancient documents of established authenticity. When regular or public records are kept, the absence of such records may also be used as admissible hearsay evidence.
Hearsay exceptions that apply only where the declarant is unavailable
1. Dying declarations and other statements under belief of impending death:
In the law of evidence, a dying declaration is testimony that would normally be barred as hearsay but may nonetheless be admitted as evidence in certain kinds of cases because it constituted the last words of a dying person.
Under the Federal Rules of Evidence, a dying declaration is admissible if:
1. it constituted the last words of a person who was dying or thought he was dying, and
2. that person was aware that he or she was dying, and
3. that person made a statement, based on their actual knowledge, that relates in some way to the cause or circumstances of his or her death.
The declarant does not actually have to die for the statement to be admissible, but they need to have had a genuine belief that they were going to die, and they must be unavailable to testify in court. Furthermore, the statement must relate to the circumstances or the cause of the declarant's own death. As with all testimony, the dying declaration will be inadmissible unless it is based on the declarant's actual knowledge. In U.S. federal courts, the dying declaration exception is limited to civil cases and homicide prosecutions. It cannot be used in any other kind of criminal proceeding.
2. Declarations against interest: Such declarations are an exception to the rule on hearsay in which a person's statement may be used, where generally the content of the statement is so predjudicial to the person making it (such as confessing to a crime or admitting liability for a tort) that they would not have made the statment unless they believed the statement was true. This differs from a party admission because here the declarant does not have to be a party to the case, but must have a basis for knowing that the statement is true.
3. Prior testimony: if the testimony was given under oath and the party against whom the testimony is being proffered was present and had the opportunity to cross examine the witness at that time. This is often used to enter depositions into the court record at trial.
4. Admission of guilt: if if a statement is made, verbal or otherwise, as an admission of guilt of the matter at hand, that statement would not be regarded as hearsay. In other words, self-incriminating statements or confessions are not hearsay.
However, some statements are defined as hearsay, but may nevertheless be admissible as evidence in court. These statements relate to exceptions to the general rule on hearsay. Some exceptions to the hearsay rule apply only when the declarant is unavailable for testimony at the trial or hearing.
Hearsay exceptions that apply even where the declarant is available
1. Excited utterances: These are statements relating to startling events or condition made while the declarant was under the stress of excitement caused by the event or condition. An excited utterance does not have to be made at the same time of the startling event. A statement made minutes, hours or even days after the startling event can be excited utterances, so long as the declarant is still under the stress of the startling event.
2. Present sense impressions: These are statements expressing the declarant's impression of a condition existing at the time the statement was made. Unlike an excited utterance, it need not be made in response to a startling event. Instead, it is admissible because it is a condition that the witness would likely have been experiencing at the same time as the declarant, and would instantly be able to corroborate.
3. Declarations of present state of mind: Much like a present-sense impression describes the outside world, declarant's statement to the effect of of his or her emotions will be admissible to prove that the declarant was indeed in that state of mind. This is normally used in cases where the declarant's mental state is at issue. Present-state-of-mind statements are also used as circumstantial evidence of subsequent acts committed by the declarant.
4. Statements made in the course of medical treatment: These are statements made by a patient to a medical professional to help in diagnosis and treatment. Any statements contained therein that attribute fault or causation to an individual will generally not be admissible under this exception, unless it involves a small child as stipulated under the "Tender Years" doctrine.
5. Business records exception: business records created during the ordinary course of business are considered reliable and can usually be brought in under this exception if the proper foundation is laid when the records are introduced into evidence.
6. Guantanamo Bay exception: The military tribunals used to try some Guantanamo Bay prisoners allow any evidence, including hearsay, "if the military judge determines that the evidence would have probative value to a reasonable person".
7. Other exceptions, declarant's availability immaterial: In the United States Federal Rules of Evidence, separate exceptions are made for public records, family records, and records in ancient documents of established authenticity. When regular or public records are kept, the absence of such records may also be used as admissible hearsay evidence.
Hearsay exceptions that apply only where the declarant is unavailable
1. Dying declarations and other statements under belief of impending death:
In the law of evidence, a dying declaration is testimony that would normally be barred as hearsay but may nonetheless be admitted as evidence in certain kinds of cases because it constituted the last words of a dying person.
Under the Federal Rules of Evidence, a dying declaration is admissible if:
1. it constituted the last words of a person who was dying or thought he was dying, and
2. that person was aware that he or she was dying, and
3. that person made a statement, based on their actual knowledge, that relates in some way to the cause or circumstances of his or her death.
The declarant does not actually have to die for the statement to be admissible, but they need to have had a genuine belief that they were going to die, and they must be unavailable to testify in court. Furthermore, the statement must relate to the circumstances or the cause of the declarant's own death. As with all testimony, the dying declaration will be inadmissible unless it is based on the declarant's actual knowledge. In U.S. federal courts, the dying declaration exception is limited to civil cases and homicide prosecutions. It cannot be used in any other kind of criminal proceeding.
