Learn about why hundreds of ducks are employees at a wine vineyard; a musical invention that was the Spotify of the Victorian era; and a delicious mathematical principle known as the ham sandwich theorem.
Learn about why hundreds of ducks are employees at a wine vineyard; a musical invention that was the Spotify of the Victorian era; and a delicious mathematical principle known as the ham sandwich theorem.
Hundreds of Ducks Are Employees at a Vineyard by Joanie Faletto
https://curiosity.com/topics/hundreds-of-ducks-are-employees-at-a-vineyard-curiosity
The Telharmonium was the Victorian version of Spotify by Steffie Drucker
The Ham Sandwich Theorem Is a Delicious and Puzzling Mathematical Principle by Ashley Hamer
https://curiosity.com/topics/the-ham-sandwich-theorem-is-a-delicious-and-puzzling-mathematical-principle-curiosity
Subscribe to Curiosity Daily to learn something new every day with Cody Gough and Ashley Hamer. You can also listen to our podcast as part of your Alexa Flash Briefing; Amazon smart speakers users, click/tap “enable” here: https://curiosity.im/podcast-flash-briefing
Find episode transcript here: https://curiosity-daily-4e53644e.simplecast.com/episodes/ducks-are-employees-at-a-vineyard-the-victorian-version-of-spotify-and-a-mathematical-theorem-for-cutting-a-ham-sandwich
CODY: Hi! You’re about to get smarter in just a few minutes with Curiosity Daily from curiosity-dot-com. I’m Cody Gough.
ASHLEY: And I’m Ashley Hamer. Today, you’ll learn about why hundreds of ducks are employees at a wine vineyard; a musical invention that was the Spotify of the Victorian era; and a delicious mathematical principle known as the ham sandwich theorem.
[CODY AD LIB April Fool’s Day]
CODY: Let’s satisfy some curiosity.
What would you think if you saw a herd of ducks, several-hundred strong, running in formation through a vineyard? You might wonder whether you've had too much wine. But at the Vergenoegd [VEHR-uh-nood] Wine Estate in Stellenbosch [STELL-in-bosh], South Africa, this is a daily and surprisingly orderly occurrence.
These are Indian Runner ducks, and they’re employed at the vineyard to help with pest control. While that might sound unusual, putting ducks to work actually has a long history, both at this vineyard and around the world.
The ducks work five hours a day, five days a week. Picture this scene, which happens every morning at 9:45: the ducks are released en masse, running in formation, bodies and beaks in the same direction. They even manage to turn at the same time. The web-footed staff members aren’t a new addition, either. The estate has had runner ducks for 30 years.
These aren’t your average duck-pond ducks, though. They have a unique body type that’s been described as a “bowling pin with legs,” and they have a posture similar to a penguin. They’re about 20 to 30 inches tall, which makes them tall enough to grab slugs and snails from higher plants, and skinny enough to fit through the vines. And they don’t waddle — as their name suggests, they do, in fact, run! And that’s pretty important, considering the vineyard has 140 acres of vines to debug. The ducks help reduce the use of pesticides and make the vineyard a unique tourist attraction to boot. The ducks get something out of it too, of course — they get to gorge on pests all day long.
This is nothing new: Runner ducks have a very long history. They’ve been used by rice farmers in China for hundreds of years. Farmers have been selecting the best foragers to breed, so over time the species have become taller, skinnier and better at running, making them the perfect farmhands. I’ll drink to that!
They say that there’s nothing new under the sun — and believe it or not, you can include streaming music services on that list. Because check this out: at the turn of the 20th century, lawyer Thaddeus Cahill [KAY-hill] invented the telharmonium. And the machine was basically the Victorian-era Spotify.
The telharmonium was an electrically powered keyboard the size of a room that was patented in 1897. And it transmitted live music from a hub in downtown Manhattan to homes, restaurants, and hotels across the city over the telephone.
Why not use the radio, you might ask? Because that wouldn’t be possible for another 20 years. Even the phonograph had only been in wide use for about a decade. And unlike the phonograph, the telharmonium’s music was live. Cahill recruited musicians to play the keyboard instrument 24 hours a day, usually two at a time.
