20100620

假如全世界智商最高的人是個女人

現時全世界智商最高的人是誰?除非我們可以測試所有人的智商,否則便無法知道答案。不過,假如問題是「根據《健力士世界紀錄大全》,現時全世界智商最高的人是誰?」答案便是:Marilyn vos Savant。她的智商是228,是她十歲時做的一個智力測驗的結果。

從1986年開始,vos Savant替Parade雜誌寫一個叫"Ask Marilyn"的專欄,解答讀者上至天文地理、下至怪力亂神的問題,當時她四十歲,今年八月她便六十四了,這專欄還一直在寫,已接近二十四年。

在她解答過的所有問題中,最引人注目的應該是1990年時一個讀者問的一條概率問題:

在一個電視遊戲節目裏,主持人要你從A, B, C三道門中選擇一道,而門後的東西就是你的獎品。其中一道門之後是一輛新車,另外兩道門之後各有一頭羊(你當然想要汽車)。你選了A門,主持人知道各道門之後有些甚麼,這時他打開C門給你看,那是一頭羊;他接著問你:「我給你一個機會改選B門,你想改嗎?」改選B門會不會增加你得到汽車的機會?

一般人的想法是:現在只剩下A和B兩道門,是車是羊,都是一半的機會,改選B門當然不會增加你得到汽車的機會。Marilyn的答案卻是:你應該改選B門,因為A門之後是車的機會仍是三份一,但B門之後是車的機會現在是三份二。

她這答案一出,即引來數以千計的讀者來信,絕大部份是指她的答案錯誤,其中一些更來自著名大學的數學教授!不少來信的語氣頗不友善,矛頭直指Marilyn那個「全世界智商最高」的銜頭;例如一個博士這樣寫:「這個國家的數學盲已夠多了,我們不需要全世界智商最高的人令更多人成為數學盲。真丟臉!」

於是Marilyn再寫一篇,堅持自己的答案是對的,並進一步解釋答案。結果呢?更多的讀者來信指責她不肯認錯,而事件也引起全國報章的注意。Marilyn並不退縮,寫第三篇回應,呼籲全國的數學教師做一個實驗,著學生模擬那個電視遊戲節目,玩「改選B門」和「不改選B門」各二百次;如果她的答案是對的,這個實驗的結果應該與之吻合,即是「改選B門」而得到汽車的次數會較多。

果然有很多教師和學生響應,並把實驗結果寄給Marilyn,而實驗證明她的答案正確!有些曾罵過她的大學教授還再次來信,但這次承認她是對的,並向她道歉。

我不在這裏解釋她的答案了,有興趣的可以到Wikipedia查"Monty Hall Problem"一條,或看看這本書。"Ask Marilyn" 專欄曾結集成書,這條問題和讀者的回應也收在裏面,頗值一讀。

我想,假如Marilyn沒有「全世界智商最高」的銜頭,又假如她有這銜頭卻不是女人,讀者的反應可能不一樣。有個讀者就這樣寫:「說不定女人看數學問題跟男人的看法有點不同。」到實驗結果出了,仍有個男讀者來信說:「我還是認為你是錯的,真的有女性的邏輯這回事。」

34 則留言:

  1. Wong,

    嘆為觀止。註定我不是發達的料子。

    另一數學謎題:她1986年開始寫專欄時是二十歲,為甚麼二十四年後的今年她已六十三歲?

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  2. 讀者的反應可能不一樣, possible to have more reaction boxes, please? many thanks in advance :)

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  3. Meshi,

    哎呀,給你捉著了,計錯數,已更正。你看得真小心。

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  4. catcat,

    Sorry, Blogger不容許加boxes。

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  5. 有心, 有心, thanks thanks.
    catcat wants to be more blessed than high IQ loh.

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  6. catcat,

    Having a high IQ does not mean much.

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  7. that's so true... esp within personal relationship woman with high IQ means a disadvantage sometimes. (not applied to a dump dump cat here)
    假如男的有這銜頭, 反應真的可能不一樣.