2. Declarations against interest: Such declarations are an exception to the rule on hearsay in which a person's statement may be used, where generally the content of the statement is so predjudicial to the person making it (such as confessing to a crime or admitting liability for a tort) that they would not have made the statment unless they believed the statement was true. This differs from a party admission because here the declarant does not have to be a party to the case, but must have a basis for knowing that the statement is true.
3. Prior testimony: if the testimony was given under oath and the party against whom the testimony is being proffered was present and had the opportunity to cross examine the witness at that time. This is often used to enter depositions into the court record at trial.
4. Admission of guilt: if if a statement is made, verbal or otherwise, as an admission of guilt of the matter at hand, that statement would not be regarded as hearsay. In other words, self-incriminating statements or confessions are not hearsay.
Friday, June 22, 2007
Anamorphic illusions
Anamorphic illusions refer to optical illusions which are drawn with special distortions in order to create an impression with 3 dimensional effects when observed from one particular viewpoint.
Friday, May 04, 2007
What if Earth never had its own moon?
(By Professor Neil F. Comins of the Department of Astronomy and Physics at the University of Maine in his research findings “What if the moon didn't exist?” — 1993 Harper Collins Publication)
The earth has a substantially large moon orbiting around it, which could not have possibly bulge off due to the earth's high rotational speed or have been captured by the earth's gravity, due to the moon's large mass.
The most likely explanation for the moon's existence would be a colossal accident in space, a collision of unimaginable magnitude where a Mars-sized planet crashed into the earth around 4.25 billion years ago (the age of the Moon). The probability of two planets colliding in the same solar system is extremely remote. Any "normal" collision would not have resulted in the formation of the moon, since the ejecta would not have been thrown far enough from the earth to form the moon. The small planet, before it collided with the earth, must have had an unusually elliptical orbit (unlike the orbit of any other planet in the Solar System), which resulted in a virtual head-on collision.
The collision of the small planet with the earth would have resulted in the ejection of 5 billion cubit miles of the earth's crust and mantle into orbit around the earth. This ring of material, the theory states, would have coalesced to form the moon. In addition, the moon is moving away from the earth (currently at 2 inches per year), as it has been since its creation. If we calculate backwards we discover that the moon must have formed just outside the Roche limit, the point at which an object would be torn apart by the earth's gravity (7,300 miles above the earth's surface). A collision which would have ejected material less than the Roche limit would have formed only rings around the earth. Computer models show that a collision of a small planet with the earth must have been very precise in order for any moon to have been formed at all.
The creation of the moon had a cataclysmal effect on the evolution of life on earth. The collision of the small planet with the earth also resulted in the ejection of the majority of the earth's primordial atmosphere. If this collision had not occurred, we would have had an atmosphere similar to that of Venus, which is 80 times that of the earth (equivalent to being one mile beneath the ocean). Such a thick atmosphere on Venus resulted in a runaway greenhouse affect, leaving a dry planet with a surface temperature of 800°F. The earth would have suffered a similar fate if the majority of its primordial atmosphere had not been ejected into outer space. In fact, the Earth is 20% more massive than Venus and further away from the Sun, both factors of which should have lead to a terrestrial atmosphere much thicker than that of Venus. For some strange reason, we have a very thin atmosphere - just the right density to maintain the presence of liquid, solid and gaseous water necessary to life.
Assuming our earth never had any moon, scientists would first train their eyes on the geo-physical aspects of earth in the new context. It is the tides pattern that would be most significant. There would be no gravitational pull by the moon and whatever tides the earth had would depend only on the pull by the sun. The tides would necessarily be very gentle and restricted within the same range. The tide behaviour would have other far-reaching effects. Powerful tides in our world hit the ocean floor and shorelines in great force and tend to apply a sort of brake on the speed of earths rotation.
During a span of 4.5 billion years the strong gravitational pull of the moon and its effect on tides had been able to lengthen our earthly days from 6 hours at the beginning to 24 hours by slowing down the speed of rotation. Likewise, the gravitational attraction of the earth on the moon has reduced its rotational period to 29 days. A moonless earth, the Professor calculates, would have 8-hour day and a year comprising 1,095 eight-hour days. Its rotation speed would be three times higher than at of our good earth.
Such a rapid rotational period would have resulted in surface wind velocities in excess of 200 miles per hour. Winds are generated by the planet's rotation and the heating and cooling of its air. The rotation drags air along the planet's surface. The faster rotation of the moonless earth would drag air along its equatorial surface much more forcefully than on our earth. There would be much less wind movement to north and south leading to an exceptional global climatic pattern. The fast rotation would cause wind whipping at tremendous speed over the torrid zone, regularly topping 200 miles per hour, while violent hurricanes would continuously hit the surface. A similar situation exists on the Jupiter and the Saturn each having 10-hour days where storms with wind speed around 300 mph rage the surface for years and even for centuries.
