Self-Motivation
David Goggins
Former Navy Seal
Career Development
Bryan Cranston
Actor
Critical Thinking
Liv Boeree
International Poker Champion
Emotional Intelligence
Amaryllis Fox
Former CIA Clandestine Operative
Management
Chris Hadfield
Retired Canadian Astronaut & Author
Learn
from the world's big
thinkers
Start Learning

The evolution of mathematics, from agriculture to quantum mechanics

Why is math the universal language? NASA's Michelle Thaller solves that one.

MICHELLE THALLER: Oğuzhan, you asked, why is mathematics the universal language? And this is something I've actually thought a lot about. Mathematics is in some ways kind of scary in how useful it is at really describing how the universe works around us. Now, to give you an idea, the origin of mathematics seems very straightforward. We can count on our fingers up to 10, and maybe it was useful to understand how many sheep you had? So you could start counting sheep and then you either added or subtracted sheep as you got more or as you lost some. It was a simple thing. We learned how to count. We learned how to add and subtract. The idea of multiplying and dividing is a little more abstract, but that also makes sense. That's something that we can kind of visualize.

But then what amazes me is that this led us on a tremendously complicated journey that's still going on to this day. And we had no idea where this would lead us. If you can do multiplication and subtraction, it's not too long before you begin to develop the basic building blocks of calculus. And calculus describes how moving objects can change, how things can accelerate. If you want to describe an apple falling from a tree to the ground or a ball rolling down a hill, that's calculus. It's the mathematics of how things can change over time. That's really interesting, and the amazing thing is it works so well. If you use these equations to predict how a ball will roll down a hill, reality matches that. It really does tell you how something is going to behave. So now we've gone from counting on our fingers how many sheep we have to being able to predict what the universe around us is going to do. That's incredibly powerful.

Now we look around us and we see things like planets orbiting the stars or the galaxy turning around, and we realize those equations of motion apply to everything else in the universe. It's not just here. It's not just on the surface of the Earth, but we can look at things literally billions of light years out in space, and they're following those same rules of mathematics. But now things got strange. We started to play with calculus. We started to see where it would go. What happens if you put in more variables and you solve for more things at once? And we end up with some very strange abstract concepts that turned out to be surprisingly useful. One of the things that kind of worries me is something called imaginary numbers. Imaginary numbers are numbers that don't really make sense in our proper definition of mathematics. Take, for example, the square root of negative 1. Now, in mathematics, if you multiply something by itself it always turns out to be a positive number. That's never a negative number. But somebody said, what happens if we start to do the mathematics of how an imaginary number -- this can't be real. The square root of negative 1 doesn't make any sense. But it turns out to be able to describe how things rotate, and that became the foundation of quantum mechanics. And here's the thing, now when you use a number that shouldn't exist -- that doesn't make any sense -- it predicts exactly how an atom will vibrate, It will predict how quantum mechanics at a very small scale runs, and it needs a type of math that doesn't make any real sense to us but it works. It works perfectly.

So we keep getting led farther and farther down this rabbit hole. Where does math lead us? Now we realize that you can describe physics incredibly well if you allow the universe to exist in many different dimensions-- more than three dimensions that we're familiar with. In fact, specifically, if you want to do particle physics, it requires 11 dimensions. That's not something our minds comprehend, but we can do the math. We can do the math of how things would behave if they could move in 11 different directions. And it turns out to predict exactly the results we get from particle physics. That's kind of scary. Does that mean that's real? Are there really 11 dimensions? The math works so well, and the predictions are so strong that it can't just be nonsense. But now we've gone to the limit of what I can tell you; is it real or not? Our math has given us something incredibly useful, but it's taken us completely out of our realm of common sense, of human scale of how our minds work and even our sense of space and time. I don't think that journey's over yet. Where is math going to lead us? It may lead us to understand things like the universe is a type of a hologram? That was a mathematical solution to How things work around a black hole, and it works really, really well. So I think it's wonderful and a little bit scary that you start counting on your fingers. You get to 11 dimensions of space and time. And where else?

  • Mathematics has snowballed from counting to 10 on our fingers, to calculus, to abstract concepts like imaginary numbers that move in 11 dimensions and predict particles physics.
  • The math that led us down the rabbit hole of quantum mechanics is bizarre and while we can crunch the numbers, we can't really understand what they mean.
  • If the math confirms that particles can move in 11 dimensions, is that a fundamental truth of the universe?


Remote learning vs. online instruction: How COVID-19 woke America up to the difference

Educators and administrators must build new supports for faculty and student success in a world where the classroom might become virtual in the blink of an eye.

