Daily Archives: November 19, 2012

機會率悲劇 1.2

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Monty Hall problem 1.2

這段改編自 2010 年 4 月 3 日的對話。

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「機會均等假設」如果胡亂使用，會得到很多荒唐的結論。例如，小明跟媽媽說：「在這次考試，我的成績有兩個可能。要麼我考到全班第一，要麼我考不到全班第一。所以，今次我有一半的機會，考到全班第一。」

媽媽回答：「荒謬！」

小明再解釋：「『考到全班第一』和『考不到全班第一』已經窮盡了，這次考試結果的所有可能。你不會想像到，有第三個情況出現。」

那樣，小明的媽媽，應該如何反駁他呢？

只有兩個可能的結果，並不代表各自的機會率是二分之一。除非題目假設，又或者有以往的實驗數據支持，例如小明在以往的考試中，平次每兩次中，就會有一次考第一；否則，你不能自己假設，機會率會平均分配於各個可能性。

而這個「故亂假設機會均等」的思考錯誤，往往形成塵世間很多悲劇，例如選錯配偶和選錯事業。「我加入這一行，要麼成功，要麼失敗。所以，我成功的機會有一半。」那即使不是顯意識的思考，大概也會是潛意識的想法。

這個錯誤來自，不必要地選擇無知。正當的做法是，先做功課，先做好資料搜集。以自己當時可以得到，最多和最準確的資訊，去評價自己，加入某一行時，成功和失敗的機會率，各佔多少。即使那個機會率不會十分詳細，例如「成功的機會是 57%」，你也至少要有個大概，知道成功的機會較大，還是失敗。如果成功的機會較大，是約略大多少呢？是不是大到，值得你投資未來五年的人生，去作嘗試呢？

雖然，那也不保證一定成功，但是至起碼，即使錯了，也可以問心無愧。而且，如果你是在做足功課的情況下失敗，你吸收到的知識經驗，將會是最豐富的。那將大大提高你，未來成功的機會率。

— Me@2012.11.19

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2012.11.19 Monday (c) All rights reserved by ACHK

EPR paradox, 5

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One important question raised by this ambiguity is whether Einstein’s theory of relativity is compatible with the experimental results demonstrating nonlocality. Relativistic quantum field theory requires interactions to propagate at speeds less than or equal to the speed of light, so “quantum entanglement” cannot be used for faster-than-light-speed propagation of matter, energy, or information.

Measurements of one particle will be correlated with measurements on the other particle, but this is only known after the experiment is performed and notes are compared, therefore there is no way to actually send information faster than the speed of light.

On the other hand, relativity predicts causal ambiguities will result from the nonlocal interaction. In terms of the EPR experiment, in some reference frames measurement of photon A will cause the wave function to collapse, but in other reference frames the measurement of photon B will cause the collapse.

— 02:57, 16 June 2012

— Wikipedia on Action at a distance (physics)

Correlation does not imply causation.

If two events A and B have no causal relationship, they can have different time orders in different frames of reference. In some frames, A happened at a time earlier than B. In some other frames, B happened at a time earlier than A.

However, if they have causal relationship, their time order is the same with respect to any frame of reference.

— Me@2012-11-18 10:44:59 PM

2012.11.19 Monday (c) All rights reserved by ACHK