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Can Math Help You Find Mr. or Miss Right?

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Are they really right for you? Don't leave it to your heart to decide... let the math do the judging! Here are three mathematical theories to help determine if your marriage will last (or if it should happen at all).

1. The Mathematics of Marriage

In their book, The Mathematics of Marriage, mathematician James D. Murray and psychologist John Gottman describe their use of calculus to study interactions between couples. Using a model Gottman developed in 1979, the pair surveyed 700 newly married couples in King County, Washington in 1992. They analyzed couples' 15 minute conversations using a scoring system that assigned a number based on each statement, expression, and even pulse rates. Then they model quantified the ratio of positive to negative interactions during the talk. The magic ratio was 5:1. When the ratio falls below this, a relationship may be in trouble.

These numbers were plotted as a function of time and were used to make predictions as to whether the couple would i) divorce, or ii) stay married a) happily, or b) unhappily. They called this the "Dow Jones for Marital Conversation." Every 1-2 years until 2004 the couples were asked to complete a questionnaire assessing their marriage. The predictions on which couples would get divorced was 94% accurate, and typically divorce occurred after 4 years.

2. The 37% Rule

In 1997, Dr. Peter Todd of the Max Planck Institute in Munich described his 37% rule, also known as the secretary rule. Imagine if you have to fill 1 secretarial position and have n # of applicants, ranked from best to worst. Now, here's where the math gets hairy. Assuming you skip the worst ones (n/e of the applicants where e is the base of the natural logarithm), and you only interview applicants who are better than those you have already interviewed (n/e + 1 is better than all previous n/e interviews), the probability of selecting the best applicant from the pool rounds to 1/e, or around 37%. Hence, you should be able to pick the best secretary after interviewing 37% of the applicants.

If there are about 100 potential "mates" you don't have to date 37 people to finally meet Mr. Right, #37. Instead, Dr. Todd advises you set your "aspiration level," what you are looking for in a partner, to a range. Then date only those who are in the top 25% of that range. Your sample size, therefore, is reduced to only 10 dates. One of those should make the cut.

3. The "What are the Chances My Marriage Will Last?" Equation

Picture 66.pngGarth Sundem, author of GeekLogic created his own equations to determine: 1. What are the Chances My Marriage Will Last? 2. Should We Get Married? and 3. How Many Kids Should we Have?The "What are the Chances my Marriage Will Last?" is based on an 11,000 person study by the CDC that explored factors that help and hurt a marriage's chances of working. Here's the equation:

where"¨ A= Her age at time of marriage

E=Current combined years of post-high-school education

K= Number of kids from this marriage

R= How religious is the couple (1-10 with 10 being "the Pope")

D= Combined number of divorces of couple's parents

P= Combined previous marriages

T= Years at which you are computing the chances

H.E.A. = % chance of Happily Ever After
But don't worry about calculating it out yourself. Over at Political Calculations, you can type in your personal data and it spits out the probability you and your partner will still be married at a given year of anniversary.

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iStock // Ekaterina Minaeva
Man Buys Two Metric Tons of LEGO Bricks; Sorts Them Via Machine Learning
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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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© Nintendo
Nintendo Will Release an $80 Mini SNES in September
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© Nintendo

Retro gamers rejoice: Nintendo just announced that it will be launching a revamped version of its beloved Super Nintendo Classic console, which will allow kids and grown-ups alike to play classic 16-bit games in high-definition.

The new SNES Classic Edition, a miniature version of the original console, comes with an HDMI cable to make it compatible with modern televisions. It also comes pre-loaded with a roster of 21 games, including Super Mario Kart, The Legend of Zelda: A Link to the Past, Donkey Kong Country, and Star Fox 2, an unreleased sequel to the 1993 original.

“While many people from around the world consider the Super NES to be one of the greatest video game systems ever made, many of our younger fans never had a chance to play it,” Doug Bowser, Nintendo's senior vice president of sales and marketing, said in a statement. “With the Super NES Classic Edition, new fans will be introduced to some of the best Nintendo games of all time, while longtime fans can relive some of their favorite retro classics with family and friends.”

The SNES Classic Edition will go on sale on September 29 and retail for $79.99. Nintendo reportedly only plans to manufacture the console “until the end of calendar year 2017,” which means that the competition to get your hands on one will likely be stiff, as anyone who tried to purchase an NES Classic last year will well remember.

In November 2016, Nintendo released a miniature version of its original NES system, which sold out pretty much instantly. After selling 2.3 million units, Nintendo discontinued the NES Classic in April. In a statement to Polygon, the company has pledged to “produce significantly more units of Super NES Classic Edition than we did of NES Classic Edition.”

Nintendo has not yet released information about where gamers will be able to buy the new console, but you may want to start planning to get in line soon.