Credit: Shutterstock
Sponsored by Charles Koch Foundation
  • If you or someone you know is attending school remotely, you are more than likely learning through emergency remote instruction, which is not the same as online learning, write Rich DeMillo and Steve Harmon.
  • Education institutions must properly define and understand the difference between a course that is designed from inception to be taught in an online format and a course that has been rapidly converted to be offered to remote students.
  • In a future involving more online instruction than any of us ever imagined, it will be crucial to meticulously design factors like learner navigation, interactive recordings, feedback loops, exams and office hours in order to maximize learning potential within the virtual environment.
Keep reading Show less

White dwarfs hold key to life in the universe, suggests study

New study shows white dwarf stars create an essential component of life.

NASA and H. Richer (University of British Columbia)
Surprising Science
  • White dwarf stars create carbon atoms in the Milky Way galaxy, shows new study.
  • Carbon is an essential component of life.
  • White dwarfs make carbon in their hot insides before the stars die.
Keep reading Show less

"Forced empathy" is a powerful negotiation tool. Here's how to do it.

Master negotiator Chris Voss breaks down how to get what you want during negotiations.

Photo by Joe Raedle/Getty Images
Personal Growth
  • Former FBI negotiator Chris Voss explains how forced empathy is a powerful negotiating tactic.
  • The key is starting a sentence with "What" or "How," causing the other person to look at the situation through your eyes.
  • What appears to signal weakness is turned into a strength when using this tactic.
Keep reading Show less

Octopus-like creatures inhabit Jupiter’s moon, claims space scientist

A leading British space scientist thinks there is life under the ice sheets of Europa.

Credit: NASA/JPL-Caltech/SETI Institute
Surprising Science
  • A British scientist named Professor Monica Grady recently came out in support of extraterrestrial life on Europa.
  • Europa, the sixth largest moon in the solar system, may have favorable conditions for life under its miles of ice.
  • The moon is one of Jupiter's 79.
Keep reading Show less

How to catch a glimpse of Comet NEOWISE before it’s gone

Unless you plan to try again in 6,800 years, this week is your shot.

Image source: Sven Brandsma/Unsplash
Surprising Science
  • Comet NEOWISE will be most visible in the U.S. during the evenings from July 14-19, 2020.
  • After July 23rd, NEOWISE will be visible only through good binoculars and telescopes.
  • Look in the northwestern sky below the Big Dipper after dusk while there's a chance.

UPDATE: NASA is broadcasting a NASA Science Live episode highlighting Comet NEOWISE. NASA experts will discuss and answer public questions beginning at 3PM EST on Wednesday, July 15. Tune in via the agency's website, Facebook Live, YouTube, Periscope, LinkedIn, Twitch, or USTREAM.

Before last evening, July 14, 2020, the easiest way to see Comet NEOWISE — the brightest comet to zoom past Earth since 1977's Comet Hale-Bopp — from the United States was to catch it about an hour before sunrise. Now, however, you can see it in the evening, where it will remain for until the 19th. This is a definite don't-miss event — NEOWISE won't be coming back our way for another 6,800 years. It's the first major comet of the millennium, and by all accounts, it's unforgettable.

NEOWISE just got back from the Sun

Comet NEOWISE is named after the NASA infrared space telescope that first spotted it on March 27th. Its official moniker is C/2020 F3. It's estimated that the icy comet is about three miles across, not counting its tail.

NEOWISE is now heading away from our Sun, having made it closet approach, 27.4 million miles, to our star on July 3. The heat from that encounter is what's given NEOWISE its tail: It caused gas and dust to be released from the icy object, creating the tail of debris that looks so magical from here.

As NEOWISE moves closer to Earth, paradoxically, it will be less and less visible. By about July 23rd, you'll need binoculars or a telescope to see it at all. All of which makes this week prime time.

An evening delight

star constellation in sky

Image source: Allexxandar/Shutterstock/Big Think

First, find an unobstructed view of the northwest sky, free of streetlights, car headlights, apartment lights, and so on. And then, according to Sky & Telescope:

"Start looking about one hour after sunset, when you'll find it just over the northwestern horizon as the last of twilight fades into darkness."

It should be easy to spot since it's near to one of the most recognizable constellations up there, the Big Dipper. "Look about three fists below the bottom of the Big Dipper, which is hanging down by its handle high above, and from there perhaps a little to the right." Et voilà: Comet NEOWISE.

Says Sky & Telescope's Diana Hannikainen, "Look for a faint, fuzzy little 'star' with a fainter, fuzzier little tail extending upward from it."

The comet should be visible with the naked eye, though binoculars and a simple telescope may reveal more detail.

You may also be able to snap a photo of this special visitor, though you'll need the right gear to do so. A dedicated camera is more likely to capture a good shot than a telephone, but in either case, you'll need a tripod or some other means of holding the camera dead still as it takes a timed exposure of several seconds (not all phones can do this).

Quantcast