Hero 4

Seen by itself the David’s body might be some unusually taut and vivid work of antiquity; it is only when we come to the head that we are aware of a spiritual force that the ancient world never knew. I suppose that this quality, which I may call heroic, is not a part of most people’s idea of civilisation. It involves a contempt for convenience and a sacrifice of all those pleasures that contribute to what we call civilised life. It is the enemy of happiness. And yet we recognise that to despise material obstacles, and even to defy the blind forces of fate, is man’s supreme achievement; and since, in the end, civilisation depends on man’s extending his powers of mind and spirit to the utmost, we must reckon the emergence of Michelangelo as one of the great events in the history of western man.

— Ch. 5: The Hero as Artist

— Civilisation (1969)

— Kenneth Clark

2012.11.21 Wednesday ACHK

Monty Hall problem 1.3

Frequency probability and Bayesian probability, 3.1

機會率哲學 3.1

這段改編自 2010 年 4 月 3 日的對話。

除了錯誤使用「機會均等假設」外,思考「蒙提霍爾問題」時,另一個典型錯誤是,一般人不明顯知道,各道門的中獎機會率,在遊戲中途可能有變,即使房車和山羊的位置,都維持原本。

「機會率」除了描述客觀的物理系統外,還會反映觀察者的主觀知識狀態。換句話說,隨著那位遊戲參賽者,對他所觀察的系統,獲得多一點資料,各個機會率就會有變。例如,第三道門原本的中獎機會,相對於參賽者來說,是三分之一。但是,當主持人打開了它,導致參賽者知道「門後是山羊」後,相對於參賽者來說,第三道門中獎機會率,就立刻變成零。

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即使外在客觀的系統沒有變,只要觀察者對該系統的主觀知識,有所增加,事件各個可能結果,所對應的機會率,就要全部重新運算。

同理,雖然根據題目的假設,原初每道門的中獎機會均等,都是三分之一,但是,因為參賽者在中途,獲得了多一點資料,餘下兩道門中獎的機會率,未必仍然和對方相同。   

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而正確的答案是,餘下的兩道門中獎機會,不再均等。原本的被選的那一道,中獎的機會是三分之一;另一道門中獎的機會,則變成了三分之二。

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— Me@2012.11.21

2012.11.21 Wednesday (c) All rights reserved by ACHK