Another fortuitous result of the collision of the Mars-sized planet with the Earth is the presence of the Earth's large and heavy metallic core. In fact, the Earth has the highest density of any of the planets in our Solar System. This large nickel-iron core is responsible for our large magnetic field. This magnetic field produces the Van-Allen radiation shield, which protects the Earth from radiation bombardment. If this shield were not present, life would not be possible on the Earth. The only other rocky planet to have any magnetic field is Mercury. But its field strength is 100 times less than the Earth's. Even Venus, our sister planet, has no magnetic field. The Van-Allen radiation shield is a design unique to the Earth.
The earth has a substantially large moon orbiting around it, which could not have possibly bulge off due to the earth's high rotational speed or have been captured by the earth's gravity, due to the moon's large mass.
The most likely explanation for the moon's existence would be a colossal accident in space, a collision of unimaginable magnitude where a Mars-sized planet crashed into the earth around 4.25 billion years ago (the age of the Moon). The probability of two planets colliding in the same solar system is extremely remote. Any "normal" collision would not have resulted in the formation of the moon, since the ejecta would not have been thrown far enough from the earth to form the moon. The small planet, before it collided with the earth, must have had an unusually elliptical orbit (unlike the orbit of any other planet in the Solar System), which resulted in a virtual head-on collision.
The collision of the small planet with the earth would have resulted in the ejection of 5 billion cubit miles of the earth's crust and mantle into orbit around the earth. This ring of material, the theory states, would have coalesced to form the moon. In addition, the moon is moving away from the earth (currently at 2 inches per year), as it has been since its creation. If we calculate backwards we discover that the moon must have formed just outside the Roche limit, the point at which an object would be torn apart by the earth's gravity (7,300 miles above the earth's surface). A collision which would have ejected material less than the Roche limit would have formed only rings around the earth. Computer models show that a collision of a small planet with the earth must have been very precise in order for any moon to have been formed at all.
The creation of the moon had a cataclysmal effect on the evolution of life on earth. The collision of the small planet with the earth also resulted in the ejection of the majority of the earth's primordial atmosphere. If this collision had not occurred, we would have had an atmosphere similar to that of Venus, which is 80 times that of the earth (equivalent to being one mile beneath the ocean). Such a thick atmosphere on Venus resulted in a runaway greenhouse affect, leaving a dry planet with a surface temperature of 800°F. The earth would have suffered a similar fate if the majority of its primordial atmosphere had not been ejected into outer space. In fact, the Earth is 20% more massive than Venus and further away from the Sun, both factors of which should have lead to a terrestrial atmosphere much thicker than that of Venus. For some strange reason, we have a very thin atmosphere - just the right density to maintain the presence of liquid, solid and gaseous water necessary to life.
Assuming our earth never had any moon, scientists would first train their eyes on the geo-physical aspects of earth in the new context. It is the tides pattern that would be most significant. There would be no gravitational pull by the moon and whatever tides the earth had would depend only on the pull by the sun. The tides would necessarily be very gentle and restricted within the same range. The tide behaviour would have other far-reaching effects. Powerful tides in our world hit the ocean floor and shorelines in great force and tend to apply a sort of brake on the speed of earths rotation.
During a span of 4.5 billion years the strong gravitational pull of the moon and its effect on tides had been able to lengthen our earthly days from 6 hours at the beginning to 24 hours by slowing down the speed of rotation. Likewise, the gravitational attraction of the earth on the moon has reduced its rotational period to 29 days. A moonless earth, the Professor calculates, would have 8-hour day and a year comprising 1,095 eight-hour days. Its rotation speed would be three times higher than at of our good earth.
Such a rapid rotational period would have resulted in surface wind velocities in excess of 200 miles per hour. Winds are generated by the planet's rotation and the heating and cooling of its air. The rotation drags air along the planet's surface. The faster rotation of the moonless earth would drag air along its equatorial surface much more forcefully than on our earth. There would be much less wind movement to north and south leading to an exceptional global climatic pattern. The fast rotation would cause wind whipping at tremendous speed over the torrid zone, regularly topping 200 miles per hour, while violent hurricanes would continuously hit the surface. A similar situation exists on the Jupiter and the Saturn each having 10-hour days where storms with wind speed around 300 mph rage the surface for years and even for centuries.
Another fortuitous result of the collision of the Mars-sized planet with the Earth is the presence of the Earth's large and heavy metallic core. In fact, the Earth has the highest density of any of the planets in our Solar System. This large nickel-iron core is responsible for our large magnetic field. This magnetic field produces the Van-Allen radiation shield, which protects the Earth from radiation bombardment. If this shield were not present, life would not be possible on the Earth. The only other rocky planet to have any magnetic field is Mercury. But its field strength is 100 times less than the Earth's. Even Venus, our sister planet, has no magnetic field. The Van-Allen radiation shield is a design unique to the Earth.
