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?


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Credit: NASA
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CRISPR therapy cures first genetic disorder inside the body

It marks a breakthrough in using gene editing to treat diseases.

Credit: National Cancer Institute via Unsplash
Technology & Innovation

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

For the first time, researchers appear to have effectively treated a genetic disorder by directly injecting a CRISPR therapy into patients' bloodstreams — overcoming one of the biggest hurdles to curing diseases with the gene editing technology.

The therapy appears to be astonishingly effective, editing nearly every cell in the liver to stop a disease-causing mutation.

The challenge: CRISPR gives us the ability to correct genetic mutations, and given that such mutations are responsible for more than 6,000 human diseases, the tech has the potential to dramatically improve human health.

One way to use CRISPR to treat diseases is to remove affected cells from a patient, edit out the mutation in the lab, and place the cells back in the body to replicate — that's how one team functionally cured people with the blood disorder sickle cell anemia, editing and then infusing bone marrow cells.

Bone marrow is a special case, though, and many mutations cause disease in organs that are harder to fix.

Another option is to insert the CRISPR system itself into the body so that it can make edits directly in the affected organs (that's only been attempted once, in an ongoing study in which people had a CRISPR therapy injected into their eyes to treat a rare vision disorder).

Injecting a CRISPR therapy right into the bloodstream has been a problem, though, because the therapy has to find the right cells to edit. An inherited mutation will be in the DNA of every cell of your body, but if it only causes disease in the liver, you don't want your therapy being used up in the pancreas or kidneys.

A new CRISPR therapy: Now, researchers from Intellia Therapeutics and Regeneron Pharmaceuticals have demonstrated for the first time that a CRISPR therapy delivered into the bloodstream can travel to desired tissues to make edits.

We can overcome one of the biggest challenges with applying CRISPR clinically.

—JENNIFER DOUDNA

"This is a major milestone for patients," Jennifer Doudna, co-developer of CRISPR, who wasn't involved in the trial, told NPR.

"While these are early data, they show us that we can overcome one of the biggest challenges with applying CRISPR clinically so far, which is being able to deliver it systemically and get it to the right place," she continued.

What they did: During a phase 1 clinical trial, Intellia researchers injected a CRISPR therapy dubbed NTLA-2001 into the bloodstreams of six people with a rare, potentially fatal genetic disorder called transthyretin amyloidosis.

The livers of people with transthyretin amyloidosis produce a destructive protein, and the CRISPR therapy was designed to target the gene that makes the protein and halt its production. After just one injection of NTLA-2001, the three patients given a higher dose saw their levels of the protein drop by 80% to 96%.

A better option: The CRISPR therapy produced only mild adverse effects and did lower the protein levels, but we don't know yet if the effect will be permanent. It'll also be a few months before we know if the therapy can alleviate the symptoms of transthyretin amyloidosis.

This is a wonderful day for the future of gene-editing as a medicine.

—FYODOR URNOV

If everything goes as hoped, though, NTLA-2001 could one day offer a better treatment option for transthyretin amyloidosis than a currently approved medication, patisiran, which only reduces toxic protein levels by 81% and must be injected regularly.

Looking ahead: Even more exciting than NTLA-2001's potential impact on transthyretin amyloidosis, though, is the knowledge that we may be able to use CRISPR injections to treat other genetic disorders that are difficult to target directly, such as heart or brain diseases.

"This is a wonderful day for the future of gene-editing as a medicine," Fyodor Urnov, a UC Berkeley professor of genetics, who wasn't involved in the trial, told NPR. "We as a species are watching this remarkable new show called: our gene-edited future."

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