1) Which is the only country in the world to have dropped bombs on over twenty different countries since 1945?
2) Which is the only country to have used nuclear weapons?
3) Which country was responsible for a car bomb which killed 80 civilians in Beirut in 1985, in a botched assassination attempt, thereby making it
the most lethal terrorist bombing in modern Middle East history?
4) Which country's illegal bombing of Libya in 1986 was described by the UN
Legal Committee as a "classic case" of terrorism?
5) Which country rejected the order of the International Court of Justice (ICJ) to terminate its "unlawful use of force" against Nicaragua in 1986,
and then vetoed a UN Security Council resolution calling on all states to observe international law?
6) Which country was accused by a UN-sponsored truth commission of providing "direct and indirect support" for "acts of genocide" against
the Mayan Indians in Guatemala during the 1980s?
7) Which country unilaterally withdrew from the Anti-Ballistic Missile (ABM) Treaty in December 2001?
8) Which country renounced the efforts to negotiate a verification process for the Biological Weapons Convention and brought an international
conference on the matter to a halt in July 2001?
9) Which country prevented the United Nations from curbing the gun trade at
a small arms conference in July 2001?
10) Aside from Somalia, which is the only other country in the world to have refused to ratify the UN Convention on the Rights of the Child?
11) Which is the only Western country which allows the death penalty to be
applied to children?
12) Which is the only G7 country to have refused to sign the 1997 Mine Ban Treaty, forbidding the use of landmines?
13) Which is the only G7 country to have voted against the creation of the
International Criminal Court (ICC) in 1998?
14) Which was the only other country to join with Israel in opposing a 1987
General Assembly resolution condemning international terrorism?
15) Which country refuses to fully pay its debts to the United Nations yet reserves its right to veto United Nations resolutions?
answer to all 15 questions:
The United States of America
Wednesday, February 21, 2007
Fermat’s Last Theorem
Fermat’s Last Theorem, in mathematics, famous theorem which has led to important discoveries in algebra and analysis. It was proposed by the French mathematician Pierre de Fermat. While studying the work of the ancient Greek mathematician Diophantus, Fermat became interested in the chapter on Pythagorean numbers—that is, the sets of three numbers, a, b, and c, such as 3, 4, and 5, for which the equation a^2 + b^2 = c^2 is true. He wrote in pencil in the margin, “I have discovered a truly remarkable proof which this margin is too small to contain.” Fermat added that when the Pythagorean Theorem is altered to read a^n + b^n = c^n, the new equation cannot be solved in integers for any value of n greater than 2. That is, no set of positive integers a, b, and c can be found to satisfy, for example, the equation a^3 + b^3 = c^3 or a^4 + b^4 = c^4.
Fermat’s simple theorem turned out to be surprisingly difficult to prove. For more than 350 years, many mathematicians tried to prove Fermat’s statement or to disprove it by finding an exception. In June 1993, Andrew Wiles, an English mathematician at Princeton University, claimed to have proved the theorem; however, in December of that year reviewers found a gap in his proof. On October 6, 1994, Wiles sent a revised proof to three colleagues. On October 25, 1994, after his colleagues judged it complete, Wiles published his proof.
Despite the special and somewhat impractical nature of Fermat’s theorem, it was important because attempts at solving the problem led to many important discoveries in both algebra and analysis.
Note a^n means "a" raised to nth power
Fermat’s simple theorem turned out to be surprisingly difficult to prove. For more than 350 years, many mathematicians tried to prove Fermat’s statement or to disprove it by finding an exception. In June 1993, Andrew Wiles, an English mathematician at Princeton University, claimed to have proved the theorem; however, in December of that year reviewers found a gap in his proof. On October 6, 1994, Wiles sent a revised proof to three colleagues. On October 25, 1994, after his colleagues judged it complete, Wiles published his proof.
Despite the special and somewhat impractical nature of Fermat’s theorem, it was important because attempts at solving the problem led to many important discoveries in both algebra and analysis.