Saturday, April 28, 2007
Game theory: Nash Equilibrium
We have applied game theory from a simpler Prisoners' Dilemma situation to a more realistic game model in a real-world example of strategic thinking, say choosing an information system in the followings.
For this example, the players will be a company considering the choice of a new information system, and a supplier who is considering producing it. The two choices are to install a technically advanced or a more proven system with less functionality. We'll assume that the more advanced system really does supply a lot more functionality.
Again, in this case, we can express all this compactly in a payoff table. Basically, the table would indicate that if both the company and supplier choose the technically advanced information system, each earns $20 million in profits from the system, but if the company chooses the advanced system and the supplier does not choose to produce it or vice versa, then both earn nil profits for the period under consideration. However, if both choose the proven information system, then both earn only $5 million of profits each.
We see that both players can be better off, on net, if an advanced system is installed. But the worst that can happen is for one player to commit to an advance system while the other player stays with the proven one. In that case there is no deal, and no payoffs for anyone. The problem is that the supplier and the user must establish a compatible standard, in order to work together, and since the choice of a standard is a strategic choice, their strategies have to mesh.
Although it looks a lot like the Prisoners' Dilemma at first glance, this is a more complicated game. We'll take several complications in turn:
1. By observing the table carefully, we would notice that there are no dominated strategies in this game. The best strategy for each participant depends on the strategy chosen by the other participant. Thus, we need a new concept of game-equilibrium that will allow for that complication. When there are no dominant strategies, we often use an equilibrium conception called the Nash Equilibrium, named after Nobel Memorial Laureate John Nash.
2. Nash Equilibrium occurs when there is a set of strategies with the property that no player can benefit by changing his / her strategy while the other players keep their strategies unchanged. In this case, this set of strategies and the corresponding payoffs constitute the Nash Equilibrium.
3. The Nash Equilibrium is a pretty simple idea: we have a Nash Equilibrium if each participant chooses the best strategy, given the strategy chosen by the other participant. In the example, if the user opts for the advanced system, then it is best for the supplier to do that too. So (Advanced, Advanced) is a Nash-equilibrium.
4. If the user chooses the proven system, it's best for the supplier to do that too. There are as such two Nash Equilibria. It may seem easy enough to opt for the advanced system which is better all around, but if each participant believes that the other will stick with the proven system, then it will be best for each player to choose the proven system. This is a danger typical of a class of games called coordination games -- and what we have learned is that the choice of compatible standards is a coordination game.
5. We have assumed that the payoffs are known and certain. In the real world, every strategic decision is risky -- and a decision for the advanced system is likely to be riskier than a decision for the proven system. Thus, we would have to take into account the players' subjective attitudes toward risk, in other words their risk aversion, to make the example fully realistic.
6. The example assumes that payoffs are measured in money. Thus, we are not only leaving risk aversion out of the picture, but also any other subjective rewards and penalties that cannot be measured in money. Economists have ways of measuring subjective rewards in money terms. To simplify the analysis, we assume that all rewards and penalties are measured in money and are transferable from the user to the supplier and vice versa.
7. Real choices of information systems are likely to involve more than two players, at least in the long run. The user may choose among several suppliers, and suppliers may have many customers. That makes the coordination problem harder to solve. Suppose, for example, that "beta" is the advanced system and "VHS" is the proven system, and suppose that about 90% of the market uses "VHS." Then "VHS" may take over the market from "beta" even though "beta" is the better system. Many economists, game theorists and others believe this is a main reason why certain technical standards gain dominance.
8. On the other hand, the user and the supplier don't have to just sit back and wait to see what the other person does. They can sit down and talk it out, and commit themselves to a contract. In fact, they have to do so, because the amount of payment from the user to the supplier also has to be agreed upon. In other words, unlike the Prisoners' Dilemma, this is a cooperative game, not a non-cooperative game. On the one hand, that will make the problem of coordinating standards easier, at least in the short run. On the other hand, Cooperative games call for a different approach to solution.
For this example, the players will be a company considering the choice of a new information system, and a supplier who is considering producing it. The two choices are to install a technically advanced or a more proven system with less functionality. We'll assume that the more advanced system really does supply a lot more functionality.
Again, in this case, we can express all this compactly in a payoff table. Basically, the table would indicate that if both the company and supplier choose the technically advanced information system, each earns $20 million in profits from the system, but if the company chooses the advanced system and the supplier does not choose to produce it or vice versa, then both earn nil profits for the period under consideration. However, if both choose the proven information system, then both earn only $5 million of profits each.
We see that both players can be better off, on net, if an advanced system is installed. But the worst that can happen is for one player to commit to an advance system while the other player stays with the proven one. In that case there is no deal, and no payoffs for anyone. The problem is that the supplier and the user must establish a compatible standard, in order to work together, and since the choice of a standard is a strategic choice, their strategies have to mesh.
