This is a very controversial question. People posted a lot of discussions on the issue. Basically, it is quite a personal favor and depends on great varieties of the chessboard.
let's just assume there are 2 rooks and a Queen, all pawns are stripped. my opinion is, the queen attack direction is a point source, but 2 rooks can be from totally difference direction(row an columns). The total square covered by a Queen is 7x4+1=29, which is 45% of the board. the 2 rooks, if they are not covering each other, it can cover at almost 7x4-2+2=28, a little smaller. If the 2 rooks are on the same row or column, the covered area reduced to 22, 7 squares lesser, which almost a row. however, since the tools are covered each other, they are not threaten by the queen any more. while a single queen movement is truly restricted.
in order I checkmate, the Queen has to work together with the King. the only way to checkmate is the King pushing the other King in close range. in case of 2 rooks, the checkmate can be done by theirs own as long as they are not on same file. thus, If the queen can forcing the rooks on same files and moving her king toward the other king. possible checkmate.
this is an ideal case, since the 2 rooks can also get help from their king to not occupy the same file by staying close to their king. this also proving a castle for the king to avoid check and forcing draw.
now, we think about checking and avoiding checking in the queen side. to check the queen's king, the rooks have to put on the same file of the king. if the queen is on the same file of the king, the number of possible checking square is 5 for a single rook. for 2 rooks, as they are not threaten by the queen, they can always check, either directly or behind the queen. in fact, the Queen should be avoid to stay on the same file with her king, otherwise, a pinning will loss the queen! thus, the danger square of the queen or the effective cover area of 2 rooks is 28.
In the 2 rooks side, their king can be attacked from any direction if the rook are far away. however, when the rooks are near, the possible attack direction reduced to 1.
OK, i am tried. the last thing we should think about is the possibly of forking a single rook.
Friday, July 27, 2012
Thursday, July 19, 2012
logic 101 (class 3, set)
Somehow, "half-knowledge (mis-understood) is more dangerous then foolish". it is because, people like to guess the non-told part, or be confused for the non-told. lets go deeper into logic.
before, lets go back to a fundamental thing : set.
set is a group of objects
for example, a family is a set, it contains family members. the stuffs on a desk form a set. the people in a country form a set. nevertheless, there is an empty set. say, the tree in Antarctica. Thus, by naming the common property of some objects or a rule on selection, we have a set. in reverse, all elements in a set share some common properties or rules.
among a set, there may be some "sub-set", say, the kids in a family, the women in a country. this concept should be easily be understood.
To get the feeling of set, we usually draw a picture. the area inside a circle represent a set, and another circle inside the circle represent a sub-set.
Now, we have to introduce 2 simple concepts: AND and OR
AND : the common objects in 2 or more sets.
OR : any thing in 2 or more sets
in a picture, AND is the common area of 2 circles. OR is the total area of 2 circles. We should be very careful that, in logic, the OR has only 1 meaning. but in human language, which also follow some logic, "or" can be mean "either A or B, but not both", or "either A or B or both."
the application of it is very powerful. say, we have a set of "what to do in raining", thus, we have many elements inside, say, "bring umbrella" , "stay indoor", etc. If we draw a circle A of "what to do in raining", the circle B of "bring umbrella" is another circle that cross circle A. and "stay indoor" also another circle crossing A but never touch B.
what does it means?? it mean that, there are some are of B, which is not lay in A. thus, when someone bring an umbrella, it does not mean it is raining! we just illustrated the logic why "If A then B" and "if B then A" are not equal by graph!!
and we can see, the circle B and C don't touch each other, which mean, when we stay home, we never bring umbrella and vice versa. then we have a logic,
if B then not C equal if C then not B
ok, Now, we introduce "a universal set", which contain everything we are concerning. (it is not the set of everything, which does not exist.) we draw a rectangle which contain every circles.;thus, the area OUTSIDE a circle mean "not this circle". in our example, "not C" is outside the circle C.
thus, we can see, B is a subset of not C. and we have a very important concept.
if A then B equal set A is a sub-set of B
OK, lets apply on our case. we immediately see some problem that, circle A is not a subset of circle B! how come? this mean, our logic has problem. we missing an assumption that, we have to add a circle D, "out-door". i will let reader think about where the "shape" (not circle may be) should be placed.
