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5 Quirky Numbers You Should Know

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When it comes to peculiar numbers, pi is blasé. Whether you're looking for your next four-digit phone passcode or just something to talk about the next time you bump into a mathematician, we've got you covered with these intriguing collections of digits. 

1. The Münchhausen number: 3435

Named after 18th century German nobleman Baron Hieronymus von Münchhausen—whose tall tales were turned into fictional stories that included riding a cannonball and visiting the moon—this number takes its name from its ability to “raise itself.” A Münchhausen number is one that equals the sum of its digits raised to each digit's power.  Since 0^0 is not well-defined, the only Münchhausen numbers are 1 and 3435 = 3^3 + 4^4 + 3^3 + 5^5 = 27 + 256 + 27 + 3125. 

The individuality of the number alone would be enough to interest us, but since it comes complete with a pun based a fictional character, it’s more than deserving of a place on our list. 

2. The Self-Descriptive Number: 6210001000 

There is precisely one base-10 number that meets the criteria for a Self-Descriptive number: a 10-digit number where the digits can be numbered 0 to 9, and any digit n is the number of ns in the number:  

6 = 0, so there are six zeros in the number.
2 = 1, so there is one two in the number.
1 = 2, so there are two ones in the number.
0 = 3, so there are zero threes in the number.
0 = 4, so there are zero fours in the number.

And so on. 

3. Kaprekar’s Constant: 6174 

Why constant? Because if you perform the following process, Kaprekar's routine, the operation will always yield 6174 in no more than seven iterations.

Take any four-digit number, using at least two different digits. (Leading zeros are allowed, to keep the number of digits at four.)

Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.

Subtract the smaller number from the bigger number.

Go back to step 2. 

To illustrate the process, we’ll perform it on 7455.  

7455
7554, 4557
7554 - 4557 = 2997
2997 → 9972 - 2799 = 7173
7173 → 7731 - 1377 = 6354
6354 → 6543 - 3546 = 3087
3087 → 8730 - 0378 = 8352
8352 → 8532 - 2358 = 6174, in six iterations of the routine.

Go on.  Try it yourself.  We'll wait. 

4. The Hardy–Ramanujan number: 1729 

This number got its start when British mathematician G. H. Hardy visited Indian mathematician Srinivasa Ramanujan while Ramanujan was ill in the hospital. Hardy later recalled: 

I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. ‘No,’ [Ramanujan] replied, ‘it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.’

The two cubes are 1729 = 1^3 + 12^3 = 9^3 + 10^3. Numbers that are the smallest number expressible as the sum of two positive cubes in n distinct ways are called “taxicab numbers” for just this reason. 

5. The Golden Ratio: 1.618...

This one is more of a mathematical expression where, if variables a and b are greater than zero, a + b : a :: a : b, which basically means that the sum of the variables is to the first variable as the first variable is to the second. 

This ratio has been known since the Ancient Greeks, and some people see it represented in architectural works. For instance, the Great Mosque of Kairouan is often cited as a nearly perfect representation (but the jury is still out). Somewhere along the line people got the idea that this ratio is super sexy—though Euclid himself recorded it simply as “an extreme and mean ratio” in the Elements—and some modern designers deliberately incorporate it into their designs. More recently, its been found in certain patterns in nature.

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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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