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The Science of Gift-Giving (and how Santa does it)

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An article from a 1990 issue of Spy magazine that examines the physics of Santa's toy delivery journey has been floating around the Internet for as long as I can remember. It's ubiquity at a certain time of year sort of makes it the web version of the "Yes, Virginia, there is a Santa Claus" editorial. If you haven't seen it, here it is:

1) No known species of reindeer can fly. BUT there are 300,000 species of living organisms yet to be classified, and while most of these are insects and germs, this does not COMPLETELY rule out flying reindeer which only Santa has ever seen.

2) There are 2 billion children (persons under 18) in the world. BUT since Santa doesn't (appear) to handle the Muslim, Hindu, Jewish and, Buddhist children, that reduces the workload to 15% of the total - 378 million according to Population Reference Bureau. At an average (census) rate of 3.5 children per household, that's 91.8 million homes. One presumes there's at least one good child in each.

3) Santa has 31 hours of Christmas to work with, thanks to the different time zones and the rotation of the earth, assuming he travels east to west (which seems logical). This works out to 822.6 visits per second.

This is to say that for each Christian household with good children, Santa has 1/1000th of a second to park, hop out of the sleigh, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left, get back up the chimney, get back into the sleigh and move on to the next house. Assuming that each of these 91.8 million stops are evenly distributed around the earth (which, of course, we know to be false but for the purposes of our calculations we will accept), we are now talking about .78 miles per household, a total trip of 75-1/2 million miles, not counting stops to do what most of us must do at least once every 31 hours, plus feeding etc.

This means that Santa's sleigh is moving at 650 miles per second, 3,000 times the speed of sound. For purposes of comparison, the fastest man-made vehicle on earth, the Ulysses space probe, moves at a poky 27.4 miles per second - a conventional reindeer can run, tops, 15 miles per hour.

4) The payload on the sleigh adds another interesting element. Assuming that each child gets nothing more than a medium-sized lego set (2 pounds), the sleigh is carrying 321,300 tons, not counting Santa, who is invariably described as overweight. On land, conventional reindeer can pull no more than 300 pounds. Even granting that "flying reindeer" (see point #1) could pull TEN TIMES the normal amount, we cannot do the job with eight, or even nine. We need 214,200 reindeer. This increases the payload - not even counting the weight of the sleigh - to 353,430 tons. Again, for comparison - this is four times the weight of the Queen Elizabeth.

5) 353,000 tons traveling at 650 miles per second creates enormous air resistance - this will heat the reindeer up in the same fashion as spacecrafts re-entering the earth's atmosphere. The lead pair of reindeer will absorb 14.3 QUINTILLION joules of energy. Per second. Each. In short, they will burst into flame almost instantaneously, exposing the reindeer behind them, and create deafening sonic booms in their wake. The entire reindeer team will be vaporized within 4.26 thousandths of a second. Santa, meanwhile, will be subjected to centrifugal forces 17,500.06 times greater than gravity. A 250-pound Santa (which seems ludicrously slim) would be pinned to the back of his sleigh by 4,315,015 pounds of force.

In conclusion - If Santa ever DID deliver presents on Christmas Eve, he's dead now.

Santa Claus, Ph.D.

If, that's a little depressing, then consider the alternate view of Larry Silverberg, a professor of mechanical and aerospace engineering at North Carolina State University. Silverberg posits that Santa is smart enough to know that traveling across all those millions of miles in one night is a fool's errand. Instead, Santa relies on his advanced understanding of the space-time continuum (you gotta do something for kicks at the North Pole) to create what Silverberg calls "relativity clouds," small rips in time that allow Santa to bounce around the world at his leisure, deposit himself right in people's living rooms and deliver presents in nanoseconds.

And he doesn't actually have to carry all those presents on the sleigh with him. Rather, at each house Santa uses nanotechnology to reverse-engineer toys, atom by atom, from soot, snow, cookies and other materials readily available to him.

Good tidings to you

If you were naughty this year and you're getting the cold shoulder from Santa, Martin Nowak, director of the Program for Evolutionary Dynamics at Harvard University, can explain the reasoning behind the presents from your friends and family. In the journal Proceedings of the Royal Society B, Nowak and Sebastien Roch of the University of California, Berkeley examined phenomena they call "upstream reciprocity" "“ if someone is nice to you, the good feelings that are created may spur you to be nice to somebody else "“ and "network reciprocity" "“ being nice to people who are likely to be nice to someone else, with the assumption that a chain reaction will start and eventually someone will be nice to you. The scientists performed a mathematical analysis and calculated random chains of altruistic acts between people and found that a person who has been acted to kindly or been given a present may return the favor to several other people and create an "epidemic" of altruism.

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iStock // Ekaterina Minaeva
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technology
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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iStock
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Live Smarter
Working Nights Could Keep Your Body from Healing
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iStock

The world we know today relies on millions of people getting up at sundown to go put in a shift on the highway, at the factory, or in the hospital. But the human body was not designed for nocturnal living. Scientists writing in the journal Occupational & Environmental Medicine say working nights could even prevent our bodies from healing damaged DNA.

It’s not as though anybody’s arguing that working in the dark and sleeping during the day is good for us. Previous studies have linked night work and rotating shifts to increased risks for heart disease, diabetes, weight gain, and car accidents. In 2007, the World Health Organization declared night work “probably or possibly carcinogenic.”

So while we know that flipping our natural sleep/wake schedule on its head can be harmful, we don’t completely know why. Some scientists, including the authors of the current paper, think hormones have something to do with it. They’ve been exploring the physiological effects of shift work on the body for years.

For one previous study, they measured workers’ levels of 8-OH-dG, which is a chemical byproduct of the DNA repair process. (All day long, we bruise and ding our DNA. At night, it should fix itself.) They found that people who slept at night had higher levels of 8-OH-dG in their urine than day sleepers, which suggests that their bodies were healing more damage.

The researchers wondered if the differing 8-OH-dG levels could be somehow related to the hormone melatonin, which helps regulate our body clocks. They went back to the archived urine from the first study and identified 50 workers whose melatonin levels differed drastically between night-sleeping and day-sleeping days. They then tested those workers’ samples for 8-OH-dG.

The difference between the two sleeping periods was dramatic. During sleep on the day before working a night shift, workers produced only 20 percent as much 8-OH-dG as they did when sleeping at night.

"This likely reflects a reduced capacity to repair oxidative DNA damage due to insufficient levels of melatonin,” the authors write, “and may result in cells harbouring higher levels of DNA damage."

DNA damage is considered one of the most fundamental causes of cancer.

Lead author Parveen Bhatti says it’s possible that taking melatonin supplements could help, but it’s still too soon to tell. This was a very small study, the participants were all white, and the researchers didn't control for lifestyle-related variables like what the workers ate.

“In the meantime,” Bhatti told Mental Floss, “shift workers should remain vigilant about following current health guidelines, such as not smoking, eating a balanced diet and getting plenty of sleep and exercise.”

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