Mathematics | The Knowledge Dynasty


New algorithm lets you make anything in origami

They say if you fold 1,000 origami cranes out of individual sheets of paper your deepest wishes will be granted. I tried it once: I was a lonely college kid and I ended up with pink eye. However, a new paper out of MIT describes a way to possibly make 1,000 origami cranes out of one piece of paper, a unique feat that is now a possibility thanks to a new origami algorithm.

Computer science has long struggled with computational origami. In 2008 Tomohiro Tachi first piece of software that can create folding patterns, usually out of long strips of paper. The new algorithm, however, uses a simpler, large sheet of paper and is more watertight, meaning it has more folds and fewer joints.

The new algorithm is supposed to give you much better, more practical foldings, said one of the researchers, Erik Demaine. We dont know how to quantify that mathematically, exactly, other than it seems to work much better in practice. But we do have one mathematical property that nicely distinguishes the two methods. The new method keeps the boundary of the original piece of paper on the boundary of the surface youre trying to make. We call this watertightness.

The algorithm, which will be added to the folding software to improve the system, means you can fold nearly anything including the 1,000 simple cranes with a big enough piece of paper.

What was known before was either cheating winding the polyhedron with a thin strip or not guaranteed to succeed, said math professor Joseph ORourke. Their new algorithm is guaranteed to produce a folding, and it is the opposite of cheating in that every facet of the polyhedron is covered by a seamless facet of the paper, and the boundary of the paper maps to the boundary of the polyhedral manifold their watertight property. Finally, the extra structural flash needed to achieve their folding can all be hidden on the inside and so is invisible.

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The only way to prove you aren’t a robot is to solve this chess puzzle

Check it out, Mate!

Image: James Tagg

Check out the chess board above: looks wrong, right?

If you’ve ever played chess, you know something’s amiss, here. For one thing, someone chose to exchange a pawn for another bishop instead of a queen. For another, virtually all the action’s moved to the left side of a board.

It’s hard to imagine how the game got here: it’s even harder to imagine what happens next, let alone a scenario in which four white pawns and a white king could play to a draw, or even win this game.

The Penrose Chess Puzzle: Can you find the solution that results in either a white win or a game draw?

Image: James tagg

Yet: scientists at the newly-formed Penrose Institute say it’s not only possible, but that human players see the solution almost instantly, while chess computers consistently fail to find the right move.

“We plugged it into Fritz, the standard practice computer for chess players, which did three-quarters of a billion calculations, 20 moves ahead,” explained James Tagg Co-Founder and Director of the Penrose Institute, which was founded this week to understand human consciousness through physics.

“It says that one-side or the other wins. But,” Tagg continued, “the answer that it gives is wrong.”

Tagg and his co-founder, Mathematical Physicist and professor Sir Roger Penrose who successfully proved that black holes have a singularity in them cooked up the puzzle to prove a point: Human brains think differently.

(Those who figure out the puzzle can send their answers to Penrose to be entered to win the professor’s latest book.)

“Humans can look at a problem like this strange chess board configuration,” said Tagg, “and understand it. What a computer does is brute force calculation, which is different.” This is set up, rather exquisitely, to show the difference, he added.

They forced the computer out of its comfort zone by, at least in part, making an unusual choice: the third bishop.

“All those bishops can move in lots of different ways, so you get computation explosion. To calculate it out would suck up more computing power than is available on earth,” claimed Tagg.

Tagg told us that there is, in fact, a natural way to get to this board configuration.

We’re trying to figure it out here, but lacked an extra black bishop. So we tagged one to keep track.

Image: lance ulanoff/mashable

Sir Richard Penrose’s brother is, according to Tagg, a very strong chess player. He assures me that it’s a position you can get to, but I have not played it through. Question is, is there a rational game that gets you there?

In fact, those who can figure out that second puzzle and get the answer to Penrose, could also receive a free copy of Professor Penrose’s book.

Chess computers fail at Penrose’s chess puzzle because they have a database of end-games to choose from. This board is not, Tagg and Penrose believe, in the computer’s playbook. “We’re forcing the chess machine to actually think about the position, as opposed to cheat and just regurgitate a pre-programmed answer, which computers are perfect at,” said Tagg.

So far, Tagg and the Penrose Institute haven’t heard from any artificial intelligence experts refuting their claims. “I’m quite surprised,” said Tagg.

Mashable has contacted several AI experts for comment and will update this post with their response.

Aside from the fun of solving this puzzle (Tagg said hundreds already have and claim they have done so in seconds), it poses a deeper question: Are we executing some fiendishly clever algorithm in our brain, that cuts through the chaff? It is just a higher level of computation, one that computers can still aspire to or something unique to brain-matter-based thought?

Tagg said Penrose Institute falls into the latter camp.

Penrose and Tagg don’t think you can simply call a brain a machine. It sits in skull, made of gray matter and we don’t understand how it works. “Simply calling it a clever computer, this sort of puzzle shows that it clearly is not,” he said.

You can send your Chess Puzzle solution to the Penrose Institute here:

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The Weather Channel takes on stereotypes in STEM

Female meteorologists have a simple request: Stop labeling us educated, highly trained scientists as “weather girls.” And maybe stop commenting on our dresses and lipstick and start asking about our forecasts.

“Women on television can also be scientists. It’s that simple,” said Ginger Zee, a meteorologist on Good Morning America and ABC World News Tonight.

On Sunday, The Weather Channel (TWC) debuted a two-part series exploring the unique challenges that women face in science, technology, engineering and mathematics (STEM).

In the clip shown here, Zee and two other leading meteorologists Janice Huff of WNBC-New York and Jen Carfagno join Marshall Shepard, host of TWC’s Weather Geek program, to discuss ways to encourage young women to embrace science from an early age.

Left to right: Marshall Shepard, Jen Carfagno, Janice Huff and Ginger Zee on the set of “Women in Science Wx Geeks.”

Image: the weather channel

“More than ever, there are opportunities for girls and women who are interested in science to … find extra help and support along the way,” Carfagno, who hosts TWC’s AMHQ program, told Mashable.

She noted that stereotypes about women in science extend far beyond the 1950s-notion of the well-heeled weather girl. Think about the recurring movie plot, in which a frizzy, bespectacled geek suddenly gets hair gel, contact lenses and stops droning on about all that “dull” science stuff.

“Society still hangs on to that, and it’s a sort of underlying theme I feel that’s hard to shake,” Carfagno said.

Given those lingering cultural perceptions, and the fact that more men work in meteorology than women, “We decided we really need to do a show about women in science,” she said.

Part one of TWC‘s “Wx Geeks” special on women in science airs Jan. 29 at 12 p.m. ET. Part two airs Feb. 5 at the same time.

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