師長經常說, 網上的人寫東西亂七八糟, 內容空洞, 文句不通, 言語粗鄙, 又容易沉迷, 因此勸我們要少上網, 多溫習功課. 我其實是不相信的. 我身邊的朋友中沒有人寫東西亂七八糟, 內容空洞, 文句不通, 言語粗鄙, 他們非常用功, 更不會沉迷沒意思的東西. 我心想, 怎會有這樣的人呢? 更何況每個上網的朋友都告訴我, 網上有豐富資訊, 有教科書沒教的事, 並時常介紹網站給我. 但我也不太相信. 怎會有教科書沒教的東西呢? 但看了這個網頁後, 我完全相信老師了.
http://forum7.hkgolden.com/view.aspx?message=1683450&highlight_id=0&page=1
網頁引述的調查 (ref. 香港青年協會) 真是令人難以置信. 七成青少年說粗口, 四成喝酒, 說笑吧? 甚至大部份人認同吸菸, 濫藥等罪行, 真是誇張失實. 我敢說我校的同學沒有一人會這樣. 師長說, 網上資訊極不準確, 相信一成也會雙目失明. 現在我不得不相信了.
更奇怪的是下面的討論. 他們的回應我完全看不明白, 有些字更是從來沒有看過的, 在教科書又找不到, 查看yahoo字典的解釋後也不明白, 希望看得懂的人說說下列字, 詞的意思:
屌/屌你老母, 撚, 鳩, 柒, 仆街 (這個最近在報紙看過, 聽說是粗口. 真的嗎? 議員們不都是剛正不阿, 受良好教育的人嗎? 為什麼會說這樣的話?)
還有就是, 他們竟然寫口語和同音字. 難道他們不知道這是錯的嗎?
我很後悔浪費時間看這個網頁. 不過也好, 總算是了解一下狀況. 那些經常叫我上網的同學, 相信是非常沉迷吧. 明天我會勸他們應該珍惜光陰, 不要再把時間用在沒建設性的事上.
2009-04-28
2009-04-07
稍為反省一下該如何思考
圍棋, 象棋等要求棋手在下每一手棋前考慮足夠的變化, 而且需要一定深度(search depth), 即考慮每一種下法在數手以後的結果, 而且最好有一定速度 (趙治勛指出, 專業棋手大都能在六十秒內看出最佳著法). 自問思考每一手棋的時間實在太少, 在IGS一般對局中, 要求棋手每十分鐘下廿五手棋, 就是大概二十秒一手. 但除特殊情況(特別是對殺)外, 一般用時都遠少於此. 太多"想當然"的時候, 就會失去細算的意欲, 這樣定難有大進步. 因此以後將強逼自己在每一手中至少花十秒時間(需要預留一些去應付較複雜的情況).
除了足夠 的變化, 深度和速度外, 思考問題比這更多一項要求, 就是要想得精微. 在棋戲中, 時間與空間都是discret的, 而且每個step size的大小一樣, 因此就不需考慮resolution, 但思考問題則不然. 即使是用game tree by exhaustion, 由不同的人來做, 所得的圖象的resolution也會是大大不同的. 這就是我們要讀"哲學家"的著作的原因. 並非因為他們特別正確, 而是要學習他們做學問是如何細緻精密, 如何忘記"常識"的偏見.
要評論自己想問題, 只能說是嚴重地low resolution. 同樣地, 由於太多"想當然", 很快就會得到結論, 然後遊蕩到下一個問題. 這樣對知識的廣是有幫助的, 但每事則只能得到皮毛. 這是令人難以接受的. 因此, 提高resolution, 不論是spatial, time還是spectral resolution, 都是最逼切要做的.
除了足夠 的變化, 深度和速度外, 思考問題比這更多一項要求, 就是要想得精微. 在棋戲中, 時間與空間都是discret的, 而且每個step size的大小一樣, 因此就不需考慮resolution, 但思考問題則不然. 即使是用game tree by exhaustion, 由不同的人來做, 所得的圖象的resolution也會是大大不同的. 這就是我們要讀"哲學家"的著作的原因. 並非因為他們特別正確, 而是要學習他們做學問是如何細緻精密, 如何忘記"常識"的偏見.
要評論自己想問題, 只能說是嚴重地low resolution. 同樣地, 由於太多"想當然", 很快就會得到結論, 然後遊蕩到下一個問題. 這樣對知識的廣是有幫助的, 但每事則只能得到皮毛. 這是令人難以接受的. 因此, 提高resolution, 不論是spatial, time還是spectral resolution, 都是最逼切要做的.
2009-04-04
The Physics of Mark 6
in response to MRC@Mark 6
Q: What is the physics behind the Mark 6 machine?
A: Newtonian mechanics, i.e. F=ma and conservation of momentum.
Q: How are the initial conditions of each trail differ from each other?
A: Let's see some examples.
六合彩 第129期
六合彩 第 96期
Obviously there is great difference in the position of blades of the windmill, and the way the balls fall.