Note a^n means "a" raised to nth power
Monday, January 15, 2007
What does love mean?
A group of professional people posed this question to a group of 4 to 8 year-olds,
"What does love mean?"
The answers they got were broader and deeper than anyone could have imagined. See what you think:
"When my grandmother got arthritis, she couldn't bend over and paint her
toenails anymore. So my grandfather does it for her all the time, even when his hands got
arthritis too. That's love."
Rebecca- age 8
"When someone loves you, the way they say your name is different. You just know that your name is safe in their mouth."
Billy - age 4
"Love is when a girl puts on perfume and a boy puts on shaving cologne and they go out and smell each other."
Karl - age 5
"Love is when you go out to eat and give somebody most of your French fries without making them give you any of theirs."
Chrissy - age 6
"Love is what makes you smile when you're tired."
Terri - age 4
"Love is when my mommy makes coffee for my daddy and she takes a sip before giving it to him, to make sure the taste is OK."
Danny - age 7
"Love is when you kiss all the time. Then when you get tired of kissing, you still want to be together and you talk more. My Mommy and Daddy are like that. They look gross when they kiss"
Emily - age 8
"Love is what's in the room with you at Christmas if you stop opening presents and listen."
Bobby - age 7 (Wow!)
"If you want to learn to love better, you should start with a friend who you hate,"
Nikka - age 6
(We need a few million more Nikka's on this planet)
"Love is when you tell a guy you like his shirt, then he wears it everyday."
Noelle - age 7
"Love is like a little old woman and a little old man who are still friends even after they know each other so well."
Tommy - age 6
"During my piano recital, I was on a stage and I was scared. I looked at all the people watching me and saw my daddy waving and smiling. He was the only one doing that. I wasn't scared anymore."
Cindy - age 8
"My mommy loves me more than anybody . You don't see anyone else kissing me to sleep at night."
Clare - age 6
"Love is when Mommy gives Daddy the best piece of chicken."
Elaine-age 5
"Love is when Mommy sees Daddy smelly and sweaty and still says he is handsomer than Brad Pitt."
Chris - age 7
"Love is when your puppy licks your face even after you left him alone all day."
Mary Ann - age 4
"I know my older sister loves me because she gives me all her old clothes and has to go out and buy new ones."
Lauren - age 4
"When you love somebody, your eyelashes go up and down and little stars come out of you." (what an image)
Karen - age 7
"You really shouldn't say 'I love you' unless you mean it. But if you mean it, you should say it a lot. People forget."
Jessica - age 8
And the final one -- Author and lecturer Leo Buscaglia once talked about a
contest he was asked to judge.
The purpose of the contest was to find the most caring child.
The winner was a four year old child whose next door neighbor was an elderly
gentleman who had recently lost his wife.
Upon seeing the man cry, the little boy went into the old gentleman's yard,
climbed onto his lap, and just sat there.
When his Mother asked what he had said to the neighbor, the little boy said,
"Nothing, I just helped him cry"
Monday, May 10, 2004
Ten Golden Rules to start a Day
1. TODAY I WILL NOT STRIKE BACK: If someone is rude, if someone is impatient, if someone is unkind...I will not respond in a like manner.
2. TODAY I WILL ASK ALLAH TO BLESS MY “ENEMY”: If I come across someone who treats me harshly or unfairly, I will quietly ask Allah to bless that individual. I understand the “enemy” could be a family member, neighbor, co-worker, or a stranger.
3. TODAY I WILL BE CAREFUL ABOUT WHAT I SAY: I will carefully choose and guard my words being certain that I do not spread gossip.
4. TODAY I WILL GO THE EXTRA MILE: I will find ways to help share the burden of another person.
5. TODAY I WILL FORGIVE: I will forgive any hurts or injuries that come my way.
6. TODAY I WILL DO SOMETHING NICE FOR SOMEONE, BUT I WILL DO IT SECRETLY: I will reach out anonymously and bless the life of another.