Although it looks a lot like the Prisoners' Dilemma at first glance, this is a more complicated game. We'll take several complications in turn:
1. By observing the table carefully, we would notice that there are no dominated strategies in this game. The best strategy for each participant depends on the strategy chosen by the other participant. Thus, we need a new concept of game-equilibrium that will allow for that complication. When there are no dominant strategies, we often use an equilibrium conception called the Nash Equilibrium, named after Nobel Memorial Laureate John Nash.
2. Nash Equilibrium occurs when there is a set of strategies with the property that no player can benefit by changing his / her strategy while the other players keep their strategies unchanged. In this case, this set of strategies and the corresponding payoffs constitute the Nash Equilibrium.
3. The Nash Equilibrium is a pretty simple idea: we have a Nash Equilibrium if each participant chooses the best strategy, given the strategy chosen by the other participant. In the example, if the user opts for the advanced system, then it is best for the supplier to do that too. So (Advanced, Advanced) is a Nash-equilibrium.
4. If the user chooses the proven system, it's best for the supplier to do that too. There are as such two Nash Equilibria. It may seem easy enough to opt for the advanced system which is better all around, but if each participant believes that the other will stick with the proven system, then it will be best for each player to choose the proven system. This is a danger typical of a class of games called coordination games -- and what we have learned is that the choice of compatible standards is a coordination game.
5. We have assumed that the payoffs are known and certain. In the real world, every strategic decision is risky -- and a decision for the advanced system is likely to be riskier than a decision for the proven system. Thus, we would have to take into account the players' subjective attitudes toward risk, in other words their risk aversion, to make the example fully realistic.
6. The example assumes that payoffs are measured in money. Thus, we are not only leaving risk aversion out of the picture, but also any other subjective rewards and penalties that cannot be measured in money. Economists have ways of measuring subjective rewards in money terms. To simplify the analysis, we assume that all rewards and penalties are measured in money and are transferable from the user to the supplier and vice versa.
7. Real choices of information systems are likely to involve more than two players, at least in the long run. The user may choose among several suppliers, and suppliers may have many customers. That makes the coordination problem harder to solve. Suppose, for example, that "beta" is the advanced system and "VHS" is the proven system, and suppose that about 90% of the market uses "VHS." Then "VHS" may take over the market from "beta" even though "beta" is the better system. Many economists, game theorists and others believe this is a main reason why certain technical standards gain dominance.
8. On the other hand, the user and the supplier don't have to just sit back and wait to see what the other person does. They can sit down and talk it out, and commit themselves to a contract. In fact, they have to do so, because the amount of payment from the user to the supplier also has to be agreed upon. In other words, unlike the Prisoners' Dilemma, this is a cooperative game, not a non-cooperative game. On the one hand, that will make the problem of coordinating standards easier, at least in the short run. On the other hand, Cooperative games call for a different approach to solution.
Wednesday, March 28, 2007
Game theory: Prisoners’ Dilemma
Game theory is a branch of applied mathematics that deals with the analysis of games (i.e., situations involving parties with conflicting interests). It is a mathematical method of decision-making which involves searching for the best strategy contingent upon what another player will or will not do. Typically, a competitive situation is analyzed to determine the optimal course of action for an interested topic. It is generally taught in mathematics classes such as applied combinatorics, and in economics classes such as industrial organization. In addition to the mathematical elegance and complete "solution" which is possible for simple games, the principles of game theory also find applications to complicated games such as cards, checkers, and chess, as well as real-world problems as diverse as economics, property division, politics, and warfare.
Game theory has two distinct branches: combinatorial game theory and classical game theory.
Combinatorial game theory covers two-player games of perfect knowledge such as go, chess, or checkers. Notably, combinatorial games have no chance element, and players take turns.
In classical game theory, players move, bet, or strategize simultaneously. Both hidden information and chance elements are frequent features in this branch of game theory, which is also a branch of economics.
The Prisoners’ Dilemma is a non-zero sum problem founded in game theory initially discussed by Albert W. Tucker. Tucker's invention of the Prisoners' Dilemma example did not come out via a research paper, but in a classroom. In 1950, while addressing an audience of psychologists at Stanford University in his capacity of visiting professor, Tucker created the Prisoners' Dilemma to illustrate the difficulty of analyzing certain kinds of games.
Tucker’s actual Prisoners' Dilemma example is as follows:
Two burglars, Bob and Al, are captured near the scene of a burglary and are given the "third degree" separately by the police. Each has to choose whether or not to confess and implicate the other. If neither man confesses, then both will serve one year on a charge of carrying a concealed weapon. If each confesses and implicates the other, both will go to prison for 10 years. However, if one burglar confesses and implicates the other, and the other burglar does not confess, the one who has collaborated with the police will go free, while the other burglar will go to prison for 20 years on the maximum charge.
