由機會率的理論問題談到愛情

(翻譯自: http://eulertruthbible.wordpress.com/2008/02/15/philosophical-difficulti...)

這本來是一條我在上心理學的統計科時想起的難題，後來上數學的統計科時也沒有什麼頭緒。
其大意是質疑機會率的第一支柱的外向合理性(external validity)，也在挑戰科學哲學的基礎，機會率的一支柱為只要做實驗的次數愈多，就愈接近理論上的慨念值，如角子的兩面出現的機會為二份一，理論上，如果可以做一萬次實驗，一億次實驗，在一個一般硬幣中每一面被撙出的數量就會相當接近總數的一半。但是這看來像是自己引證自己 (tautology)，因為你根本不能在做實驗前預先知道某一面出面真正的機會率為多少，這個理論值其實是猜出來的，而且是一個未經驗證的理論，唯一驗證的方式就是做實驗﹐所以實驗值和理論值相等根本只是邏緝上的必然，是遊戲一開始時的規則決定了它的結果，這實驗其實並沒有為我們增加任何的新知識。換句話說，慨率論的慨念有點不完整。

舉一個具體的例子，例如我擲骰去決定每一面出現的慨率，有什麼東西可以保證我做了一億次實驗的結果一定會比一萬次實驗的結果更接近理論值呢?因為每次實驗都是獨立的，因此知道了第1000次的結果不代表我知道第1001次的結果,知道了第1001次的結果不代表我知道第1002次的結果，遑論由第 1000次的結果去估計第1002次的結果，更不可能由第1000次的結果去估計第10000次的結果，所以機會率的第一支柱，實驗愈多就愈接近理論上的慨念值由頭到尾都是一個假設。一如真相是不是愈辯愈明一樣，似乎無法由此理論框架去解決。

進一步更深入的問題，當它用在科學上時，就是時間永不停留，這一秒和下一秒物體的物理狀態/參數也是不一樣，所以如果拿心理教授舉的例子: 為了謹重起見，為了公平起見，所以和別人賽跑一定要跑1000圈去定輸羸，但是如果是連續跑1000圈，則令你在第1圈勝出的因素和令你在第2圈落後的因素不能保證是一樣;要是分開1000天每天去跑一圈比賽，就更加不公平，因每一天兩位的身體、精神狀態都略有不同，如何能保證每一天都是在一切影響賽跑結果的主要因素都一樣下去比賽呢?是不是在理論上根本不能保證完全公平的比賽，即在科學中我們永遠不能保證找到的是真相?

此一問題用在心理學/社會科學上就更顯箸了，因為心理因素更不可能像科學實驗一樣準確測量出來，所以就成疑問了。怪不得我有不少大學同學以為心理學並不算一門科學，因為科學可以很精細的定義每一因素及量度，但心理學在很大程度上接近一個思想遊戲，一個自我封閉的系統。基於心理學「知識」的奇異性質，所以學心理學的人不一定比其他人更了解別人的心理，不一定更了解自己，最多是知多了一些如何研究別人心理的方法，學心理學的意義因此不是令人更「醒目」，研究結果也印證這一點，心理學家不一定比其他人更有生活上的優勢，最多是更會思考而已。更會思考的人或者較難被騙，但不一定更快樂;正如書中也不一定有如顏玉。

想說及冰漓的也只是這一個教訓，我因為失戀之後才讀心理學，所以我常常鑽研愛情心理學，但是檢討了一千次還是找不出如何把剛學到的心理學知識用到情場上，事後諸葛分析到頭頭是道，不等於我或你成情場鬼見愁，我是有一定的魅力，但和心理學的內容似乎沒有直接關係。理性是不可能分析出任何愛情的真偽，我也永遠無法在理論上完全證明對你的愛有幾深，是否永恆不變，什麼心理學原理或邏緝決定它是永恆不變，你信就是信，不信就是不信，我的說話在當時完全為真，但是要時因為你的懷疑，你覺得要多試十個，以為多一點情愛的經驗後來的婚姻才會美滿的話，則你對心理學的領悟還是生吞活剝，未窺全豹，因為在現實上常常發生的是緣份一閃即逝﹐如我今天現在不選擇在家中寫文而是在外面找異性攀談的話，天知今晚會發生什麼事?天知我會不會在哪一位異性的床上?天知會不會和另一位異性即時通電呢?

我想假設要是有人依你的理論堅持由一試到十段感情，之後得出結論是第1,3,5位各有千秋，不相伯仲，值得深入發展，但第1,3,5先生又會不會坐在哪裏等侯她的恩寵?會不會本來第一段是一見鐘情，第二天可共諧連理，卻因為信了這一套看來很對的理論而錯失了一段良緣呢?還是以為只要是註定則無論怎做也不能破壞它呢?你以為你一直應用半通不通的心理學/哲學到底是幫人還是在害人?你為什麼不去珍惜把握已有的緣份去令我倆成令人羨慕一對，去完成你我認同的夢想，去把生命活得更有意義，去把世界改造得更美好，反而終日只生活在思想世界中。

你有能力去寫熾愛，但你卻沒有能力去接受熾愛的洗禮﹐我更不知你是不是天生沒有能力去熾愛除了你之外的人，你有能力去充心理專家，但是對於我你卻永遠在逃避。

我相信愛情﹐你在謀殺愛情，因為世界不完美，所以太好的東西就是存在也不應存在，世上是沒有完美的愛情，只會在你思想中才存在，所以你要否定在你思想世界以外的愛情。為了證明你邏緝無懈可擊，為了證明自己比其他更聰明﹐為了繼續保持萬人迷的形象，你寧不要愛情。

夫複何言?金錢、權勢、知識、智力都不能換愛情，我一生擁有一切和一事無成有什麼分別?
冰漓，告訴我，我真的不明白，為什麼我不能和你相愛?你又明白為什麼呢?你到底知不知道自己在做什麼?你以為生命真的有無盡的選擇，香港真的如中共宣傳所說有美好的明天，當我們全部都在獄牢要為一塊麵包互鬥至死時?

