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Understanding the Monty Hall Problem

The Monty Hall problem is a logic puzzle named for the host of the gameshow Let's Make a Deal. It's one of my favorite such problems, because it's an example of math completely contradicting my gut instinct. Even though I know the math says to do one thing, my gut consistently says the other -- and thus every time the problem is explained, I get a little window into my fallible human brain. In fact, I used to be so tied to my gut on this one that I would fail to explain the Monty Hall problem correctly when describing it to others, because I always assumed my gut instinct was actually correct. (Yes, I took Math for Liberal Arts Majors.)

Marilyn vos Savant posed the problem in one of her columns like so:

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 No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

I won't spoil the answer. Think on it for a moment. Do you switch or not? Now watch this AsapSCIENCE video for a brief explanation of what math says is the right thing to do...and what my gut says is crazy:

Having said all this, it's important to note that we have a shared assumption that a car is better than a goat. But if we're talking about one of those awesome unicorn goats, maybe you want that instead.

Also relevant: previous coverage of Monty Hall, plus an interview with the man. And although they're not strictly related, the Monty Hall Problem occupies the same space in my brain as The Abilene Paradox.

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Art
The Simple Optical Illusion That Makes an Image Look Like It's Drawing Itself
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Artist James Nolan Gandy invents robot arms that sketch intricate mathematical shapes with pen and paper. When viewed in real time, the effect is impressive. But it becomes even more so when the videos are sped up in a timelapse. If you look closely in the video below, the illustration appears to materialize faster than the robot can put the design to paper. Gizmodo recently explained how the illusion works to make it look like parts of the sketch are forming before the machine has time to draw them.

The optical illusion isn’t an example of tricky image editing: It’s the result of something called the wagon wheel effect. You can observe this in a car wheel accelerating down the highway or in propeller blades lifting up a helicopter. If an object makes enough rotations per second, it can appear to slow down, move backwards, or even stand still.

This is especially apparent on film. Every “moving image” we see on a screen is an illusion caused by the brain filling in the gaps between a sequence of still images. In the case of the timelapse video below, the camera captured the right amount of images, in the right order, to depict the pen as moving more slowly than it did in real life. But unlike the pen, the drawing formed throughout the video isn't subject to the wagon-wheel effect, so it still appears to move at full speed. This difference makes it look like the sketch is drawing itself, no pen required.

Gandy frequently shares behind-the-scenes videos of his mechanical art on his Instagram page. You can check out some of his non-timelapse clips like the one below to better understand how his machines work, then visit his website to browse and purchase the art made by his 'bots.

And if you think his stuff is impressive, make sure to explore some of the incredible art robots have made in the past.

[h/t Gizmodo]

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science
Narcissists Are More Likely to Be Compulsive Facebook Users
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Updating your Facebook status throughout the day is probably a sign you need a different hobby, but according to a new study, the habit can also indicate something else. As PsyPost reports, people with Facebook addiction are also likely to be narcissists.

For their recent study published in the journal PLOS One, scientists from Ruhr-Universität Bochum in Germany followed the Facebook activity of 179 German students over the course of a year. They were looking for cases of so-called Facebook Addiction Disorder (FAD) based on the Bergen Facebook Addiction Scale, a system developed by University of Bergen researchers that measures factors like mood modification, withdrawal, and relapse in relation to Facebook use.

They wanted to find out whether FAD was linked to other mental health problems. In addition to gauging Facebook compulsion, they also surveyed subjects on their depression and anxiety levels, social support systems, physical health, narcissism, and general satisfaction with life. The results showed a strong correlation between FAD and narcissism. Rather than Facebook making its users more narcissistic, the researchers state that people with narcissistic personalities are at a greater risk of developing the social media addiction.

"Facebook use holds a particular meaning for narcissistic people," they write in the paper. "On Facebook, they can quickly initiate many superficial relationships with new Facebook-friends and get a large audience for their well-planned self-presentation. The more Facebook-friends they have, the higher is the possibility that they attain the popularity and admiration they are seeking; whereas in the offline world they might not be as popular since their interaction partners can quickly perceive their low agreeableness and exaggerated sense of self-importance."

The researchers also found a connection between Facebook addiction and higher levels of stress, depression, and anxiety.

Studies investigating Facebook Addiction Disorder have been conducted in the past, but there’s still not enough research to classify it as an official behavioral addiction. The researchers hope their work will lead to similar studies pinning down a link between FAD and mental health consequences.

[h/t PsyPost]

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