Here’s how it worked: Customers would pick up their phone and ask the operator to connect them to the instrument. The music would then burst forth from their telephone receiver. To amplify the sound, they’d just put a big paper funnel on the receiver. This old-timey streaming service cost 20 cents an hour — which is around $6 an hour in today’s money.
But live streaming wasn’t the only cool thing about the telharmonium. See, Cahill was inspired to build this instrument by a German physicist named Hermann Helmholtz. Helmholtz had shown that every musical note was made up of many harmonics, or higher tones, that give the note its color — so like, a Bb on a clarinet sounds different than on a violin because of each instrument’s particular blend of harmonics. Helmoltz even used this concept to create an electromechanical, one-note synthesizer that could mimic the sound of German vowels! He also believed that these particular harmonic blends made many instruments sub-par. As far as he was concerned, the best instrument was the organ, because you could alter its tone any way you wanted. Cahill took Helmholtz’s ideas and ran with them, and he designed the telharmonium to be what he hoped was the perfect instrument.
So what halted this musical revolution? Primarily cost: The 200 tons of machinery that powered the telharmonium drew a tremendous amount of electricity. The first instrument cost $200,000 — which today would be more than $6 million! And expanding the system would require cities to build a new power plant for every 10,000 new listeners. On top of that, the sound quality was lousy. The music was faint and distorted, and would sometimes bleed into other people’s phone calls. Certainly not like the crystal clear quality you get when you listen to Curiosity Daily on Spotify today.
Still, Cahill’s invention paved the way for modern electronic music. I mean, the telharmonium was basically the world’s first synthesizer. His design gave way to the electric organ, which eventually birthed the analog synthesizer, the electronic keyboard, and the digital piano. Cahill once dreamed that music would lull people to sleep and wake them the next day. And in a way, his dream came true.
You can easily cut a ham sandwich in half with one slice, right? But what if you knocked the plate over and left the bread and ham in a big mess? Could you still cut them in half with one single cut? Well, there's a mathematical principle that says yes, it’s still technically possible. And it’s called the ham sandwich theorem. (What else would they call it?)
To explain this, let's start simpler and imagine the problem with pancakes. This is called, obviously, the pancake theorem. If you have a single pancake, it’s easy to cut it into two equal halves. If you add a second pancake next to it on the plate — no matter how it’s shaped or where it is — you’ll eventually find a line that will divide them equally.
If you really want to get into the math of the pancake theorem, it technically says that in the case n = 2 (CODY: so, if you have two objects), given two disjoint regions of the plane (CODY: regions that aren't next to each other), there's a line that simultaneously divides both regions into two pieces of equal area. Easy.
Ok, back to the ham sandwich. For one more twist to our scenario, let's remove the force of gravity. So now your ham sandwich is floating in three pieces in the air, and your knife can grow as long and tall as you need it to. The ham sandwich theorem says that no matter where the pieces of that sandwich are in three-dimensional space — whether they’re touching, across the kitchen, or across the universe from each other — there is a way to slice your infinitely long, infinitely tall knife through all three pieces to get exactly equal halves of each.
In mathematical terms, the ham sandwich theorem states that given n objects floating in n-dimensional space (CODY: in our case, that's 3 objects floating in 3-dimensional space), there exists a single [n - 1]-dimensional (CODY: again, in our case, that's 3-1, or 2-dimensional) plane that simultaneously cuts all n objects into two pieces of equal volume.
So if you're ever floating out in space with a friend who's really particular about splitting food equally, you know for certain that you can cut your ham sandwich to fairly share it with them. The only problem? The ham sandwich theorem doesn't tell you where to cut it. For that, you're on your own.
ASHLEY: Let’s recap the main things we learned today
[ad lib optional]
CODY: Today’s stories were written by Ashley Hamer, Steffie Drucker, and Joanie Faletto, and edited by Ashley Hamer, who’s the managing editor for Curiosity Daily.
ASHLEY: Scriptwriting was by Cody Gough and Sonja Hodgen. Curiosity Daily is produced and edited by Cody Gough.
CODY: Join us again tomorrow to learn something new in just a few minutes.
ASHLEY: And until then, stay curious!