Seize the moment!

To win a lottery using Mathematics(2)

It would be difficult to illustrate without giving an concrete example, suppose you define the higher the sum of score of three dice as an indication of luckiness. At one day, you are not feeling lucky, and you draw the lowest sum of all: one, one, one, that has 1 out of 216 chance to happen. i.e. If we can rank what is most lucky and what is most unlucky, you are in the 216th of 216 ranks. Then you brought a quick pick of 6 numbers: 1,2,3,4,5,6; since you know that is not your lucky day, the chance of this number to appear in the lottery is 1/216. You can thus advise your friend not to pick any number from 1 to 6, which increase their chance of winning slightly. You can repeat the process to eliminate other numbers like 7,8,9,10,11,12; 13,14,15,16,17,18; 19,20,21,22,23,24; 25,26,27,28,29,30… until all but 6 number remained. That is something unusual given the computer picked number are most likely to repeated in each ticket. To fit the definition of being unlucky, it should reduce your chance of winning the lottery regardless of which strategy you devised to defeat it. So you should be expected to see a lot of overlapping numbers from each of the ticket your brought, because that would realistically defeat the scheme I devise here, otherwise the idea of a luckiness index is invalid. Say you have the worst luck of all, you have a repeat rate of five out of six(i.e., Given the first quick pick is 1,2,3,4,5,6; next quick pick is 2,3,4,5,6,7; and the 3th quick pick is 3,4,5,6,7,8), and it take you 37 more picks to eliminate all but 6 number out of 49. Nevertheless, you can pretty assured that the remaining number has a much higher chance (215/216) of appearing in the lottery.
On the other end, if you have the best of luck but not enough to win a lottery, this method could increase your chance of winning the lottery. How? Because which number doesn't appear in the quick pick must have a much lower chance to appear in lottery. You can apply this method in opposition direction. Since you are luck, it follows that the number of repeated number should be less for you to eliminate the one which has lower chance of winning the lotter.
Suppose we now have 216 people has luck ranked from 1 to 216th. If each of them buy a quick pick lottery ticket, since there is only one combination 6 out of 49 number that can win a lottery regardless of the luck of each buyer. We could easily use a computer program to guess which six number better fitted with 216 hypothesis that the chance of winning the lottery is reflected in luckiness index by throwing the dice three times. Of course, to further increase the number of quick pick that each person brought. For instance, each of them can get 6 quick pick, what the computer software has to do now is first evaluate 1296 hypothesis of different level of luckiness to get a coherent picture of the chance of each number appears in the lottery number; then evaluate the 36 hypothesis for fixed level of luckiness. So the computer can arrive at a coherent picture of the probability distribution of each number, and advise the best number to pick from.

Who would like to write such a computer software? It is just a lot of Mathematics. It can even apply this method in opposite, advising the buyer how many more quick picks to buy to maximize his/her chance of winning the lottery.

The opposite of unlucky is lucky. Shouldn't that lucky is the opposite of opposite of lucky?

To win a lottery through Mathematics?

There are various approaches to increase the chance of winning in a lottery, in a sense, they attempt to encircle the winning lottery numbers. However, we all know that it is mathematically impossible to accurately predict the winning number by sheer calculation. That is because of Gauss’s theorem which require minimum n different equations to solve for n unknown, but any approaches would give less equation than what is needed for solving the unknown.

My solution is to add one more variable into the equations: Luck. That is assume the luck factor is uniformly distributed across day, and that is knowable using methods of testing. (For instance, if u desire large number then throw dice for three consecutive times and get three six. So you are lucky because it has a chance of 1/216, which translated into you have the luck of 1-1/216=215/216 chance of winning.) Theoretically, since we now know the chance of winning and the number you pick then we can reverse-engineer the lottery numbers (use the number auto-selection lottery tickets since it is neutral in a sense). To increase the certainty of the winning numbers, a more sophisticated method is to ask several of your friends to get their luck factor, and ask them to pick the numbers. Since it is known that the chance of you and your friend for winning the lottery, we could thus estimate the number that has the highest chance of winning the lottery by correlate the numbers they pick and the chance of winning.

Actually, I do have an easier method for practice, but that require a sensitivity of your own luck. My method is to choose a day which you had absolutely worst luck. Do not choose the numbers yourself but use auto-selection from the computer(or in any sense that is selected for you by other.) Get as many of those lottery tickets as possible, then eliminate the repeated numbers. Then you have a set of numbers that you know which is extremely unlikely to win(otherwise you would win just by buying these auto-selected number). So what is left is what has a much higher probability to win. Suppose it require you to pick 9 out of 64, what you need is just to find a way to eliminate 55 numbers. If you buy a number of auto-selection lottery tickets, which you just happen to have 55 non-repeating numbers, then you just need to ask a friend to buy the remaining 9 numbers. Make sure s/he will pay you, and make sure you granted me one wish, it is your obligation to fulfill that wish regardless of its nature in case you win the lottery using this method.