Tuesday, July 17, 2012
logic 101 (class 2)
i just posted about logic yesterday, and i saw one logic error in facebook today. (facepalm)
let put it in here,
man cannot change destiny, but personality can change it.
it seems OK, right. lets just don't discuss what is "destiny" in here, and i reply the post by asking,
can man change his personality?
by i asking this question is that, the sentence indicated that "man" and "his personality" are independent. and this is natural to ask that "what defined the personality?" it can be anything but "man", say, weather, horoscope, etc. i just want to clarify that. If man cannot change his personality, then the so call "destiny" is really out of man control. and we are all helpless in front of "destiny", like a chess piece.
my friend replied,
man definite can change his personality.
thus, we can see, "man can change destiny", which contradicted to the statement. because by associative law, we have
man definite can change his personality.
personality can change destiny.
thus, man can change destiny
but, man cannot change destiny !
Contradiction!!
Now, we can understand the contradiction, which can be symbolic into.
Given B, if A then not B.
let put it in here,
man cannot change destiny, but personality can change it.
it seems OK, right. lets just don't discuss what is "destiny" in here, and i reply the post by asking,
can man change his personality?
by i asking this question is that, the sentence indicated that "man" and "his personality" are independent. and this is natural to ask that "what defined the personality?" it can be anything but "man", say, weather, horoscope, etc. i just want to clarify that. If man cannot change his personality, then the so call "destiny" is really out of man control. and we are all helpless in front of "destiny", like a chess piece.
my friend replied,
man definite can change his personality.
thus, we can see, "man can change destiny", which contradicted to the statement. because by associative law, we have
man definite can change his personality.
personality can change destiny.
thus, man can change destiny
but, man cannot change destiny !
Contradiction!!
Now, we can understand the contradiction, which can be symbolic into.
Given B, if A then not B.
Monday, July 16, 2012
logic 101
i planned to write about logic for public long time ago. coz i saw many people made logic mistake during debates and arguments, especially more and more people joined discussions on public issues. And never the less, the new HK chief executive always using "double negation" statement, or logic, to fool people around.
here i will give a fundamental logic with minimum mathematical jargon, hope people from any background will understand it easily.
***************
first rule of logic is, we only talk about something that can be proved to be right or wrong. Expressing a feeling is not part of logic.
Eunice is beautiful. <-- this is not a logical statement, since it cannot be right or wrong.
Bill Gate is rich. <--- this is a logical statement, since we can prove Bill Gate is rich or not. of course this can also be an expression of feeling.
Most people understand the conclusive logic.
if A has property B and C is part of A, then C has property B.
an example is : All human will die, John is a human, then John will die. a little explanation is, C is part of A. if C is not part of A, then the logic fail. an example is, i like apple, i am human, then human likes apple. obviously, we know that NOT all human likes apple!
we can generalized the logic as
if A then B
which mean, A will cause B, expressing a relationship/consequence. for example, if my cell phone run out of battery, then i could not use the phone.
Most people can use associative law very easily:
if A then B and B then C, then A then C.
an example is, if i work hard, then high score in exam, and if high score in exam, my parent happy. then, if i work hard, then my parent happy.