The strategies in this case are those of whether to confess or don't confess. The payoffs or penalties in this case, are the sentences served. We can express all this compactly in a payoff table which has become quite standard in game theory. Basically, the table would indicate that if they both confess, each gets 10 years, but if Al confesses and Bob does not, Bob gets 20 and Al goes free, and vice versa. However, if both do not confess, then both get 1 year each.
A dilemma arises in deciding the best course of action in the absence of knowledge of the other prisoner's decision, as in what strategies are "rational" if both men want to minimize the time they spend in jail. Each prisoner's best strategy would appear to be to turn the other in. Al might reason as follows: "Two things can happen: Bob can confess or Bob can keep quiet. Suppose Bob confesses. Then I get 20 years if I don't confess, 10 years if I do, so in that case it's best to confess. On the other hand, if Bob doesn't confess, and I don't either, I get a year; but in that case, if I confess I can go free. Either way, it's best if I confess. Therefore, I'll confess."
But Bob will presumably reason in the same manner. Therefore, given that both of them confess, both will go to prison for 10 years each. Yet, if they had acted "irrationally" and kept quiet, they each could have gotten off with one year each.
What has happened here is that the two prisoners have fallen into something known as "dominant strategy equilibrium".
A dominant strategy is defined as follows:
If we were to allow an individual player in a game to evaluate separately each of the strategy combinations he may face, and, for each combination, choose from his own strategies the one that gives the best payoff. If the same strategy is chosen for each of the different combinations of strategies the player might face, that strategy is called a "dominant strategy" for that player in that game.
Therefore, dominant strategy equilibrium occurs if, in a game, each player has a dominant strategy, and each player plays the dominant strategy, then that combination of the dominant strategies and the corresponding payoffs are said to constitute the dominant strategy equilibrium for that game.
In the Prisoners' Dilemma game, to confess is a dominant strategy, and when both prisoners confess, dominant strategy equilibrium occurs. In this case, the individually rational action results in both persons being made worse off in terms of their own self-interested purposes. This revelation has wide implications in modern social science. This is because there are many interactions in the modern world that seem very much like this, from arms races through road congestion and pollution to the depletion of fisheries and the overexploitation of some subsurface water resources. These are all quite different interactions in detail, but are interactions in which individually rational action leads to inferior results for each person, and the Prisoners' Dilemma suggests something of what is going on in each of them.
A number of critical issues can be raised with the Prisoners' Dilemma in view of its simplified and abstract conception of many real life interactions, and each of these issues has been the basis of a large scholarly literature:
1. The Prisoners' Dilemma is a two-person game, but many of the applications of the idea are really many-person interactions;
2. We have assumed that there is no communication between the two prisoners. If they could communicate and commit themselves to coordinated strategies, we would expect a quite different outcome;
3. In the Prisoners' Dilemma, the two prisoners interact only once. Repetition of the interactions might lead to quite different results;
4. Compelling as the reasoning that leads to the dominant strategy equilibrium may be, it is not the only way this problem might be reasoned out. Perhaps it is not really the most rational answer after all.
The Prisoners' Dilemma has wide applications to economics and business. Let’s take an example of two firms, say A and B, selling similar products. Each must decide on a pricing strategy. They best exploit their joint market power when both charge a high price; each makes a profit of $10 million per month. If one sets a competitive low price, it wins a lot of customers away from the rival. Suppose its profit rises to $12 million, and that of the rival falls to $7 million. If both set low prices, the profit of each is $9 million. In this case, the low-price strategy is akin to the prisoner's confession, and the high-price akin to keeping silent. Let’s term the former cheating, and the latter cooperation. In this case, cheating is each firm's dominant strategy, but the result when both cheat is worse for each than that of both cooperating.
On a superficial level the Prisoners' Dilemma appears to run counter to Adam Smith's idea of the invisible hand. When each person in the game pursues his private interest, he does not promote the collective interest of the group. But often a group's cooperation is not in the interests of society as a whole. Collusion to keep prices high, for example, is not in society's interest because the cost to consumers from collusion is generally more than the increased profit of the firms. Therefore companies that pursue their own self-interest by cheating on collusive agreements often help the rest of society. Similarly cooperation among prisoners under interrogation makes convictions more difficult for the police to obtain. One must understand the mechanism of cooperation before one can either promote or defeat it in the pursuit of larger policy interests.
Would the Prisoners be able to extricate themselves from the Dilemma and sustain cooperation when each has a powerful incentive to cheat? The most common path to cooperation arises from repetitions of the game. In the above example, one month's cheating gets the cheater an extra $2 million. But a switch from mutual cooperation to mutual cheating loses $1 million. If one month's cheating is followed by two months' retaliation, therefore, the result is a wash for the cheater. Any stronger punishment of a cheater would be a clear deterrent.
This idea needs some comment and elaboration:
1. The cheater's reward comes at once, while the loss from punishment lies in the future. If players heavily discount future payoffs, then the loss may be insufficient to deter cheating. Thus, cooperation is harder to sustain among very impatient players.
