50% 哈佛學生都答錯嘅小學數學問題!

Daniel Kahneman 係一個近代著名嘅心理學家,而佢所做嘅研究令佢攞到 2002 年嘅諾貝爾獎。心水清嘅,應該知道諾貝爾獎並冇頒俾「心理學」呢個範疇。但係 Kahneman 嘅研究,足以令佢喺心理學以外嘅範疇,攞到一個諾貝爾經濟學獎。佢嘅成就,唔單只影響心理學同經濟學,喺政治科學上面,專寫國際關係嘅雜誌 Foreign Policy 亦都將佢視為深具影響力嘅研究者。今日會分享吓佢嘅研究點樣影響到我。

佢一部分嘅研究可以濃縮到一個噉嘅結論:我哋嘅直覺好多時都會引領我哋去一個比較「舒服」嘅答案,但係一個比較「舒服」嘅答案未必係準確嘅。佢叫呢個傾向做 Cognitive Ease。

Kahneman 用咗幾個實驗去證明呢個人類諗嘢嘅傾向,其中一個係呢個 Bat and Ball Problem。

unsplash-image-c575FAuyo9s.jpg

A bat and ball together cost $1.10. The bat costs $1.00 more than the ball.

How much does the ball cost?

喺呢度問個效果未必咁好,始終大家會知道呢條問題「有伏」。但係我估大家至少有一瞬間,會有衝動去答 $0.10 (正確答案應該係 $0.05,如果你答咗 $0.10 就代表個實驗成功咗)。的確, $0.10 係一個幾吸引嘅答案,而佢「吸引」嘅原因,就係因為佢係一個「舒服」嘅答案,符合 cognitive ease。而根據 Kahnemen 嘅研究,答呢條問題嘅哈佛、MIT 同普林斯頓學生有超過 50% 答咗 $0.10;而如果啲學生係嚟自其他美國大學,就有 80% 答 $0.10。換言之即使係嚟自出名理科勁嘅 MIT,都有一半嘅學生會因為 Cognitive Ease,而答錯一條小學生都識嘅數學題。

unsplash-image-8s8SbqgMxoI.jpg

噉呢個研究代表啲咩?係咪代表哈佛學生嘅數學好渣,連小學生識嘅嘢佢哋都唔識?好明顯唔係啦,如果佢哋喺一個考試嘅環境下面答呢條問題,應該一個錯嘅學生都冇。但係當喺一啲我哋唔係明確噉俾要求佢諗一條「數學問題」,話知你嚟自哈佛定 Princeton,錯嘅機會都超過 50%。

Quote 呢個研究嘅目的,當然唔係要笑哈佛學生啦(唔通港大學生又好叻咩?)。Quote 呢個研究嘅目的,係想講我哋所謂嘅「理性」、「思考」嘅能力係幾咁無稽。Kahneman 喺佢好多嘅實驗入面,多次證明到人嘅思考其實冇我哋諗咁理性,甚至一啲小學生都識嘅題目,當我哋唔用個腦嘅時候,連哈佛學生都會答錯。

然而樂觀啲噉睇,既然我哋犯嘅錯,用小學智力都解決到,噉去解決呢啲錯嘅方法,都應該唔難。喺呢度我想 quote 多個 Kahneman 整嘅實驗。

unsplash-image-9oGoyCX3g_A.png

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

1. Linda is a bank teller.

2. Linda is a bank teller and is active in the feminist movement.

運用少少邏輯,都應該見到 2 嘅機率低過 1。然而喺 Kahneman 嘅實驗,超過 85% 嘅參加者都覺得 Linda 同時喺銀行做 + 係女權主義者嘅機率,多過單純係喺銀行做。當然,我 quote 呢個例子唔係想笑啲參加者,而係想尋找解決呢啲思想盲點嘅方法。

而 Kahneman 喺呢個實驗嘅後續,就揾到解決嘅方法。佢用另外一個方法問咗相同嘅問題。

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

There are 100 persons who fit the description above (that is, Linda's). How many of them are:

1. Bank tellers? __ of 100

2. Bank tellers and active in the feminist movement? __ of 100

當參加者被迫用數字去諗同一條問題嘅時候,冇一個參加者會寫 2 > 1。每個參加者都準確寫出 (1) Bank tellers 嘅人數,多過 (2) Bank tellers + feminist 嘅人數。換言之,當參加者被迫用數字去諗面前嘅問題嘅時候,參加者就能夠避開佢哋嘅思想盲點。

unsplash-image-s9CC2SKySJM.jpg

放返呢啲實驗入現實,其實我哋喺現實生活中有好多時都要做唔同嘅決定。喺做呢啲決定嘅時候,相信我哋都好少會當佢哋係一條數學問題噉去處理。但係偏偏數學其實就係現實生活中不可或缺嘅一部份,而我哋嘅直覺就好少會用理性嘅方式去解決一啲本身應該理性噉解決嘅問題。尤其係一啲會影響一生嘅決定,單純靠直覺判斷,自然容易犯下大錯。

因為直覺,或者無視客觀資訊而犯錯,並唔係「一般人」嘅專利。既然成一半嘅美國頂尖大學學生都會犯呢啲錯,教育本身並唔足以解決呢個問題。甚至 Kahneman 自己一生投放咁多時間去做相關嘅研究,攞埋諾貝爾獎,佢自己都喺佢寫嘅書 Thinking, Fast and Slow 入面承認自己都有犯同樣嘅錯,被直覺衝昏咗頭腦而冇去用理性諗嘢,最終晒咗佢七年嘅時間。

unsplash-image-_zsL306fDck.jpg

既然發現呢個問題嗰個諾貝爾得獎者都會犯同樣嘅錯,我都冇原因相信自己唔會被直覺矇騙。我俾自己嘅課題,就係每次需要做決定嘅時候,無論大小,都要喺能力範圍之內搜集最多嘅資訊,並且儘量抽離,客觀噉去看待面前嘅數字,先去做決定。我未必每次都有呢個機會做到,亦未必每次做得好,但係如果我可以越勤力噉做呢個課題,相信能夠避免行好多不必要嘅冤枉路,亦防止不必要嘅失敗。

Ryan Choy

記得 Follow 埋我!

Instagram @stealtime_inhku
Telegram @RyanChoy
YouTube @Ryan Choy

Previous
Previous

AI 幾時取代律師?

Next
Next

用實力操控運氣