Now, a common mistake made by people is
if A then B = if B then A
let me give an example of this mistake. if it is raining, Mary will bring an umbrella. OK, when we saw Mary bring an umbrella, some people will say, "oh, it must be raining." or, if it is not raining, then people will ask Mary, "why do you bring umbrella?"
i see this mistake happen very common. another example is. If i respect a teacher, he is a good teacher. and what if i don't respect a teacher? is it mean he is a bad teacher? NO, i simple Didn't Say anything when i not respect a teacher!
take the example of raining. we now know that if it is raining, Mary will bring an umbrella. But how about it is sunny, what Mary will bring? WE DON"T KNOW! Mary can bring anything or nothing, we just don't know.
let make a clear illustration here. we have 4 possible combination of A, B, not A , not B.
a) if A then B
1) if not A then not B
2) if not B then not A
3) if B then A
we now should be clear that, a) is not equal to 3). and 1) is simple wrong, or we cannot know by just given a). How about 2)???
Now, this is what i want to let everyone know.
a) = 2) | if A then B = if not B then A
using if it is raining, Mary will bring an umbrella as an example. we now sure that, if Mary does not bring an umbrella, then it is not raining. we see here a double negation statement, which make many people confused.
so, to clear things, here is a conclusion.
if we given a statement, we can only know 1 extra things. and ask 2 questions to make sure we understood.
if A then B = if not B then not A
1) what if not A ??
2) what if B ??
here i will give a fundamental logic with minimum mathematical jargon, hope people from any background will understand it easily.
***************
first rule of logic is, we only talk about something that can be proved to be right or wrong. Expressing a feeling is not part of logic.
Eunice is beautiful. <-- this is not a logical statement, since it cannot be right or wrong.
Bill Gate is rich. <--- this is a logical statement, since we can prove Bill Gate is rich or not. of course this can also be an expression of feeling.
Most people understand the conclusive logic.
if A has property B and C is part of A, then C has property B.
an example is : All human will die, John is a human, then John will die. a little explanation is, C is part of A. if C is not part of A, then the logic fail. an example is, i like apple, i am human, then human likes apple. obviously, we know that NOT all human likes apple!
we can generalized the logic as
if A then B
which mean, A will cause B, expressing a relationship/consequence. for example, if my cell phone run out of battery, then i could not use the phone.
Most people can use associative law very easily:
if A then B and B then C, then A then C.
an example is, if i work hard, then high score in exam, and if high score in exam, my parent happy. then, if i work hard, then my parent happy.
Now, a common mistake made by people is
if A then B = if B then A
let me give an example of this mistake. if it is raining, Mary will bring an umbrella. OK, when we saw Mary bring an umbrella, some people will say, "oh, it must be raining." or, if it is not raining, then people will ask Mary, "why do you bring umbrella?"
i see this mistake happen very common. another example is. If i respect a teacher, he is a good teacher. and what if i don't respect a teacher? is it mean he is a bad teacher? NO, i simple Didn't Say anything when i not respect a teacher!
take the example of raining. we now know that if it is raining, Mary will bring an umbrella. But how about it is sunny, what Mary will bring? WE DON"T KNOW! Mary can bring anything or nothing, we just don't know.
let make a clear illustration here. we have 4 possible combination of A, B, not A , not B.
a) if A then B
1) if not A then not B
2) if not B then not A
3) if B then A
we now should be clear that, a) is not equal to 3). and 1) is simple wrong, or we cannot know by just given a). How about 2)???
Now, this is what i want to let everyone know.
a) = 2) | if A then B = if not B then A
using if it is raining, Mary will bring an umbrella as an example. we now sure that, if Mary does not bring an umbrella, then it is not raining. we see here a double negation statement, which make many people confused.
so, to clear things, here is a conclusion.
if we given a statement, we can only know 1 extra things. and ask 2 questions to make sure we understood.
if A then B = if not B then not A
1) what if not A ??
2) what if B ??