2. Punishment won't work unless cheating can be detected and punished. Therefore, companies cooperate more when their actions are more easily detected (setting prices, for example) and less when actions are less easily detected (deciding on non-price attributes of goods, such as repair warranties). Punishment is usually easier to arrange in smaller and closed groups. Thus, industries with few firms and less threat of new entry are more likely to be collusive.
3. Punishment can be made automatic by following strategies like "tit for tat," which was popularized by University of Michigan political scientist Robert Axelrod. In this case, you cheat if and only if your rival cheated in the previous round. But if rivals' innocent actions can be misinterpreted as cheating, then tit for tat runs the risk of setting off successive rounds of unwarranted retaliation.
4. A fixed, finite number of repetitions are logically inadequate to yield cooperation. Both or all players know that cheating is the dominant strategy in the last play. Given this, the same goes for the second-last play, then the third-last, and so on. But in practice we see some cooperation in the early rounds of a fixed set of repetitions. The reason may be either that players don't know the number of rounds for sure, or that they can exploit the possibility of "irrational niceness" to their mutual advantage.
5. Cooperation can also arise if the group has a large leader, who personally stands to lose a lot from outright competition and therefore exercises restraint, even though he knows that other small players will cheat. For example, Saudi Arabia's role of "swing producer" in the OPEC cartel is an instance of this.
Game theory has two distinct branches: combinatorial game theory and classical game theory.
Combinatorial game theory covers two-player games of perfect knowledge such as go, chess, or checkers. Notably, combinatorial games have no chance element, and players take turns.
In classical game theory, players move, bet, or strategize simultaneously. Both hidden information and chance elements are frequent features in this branch of game theory, which is also a branch of economics.
The Prisoners’ Dilemma is a non-zero sum problem founded in game theory initially discussed by Albert W. Tucker. Tucker's invention of the Prisoners' Dilemma example did not come out via a research paper, but in a classroom. In 1950, while addressing an audience of psychologists at Stanford University in his capacity of visiting professor, Tucker created the Prisoners' Dilemma to illustrate the difficulty of analyzing certain kinds of games.
Tucker’s actual Prisoners' Dilemma example is as follows:
Two burglars, Bob and Al, are captured near the scene of a burglary and are given the "third degree" separately by the police. Each has to choose whether or not to confess and implicate the other. If neither man confesses, then both will serve one year on a charge of carrying a concealed weapon. If each confesses and implicates the other, both will go to prison for 10 years. However, if one burglar confesses and implicates the other, and the other burglar does not confess, the one who has collaborated with the police will go free, while the other burglar will go to prison for 20 years on the maximum charge.
The strategies in this case are those of whether to confess or don't confess. The payoffs or penalties in this case, are the sentences served. We can express all this compactly in a payoff table which has become quite standard in game theory. Basically, the table would indicate that if they both confess, each gets 10 years, but if Al confesses and Bob does not, Bob gets 20 and Al goes free, and vice versa. However, if both do not confess, then both get 1 year each.
A dilemma arises in deciding the best course of action in the absence of knowledge of the other prisoner's decision, as in what strategies are "rational" if both men want to minimize the time they spend in jail. Each prisoner's best strategy would appear to be to turn the other in. Al might reason as follows: "Two things can happen: Bob can confess or Bob can keep quiet. Suppose Bob confesses. Then I get 20 years if I don't confess, 10 years if I do, so in that case it's best to confess. On the other hand, if Bob doesn't confess, and I don't either, I get a year; but in that case, if I confess I can go free. Either way, it's best if I confess. Therefore, I'll confess."
But Bob will presumably reason in the same manner. Therefore, given that both of them confess, both will go to prison for 10 years each. Yet, if they had acted "irrationally" and kept quiet, they each could have gotten off with one year each.
What has happened here is that the two prisoners have fallen into something known as "dominant strategy equilibrium".
A dominant strategy is defined as follows:
If we were to allow an individual player in a game to evaluate separately each of the strategy combinations he may face, and, for each combination, choose from his own strategies the one that gives the best payoff. If the same strategy is chosen for each of the different combinations of strategies the player might face, that strategy is called a "dominant strategy" for that player in that game.
Therefore, dominant strategy equilibrium occurs if, in a game, each player has a dominant strategy, and each player plays the dominant strategy, then that combination of the dominant strategies and the corresponding payoffs are said to constitute the dominant strategy equilibrium for that game.
In the Prisoners' Dilemma game, to confess is a dominant strategy, and when both prisoners confess, dominant strategy equilibrium occurs. In this case, the individually rational action results in both persons being made worse off in terms of their own self-interested purposes. This revelation has wide implications in modern social science. This is because there are many interactions in the modern world that seem very much like this, from arms races through road congestion and pollution to the depletion of fisheries and the overexploitation of some subsurface water resources. These are all quite different interactions in detail, but are interactions in which individually rational action leads to inferior results for each person, and the Prisoners' Dilemma suggests something of what is going on in each of them.