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  8. To clarify, catcat 是承認男女大不同.
    女性的邏輯,還是prefer 和比自己higher IQ, EQ and AQ 的男性一起. 假如男的是全世界智商最高的人, 真是world peace.

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  9. catcat,

    相信很多男人也不喜歡女朋友或老婆樣樣勝過自己。

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  10. Wong sir,
    You're so right!
    女性自己應該小心,犯下錯誤,乞人憎,討人厭.謝謝!

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  11. wong sir,

    Guess what, catcat just did more research on this topic… learnt that the average IQ across various occupations are different.

    Quoted: 職業與分類的平均智商﹕
    哲學家(22)平均IQ是173 is the highest !!!
    藝術家(13)平均IQ是150﹐ catcat 有藝術脾氣, but not "藝術家" hehe :)

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  12. 這道題在小說: The Curious Incident of the Dog in the Night-time 內有, 此小說好好睇

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  13. catcat,

    I would love to believe that philosophers have the highest average IQ, but I am usually skeptical of this kind of claim. How did they find out?

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  14. xinhunshaofu,

    Thanks. I will check it out.

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  15. “How did they find out ?” is an inspiring question !

    catcat 整理了下面粗糙的幾點, 為分享:

    1)美國數學家William James Sidis被認為IQ高達250 (指有IQ Test之後的統計). 注意是…被認為.

    2)IQ(智商)最初是由法國的比奈(Alfred Binet) 和他的學生所發明的一系列測試, 目的是測量兒童在其年齡段的認知能力。想利用它來識別兒童的智力障礙, 以助治療訓練。

    3)IQ(智商)=MA(智年年齡)/CA(實際年齡)×100. 將一般人的平均智商定為100。高些評為聰明, 低些評為愚笨。

    4)不能全部的人都完成智力測驗, 職業分類的平均智商可能是不足的樣本分析.

    5)最初通常測驗的三個部分包括 : 1) 語言 2) 數學 和 3) 圖像. 由於測驗的試題進程涉及不同的語言和文化, 在平均的MA與多項的變項差異下, 導致“跨世代” 和 “跨國” 的比較實際上非常困難, 甚至可視為不可能。

    6)有不少教授認為目前的智力測驗不能全部有效的測量人們的智力。最新的研究表明智力/智慧應該包括記憶力, 敏感性, 邏輯推理能力, 分析歸納能力, 觀察力, 思想交流, 空間, 數學, 運動, 個人心理調節, 人際關係等.

    怎樣是有效的測量? catcat doesn’t know. 留給d專家.

    The main points of my comment yesterday were:
    1) i believe Wong sir is much smarter than me
    2) i am very moody, 有藝術脾氣.

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  16. catcat,

    Thanks. And I am fine with 1) and 2)!

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  17. "To clarify, catcat 是承認男女大不同.
    女性的邏輯,還是prefer 和比自己higher IQ, EQ and AQ 的男性一起. 假如男的是全世界智商最高的人, 真是world peace."

    Why should women prefer a male partner who have higher IA, EQ than theirs, and vice versa for men? When, in the past, women did not have the means to earn a living on their own and be their own independent entity - yes, that logic for women to find the smartest, most competent men they possibly can makes good sense. And it's a logic of survival.

    And why should women who outdo their men be considered "乞人憎,討人厭" when it was accepted as "natural" for the man to be smarter, better than the woman in a relationship? If men can't deal with women who are just simply smarter than they are, that's their problem, not the women's.

    And I'm just talking about being smarter and more intelligent. Men or women who are arrogant of course are 乞人憎,討人厭. But then, I do think that there is higher degree of tolerance towards men who are arrogant than women who are the same. For men who are recognized to be intelligent can get away from being arrogant. But for women, if you are smart, you better be extremely humble and low-key about it.

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  18. 匿名,

    Let me clarify my position here. My comment "相信很多男人也不喜歡女朋友或老婆樣樣勝過自己" was merely descriptive; I didn't mean to suggest that it should be that way.

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  19. 匿名,

    since you quoted my comments, may i clarify?
    1) my comment is a reflection of my painful personal experience. catcat has been perceived as 乞人憎,討人厭.