7. TODAY I WILL TREAT OTHERS THE WAY I WISH TO BE TREATED: I will practice the golden rule - “Do unto others as I would have them do unto me” - with everyone I encounter.
8. TODAY I WILL RAISE THE SPIRITS OF SOMEONE I DISCOURAGED: My smile, my words, my expression of support, can make the difference to someone who is wrestling life.
9. TODAY I WILL NURTURE MY BODY: I will eat less; I will eat only healthy foods. I will thank Allah for my body.
10. TODAY I WILL GROW SPIRITUALLY: I will spend a little more time in salaah (Prayers) and dua (Supplication) today: I will begin reading something spiritual or inspirational today; I will find a quiet place (at some point during the day) and contemplate on the purpose of life.!!!
2. TODAY I WILL ASK ALLAH TO BLESS MY “ENEMY”: If I come across someone who treats me harshly or unfairly, I will quietly ask Allah to bless that individual. I understand the “enemy” could be a family member, neighbor, co-worker, or a stranger.
3. TODAY I WILL BE CAREFUL ABOUT WHAT I SAY: I will carefully choose and guard my words being certain that I do not spread gossip.
4. TODAY I WILL GO THE EXTRA MILE: I will find ways to help share the burden of another person.
5. TODAY I WILL FORGIVE: I will forgive any hurts or injuries that come my way.
6. TODAY I WILL DO SOMETHING NICE FOR SOMEONE, BUT I WILL DO IT SECRETLY: I will reach out anonymously and bless the life of another.
7. TODAY I WILL TREAT OTHERS THE WAY I WISH TO BE TREATED: I will practice the golden rule - “Do unto others as I would have them do unto me” - with everyone I encounter.
8. TODAY I WILL RAISE THE SPIRITS OF SOMEONE I DISCOURAGED: My smile, my words, my expression of support, can make the difference to someone who is wrestling life.
9. TODAY I WILL NURTURE MY BODY: I will eat less; I will eat only healthy foods. I will thank Allah for my body.
10. TODAY I WILL GROW SPIRITUALLY: I will spend a little more time in salaah (Prayers) and dua (Supplication) today: I will begin reading something spiritual or inspirational today; I will find a quiet place (at some point during the day) and contemplate on the purpose of life.!!!
Game Theory
I INTRODUCTION
Game Theory, mathematical analysis of any situation involving a conflict of interest, with the intent of indicating the optimal choices that, under given conditions, will lead to a desired outcome. Although game theory has roots in the study of such well-known amusements as checkers, tick-tack-toe, and poker—hence the name—it also involves much more serious conflicts of interest arising in such fields as sociology, economics, and political and military science.
Aspects of game theory were first explored by the French mathematician Émile Borel, who wrote several papers on games of chance and theories of play. The acknowledged father of game theory, however, is the Hungarian-American mathematician John von Neumann, who in a series of papers in the 1920s and '30s established the mathematical framework for all subsequent theoretical developments. During World War II military strategists in such areas as logistics, submarine warfare, and air defense drew on ideas that were directly related to game theory. Game theory thereafter developed within the context of the social sciences. Despite such empirically related interests, however, it is essentially a product of mathematicians.
II BASIC CONCEPTS
In game theory, the term game means a particular sort of conflict in which n of individuals or groups (known as players) participate. A list of rules stipulates the conditions under which the game begins, the possible legal “moves” at each stage of play, the total number of moves constituting the entirety of the game, and the terms of the outcome at the end of play.
A Move
In game theory, a move is the way in which the game progresses from one stage to another, beginning with an initial state of the game through the final move. Moves may alternate between players in a specified fashion or may occur simultaneously. Moves are made either by personal choice or by chance; in the latter case an object such as a die, instruction card, or number wheel determines a given move, the probabilities of which are calculable.
B Payoff
Payoff, or outcome, is a game-theory term referring to what happens at the end of a game. In such games as chess or checkers, payoff may be as simple as declaring a winner or a loser. In poker or other gambling situations the payoff is usually money; its amount is predetermined by antes and bets amassed during the course of play, by percentages or by other fixed amounts calculated on the odds of winning, and so on.