A number of critical issues can be raised with the Prisoners' Dilemma in view of its simplified and abstract conception of many real life interactions, and each of these issues has been the basis of a large scholarly literature:
1. The Prisoners' Dilemma is a two-person game, but many of the applications of the idea are really many-person interactions;
2. We have assumed that there is no communication between the two prisoners. If they could communicate and commit themselves to coordinated strategies, we would expect a quite different outcome;
3. In the Prisoners' Dilemma, the two prisoners interact only once. Repetition of the interactions might lead to quite different results;
4. Compelling as the reasoning that leads to the dominant strategy equilibrium may be, it is not the only way this problem might be reasoned out. Perhaps it is not really the most rational answer after all.
The Prisoners' Dilemma has wide applications to economics and business. Let’s take an example of two firms, say A and B, selling similar products. Each must decide on a pricing strategy. They best exploit their joint market power when both charge a high price; each makes a profit of $10 million per month. If one sets a competitive low price, it wins a lot of customers away from the rival. Suppose its profit rises to $12 million, and that of the rival falls to $7 million. If both set low prices, the profit of each is $9 million. In this case, the low-price strategy is akin to the prisoner's confession, and the high-price akin to keeping silent. Let’s term the former cheating, and the latter cooperation. In this case, cheating is each firm's dominant strategy, but the result when both cheat is worse for each than that of both cooperating.
On a superficial level the Prisoners' Dilemma appears to run counter to Adam Smith's idea of the invisible hand. When each person in the game pursues his private interest, he does not promote the collective interest of the group. But often a group's cooperation is not in the interests of society as a whole. Collusion to keep prices high, for example, is not in society's interest because the cost to consumers from collusion is generally more than the increased profit of the firms. Therefore companies that pursue their own self-interest by cheating on collusive agreements often help the rest of society. Similarly cooperation among prisoners under interrogation makes convictions more difficult for the police to obtain. One must understand the mechanism of cooperation before one can either promote or defeat it in the pursuit of larger policy interests.
Would the Prisoners be able to extricate themselves from the Dilemma and sustain cooperation when each has a powerful incentive to cheat? The most common path to cooperation arises from repetitions of the game. In the above example, one month's cheating gets the cheater an extra $2 million. But a switch from mutual cooperation to mutual cheating loses $1 million. If one month's cheating is followed by two months' retaliation, therefore, the result is a wash for the cheater. Any stronger punishment of a cheater would be a clear deterrent.
This idea needs some comment and elaboration:
1. The cheater's reward comes at once, while the loss from punishment lies in the future. If players heavily discount future payoffs, then the loss may be insufficient to deter cheating. Thus, cooperation is harder to sustain among very impatient players.
2. Punishment won't work unless cheating can be detected and punished. Therefore, companies cooperate more when their actions are more easily detected (setting prices, for example) and less when actions are less easily detected (deciding on non-price attributes of goods, such as repair warranties). Punishment is usually easier to arrange in smaller and closed groups. Thus, industries with few firms and less threat of new entry are more likely to be collusive.
3. Punishment can be made automatic by following strategies like "tit for tat," which was popularized by University of Michigan political scientist Robert Axelrod. In this case, you cheat if and only if your rival cheated in the previous round. But if rivals' innocent actions can be misinterpreted as cheating, then tit for tat runs the risk of setting off successive rounds of unwarranted retaliation.
4. A fixed, finite number of repetitions are logically inadequate to yield cooperation. Both or all players know that cheating is the dominant strategy in the last play. Given this, the same goes for the second-last play, then the third-last, and so on. But in practice we see some cooperation in the early rounds of a fixed set of repetitions. The reason may be either that players don't know the number of rounds for sure, or that they can exploit the possibility of "irrational niceness" to their mutual advantage.
5. Cooperation can also arise if the group has a large leader, who personally stands to lose a lot from outright competition and therefore exercises restraint, even though he knows that other small players will cheat. For example, Saudi Arabia's role of "swing producer" in the OPEC cartel is an instance of this.
Wednesday, February 28, 2007
Sunday, January 28, 2007
Archimedes Principles
Assume if you will a plastic toy boat loaded with cast iron toy sailors sailing in a tub of water. If all the toy sailors were to fall overboard, the level of water in the tub would theoretically lower.
This is because while in the boat, the toy sailors will displace water which is equivalent to their combined weight, whereas once they are submerged, the toy sailors will displace water which is only equivalent to their combined volume.
This phenomenon will hold true for all items whose densities are greater than that of water which is 1 gm/cm3.
This is because while in the boat, the toy sailors will displace water which is equivalent to their combined weight, whereas once they are submerged, the toy sailors will displace water which is only equivalent to their combined volume.
This phenomenon will hold true for all items whose densities are greater than that of water which is 1 gm/cm3.
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