    2) what i meant by "prefer 和比自己higher IQ, EQ and AQ 的男性一起" ? It means, even i am wrong and moody, he will have the intellgence, emotional ability and aversity management skill to reconcile the relationship. Agree here, maybe i am demanding and depending too much on my potential partner. i know my limits. Again, my personal preference.

    3) Unsure if i am smart, but agree with you that being humble and low-key is a good move.

    4) Wong Sir already taught me to improve day by day. Focus on tomorrow, let's move on. Thanks

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  20. Wong:

    I did understand that your comment was just descriptive. I was responding to Catcat's statements. I'm sorry about hijacking your discussion there.

    Catcat:

    Thank you for taking the time to respond to my comments.

    I still don't know why your statement "女性自己應該小心,犯下錯誤,乞人憎,討人厭.謝謝!" referred to women specifically in the context of women and intelligence.

    Based on your clarification above, when you said "女性的邏輯,還是prefer 和比自己higher IQ, EQ and AQ 的男性一起," you were just referring to your own logic and preference then.

    And I wasn't trying to say "being humble and low-key is a good move." I was trying to point out a gendered expectation there.

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  21. 匿名,

    All discussions are welcome here.

    It would be nice if you could use a name.

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  22. Wong Sir, my apology in advance also for using your blog as discussion forum :)

    匿名, thanks for asking and this is clearer.

    1) You're right, the original article is in context of W&I. If you follow discussion flow afterwards, you may note my mindset and attention already shifted to personal relationship between gender.

    The hard line is more like a warning to woman in relationship, especially as if i was talking to myself. As you point out now, i begin to feel that it may have sounded rude and offensive on a public blog. Thanks.

    2) Yes, catcat is a female. I was referring to my own preference for sure. But, this is also preferred by most female in my social cycle. Of course, the sample size could still be limited.

    3) Thanks for clarifying. Now i understand the line is merely descriptive.

    匿名,
    out of curiosity, are you a male or female? also mind to disclose your name/nickname?

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  23. Wong and Catcat:

    Sorry for not leaving a name. I was just trying to avoid logging onto an account.

    I'm a woman (one who perhaps lacks the feminine logic). What was your guess?

    Lin

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  24. Lin,

    I guessed you're a woman. I hope you will use this name consistently when you leave comments in the future.

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  25. 我以前是在上bayes' theorem學到類似問題(我學的是“三囚徒問題”)。全班50多人,只有幾個人能說出正確答案。但我不知道原來這和一個美國節目,和世上智商最高的人有關的!

    後過了一年,有一次機會我參加了有同樣問題的心理實驗。答完後我被問到有沒有學過bayes' theorem,我說有。但還是照樣答錯!

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  26. CYC,

    概率的推論很多時都不符合我們的直覺,很容易犯錯。

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  27. 有句話剛才沒敢說,我考研究生時的入學論文,和bayesian epistemology有關!

    這種錯誤,只能說讀書只讀到表面,又或者說好聽點:咳,人類在日常中是很難突破概率推論的制約的啊

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  28. CYC,

    我在正文裏不是提到那些數學教授都錯了嗎?

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  29. 對,對,原來這時我可以和數學教授們平起平坐!

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  30. Women are cleverer than men. No doubt. My wife think so, so I think so. No kidding.

    I once tried to explain the problem to my nephew without using much math. Let me try here. Let's think about the same (a similar) problem except that we now have 1000 rooms. Still, only one of the rooms holds the prize. You pick one room. The game show host then picks (by the rules) and shows you there is no prize in 998 rooms, from the 999 you don't pick. You are left with 2 rooms, the room you pick and the room the host does not show you yet. Now, do you want to switch? I do. Go back to the original 3 room problem. I switch too. The 3-room problem may give you the 50-50 chance illusion. Hope the 1000 room problem doesn't give you such illusion. Hope it is clear enough.
    No? For the 1000 room problem, think about (just guessing would be good enough) how big the chance is there that the room the host doesn't show you holds the prize and (as compare with) how big the chance is there that the room you pick holds the prize.

    I am no Math professor. And my IQ is still lower than Savant's.

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  31. forgot to leave my fake name --zpdrmn

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