Sunday, July 15, 2012
美國知名智褲蘭德公司的報告 ---：美國智庫對中國人的15條評論
轉貼.........美國知名智褲蘭德公司的報告 ---：美國智庫對中國人的15條評論
(值得兩岸中國人深思與警惕)
1. 中國人缺乏誠信和社會責任感。中國人不瞭解他們作為社會個體應該對國家和社會所承擔的責任和義務。普通中國人通常只關心他們的家庭和親屬，中國的文化是建立在家族血緣關係上而不是建立在一個理性的社會基礎之上。中國人只在乎他們直系親屬的福祉，對與自己毫不相關的人所遭受的苦難則視而不見。毫無疑問，這種以血緣關係為基礎的道德觀勢必導致自私，冷酷，這種自私和冷酷已經成為阻礙中國社會向前發展的最關鍵因素。
2. 中國從來就沒有成為一個法制社會，因為中國人的思維方式與守法行為格格不入。中國人老想走捷徑。他們不明白這樣一個事實：即成就來自於努⋯⋯力工作和犧牲。中國人傾向於索取而不是給予。他們需要明白一個道理：生活的真諦不在於你索取多少而在於你能給予社會和你的人類同胞多少。
3. 大多數中國人從來就沒有學到過什麼是體面和尊敬的生活意義。中國人普遍不懂得如何為了個人和社會的福祉去進行富有成效的生活。潛意識裡，中國人視他們的生活目的就是抬高自己從而獲得別人的認知。這樣一來，一個人就會對“保有面子”這樣微不足道慾望感到滿足。“面子”是中國人心理最基本的組成部分，它已經成為了中國人難以克服的障礙，阻礙中國人接受真理並嘗試富有意義的生活。這個應受譴責的習性使得中國人生來就具有無情和自私的特點，它已成為中國落後的主要原因。
4. 中國人沒有勇氣去追求他們認為正確的事情。首先，他們沒有從錯誤中篩選正確事物的能力，因為他們的思想被貪婪所佔據。再有，就算他們有能力篩選出正確的事情，他們也缺乏勇氣去把真理化為實踐。
5. 中國人習慣接受廉價和免費的事物，他們總是夢想奇跡或者好運，因為他們不願意付出努力，他們總想不勞而獲。很少有中國人明白一個事實：威望和成就是通過一步步努力的工作和犧牲實現的，不付出就沒有所得。簡單來說，如果是為了謀生，那一個人只有去索取；但如果是為了生活，一個人必須要去奉獻。
6. 由於在貧窮的環境下生長並且缺少應有的教育，大多數中國人不懂得優雅的舉止和基本的禮貌。他們中的大多數人著裝笨拙粗鄙卻不感到害羞。他們在青少年時所受的教育就是如何說謊並從別人那裡索取，而不是去與別人去分享自己的所有。
7. 中國是一個物產豐富的國家。但無限制生育政策所帶來惡果使得中國成為了無限廉價勞動力的輸出國。這些輸出也包括那些受過教育的勞力輸出，除了他們的教育水平，實則和其他一般苦力沒有本質上的區別。
8. 中國大規模生產的便宜產品降低了鍵入這些產品的地區的商業信用度。由於技術落後，管理失敗，中國製造的單位能耗要比發達國家如日本、美國高出很多。因此，隨著出口額的增加，中國在擴大生產的同時喪失著寶貴的能源。同時，這種行為也嚴重地污染了環境，使中國變為全世界最不適宜人類居住的國家。
9. 目前中國正在遭受著資本主義社會兩大邪惡的折磨，環境的破壞與人性的喪失。由於中國人天生的貪婪的本性，他們可以毫無保留的接受資本主義的陰暗面即無止境追求物質利益、忽視人的尊嚴。中國人對西方的技術與產品狂熱追求卻對西方管理文化所強調的坦率、直接、誠實這些品質漠不關心。