C Extensive and Normal Form
One of the most important distinctions made in characterizing different forms of games is that between extensive and normal. A game is said to be in extensive form if it is characterized by a set of rules that determines the possible moves at each step, indicating which player is to move, the probabilities at each point if a move is to be made by a chance determination, and the set of outcomes assigning a particular payoff or result to each possible conclusion of the game. The assumption is also made that each player has a set of preferences at each move in anticipation of possible outcomes that will maximize the player's own payoff or minimize losses. A game in extensive form contains not only a list of rules governing the activity of each player, but also the preference patterns of each player. Common parlor games such as checkers and ticktacktoe and games employing playing cards such as “go fish” and gin rummy are all examples.
Because of the enormous numbers of strategies involved in even the simplest extensive games, game theorists have developed so-called normalized forms of games for which computations can be carried out completely. A game is said to be in normal form if the list of all expected outcomes or payoffs to each player for every possible combination of strategies is given for any sequence of choices in the game. This kind of theoretical game could be played by any neutral observer and does not depend on player choice of strategy.
D Perfect Information
A game is said to have perfect information if all moves are known to each of the players involved. Checkers and chess are two examples of games with perfect information; poker and bridge are games in which players have only partial information at their disposal.
E Strategy
A strategy is a list of the optimal choices for each player at every stage of a given game. A strategy, taking into account all possible moves, is a plan that cannot be upset, regardless of what may occur in the game.
III KINDS OF GAMES
Game theory distinguishes different varieties of games, depending on the number of players and the circumstances of play in the game itself.
A One-Person Games
Games such as solitaire are one-person, or singular, games in which no real conflict of interest exists; the only interest involved is that of the single player. In solitaire only the chance structure of the shuffled deck and the deal of cards come into play. Single-person games, although they may be complex and interesting from a probabilistic view, are not rewarding from a game-theory perspective, for no adversary is making independent strategic choices with which another must contend.
B Two-Person Games
Two-person, or dual, games include the largest category of familiar games such as chess, backgammon, and checkers or two-team games such as bridge. (More complex conflicts—n-person, or plural, games—include poker, Monopoly, Parcheesi, and any game in which multiple players or teams are involved.) Two-person games have been extensively analyzed by game theorists. A major difficulty that exists, however, in extending the results of two-person theory to n-person games is predicting the interaction possible among various players. In most two-party games the choices and expected payoffs at the end of the game are generally well-known, but when three or more players are involved, many interesting but complicating opportunities arise for coalitions, cooperation, and collusion.
C Zero-Sum Games
A game is said to be a zero-sum game if the total amount of payoffs at the end of the game is zero. Thus, in a zero-sum game the total amount won is exactly equal to the amount lost. In economic contexts, zero-sum games are equivalent to saying that no production or destruction of goods takes place within the “game economy” in question. Von Neumann and Oskar Morgenstern showed in 1944 that any n-person non-zero-sum game can be reduced to an n + 1 zero-sum game, and that such n + 1 person games can be generalized from the special case of the two-person zero-sum game. Consequently, such games constitute a major part of mathematical game theory. One of the most important theorems in this field establishes that the various aspects of maximal-minimal strategy apply to all two-person zero-sum games. Known as the minimax theorem, it was first proven by von Neumann in 1928; others later succeeded in proving the theorem with a variety of methods in more general terms.
IV APPLICATIONS
Applications of game theory are wide-ranging and account for steadily growing interest in the subject. Von Neumann and Morgenstern indicated the immediate utility of their work on mathematical game theory by linking it with economic behavior. Models can be developed, in fact, for markets of various commodities with differing numbers of buyers and sellers, fluctuating values of supply and demand, and seasonal and cyclical variations, as well as significant structural differences in the economies concerned. Here game theory is especially relevant to the analysis of conflicts of interest in maximizing profits and promoting the widest distribution of goods and services. Equitable division of property and of inheritance is another area of legal and economic concern that can be studied with the techniques of game theory.
