{"id":62275,"date":"2024-09-25T09:56:54","date_gmt":"2024-09-25T16:56:54","guid":{"rendered":"http:\/\/www.todayifoundout.com\/?p=62275"},"modified":"2024-09-25T09:56:54","modified_gmt":"2024-09-25T16:56:54","slug":"the-story-behind-the-most-heated-controversial-and-downright-toxic-debate-in-the-history-of-mathematics","status":"publish","type":"post","link":"https:\/\/www.todayifoundout.com\/index.php\/2024\/09\/the-story-behind-the-most-heated-controversial-and-downright-toxic-debate-in-the-history-of-mathematics\/","title":{"rendered":"The Story Behind the Most Heated, Controversial, and Downright Toxic Debate in the History of Mathematics"},"content":{"rendered":"

\"\"<\/a>Imagine you are a contestant on the classic game show<\/span><\/span> Let\u2019s make a Deal. <\/i><\/span><\/span>The host, Monty Hall, presents you with three closed doors. Behind one is a brand-new sports car, while behind the other two is a goat. <\/span><\/span><\/span><\/span><\/span><\/p>\n

You make your choice and prepare to discover whether you will leave the studio the proud owner of a set new ride or of a four-legged garbage disposal. But at the last moment, Monty offers to make your choice a little easier; he opens one of the doors, revealing a goat, and gives you the option to either change your guess or stick with your original choice. What do you do?<\/span><\/span><\/span><\/span><\/span><\/p>\n

This is the Monty Hall Problem, first posed by American statistician Steve Selvin in a 1975 letter to the journal <\/span><\/span>American Statistician. <\/i><\/span><\/span>For 15 years after its introduction, the puzzle was discussed by a number of academic publications but failed to make much of an impact. But when in September 1990 reader Craig F. Whitaker submitted the question to <\/span><\/span>Parade <\/i><\/span><\/span>Magazine\u2019s <\/span><\/span>Ask Marylin <\/i><\/span><\/span>column, it unexpectedly triggered one of the most heated, controversial, and downright toxic debates in the history of mathematics. <\/span><\/span><\/span><\/span><\/span><\/p>\n

Ask Marylin, <\/i><\/span><\/span>which has run in <\/span><\/span>Parade<\/i><\/span><\/span> since 1986, is written by Marylin sos Savant, who for many years was widely known as the \u201cWorld\u2019s Smartest Person.\u201d Born in St. Louis, Missouri in 1946, in 1956 at the age of 10 vos Savant took the standard 1937 Stanford-Binet Test, achieving an unprecedented IQ score of 228. Later in the 1980s she scored a 46\/48 on the Hoeflin Mega Test, which revised her IQ down to a more reasonable but still impressive 186. Based on these two scores, vos Savant held the Guinness World Record for the highest recorded IQ from 1986 to 1989 when the category was finally retired. <\/span><\/span><\/span><\/span><\/span><\/p>\n

At first glance the answer to the Monty Hall Problem appears obvious: your chances of picking the car, originally 1 in 3, have now been increased to 1 in 2. However, as you\u2019ve been given no additional information as to which door the car sits behind, it makes no difference whether you stick with your original guess or switch; your odds of winning remain the same. However, in her reply to Craig Whittaker\u2019s statement of the problem, vos Savant gave an altogether different answer, arguing that the best strategy was, in fact, to switch your first guess:<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u201cYes; you should switch. The first door has a 1\/3 chance of winning, but the second door has a 2\/3 chance. Here\u2019s a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what\u2019s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You\u2019d switch to that door pretty fast, wouldn\u2019t you?\u201d<\/i><\/span><\/span><\/p>\n

The reaction to this counter-intuitive solution was swift and surprisingly hostile, with vos Savant being bombarded with letters from hundreds of readers – several with PhDs in statistics and related fields – staunchly refuting her analysis. These ranged from the relatively polite but dismissive:<\/span><\/span><\/p>\n

\u201cYour answer to the question is in error. But if it is any consolation, many of my academic colleagues have also been stumped by this problem.\u201d<\/i><\/span><\/span><\/span><\/p>\n

-Barry Pasternack, Ph.D.<\/i><\/span><\/span><\/span><\/p>\n

California Faculty Association<\/i><\/span><\/span><\/span><\/p>\n

\u2026to the arrogant and condescending:<\/span><\/span><\/p>\n

\u201cSince you seem to enjoy coming straight to the point, I\u2019ll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1\/2. As a professional mathematician, I\u2019m very concerned with the general public\u2019s lack of mathematical skills. Please help by confessing your error and in the future being more careful.\u201d<\/i><\/span><\/span><\/span><\/p>\n

-Robert Sachs, Ph.D.<\/i><\/span><\/span><\/span><\/p>\n

George Mason University<\/i><\/span><\/span><\/span><\/p>\n

\u201cYou blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I\u2019ll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don\u2019t need the world\u2019s highest IQ propagating more. Shame!\u201d<\/i><\/span><\/span><\/span><\/p>\n

-Scott Smith, Ph.D.<\/i><\/span><\/span><\/span><\/p>\n

University of Florida<\/i><\/span><\/span><\/span><\/p>\n

\u2026to the downright misogynistic:<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u201cMaybe women look at math problems differently than men.\u201d<\/i><\/span><\/span><\/span><\/p>\n

-Don Edwards<\/i><\/span><\/span><\/span><\/p>\n

Sunriver, Oregon <\/i><\/span><\/span><\/span><\/p>\n

In response to this deluge of criticism, vos Savant devoted her three next columns to patiently re-explaining the logic of her solution, but the majority of her respondents remained unconvinced, with one writing nearly a year later:<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u201cI still think you\u2019re wrong. There is such a thing as female logic.\u201d<\/i><\/span><\/span><\/span><\/span><\/span><\/p>\n

