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Indiana Once Tried to Change Pi to 3.2

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Any high school geometry student worth his or her protractor knows that pi is an irrational number, but if you’ve got to approximate the famed ratio, 3.14 will work in a pinch. That wasn’t so much the case in late-19th-century Indiana, though. That’s when the state’s legislators tried to pass a bill that legally defined the value of pi as 3.2.

The very notion of legislatively changing a mathematical constant sounds so crazy that it just has to be an urban legend, right? Nope. As unbelievable as it sounds, a bill that would have effectively redefined pi as 3.2 came up before the Indiana legislature in 1897.

The story of the “Indiana pi bill” starts with Edward J. Goodwin, a Solitude, Indiana, physician who spent his free time dabbling in mathematics. Goodwin’s pet obsession was an old problem known as squaring the circle. Since ancient times, mathematicians had theorized that there must be some way to calculate the area of a circle using only a compass and a straightedge. Mathematicians thought that with the help of these tools, they could construct a square that had the exact same area as the circle. Then all one would need to do to find the area of the circle was calculate the area of the square, a simple task.

Sounds like a neat trick. The only problem is that it’s impossible to calculate the area of a circle in this way. It just won’t work. Furthermore, when Goodwin was toying with this problem, mathematicians already knew it was impossible; Ferdinand von Lindemann had proven that the task was a fool’s errand in 1882.

Goodwin wasn’t going to let something trivial like the proven mathematical impossibility of his task deter his efforts, though. He persevered, and in 1894 he even convinced the upstart journal American Mathematical Monthly to print the proof in which he “solved” the squaring-the-circle problem. Goodwin’s proof didn’t explicitly deal with approximating pi, but when you’re quite literally trying to fit a square peg in a round hole, weird things happen. One of the odd side effects of Goodwin’s machinations was that the value of pi morphed into 3.2.

Let's Make a Deal

Although Goodwin’s “proof” was anything but, he was pretty cocky about its infallibility. He didn’t just publish his faulty method in journals; he copyrighted it. Goodwin figured everyone would be lining up to use his revolutionary new trick, and his plan was to collect royalties from businesses and mathematicians who sought to exploit his method.

Goodwin wasn’t totally greedy, though, and that’s where the Indiana legislature entered the picture. Goodwin couldn’t bear the thought of Hoosier schoolchildren being deprived of the fruits of his brilliance just because the state couldn’t foot the bill for his royalties. So he magnanimously offered to let the state use his masterpiece free of charge.

Indiana wasn’t going to get such an awesome deal totally for free, though. The state could avoid paying royalties if and only if the legislature would accept and adopt this “new mathematical truth” as state law. Goodwin convinced Representative Taylor I. Record to introduce House Bill 246, which outlined both this bargain and the basics of his method.

Again, Goodwin’s method and the accompanying bill never mention the word “pi,” but on the topic of circles, it clearly states, “[T]he ratio of the diameter and circumference is as five-fourths to four.” Yup, that ratio is 3.2. Goodwin isn’t afraid to lambaste the old approximation of pi, either. The bill angrily condemns 3.14 as “wholly wanting and misleading in its practical applications.”

Goodwin’s blasting of the old approximation isn’t even the funniest part of the bill’s text. The third and final section extols his other mathematical breakthroughs, including solving the similarly impossible problems of angle trisection and doubling the cube, before reminding any reader who wasn’t sufficiently awestruck at his magnificence, “And be it remembered that these noted problems had been long since given up by scientific bodies as insolvable mysteries and above man's ability to comprehend.“

Math Problem

To anyone who passed the aforementioned high school geometry class, this bill was patently absurd. Apparently Indiana legislators weren’t a pack of math whizzes, though. After the bill bounced around between committees, the Committee on Education finally sent it out for a vote, and the bill passed the House unanimously. No, not a single one of Indiana’s 67 House members raised an eyebrow at a proof that effectively redefined pi as 3.2.

Luckily the state’s senators had a bit more numerical acumen. Well, some of them did. Eventually. After sailing through the House, the bill first went to the Senate’s Committee on Temperance, which also recommended that it pass. By this point, news of Indiana attempting to legislate a new value of pi and endorse an airtight solution to an unsolvable math problem had become national news, and papers all over the country were mocking the legislature’s questionable calculations.

All this attention ended up working in Indiana’s favor. While the state’s lawmakers couldn’t follow Goodwin’s bizarre brand of mathe-magic well enough to refute his proof, there were other smart Hoosiers who could. Professor C.A. Waldo of Purdue University was in Indianapolis while the pi hoopla was unfolding, and after watching part of the debate at the statehouse he was so thoroughly horrified that he decided to intervene.

The legislators may have been nearly bamboozled by Goodwin’s pseudo-math, but Waldo certainly wasn’t. Waldo got the ear of a group of senators after watching the absurd debate and explained why Goodwin’s theory was nonsense. (It seemed that most of the legislators didn’t really understand what was going on in the bill; they just knew that by approving it the state would get to use a new theory for free.)

