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Too Much Time On My Hands: Why Do We Have Leap Years?

David K. Israel explained the leap second the other day, so in the last few hours of this leap year, let's also look at that extra day we had way back in February.

Our average calendar year (the usual 365 days) is a little out of sync with the astronomical year "“ the 365 days, 5 hours, 48 minutes and 46 seconds it takes the earth to go once around the sun. That little chunk of extra time doesn't seem like much (you could probably let 5 hours, 48 minutes and 46 seconds slip by while reading this blog), but over time it adds up. Every four common calendar years, the calendar would be about a full day behind of the astronomical year. As time went on (we're talking a few hundred years), our calendar months would start to fall earlier in the year. We'd have Christmas in the summer and Fourth of July barbecues in the dead of winter. It would be chaos.

To prevent that drift and keep the calendar and astronomical years in sync, we created the leap year and add one extra day to the calendar every four years (most of the time, we'll get to that in a minute). Over a four year period, then, we average 365.25 days per year and just about keep pace with the astronomical year. But a solar year is just shy of 365.25 days "“ 365.2422 days, actually "“ so if we added a leap day strictly every four years, we'd eventually get ahead of the astronomical calendar and months would fall later in the year.

To prevent that other drift, we space our leap years out by the following rules:

1. Years divisible by 4 are leap years (e.g. 2008).

2. Years divisible by 4 and 100 are not leap years (e.g. 1900), unless"¦

3. Those years are also divisible by 400 (e.g. 2000), in which case, they are leap years.

In the long run, then, we average 365.2425 days in a year, which is close enough to the astronomical year that it will take over 3,000 years for the calendar and astronomical years to be off by a day.

If you've got a burning question that you'd like to see answered here, shoot me an email at flossymatt (at) gmail.com. Twitter users can also make nice with me and ask me questions there. Be sure to give me your name and location (and a link, if you want) so I can give you a little shout out.

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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
Original image
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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Opening Ceremony
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These $425 Jeans Can Turn Into Jorts
May 19, 2017
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Opening Ceremony

Modular clothing used to consist of something simple, like a reversible jacket. Today, it’s a $425 pair of detachable jeans.

Apparel retailer Opening Ceremony recently debuted a pair of “2 in 1 Y/Project” trousers that look fairly peculiar. The legs are held to the crotch by a pair of loops, creating a disjointed C-3PO effect. Undo the loops and you can now remove the legs entirely, leaving a pair of jean shorts in their wake. The result goes from this:

501069-OpeningCeremony2.jpg

Opening Ceremony

To this:

501069-OpeningCeremony3.jpg

Opening Ceremony

The company also offers a slightly different cut with button tabs in black for $460. If these aren’t audacious enough for you, the Y/Project line includes jumpsuits with removable legs and garter-equipped jeans.

[h/t Mashable]

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