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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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Kohske Takahashi, i-Perception (2017)
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Can You Figure Out This Newly Discovered Optical Illusion?
Kohske Takahashi, i-Perception (2017)
Kohske Takahashi, i-Perception (2017)

Ready to have your mind boggled? Take a look at the image above. What shape are the lines? Do they look like curves, or zigzags?

The image, spotted by Digg, is a new type of optical illusion published in the aptly named journal i-Perception. Discovered by Japanese psychologist Kohske Takahashi, it’s called the “curvature blindness illusion,” because—spoiler—the contrast of the lines against the gray background makes our eye see some of the lines as zigzags when, in fact, they’re all smooth curves.

The illusion relies on a few different factors, according to the three experiments Takahashi conducted. For it to work, the lines have to change contrast just at or after the peak of the curve, reversing the contrast against the background. You’ll notice that the zigzags only appear against the gray section of the background, and even against that gray background, not every line looks angled. The lines that look curvy change contrast midway between the peaks and the valleys of the line, whereas the lines that look like they contain sharp angles change contrast right at the peak and valley. The curve has to be relatively gentle, too.

Go ahead, stare at it for a while.

[h/t Digg]

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Vivid Imagery Makes Poetry More Pleasurable, According to Psychologists
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iStock

Contrary to what English teachers led us to believe, most readers don’t judge poetry based on factors like alliteration and rhyme. In fact, a new study published in the journal Psychology of Aesthetics, Creativity, and the Arts suggests that vivid imagery (i.e. sense-evoking description) is what makes a poem compelling, according to Smithsonian.

To determine why some poetic works are aesthetically pleasing while others are less so, researchers from New York University and the Max Planck Institute for Empirical Aesthetics in Frankfurt, Germany, had more than 400 online volunteers read and rate 111 haikus and 16 sonnets. Participants answered questions about each one, including how vivid its imagery was, whether it was relaxing or stimulating, how aesthetically pleasing they found it, and whether its content was positive or negative.

Not surprisingly, taste varied among subjects. But researchers did find, overall, that poems containing colorful imagery were typically perceived as more pleasurable. (For example, one favorite work among subjects described flowers as blooming and spreading like fire.) Emotional valence—a poem's emotional impact—also played a smaller role, with readers ranking positive poems as more appealing than negative ones. Poems that received low rankings were typically negative, and lacked vivid imagery.

Researchers think that vivid poems might also be more interesting ones, which could explain their popularity in this particular study. In the future, they hope to use similar methodology to investigate factors that might influence our enjoyment of music, literature, and movies.

[h/t Smithsonian]

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