After receiving Waldo’s coaching, the Senate realized that the new bill was a very, very bad idea. Senator Orrin Hubbel moved that a vote on the bill be postponed indefinitely, and Goodwin’s new math died a quiet legislative death. The Indiana legislature hasn’t tried to rewrite the basic principles of math in all the years since. 

This post originally appeared in 2011. Image credit: Instructables member hertzgamma. You can read the text of the bill here.

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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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8 Common Dog Behaviors, Decoded
May 25, 2017
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Dogs are a lot more complicated than we give them credit for. As a result, sometimes things get lost in translation. We’ve yet to invent a dog-to-English translator, but there are certain behaviors you can learn to read in order to better understand what your dog is trying to tell you. The more tuned-in you are to your dog’s emotions, the better you’ll be able to respond—whether that means giving her some space or welcoming a wet, slobbery kiss. 

1. What you’ll see: Your dog is standing with his legs and body relaxed and tail low. His ears are up, but not pointed forward. His mouth is slightly open, he’s panting lightly, and his tongue is loose. His eyes? Soft or maybe slightly squinty from getting his smile on.

What it means: “Hey there, friend!” Your pup is in a calm, relaxed state. He’s open to mingling, which means you can feel comfortable letting friends say hi.

2. What you’ll see: Your dog is standing with her body leaning forward. Her ears are erect and angled forward—or have at least perked up if they’re floppy—and her mouth is closed. Her tail might be sticking out horizontally or sticking straight up and wagging slightly.

What it means: “Hark! Who goes there?!” Something caught your pup’s attention and now she’s on high alert, trying to discern whether or not the person, animal, or situation is a threat. She’ll likely stay on guard until she feels safe or becomes distracted.

3. What you’ll see: Your dog is standing, leaning slightly forward. His body and legs are tense, and his hackles—those hairs along his back and neck—are raised. His tail is stiff and twitching, not swooping playfully. His mouth is open, teeth are exposed, and he may be snarling, snapping, or barking excessively.

What it means: “Don’t mess with me!” This dog is asserting his social dominance and letting others know that he might attack if they don’t defer accordingly. A dog in this stance could be either offensively aggressive or defensively aggressive. If you encounter a dog in this state, play it safe and back away slowly without making eye contact.

4. What you’ll see: As another dog approaches, your dog lies down on his back with his tail tucked in between his legs. His paws are tucked in too, his ears are flat, and he isn’t making direct eye contact with the other dog standing over him.

What it means: “I come in peace!” Your pooch is displaying signs of submission to a more dominant dog, conveying total surrender to avoid physical confrontation. Other, less obvious, signs of submission include ears that are flattened back against the head, an avoidance of eye contact, a tongue flick, and bared teeth. Yup—a dog might bare his teeth while still being submissive, but they’ll likely be clenched together, the lips opened horizontally rather than curled up to show the front canines. A submissive dog will also slink backward or inward rather than forward, which would indicate more aggressive behavior.

5. What you’ll see: Your dog is crouching with her back hunched, tail tucked, and the corner of her mouth pulled back with lips slightly curled. Her shoulders, or hackles, are raised and her ears are flattened. She’s avoiding eye contact.

What it means: “I’m scared, but will fight you if I have to.” This dog’s fight or flight instincts have been activated. It’s best to keep your distance from a dog in this emotional state because she could attack if she feels cornered.

6. What you’ll see: You’re staring at your dog, holding eye contact. Your dog looks away from you, tentatively looks back, then looks away again. After some time, he licks his chops and yawns.

What it means: “I don’t know what’s going on and it’s weirding me out.” Your dog doesn’t know what to make of the situation, but rather than nipping or barking, he’ll stick to behaviors he knows are OK, like yawning, licking his chops, or shaking as if he’s wet. You’ll want to intervene by removing whatever it is causing him discomfort—such as an overly grabby child—and giving him some space to relax.

7. What you’ll see: Your dog has her front paws bent and lowered onto the ground with her rear in the air. Her body is relaxed, loose, and wiggly, and her tail is up and wagging from side to side. She might also let out a high-pitched or impatient bark.

What it means: “What’s the hold up? Let’s play!” This classic stance, known to dog trainers and behaviorists as “the play bow,” is a sign she’s ready to let the good times roll. Get ready for a round of fetch or tug of war, or for a good long outing at the dog park.

8. What you’ll see: You’ve just gotten home from work and your dog rushes over. He can’t stop wiggling his backside, and he may even lower himself into a giant stretch, like he’s doing yoga.

What it means: “OhmygoshImsohappytoseeyou I love you so much you’re my best friend foreverandeverandever!!!!” This one’s easy: Your pup is overjoyed his BFF is back. That big stretch is something dogs don’t pull out for just anyone; they save that for the people they truly love. Show him you feel the same way with a good belly rub and a handful of his favorite treats.

The best way to say “I love you” in dog? A monthly subscription to BarkBox. Your favorite pup will get a package filled with treats, toys, and other good stuff (and in return, you’ll probably get lots of sloppy kisses). Visit BarkBox to learn more.

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