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How to Solve a Rubik's Cube in Only 23 Moves

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I've never solved a Rubik's Cube. I'm that guy who takes the stickers off puts them where I want them in order to get it over with. (Much to the consternation of any legitimate puzzle-solver who might try to use my cube in the future.) So it was with some amazement that I learned that Rubik's Cube solutions are an area of active mathematical research. There are scholars out there working on ideal cube-solving algorithms, and major progress is being made towards "God's algorithm" -- more on that in a moment.

Math god Tom Rokicki recently proved that all possible Rubik's Cube configurations can be solved in 23 turns or fewer. In order to arrive at this conclusion he needed massive computing power -- the research was done on supercomputers at Sony Pictures Imageworks (in the idle time between rendering special effects for Hollywood movies). Rokicki's conclusion states that for any legal Rubik's Cube configuration, a solution exists in 21, 22, or 23 moves. (And a few special-case cube configurations may be solvable in 20 or fewer.) Now the trick is...what are those moves?

Rokicki's research is interesting in that it doesn't actually tell you specifically how to solve a given cube (contrary to my catchy blog title above) -- it just proves that a solution exists for all possible legal cube configurations, and that solution is guaranteed to be achievable in 23 moves or fewer.

This research is one step in a process that may arrive at "God's algorithm," a theoretically ideal solution to a puzzle. From Wikipedia's page on the algorithm to end all algorithms:

God's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other combinatorial puzzles and mathematical games. It stands for any practical algorithm that produces a solution having the least possible number of moves, the idea being that an omniscient being would know an optimal step from any given configuration.

...It is unknown whether a practical God's algorithm exists for Rubik's Cube.

Further reading: Rokicki's paper on 25-move solutions, a nice Slashdot explanation of the implications of the research, more on God's algorithm, and a highly math-intensive page on Optimal solutions for Rubik's Cube.

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The Brain Chemistry Behind Your Caffeine Boost
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iStock

Whether it’s consumed as coffee, candy, or toothpaste, caffeine is the world’s most popular drug. If you’ve ever wondered how a shot of espresso can make your groggy head feel alert and ready for the day, TED-Ed has the answer.

Caffeine works by hijacking receptors in the brain. The stimulant is nearly the same size and shape as adenosine, an inhibitory neurotransmitter that slows down neural activity. Adenosine builds up as the day goes on, making us feel more tired as the day progresses. When caffeine enters your system, it falls into the receptors meant to catch adenosine, thus keeping you from feeling as sleepy as you would otherwise. The blocked adenosine receptors also leave room for the mood-boosting compound dopamine to settle into its receptors. Those increased dopamine levels lead to the boost in energy and mood you feel after finishing your morning coffee.

For a closer look at how this process works, check out the video below.

[h/t TED-Ed]

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Sophie Nightingale / University of Warwick
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Can You Spot Which Photo Is Fake? Most People Can’t
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Sophie Nightingale / University of Warwick

In a digital world, it’s easier than ever to fool people. Sophisticated Photoshop jobs, social media, and viral news cycles mislead readers into mistaking shots from a Lebanese music video for real scenes of destruction from Aleppo, thinking that Vladimir Putin was the center of attention at the G-20 summit, or believing that Elizabeth Taylor and Marilyn Monroe posed together for a photo shoot in the park.

While it would be nice to tell ourselves that we would never be duped by such fake images, the truth is, most people can’t distinguish between a manipulated photo and a real one. That’s the takeaway from a new study in Cognitive Research: Principle and Implications. As the team at Science reports, the participants were only able to pinpoint fake images two-thirds of the time.

First, psychologists from the University of Warwick asked more than 700 volunteers to look at real and fake images and identify the changes. The researchers used 10 color photographs sourced from Google searches, manipulating them through airbrushing, adding elements in, subtracting elements, and distorting shadows, and shearing trees. They applied each of these five manipulation techniques separately to a portion of the photos, eventually creating 30 manipulated photos and 10 real ones. All the participants saw one of each of the manipulation types in different photos.

An older man stands in the street in front of a house.
Can you spot the differences between the manipulated image at the top of the page and the original version above?
Sophie Nightingale / University of Warwick

The participants performed slightly above chance rates, identifying photos correctly as real only 58 percent of the time and spotting manipulations 66 percent of the time. Even when they did identify a manipulated photo, though, they didn’t necessarily know where it had been altered.

In a second study, the researchers did the same thing, but using photos study co-author Sophie J. Nightingale took with her Nikon camera, controlling for the fact that images found online could be manipulated before the researchers even downloaded them. They then had almost 660 people take an online survey testing their ability to spot fakes. They had to look at photos and label whether it was fake and if they could see where it was manipulated, whether it was fake but they didn’t know where it had been altered, or whether it was an original. At the end of the study, the subjects identified just 62 percent of the fake images correctly.

Woman standing outside
The first image is the original. The second was manipulated to add in a water spout, airbrush the woman's face, and make other slight changes.
Sophie Nightingale / University of Warwick

The results were the same regarding images that had been manipulated in both overtly unrealistic ways and photos that featured more plausible changes. One reason might be the way that our visual system simplifies information. As long as object geometries and shadows are roughly correct, our eyes accept them as accurate.

“It remains to be determined whether it is possible to train people to make use of physically implausible inconsistencies,” the researchers write. “Perhaps one possibility would entail ‘teaching' the visual system to make full use of physical properties of the world as opposed to automatically simplifying them.”

You can still take a 10-minute online survey for the project here and test your own manipulation awareness skills. (I had to take wild guesses on most of them.)

If this makes you weep for the future of the world, at least know that it’s a timeless problem. Manipulated, misleading images have been around since the earliest days of photography.

[h/t Science]

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