10. 由於中國文化不鼓勵敢於冒險這種優良品質 (??)，所以中國人極力避免冒險，他們也不想尋求機會來改善自己的生活。中國人對於生活的平衡性和意義性並不感興趣，相反他們更執迷於對物質的索取，這點上要遠遠勝於西方人。大多數中國人發現他們不懂得“精神靈性”、“自由信仰”以及“心智健康”這樣的概念，因為他們的思想尚不能達到一個生命(補：即肉體和靈性的並存)存在的更高層次。他們的思想還停留在專注於動物本能對性和食物那點貪婪可憐的慾望上。
11. 在中國人的眼中，受教育不是為了尋求真理或者改善生活質量，而只是身份和顯赫地位的象徵和標誌。中國的知識分子從別人那裡得到尊敬並不是因為他們為了別人的幸福做過什麼，而只是因為他們獲得佔有了相當的知識。事實上，他們中的大多數只不過是一群僅僅通曉考試卻從不關心真理和道德的食客。
12.中國的教育體系很大程度上已經成為一種失敗和恥辱。它已經不能夠服務於教育本應所服務的對象：社會。這個教育體系不能提供給社會許多有用的個體。它只是製造出一群投機分子，他們渴望能夠受益於社會所提供的好處卻毫不關心回報。
13. 中國可以培養出大批的高級人才，但卻很少可以培養出合格的可以獨立主持的管理級專家。服務於一個公司或者社會，光有技術是不夠的；還需要有勇氣、膽量、正直和誠實的領導才能，這恰恰是大多數中國人所缺少的品性。正如亞瑟•史密斯(一位著名的西方傳教士)一個世紀前所指出的，中國人最缺乏的不是智慧，而是勇氣和正直的純正品性。這個評價，雖然歷經百年，如今依舊準確診斷出中國綜合症的原因。
14 .大多數中國畢業生對選擇出國並為外國工作不會感到內疚，事實上他們首先欠下了中國人民在教育上為他們所做出的犧牲。隨著傳統文化價值觀的破壞和逐步衰弱，大多數的中國人(包括受過教育的人)都徘徊在精神和內心世界的路口，像迷失的狗一樣不知何去何從。
15.……………………(最後一條留給我們的讀者)
(值得兩岸中國人深思與警惕)
1. 中國人缺乏誠信和社會責任感。中國人不瞭解他們作為社會個體應該對國家和社會所承擔的責任和義務。普通中國人通常只關心他們的家庭和親屬，中國的文化是建立在家族血緣關係上而不是建立在一個理性的社會基礎之上。中國人只在乎他們直系親屬的福祉，對與自己毫不相關的人所遭受的苦難則視而不見。毫無疑問，這種以血緣關係為基礎的道德觀勢必導致自私，冷酷，這種自私和冷酷已經成為阻礙中國社會向前發展的最關鍵因素。
2. 中國從來就沒有成為一個法制社會，因為中國人的思維方式與守法行為格格不入。中國人老想走捷徑。他們不明白這樣一個事實：即成就來自於努⋯⋯力工作和犧牲。中國人傾向於索取而不是給予。他們需要明白一個道理：生活的真諦不在於你索取多少而在於你能給予社會和你的人類同胞多少。
3. 大多數中國人從來就沒有學到過什麼是體面和尊敬的生活意義。中國人普遍不懂得如何為了個人和社會的福祉去進行富有成效的生活。潛意識裡，中國人視他們的生活目的就是抬高自己從而獲得別人的認知。這樣一來，一個人就會對“保有面子”這樣微不足道慾望感到滿足。“面子”是中國人心理最基本的組成部分，它已經成為了中國人難以克服的障礙，阻礙中國人接受真理並嘗試富有意義的生活。這個應受譴責的習性使得中國人生來就具有無情和自私的特點，它已成為中國落後的主要原因。
4. 中國人沒有勇氣去追求他們認為正確的事情。首先，他們沒有從錯誤中篩選正確事物的能力，因為他們的思想被貪婪所佔據。再有，就算他們有能力篩選出正確的事情，他們也缺乏勇氣去把真理化為實踐。