In the social sciences, n-person game theory has interesting uses in studying, for example, the distribution of power in legislative procedures. This problem can be interpreted as a three-person game at the congressional level involving vetoes of the president and votes of representatives and senators, analyzed in terms of successful or failed coalitions to pass a given bill. Problems of majority rule and individual decision making are also amenable to such study.
Sociologists have developed an entire branch of game theory devoted to the study of issues involving group decision making. Epidemiologists also make use of game theory, especially with respect to immunization procedures and methods of testing a vaccine or other medication. Military strategists turn to game theory to study conflicts of interest resolved through “battles” where the outcome or payoff of a given war game is either victory or defeat. Usually, such games are not examples of zero-sum games, for what one player loses in terms of lives and injuries is not won by the victor. Some uses of game theory in analyses of political and military events have been criticized as a dehumanizing and potentially dangerous oversimplification of necessarily complicating factors. Analysis of economic situations is also usually more complicated than zero-sum games because of the production of goods and services within the play of a given “game.”
Game Theory, mathematical analysis of any situation involving a conflict of interest, with the intent of indicating the optimal choices that, under given conditions, will lead to a desired outcome. Although game theory has roots in the study of such well-known amusements as checkers, tick-tack-toe, and poker—hence the name—it also involves much more serious conflicts of interest arising in such fields as sociology, economics, and political and military science.
Aspects of game theory were first explored by the French mathematician Émile Borel, who wrote several papers on games of chance and theories of play. The acknowledged father of game theory, however, is the Hungarian-American mathematician John von Neumann, who in a series of papers in the 1920s and '30s established the mathematical framework for all subsequent theoretical developments. During World War II military strategists in such areas as logistics, submarine warfare, and air defense drew on ideas that were directly related to game theory. Game theory thereafter developed within the context of the social sciences. Despite such empirically related interests, however, it is essentially a product of mathematicians.
II BASIC CONCEPTS
In game theory, the term game means a particular sort of conflict in which n of individuals or groups (known as players) participate. A list of rules stipulates the conditions under which the game begins, the possible legal “moves” at each stage of play, the total number of moves constituting the entirety of the game, and the terms of the outcome at the end of play.
A Move
In game theory, a move is the way in which the game progresses from one stage to another, beginning with an initial state of the game through the final move. Moves may alternate between players in a specified fashion or may occur simultaneously. Moves are made either by personal choice or by chance; in the latter case an object such as a die, instruction card, or number wheel determines a given move, the probabilities of which are calculable.
B Payoff
Payoff, or outcome, is a game-theory term referring to what happens at the end of a game. In such games as chess or checkers, payoff may be as simple as declaring a winner or a loser. In poker or other gambling situations the payoff is usually money; its amount is predetermined by antes and bets amassed during the course of play, by percentages or by other fixed amounts calculated on the odds of winning, and so on.
C Extensive and Normal Form
One of the most important distinctions made in characterizing different forms of games is that between extensive and normal. A game is said to be in extensive form if it is characterized by a set of rules that determines the possible moves at each step, indicating which player is to move, the probabilities at each point if a move is to be made by a chance determination, and the set of outcomes assigning a particular payoff or result to each possible conclusion of the game. The assumption is also made that each player has a set of preferences at each move in anticipation of possible outcomes that will maximize the player's own payoff or minimize losses. A game in extensive form contains not only a list of rules governing the activity of each player, but also the preference patterns of each player. Common parlor games such as checkers and ticktacktoe and games employing playing cards such as “go fish” and gin rummy are all examples.
Because of the enormous numbers of strategies involved in even the simplest extensive games, game theorists have developed so-called normalized forms of games for which computations can be carried out completely. A game is said to be in normal form if the list of all expected outcomes or payoffs to each player for every possible combination of strategies is given for any sequence of choices in the game. This kind of theoretical game could be played by any neutral observer and does not depend on player choice of strategy.