Q: Can we conclude that Mark 6 is sensitive to initial conditions?
A: First we have to know what is mean by "sensitive to initial conditions". Let's think of several systems.
1) A pencil rolling on the desk will eventually stop, no matter how you vary its initial speed
2) 2 identical clocks are switched on at the same time, but with different initial settings in time. Although the time displayed on each clock is different, the difference in the time displayed is more or less the same.
3) such thing would not happen if the velocity of the milk drop is slightly changed
Physicists only consider something like 3) as "sensitive to initial conditions", i.e. small difference in initial condition leads to great difference in final results. To measure this "sensitivity to initial conditions", it is assumed that final difference=initial difference*exp(constant*time). By repeating the experiment many times, we can get an average value of that constant. It is important to note that, since the experimental error of each trail is different, the value of constant of each trail is different and is NOT reproducible. Therefore we can only use the average value of the constant. If the average of constant>0, the we would say that the system is sensitive to initial conditions, or more simply, chaotic.
We can only judge if Mark 6 is chaotic by finding that constant, which can be obtained by tracking the positions and velocities of some balls. Maybe someone can do it by extracting these data from life broadcast of Mark 6.
Q: If we have perfect information on the initial conditions, is it possible to predict the result of each trail?
A: Yes, since the machine is completely deterministic. But the calculation will be terribly difficult.
Q: Is Mark 6 a biased game?
A: Yes. However this game is fair only if ALL balls have the SAME initial conditions, which is impossible. Why initial conditions manner is because they determines the initial velocity and the number of collisions with the "windmill". Similar games like roulette, and even slot machine (老虎機) are biased.
To minimize the bias, the game setters then lengthen the "processing time" e.g. in Mark 6, some balls may collide n times, while the other collide n+m times, where n is much larger than m.
Q: Is there really a trend in Mark 6 results?
A: Maybe some numbers really appear more frequently, because of bias or just by chance. The number of possible combination of 7 balls within 49 balls is of course 49C7=85900584, while there are only several hundred sets of data available, we cannot judge whether there is any bias. However we can almost immediately conclude that, any attempt to analyse Mark 6 results with time series must fail, unless you believe that weather/planetary motion/spiritual power or other time dependent factors would affect the results.
Exercise
1. Suggest some practical ways to introduce more bias on Mark 6.
Q: What is the physics behind the Mark 6 machine?
A: Newtonian mechanics, i.e. F=ma and conservation of momentum.
Q: How are the initial conditions of each trail differ from each other?
A: Let's see some examples.
六合彩 第129期
六合彩 第 96期
Obviously there is great difference in the position of blades of the windmill, and the way the balls fall.
Q: Can we conclude that Mark 6 is sensitive to initial conditions?
A: First we have to know what is mean by "sensitive to initial conditions". Let's think of several systems.
1) A pencil rolling on the desk will eventually stop, no matter how you vary its initial speed
2) 2 identical clocks are switched on at the same time, but with different initial settings in time. Although the time displayed on each clock is different, the difference in the time displayed is more or less the same.
3) such thing would not happen if the velocity of the milk drop is slightly changed
Physicists only consider something like 3) as "sensitive to initial conditions", i.e. small difference in initial condition leads to great difference in final results. To measure this "sensitivity to initial conditions", it is assumed that final difference=initial difference*exp(constant*time). By repeating the experiment many times, we can get an average value of that constant. It is important to note that, since the experimental error of each trail is different, the value of constant of each trail is different and is NOT reproducible. Therefore we can only use the average value of the constant. If the average of constant>0, the we would say that the system is sensitive to initial conditions, or more simply, chaotic.
We can only judge if Mark 6 is chaotic by finding that constant, which can be obtained by tracking the positions and velocities of some balls. Maybe someone can do it by extracting these data from life broadcast of Mark 6.
Q: If we have perfect information on the initial conditions, is it possible to predict the result of each trail?
A: Yes, since the machine is completely deterministic. But the calculation will be terribly difficult.
Q: Is Mark 6 a biased game?
A: Yes. However this game is fair only if ALL balls have the SAME initial conditions, which is impossible. Why initial conditions manner is because they determines the initial velocity and the number of collisions with the "windmill". Similar games like roulette, and even slot machine (老虎機) are biased.
To minimize the bias, the game setters then lengthen the "processing time" e.g. in Mark 6, some balls may collide n times, while the other collide n+m times, where n is much larger than m.
Q: Is there really a trend in Mark 6 results?
A: Maybe some numbers really appear more frequently, because of bias or just by chance. The number of possible combination of 7 balls within 49 balls is of course 49C7=85900584, while there are only several hundred sets of data available, we cannot judge whether there is any bias. However we can almost immediately conclude that, any attempt to analyse Mark 6 results with time series must fail, unless you believe that weather/planetary motion/spiritual power or other time dependent factors would affect the results.
Exercise
1. Suggest some practical ways to introduce more bias on Mark 6.
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