So, is it possible that the \u201cworld\u2019s smartest person” actually got it wrong? Well, actually, no. Much of the confusion regarding the Monty Hall Problem stems from the ambiguous manner in which it was stated in Craig Whittaker\u2019s original letter to <\/span><\/span>Parade<\/i><\/span><\/span> Magazine. Most of those who disagree with vos Savant\u2019s answer assume that the host\u2019s choice of which door to open is entirely random, and in this case the conclusion that the contestant\u2019s chances become 50\/50 would be correct. However, in Steve Selvin\u2019s original formulation of the problem this is not the case. After all, if the host\u2019s choice of door were random, there is a chance he would open the door with the prize behind it, ruining the game. Thus, the host must <\/span><\/span>always <\/i><\/span><\/span>open a door with a goat, and it is this detail which makes all the difference.<\/span><\/span><\/span><\/span><\/span><\/p>\n

To understand why, imagine the three possible scenarios when playing the game: you can either guess the Prize, Goat 1, or Goat 2. If you guess the Prize, then your best strategy is to stay put, since switching will lose you the game. But if you choose Goat 1 or Goat 2, then the best strategy is to switch. As the optimal strategy in 2 out of 3 possible scenarios is to switch, your chances of winning are 2\/3 if you switch compared to only 1\/3 if you stick to your original guess. So your best bet is always to switch. <\/span><\/span><\/span><\/span><\/span><\/p>\n

So how did a seemingly innocuous probability problem manage to ignite such fierce and passionate condemnation? The Monty Hall problem is what American Philosopher Willard Quine called a veridical paradox – a result that intuitively <\/span><\/span>looks <\/i><\/span><\/span>false but can nonetheless be logically proven to be true. Human intuition is particularly ill-suited to dealing with problems of probability, and when presented with a counter-intuitive solution a common reaction is simply to reject it outright. In the case of Marilyn vos Savant this knee-jerk incredulity – along with the egos of top athematicians and not a small amount of sexism – appear to have combined into the perfect storm of academic controversy. <\/span><\/span><\/span><\/span><\/span><\/p>\n

Thankfully, however, history appears to have vindicated Marilyn vos Savant, with polls showing that by 1992 56% of readers and 71% of academics had accepted her solution, compared to only 8% and 35% two years before. And even Robert Sachs of George Mason University, once among vos Savant\u2019s harshest critics, eventually wrote her to repent his former arrogance:<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u201cAfter removing my foot from my mouth I’m now eating humble pie. I vowed as penance to answer all the people who wrote to castigate me. It’s been an intense professional embarrassment.\u201d<\/i><\/span><\/span><\/span><\/p>\n

Expand for References<\/span>

\n

Kaplan, Ellen and Michael, <\/span><\/span>Chances Are\u2026: Adventures in Probability, <\/i><\/span><\/span>Penguin Books, 2007<\/span><\/span><\/span><\/span><\/span><\/p>\n

Crockett, Zachary, <\/span><\/span>The Time Everyone \u201cCorrected\u201d the World\u2019s Smartest Woman,<\/i><\/span><\/span> Priceonomics, February 19, 2015 https:\/\/priceonomics.com\/the-time-everyone-corrected-the-worlds-smartest\/<\/span><\/span><\/span><\/span><\/span><\/p>\n

Tierny, John, <\/span><\/span>Behind Monty Hall\u2019s Doors: Puzzle, Debate, and Answer? <\/i><\/span><\/span>The New York Times, July 21, 1991 https:\/\/www.nytimes.com\/1991\/07\/21\/us\/behind-monty-hall-s-doors-puzzle-debate-and-answer.html<\/span><\/span><\/span><\/span><\/span><\/p>\n

Vos Savant, Marylin, <\/span><\/span>Game Show Problem, <\/i><\/span><\/span>marylinvossavant.com<\/span><\/span><\/a><\/u><\/span><\/span> https:\/\/web.archive.org\/web\/20130121183432\/http:\/\/marilynvossavant.com\/game-show-problem\/<\/span><\/span><\/a><\/u><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"

Imagine you are a contestant on the classic game show Let\u2019s make a Deal. The host, Monty Hall, presents you with three closed doors. Behind one is a brand-new sports car, while behind the other two is a goat. You make your choice and prepare to discover whether you will leave the studio the proud owner of a set new […]<\/p>\n","protected":false},"author":188,"featured_media":62276,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,10],"tags":[],"class_list":["post-62275","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-today-i-found-out","category-science"],"_links":{"self":[{"href":"https:\/\/www.todayifoundout.com\/index.php\/wp-json\/wp\/v2\/posts\/62275","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.todayifoundout.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.todayifoundout.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.todayifoundout.com\/index.php\/wp-json\/wp\/v2\/users\/188"}],"replies":[{"embeddable":true,"href":"https:\/\/www.todayifoundout.com\/index.php\/wp-json\/wp\/v2\/comments?post=62275"}],"version-history":[{"count":1,"href":"https:\/\/www.todayifoundout.com\/index.php\/wp-json\/wp\/v2\/posts\/62275\/revisions"}],"predecessor-version":[{"id":62277,"href":"https:\/\/www.todayifoundout.com\/index.php\/wp-json\/wp\/v2\/posts\/62275\/revisions\/62277"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.todayifoundout.com\/index.php\/wp-json\/wp\/v2\/media\/62276"}],"wp:attachment":[{"href":"https:\/\/www.todayifoundout.com\/index.php\/wp-json\/wp\/v2\/media?parent=62275"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.todayifoundout.com\/index.php\/wp-json\/wp\/v2\/categories?post=62275"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.todayifoundout.com\/index.php\/wp-json\/wp\/v2\/tags?post=62275"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}