5. 中國人習慣接受廉價和免費的事物，他們總是夢想奇跡或者好運，因為他們不願意付出努力，他們總想不勞而獲。很少有中國人明白一個事實：威望和成就是通過一步步努力的工作和犧牲實現的，不付出就沒有所得。簡單來說，如果是為了謀生，那一個人只有去索取；但如果是為了生活，一個人必須要去奉獻。
6. 由於在貧窮的環境下生長並且缺少應有的教育，大多數中國人不懂得優雅的舉止和基本的禮貌。他們中的大多數人著裝笨拙粗鄙卻不感到害羞。他們在青少年時所受的教育就是如何說謊並從別人那裡索取，而不是去與別人去分享自己的所有。
7. 中國是一個物產豐富的國家。但無限制生育政策所帶來惡果使得中國成為了無限廉價勞動力的輸出國。這些輸出也包括那些受過教育的勞力輸出，除了他們的教育水平，實則和其他一般苦力沒有本質上的區別。
8. 中國大規模生產的便宜產品降低了鍵入這些產品的地區的商業信用度。由於技術落後，管理失敗，中國製造的單位能耗要比發達國家如日本、美國高出很多。因此，隨著出口額的增加，中國在擴大生產的同時喪失著寶貴的能源。同時，這種行為也嚴重地污染了環境，使中國變為全世界最不適宜人類居住的國家。
9. 目前中國正在遭受著資本主義社會兩大邪惡的折磨，環境的破壞與人性的喪失。由於中國人天生的貪婪的本性，他們可以毫無保留的接受資本主義的陰暗面即無止境追求物質利益、忽視人的尊嚴。中國人對西方的技術與產品狂熱追求卻對西方管理文化所強調的坦率、直接、誠實這些品質漠不關心。
10. 由於中國文化不鼓勵敢於冒險這種優良品質 (??)，所以中國人極力避免冒險，他們也不想尋求機會來改善自己的生活。中國人對於生活的平衡性和意義性並不感興趣，相反他們更執迷於對物質的索取，這點上要遠遠勝於西方人。大多數中國人發現他們不懂得“精神靈性”、“自由信仰”以及“心智健康”這樣的概念，因為他們的思想尚不能達到一個生命(補：即肉體和靈性的並存)存在的更高層次。他們的思想還停留在專注於動物本能對性和食物那點貪婪可憐的慾望上。
11. 在中國人的眼中，受教育不是為了尋求真理或者改善生活質量，而只是身份和顯赫地位的象徵和標誌。中國的知識分子從別人那裡得到尊敬並不是因為他們為了別人的幸福做過什麼，而只是因為他們獲得佔有了相當的知識。事實上，他們中的大多數只不過是一群僅僅通曉考試卻從不關心真理和道德的食客。
12.中國的教育體系很大程度上已經成為一種失敗和恥辱。它已經不能夠服務於教育本應所服務的對象：社會。這個教育體系不能提供給社會許多有用的個體。它只是製造出一群投機分子，他們渴望能夠受益於社會所提供的好處卻毫不關心回報。
13. 中國可以培養出大批的高級人才，但卻很少可以培養出合格的可以獨立主持的管理級專家。服務於一個公司或者社會，光有技術是不夠的；還需要有勇氣、膽量、正直和誠實的領導才能，這恰恰是大多數中國人所缺少的品性。正如亞瑟•史密斯(一位著名的西方傳教士)一個世紀前所指出的，中國人最缺乏的不是智慧，而是勇氣和正直的純正品性。這個評價，雖然歷經百年，如今依舊準確診斷出中國綜合症的原因。
14 .大多數中國畢業生對選擇出國並為外國工作不會感到內疚，事實上他們首先欠下了中國人民在教育上為他們所做出的犧牲。隨著傳統文化價值觀的破壞和逐步衰弱，大多數的中國人(包括受過教育的人)都徘徊在精神和內心世界的路口，像迷失的狗一樣不知何去何從。
15.……………………(最後一條留給我們的讀者)
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