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?


China's "artificial sun" sets new record for fusion power

China has reached a new record for nuclear fusion at 120 million degrees Celsius.

Credit: STR via Getty Images
Technology & Innovation

This article was originally published on our sister site, Freethink.

China wants to build a mini-star on Earth and house it in a reactor. Many teams across the globe have this same bold goal --- which would create unlimited clean energy via nuclear fusion.

But according to Chinese state media, New Atlas reports, the team at the Experimental Advanced Superconducting Tokamak (EAST) has set a new world record: temperatures of 120 million degrees Celsius for 101 seconds.

Yeah, that's hot. So what? Nuclear fusion reactions require an insane amount of heat and pressure --- a temperature environment similar to the sun, which is approximately 150 million degrees C.

If scientists can essentially build a sun on Earth, they can create endless energy by mimicking how the sun does it.

If scientists can essentially build a sun on Earth, they can create endless energy by mimicking how the sun does it. In nuclear fusion, the extreme heat and pressure create a plasma. Then, within that plasma, two or more hydrogen nuclei crash together, merge into a heavier atom, and release a ton of energy in the process.

Nuclear fusion milestones: The team at EAST built a giant metal torus (similar in shape to a giant donut) with a series of magnetic coils. The coils hold hot plasma where the reactions occur. They've reached many milestones along the way.

According to New Atlas, in 2016, the scientists at EAST could heat hydrogen plasma to roughly 50 million degrees C for 102 seconds. Two years later, they reached 100 million degrees for 10 seconds.

The temperatures are impressive, but the short reaction times, and lack of pressure are another obstacle. Fusion is simple for the sun, because stars are massive and gravity provides even pressure all over the surface. The pressure squeezes hydrogen gas in the sun's core so immensely that several nuclei combine to form one atom, releasing energy.

But on Earth, we have to supply all of the pressure to keep the reaction going, and it has to be perfectly even. It's hard to do this for any length of time, and it uses a ton of energy. So the reactions usually fizzle out in minutes or seconds.

Still, the latest record of 120 million degrees and 101 seconds is one more step toward sustaining longer and hotter reactions.

Why does this matter? No one denies that humankind needs a clean, unlimited source of energy.

We all recognize that oil and gas are limited resources. But even wind and solar power --- renewable energies --- are fundamentally limited. They are dependent upon a breezy day or a cloudless sky, which we can't always count on.

Nuclear fusion is clean, safe, and environmentally sustainable --- its fuel is a nearly limitless resource since it is simply hydrogen (which can be easily made from water).

With each new milestone, we are creeping closer and closer to a breakthrough for unlimited, clean energy.

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