[CLIP: Wind howls]
Rachel Feltman: When Tom Crawford climbed Mount Kilimanjaro and stood 5,895 meters [about 19,341 feet] above sea stage, he was astounded by the pure great thing about the view. Who wouldn’t be?
However in contrast to most climbers, Tom had one thing else on his thoughts, too: math.
On supporting science journalism
If you happen to’re having fun with this text, take into account supporting our award-winning journalism by subscribing. By buying a subscription you’re serving to to make sure the way forward for impactful tales in regards to the discoveries and concepts shaping our world at present.
[CLIP: “None of My Business,” by Arthur Benson]
Tom Crawford: If I can see one other peak within the distance, in my head I’m like, “I’m wondering if I might, like, calculate the peak of that primarily based on, you realize, the angle I’m at and the gap.”
Feltman: He doesn’t truly crunch these numbers. However as a mathematician on the College of Oxford, Tom’s intuition is all the time to translate the world round him into patterns and numbers—in different phrases, to show mountains into math.
Crawford: For me, the sweetness is you’ll be able to apply maths to completely something. Give me any state of affairs, any drawback, any set of information, and you need to use maths to attempt to perceive what’s taking place. And that, to me, is the attractive facet of it.
Feltman: For Science Shortly, I’m Rachel Feltman. And at present I’m joined by the world’s favourite math-teaching drag queen, Kyne Santos. For the subsequent few Fridays she’ll be taking up our feed to speak about—you guessed it—math.
Kyne, I’ve to confess: I’ve by no means been a lot of a math lover myself. So ought to I be apprehensive?
Kyne Santos: Under no circumstances! I promise you’ll discover one thing to like about math on this sequence, whether or not it was your favourite topic in class or it’s absolutely the bane of your existence.
Feltman: That may be a tall order, however I can’t consider anybody extra as much as the duty. And from what your buddy Tom simply shared with us, it looks like you’ll have loads of assist out of your fellow math followers of the world.
[CLIP: Theme music]
Santos: That’s proper. Over the subsequent three Fridays I’ll be chatting with a few of my favourite mathematicians to demystify the hidden facets of math: What’s it, actually? What the heck do mathematicians truly do? And is it actually relevant to our on a regular basis lives?
Feltman: My highschool trig trainer undoubtedly informed me so, however I’m gonna must see some receipts. So the place in mathemagic land are you taking us first?
Santos: Right now we’re beginning with the mind-boggling great thing about math: What makes mathematicians discuss it with a lot heat and romance? Then we’ll vindicate your highschool trainer by proving simply how helpful math may be.
Once I say the phrase “math,” what involves thoughts?
Feltman: Uh, I’d say chalkboards, possibly some graphing calculators, that one meme of the actually confused woman with the numbers round her—so nothing too thrilling, I’m sorry to say.
Santos: Okay, okay, I believe that’s fairly widespread. However to many mathematicians like my mountain-climbing buddy Tom, math is inherently lovely.
Mathematicians don’t simply care about which solutions they get; they’re all the time looking for probably the most elegant resolution they will. So if you perceive the how and why behind a components, you begin to see astonishing magnificence in simply how simple arithmetic may be.
Mark Jago: You are able to do maths in a means which may get you accomplished what you need to get accomplished, nevertheless it does it in a very form of clunky, sluggish, creaking means.
Santos: That’s Mark Jago, a thinker and logician from the College of Nottingham.
Jago: I used to be form of imagining my daughter—she’s simply began doing ballet. And I think about me making an attempt to do what she’s doing, proper? So I’m imagining me, a 43-year-old man who’s by no means danced earlier than, making an attempt to, like, undergo the best steps. And you may think about, like, doing the best steps—like, yeah, you bought your ft in the best place, however, you realize, it doesn’t have that form of class or attraction or no matter it’s about ballet that you really want.
And you are able to do maths like that, proper? It’s not all the time about getting the best reply. It’s usually about doing it in a means that simply makes anyone who understands what’s happening there suppose, “Wow, the best way that got here out was simply so elegant.”
Santos: Let me provide you with an instance of the form of class he’s speaking about.
