In the 1990's a lady called Marilyn vos Savant received 10,000 complaints, many from men claiming to have Ph.Ds, after writing an article discussing a simple math problem. Most of the complaints claimed she was wrong purely because she was a woman.
By all accounts, Marilyn vos Savant was a child prodigy.
Born in St. Louis, Missouri in 1946, the young savant quickly developed an aptitude for math and science. At age 10, she was given two intelligence tests -- the Stanford-Binet, and the Mega Test -- both of which placed her mental capacity at that of a 23-year-old. She went on to be listed in the Guinness Book of World Records for having the “World’s Highest IQ,” and, as a result, gained international fame.
Despite her status as the "world’s smartest woman,” vos Savant maintained that attempts to measure intelligence were “useless,” and she rejected IQ tests as unreliable. In the mid-1980s, with free rein to choose a career path, she packed her bags and moved to New York City to be a writer.
In the world of statistical mathematics there’s a simple thought experiment known colloquially as “The Monty Hall problem” which is a magnet for arguments. When vos Savant politely responded to a reader’s inquiry on the Monty Hall Problem, a then-relatively-unknown probability puzzle, she never could’ve imagined what would unfold: though her answer was correct, she received over 10,000 letters, many from noted scholars and Ph.Ds, informing her that she was a hare-brained idiot.
What ensued for vos Savant was a nightmarish journey, rife with name-calling, gender-based assumptions, and academic persecution.
The Monty Hall Problem: A Brief History
For anyone who isn’t familiar with the Monty Hall problem, it’s an age old math logic problem named after a game show from the 60’s called Let’s Make a Deal hosted by a guy called, you guessed it, Monty Hall. The problem itself was actually first devised (or at least written down) in the form we know it in the 70’s, but was named after Monty Hall for reasons you’ll see in about 40 seconds or so, depending on how fast you read.
In Let’s Make a Deal, host and magnificent haircut owner, Monty Hall would sometimes present contestants with three doors, one of which led to a brand new car or similar fantastical price while the other two contained fuck all. After a contestant selected one of the three doors, Monty would then open one of the doors they hadn’t chosen that led to nothing and then offer the contestant a chance to change their mind and pick the other, unopened door.
Statistically, if you’re ever in this situation and want to win the car, you’re always better off switching, because doing so results in a 2/3 chance of winning, whereas sticking with your gut and not being a huge pussy only results in winning 1/3 of the time. Here’s a diagram showing that regardless of what choices you make, switching will always result in a more favourable outcome.
If you’re curious about why the booby prize in this scenario is a goat, that’s because back in 1990, a curious reader wrote in to Parade magazine to ask their resident egg head, Marilyn vos Savant, the following question:
“Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice of doors?”
Marilyn (who is literally regarded as one of the smartest people on Earth by the Guinness book of World Records), answered the question by stating that switching would result in 2/3 chance of winning, as you can see in the diagram above. If you don’t believe this is the case, grab a pen and paper and try to work it out for yourself, after a few minutes you’ll see that switching invariably nets more positive results overall because math is fucking awesome. If you’re still having trouble with why switching is more likely to result in you making out like a baller, picture it this way:
When you first choose a door, the odds of you picking a door containing a prize is 1/3 whereas the odds of the other doors containing the prize is 2/3. When one of those two doors is eliminated, the odds of the remaining door containing a prize stays at 2/3 while the odds of your door stay at 1/3. This works because opening a door doesn’t retroactively change the initial probability of you being right when you first picked a door, similar to how the first number of a lottery draw matching a number on your ticket doesn’t change the odds of you actually holding a winning ticket.
A few days after the column went live featuring an explanation similar to the one above in a nicer font, Parade was inundated with hundreds of letters from angry men saying that Marilyn was full of shit. It should be pointed out that many of these men claimed to hold degrees in advanced mathematics, yet none of them seemed to be familiar with a piss-easy logic problem originally based on a century old puzzle devised by one of the most famous mathematicians in history.
Joseph Louis François Bertrand
What’s more hilarious is that even after Marilyn explained how the problem worked in excruciating detail in a follow-up article that appeared on the front page of the New York Times, thousands of complaints continued to pour in (mostly from men) who were positive that she was wrong, because how could someone with a vagina and an one of the highest IQs ever recorded know more about math than them?
Although Marilyn received literally thousands of letters of complaint about the article’s shoddy math, not a single one contained an explanation for why she was wrong. Because they couldn’t actually criticise Marilyn flawless logic, many men fell back on insisting that she was wrong, solely because she is a woman, again, without ever offering a counter explanation for why they were right.
You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I’ll 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’t need the world’s highest IQ propagating more. Shame!
Scott Smith, Ph.D.
University of Florida
May I suggest that you obtain and refer to a standard textbook on probability before you try to answer a question of this type again?
Charles Reid, Ph.D.
University of Florida
I am sure you will receive many letters on this topic from high school and college students. Perhaps you should keep a few addresses for help with future columns.
W. Robert Smith, Ph.D.
Georgia State University
You are utterly incorrect about the game show question, and I hope this controversy will call some public attention to the serious national crisis in mathematical education. If you can admit your error, you will have contributed constructively towards the solution of a deplorable situation. How many irate mathematicians are needed to get you to change your mind?
E. Ray Bobo, Ph.D.
You made a mistake, but look at the positive side. If all those Ph.D.’s were wrong, the country would be in some very serious trouble.
Everett Harman, Ph.D.
U.S. Army Research Institute
You are the goat!
Western State College
Maybe women look at math problems differently than men.
Of the 10,000 letters of complaint Marilyn received about the article, about 5-10% of them were men claiming that she had to be wrong because she was applying “woman logic” to a problem that can be solved in 30 seconds with a pen and sheet of paper. The best part is, even after Marilyn published an explanation for the problem on the front page of one of the most respected newspapers in the world as well as publishing another article in Parade to explain the problem in as simple a way as she possibly could. People still didn’t believe her because they couldn’t bring themselves to accept that a woman was smarter than them.
Eventually though, many of those who’d written in to correct vos Savant’s math backpedaled and ceded that they were in error.
An exercise proposed by vos Savant to better understand the problem was soon integrated in thousands of classrooms across the nation. Computer models were built that corroborated her logic, and support for her intellect was gradually restored. Whereas only 8% of readers had previously believed her logic to be true, this number had risen to 56% by the end of 1992, writes vos Savant; among academics, 35% initial support rose to 71%.
Among the new believers was Robert Sachs, a math professor at George Mason University, who’d originally written a nasty letter to vos Savant, telling her that she “blew it,” and offering to help "explain.” After realizing that he was, in fact, incorrect, he felt compelled to send her another letter -- this time, repenting his self-righteousness.
“After removing my foot from my mouth I'm now eating humble pie,” he wrote. “I vowed as penance to answer all the people who wrote to castigate me. It's been an intense professional embarrassment.”
Source: Factfriend.com, Zachary Crockett / priceonomics.com