D Perfect Information
A game is said to have perfect information if all moves are known to each of the players involved. Checkers and chess are two examples of games with perfect information; poker and bridge are games in which players have only partial information at their disposal.
E Strategy
A strategy is a list of the optimal choices for each player at every stage of a given game. A strategy, taking into account all possible moves, is a plan that cannot be upset, regardless of what may occur in the game.
III KINDS OF GAMES
Game theory distinguishes different varieties of games, depending on the number of players and the circumstances of play in the game itself.
A One-Person Games
Games such as solitaire are one-person, or singular, games in which no real conflict of interest exists; the only interest involved is that of the single player. In solitaire only the chance structure of the shuffled deck and the deal of cards come into play. Single-person games, although they may be complex and interesting from a probabilistic view, are not rewarding from a game-theory perspective, for no adversary is making independent strategic choices with which another must contend.
B Two-Person Games
Two-person, or dual, games include the largest category of familiar games such as chess, backgammon, and checkers or two-team games such as bridge. (More complex conflicts—n-person, or plural, games—include poker, Monopoly, Parcheesi, and any game in which multiple players or teams are involved.) Two-person games have been extensively analyzed by game theorists. A major difficulty that exists, however, in extending the results of two-person theory to n-person games is predicting the interaction possible among various players. In most two-party games the choices and expected payoffs at the end of the game are generally well-known, but when three or more players are involved, many interesting but complicating opportunities arise for coalitions, cooperation, and collusion.
C Zero-Sum Games
A game is said to be a zero-sum game if the total amount of payoffs at the end of the game is zero. Thus, in a zero-sum game the total amount won is exactly equal to the amount lost. In economic contexts, zero-sum games are equivalent to saying that no production or destruction of goods takes place within the “game economy” in question. Von Neumann and Oskar Morgenstern showed in 1944 that any n-person non-zero-sum game can be reduced to an n + 1 zero-sum game, and that such n + 1 person games can be generalized from the special case of the two-person zero-sum game. Consequently, such games constitute a major part of mathematical game theory. One of the most important theorems in this field establishes that the various aspects of maximal-minimal strategy apply to all two-person zero-sum games. Known as the minimax theorem, it was first proven by von Neumann in 1928; others later succeeded in proving the theorem with a variety of methods in more general terms.
IV APPLICATIONS
Applications of game theory are wide-ranging and account for steadily growing interest in the subject. Von Neumann and Morgenstern indicated the immediate utility of their work on mathematical game theory by linking it with economic behavior. Models can be developed, in fact, for markets of various commodities with differing numbers of buyers and sellers, fluctuating values of supply and demand, and seasonal and cyclical variations, as well as significant structural differences in the economies concerned. Here game theory is especially relevant to the analysis of conflicts of interest in maximizing profits and promoting the widest distribution of goods and services. Equitable division of property and of inheritance is another area of legal and economic concern that can be studied with the techniques of game theory.
In the social sciences, n-person game theory has interesting uses in studying, for example, the distribution of power in legislative procedures. This problem can be interpreted as a three-person game at the congressional level involving vetoes of the president and votes of representatives and senators, analyzed in terms of successful or failed coalitions to pass a given bill. Problems of majority rule and individual decision making are also amenable to such study.
Sociologists have developed an entire branch of game theory devoted to the study of issues involving group decision making. Epidemiologists also make use of game theory, especially with respect to immunization procedures and methods of testing a vaccine or other medication. Military strategists turn to game theory to study conflicts of interest resolved through “battles” where the outcome or payoff of a given war game is either victory or defeat. Usually, such games are not examples of zero-sum games, for what one player loses in terms of lives and injuries is not won by the victor. Some uses of game theory in analyses of political and military events have been criticized as a dehumanizing and potentially dangerous oversimplification of necessarily complicating factors. Analysis of economic situations is also usually more complicated than zero-sum games because of the production of goods and services within the play of a given “game.”
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