[CLIP: “Handwriting,” by Frank Jonsson]
Santos: Greater than two thousand years in the past an historical Greek mathematician named Eratosthenes used math to work out the circumference of the Earth.
Feltman: Wow, I imply, I don’t suppose I might even try this with Twenty first-century instruments! How did he get began on such an formidable venture?
Santos: I do know, it’s very mind-blowing. Eratosthenes was chief librarian on the Nice Library of Alexandria, which meant he heard quite a lot of tales from numerous vacationers and clearly had entry to quite a lot of books.
Now it’s form of unclear how he stumbled upon such an intriguing piece of knowledge that began him on his Earth-measuring journey—some say he was informed by guests from out of city; others say he learn it in a e book. However what issues is that one way or the other he realized that at midday on the summer time solstice in a faraway metropolis known as Syene, now generally known as Aswān, Egypt, the solar might completely illuminate the underside of a effectively.
Feltman: That’s, like, form of a bizarre flex, however I assume there’s some mathematical twist there.
Santos: Precisely—it comes all the way down to the angle of the solar. Eratosthenes knew that if daylight was hitting the underside of a effectively, it should imply the solar was straight above the town, casting no shadows.
However when Eratosthenes erected a pole in Alexandria and noticed it on the summer time solstice, the pole solid a shadow—that means the solar was not straight overhead.
Eratosthenes thought this should be due to the curvature of the Earth. He accurately assumed that the solar was far sufficient away that its rays have been virtually parallel after they reached Earth—that means that any distinction within the angle of daylight was because of the curvature of the planet, not the closeness of the solar.
Feltman: Okay, I’m already very impressed, however how did he show it?
Santos: Properly, he began by stamping a stick into the bottom in Alexandria on the solstice, and he measured the shadow it created to calculate the angle of the solar’s rays, which was about 7.2 levels.
Feltman: And what does that inform us, precisely?
[CLIP: “The Farmhouse,” by Silver Maple]
Santos: Okay, I’ll do my finest to clarify this merely. Think about reducing the Earth in half, with Alexandria and Syene as factors on its edge, and then you definitely’re reducing out a cake slice as skinny as the gap between the 2 cities.
Feltman: Sounds scrumptious. Go on.
Santos: Properly, if you happen to measured that slice, then the central angle between Alexandria and Syene would even be 7.2 levels. So by comparability, if you happen to measured two factors on reverse sides of the globe, the central angle could be 180 levels, proper?
Feltman: Proper, as a result of half the Earth is half of 1, like, very lumpy sort-of-sphere. Was that each one all the pieces he wanted to know to determine the planet’s circumference?
Santos: Nearly, however not fairly. He needed to put in a little bit legwork—actually. He needed to measure the gap between the 2 cities, and he did it by hiring somebody to stroll from one to the opposite. The 2 cities, Syene and Alexandria, turned out to be about 790 kilometers aside, or round 490 miles, give or take, relying on the way you outline a stadion, which is the unit of measurement he used.
Armed with these two items of knowledge, Eratosthenes then calculated the gap across the Earth to be about 39,500 kilometers. That’s round 24,500 miles. And in response to NASA, the true circumference of the Earth is 40,070 kilometers, or roughly 24,900 miles.
Feltman: Wow, that’s actually not a foul estimation for a man in, what, the third century B.C.E.?
Santos: I do know, proper? Eratosthenes’ measurement of the Earth’s circumference was truly extra correct than the one Christopher Columbus used greater than 1,000 years later.
Feltman: There’s one thing very satisfying about that [laughs].
Santos: Mhm. And Eratosthenes didn’t even want a world map or a fleet of ships or all of the colonial riches of the Spanish Empire to determine it out both. All he had was a stick within the floor—and naturally, the elegant and easy guidelines of geometry.
Math permits us to take massive issues—like determining the circumference of the planet or the gap between two mountain peaks—and rework them into easy formulation.
Feltman: I assume this can be a good time to get into how, like, truly necessary and sensible math is. It’s straightforward for knowledgeable to say that math is great and fascinating, however why ought to anybody else care about it?
Santos: Completely—let’s return to my buddy Tom. He can wax poetic about math from the mountaintops with the perfect of them, however his job has critical real-world impression. One among his analysis areas entails utilizing math to know how air pollution spreads within the ocean.
