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Math Homework I Wish I Still Got

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Call me a nerd (hey, I do write for Mental_floss), but I kind of miss my math homework. Back in the days before algebra and trig, math homework meant math problems embedded in intricate stories, arithmetic trickery and the occasional logic puzzle. In short, they were the kinds of puzzles that people secretly love to do in their free time. But once high school hit, math problems got a lot more tedious and complex and less fun. Now that I'm in college, I've completely ditched math and if it weren't for my obsession with sudoku and kakuro, I doubt I'd use my left brain at all.

So, for the sake of geeky nostalgia, here's the kind of homework I wish I could still get from math classes. Be sure to chime in with the problems you couldn't wait to get home to do.

Hanging Balance Problems

Different shapes hang in balance in elaborate, mobile-like structures. With just a few clues, it was up to you to figure how much each shape weighed in order to keep everything in balance. Looking back, those balance problems were just a sneaky way to get 5th graders thinking about algebra, but making equations with triangles and cubes is way more appealing than thinking in terms of x's and y's. These were by far my favorite form of math homework- I would even ask for extra problems and often my parents would even make their own copies to make math homework a family affair.

Crossfigures

I like crosswords. I like math (to a point). So the crossfigure seemed to be the best of both worlds. The crossfigure is just a crossword puzzle, only with numbers. The clues often played off each other (like "29-across minus four"), so solving them involved some knowhow. I didn't get them as homework so often, mostly just as a fun break from the daily grind.

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Bobo's Word Problems

Sadly, I can't give you many details on this- Bobo was a character in a series of word problems I was given for a class. Something about having a recurring character (especially one that I imagined to be a clown) just made word problems a little easier to swallow. In fact, I liked the Bobo problems so much, my sixth grade math fair project was just a series of Bobo's adventures that I solved.

Anything related to sports

Even though calculus had it's fair share of word problems, they just weren't real enough situations. When will I be trying to figure out the volume of a tank of oil that is simultaneously being filled and drained at different rates? Even the old-school arithmetic problems were a little hard to grasp- who shares apples anyways? But sports made word problems easier to handle. Figuring out different ways to make an NFL team score 20 points or figuring out a pitcher's ERA made math fun. Thankfully, fellow blogger Sandy was able to bring back that feeling with this Brain Game last month.

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iStock // Ekaterina Minaeva
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Man Buys Two Metric Tons of LEGO Bricks; Sorts Them Via Machine Learning
May 21, 2017
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iStock // Ekaterina Minaeva

Jacques Mattheij made a small, but awesome, mistake. He went on eBay one evening and bid on a bunch of bulk LEGO brick auctions, then went to sleep. Upon waking, he discovered that he was the high bidder on many, and was now the proud owner of two tons of LEGO bricks. (This is about 4400 pounds.) He wrote, "[L]esson 1: if you win almost all bids you are bidding too high."

Mattheij had noticed that bulk, unsorted bricks sell for something like €10/kilogram, whereas sets are roughly €40/kg and rare parts go for up to €100/kg. Much of the value of the bricks is in their sorting. If he could reduce the entropy of these bins of unsorted bricks, he could make a tidy profit. While many people do this work by hand, the problem is enormous—just the kind of challenge for a computer. Mattheij writes:

There are 38000+ shapes and there are 100+ possible shades of color (you can roughly tell how old someone is by asking them what lego colors they remember from their youth).

In the following months, Mattheij built a proof-of-concept sorting system using, of course, LEGO. He broke the problem down into a series of sub-problems (including "feeding LEGO reliably from a hopper is surprisingly hard," one of those facts of nature that will stymie even the best system design). After tinkering with the prototype at length, he expanded the system to a surprisingly complex system of conveyer belts (powered by a home treadmill), various pieces of cabinetry, and "copious quantities of crazy glue."

Here's a video showing the current system running at low speed:

The key part of the system was running the bricks past a camera paired with a computer running a neural net-based image classifier. That allows the computer (when sufficiently trained on brick images) to recognize bricks and thus categorize them by color, shape, or other parameters. Remember that as bricks pass by, they can be in any orientation, can be dirty, can even be stuck to other pieces. So having a flexible software system is key to recognizing—in a fraction of a second—what a given brick is, in order to sort it out. When a match is found, a jet of compressed air pops the piece off the conveyer belt and into a waiting bin.

After much experimentation, Mattheij rewrote the software (several times in fact) to accomplish a variety of basic tasks. At its core, the system takes images from a webcam and feeds them to a neural network to do the classification. Of course, the neural net needs to be "trained" by showing it lots of images, and telling it what those images represent. Mattheij's breakthrough was allowing the machine to effectively train itself, with guidance: Running pieces through allows the system to take its own photos, make a guess, and build on that guess. As long as Mattheij corrects the incorrect guesses, he ends up with a decent (and self-reinforcing) corpus of training data. As the machine continues running, it can rack up more training, allowing it to recognize a broad variety of pieces on the fly.

Here's another video, focusing on how the pieces move on conveyer belts (running at slow speed so puny humans can follow). You can also see the air jets in action:

In an email interview, Mattheij told Mental Floss that the system currently sorts LEGO bricks into more than 50 categories. It can also be run in a color-sorting mode to bin the parts across 12 color groups. (Thus at present you'd likely do a two-pass sort on the bricks: once for shape, then a separate pass for color.) He continues to refine the system, with a focus on making its recognition abilities faster. At some point down the line, he plans to make the software portion open source. You're on your own as far as building conveyer belts, bins, and so forth.

Check out Mattheij's writeup in two parts for more information. It starts with an overview of the story, followed up with a deep dive on the software. He's also tweeting about the project (among other things). And if you look around a bit, you'll find bulk LEGO brick auctions online—it's definitely a thing!

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Nick Briggs/Comic Relief
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What Happened to Jamie and Aurelia From Love Actually?
May 26, 2017
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Nick Briggs/Comic Relief

Fans of the romantic-comedy Love Actually recently got a bonus reunion in the form of Red Nose Day Actually, a short charity special that gave audiences a peek at where their favorite characters ended up almost 15 years later.

One of the most improbable pairings from the original film was between Jamie (Colin Firth) and Aurelia (Lúcia Moniz), who fell in love despite almost no shared vocabulary. Jamie is English, and Aurelia is Portuguese, and they know just enough of each other’s native tongues for Jamie to propose and Aurelia to accept.

A decade and a half on, they have both improved their knowledge of each other’s languages—if not perfectly, in Jamie’s case. But apparently, their love is much stronger than his grasp on Portuguese grammar, because they’ve got three bilingual kids and another on the way. (And still enjoy having important romantic moments in the car.)

In 2015, Love Actually script editor Emma Freud revealed via Twitter what happened between Karen and Harry (Emma Thompson and Alan Rickman, who passed away last year). Most of the other couples get happy endings in the short—even if Hugh Grant's character hasn't gotten any better at dancing.

[h/t TV Guide]

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