[CLIP: Ocean waves]
Crawford: So if you happen to’re making an attempt to know the place the air pollution goes as soon as it will get into the ocean and which areas are most vulnerable to air pollution, meaning it is advisable perceive the place the river water goes. It seems you’ll be able to resolve that drawback, like, completely by constructing a mathematical mannequin.
Santos: A mathematical mannequin is a means of utilizing equations to explain and predict actual life. For instance, you’ll be able to predict what time you’ll arrive at your vacation spot utilizing math if you realize your automotive’s velocity and the gap you’re driving. Tom can predict the trail of floating air pollution by issues such because the Earth’s rotation and the amount of water leaving the river.
Crawford: I did fieldwork to confirm the equations that I got here up with, and we have been capable of get actually, actually good outcomes. So for any river on the planet, I can say, I don’t know, with 80 p.c accuracy the place the air pollution from that river goes to finish up.
Santos: So some fields of math have very clear purposes, and we will use them instantly to deal with issues like air pollution. However there are mathematicians who research math that doesn’t essentially have many real-world purposes, prompting others to say, “What’s the purpose?” As a matter of truth, a number of the most supposedly ineffective branches of math have remodeled into technological titans that underpin our trendy civilization.
Feltman: Ooh, like what?
Santos: Tom’s favourite instance comes from Albert Einstein.
Crawford: Nearly everyone has heard of Einstein as a result of he’s such a celebrated scientist as a result of he had these unimaginable summary concepts that no person else had ever considered earlier than. However we had no sensible use for something that he did for 100 years.
Santos: That’s not actually true, however a few of Einstein’s most impactful work did take fairly a while to bear fruit—no less than in a means that on a regular basis folks can recognize.
Crawford: His concept of relativity, in a nutshell, is when one thing strikes actually, actually rapidly, the best way that factor experiences time modifications—so time slows down, which is such an alien idea to us as people. However the sensible software of it’s: if one thing is shifting actually, actually rapidly, it is advisable make this slight adjustment as a result of time doesn’t fairly behave the identical.
[CLIP: “Without Further Ado,” by Jon Björk]
Santos: This comes into play with one thing you in all probability use to get round each single day: GPS. The satellites that energy GPS whiz across the Earth at 1000’s of ft per second.
Crawford: So you’ll be like, “The place am I?” and it could present you an enormous four-, five-mile circle, being like, “You’re on this space.”
Santos: However due to Einstein’s as soon as “ineffective” concept of relativity, GPS is definitely correct inside meters.
Feltman: It’s laborious to get extra impactful than that.
Santos: Mhm. The figures and symbols that make up math can appear messy and complicated to most of us. However the subsequent time you end up scowling at some inconvenient arithmetic, take a second to understand the truth that you’ll be able to sit in an armchair and take into consideration figures and symbols and use logical reasoning to give you a profound reality about geometry, about infinity, in regards to the top of a mountain or the dimensions of the Earth—with out having to interrupt out your measuring tape. That’s the facility and great thing about math.
[CLIP: Theme music]
Santos: For Scientific American’s Science Shortly, I’m Kyne Santos.
Feltman: And I’m Rachel Feltman. This has been Episode One among our Friday Fascination miniseries “The Hidden Nature of Math.” Tune in once more subsequent week for extra.
Kyne, are you able to give us a little bit trace about what’s developing?
Santos: Completely. Let’s simply say we’ll be questioning the very nature of actuality.
Feltman: Oh, so a typical Friday. Can’t wait!
Science Shortly is produced by me, Rachel Feltman, together with Fonda Mwangi, Kelso Harper, Madison Goldberg and Jeff DelViscio. Right now’s episode was hosted by me, Rachel Feltman, and naturally, by our particular visitor, Kyne Santos. Emily Makowski, Shayna Posses and Aaron Shattuck fact-checked this sequence. Our theme music was composed by Dominic Smith. Subscribe to Scientific American for extra up-to-date and in-depth science information.
See you subsequent Friday for extra mathematical adventures. And don’t neglect to examine your feed for the newest in science information on Monday. Have a fantastic weekend!