# The evolution of mathematics, from agriculture to quantum mechanics

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

Dr. Michelle Thaller is an astronomer who studies binary stars and the life cycles of stars. She is Assistant Director of Science Communication at NASA. She went to college at Harvard University, completed a post-doctoral research fellowship at the California Institute of Technology (Caltech) in Pasadena, Calif. then started working for the Jet Propulsion Laboratory's (JPL) Spitzer Space Telescope. After a hugely successful mission, she moved on to NASA's Goddard Space Flight Center (GSFC), in the Washington D.C. area. In her off-hours often puts on about 30lbs of Elizabethan garb and performs intricate Renaissance dances. For more information, visit NASA.

**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?

## Why it’s hard to tell when high-class people are incompetent

A recent study gives new meaning to the saying "fake it 'til you make it."

- The study involves four experiments that measured individuals' socioeconomic status, overconfidence and actual performance.
- Results consistently showed that high-class people tend to overestimate their abilities.
- However, this overconfidence was misinterpreted as genuine competence in one study, suggesting overestimating your abilities can have social advantages.

- Map details dramatic shift from CNN to Fox News over 10-year period
- Does it show the triumph of "fake news" — or, rather, its defeat?
- A closer look at the map's legend allows for more complex analyses

### Dramatic and misleading

*Image: Reddit / SICResearch*

The situation today: CNN pushed back to the edges of the country.

Over the course of no more than a decade, America has radically switched favorites when it comes to cable news networks. As this sequence of maps showing TMAs (Television Market Areas) suggests, CNN is out, Fox News is in.

The maps are certainly dramatic, but also a bit misleading. They nevertheless provide some insight into the state of journalism and the public's attitudes toward the press in the US.

Let's zoom in:

- It's 2008, on the eve of the Obama Era. CNN (blue) dominates the cable news landscape across America. Fox News (red) is an upstart (°1996) with a few regional bastions in the South.

- By 2010, Fox News has broken out of its southern heartland, colonizing markets in the Midwest and the Northwest — and even northern Maine and southern Alaska.

- Two years later, Fox News has lost those two outliers, but has filled up in the middle: it now boasts two large, contiguous blocks in the southeast and northwest, almost touching.

- In 2014, Fox News seems past its prime. The northwestern block has shrunk, the southeastern one has fragmented.

- Energised by Trump's 2016 presidential campaign, Fox News is back with a vengeance. Not only have Maine and Alaska gone from entirely blue to entirely red, so has most of the rest of the U.S. Fox News has plugged the Nebraska Gap: it's no longer possible to walk from coast to coast across CNN territory.

- By 2018, the fortunes from a decade earlier have almost reversed. Fox News rules the roost. CNN clings on to the Pacific Coast, New Mexico, Minnesota and parts of the Northeast — plus a smattering of metropolitan areas in the South and Midwest.

### "Frightening map"

*Image source: Reddit / SICResearch*

This sequence of maps, showing America turning from blue to red, elicited strong reactions on the Reddit forum where it was published last week. For some, the takeover by Fox News illustrates the demise of all that's good and fair about news journalism. Among the comments?

- "The end is near."
- "The idiocracy grows."
- "(It's) like a spreading disease."
- "One of the more frightening maps I've seen."

- "LOL that's what happens when you're fake news!"
- "CNN went down the toilet on quality."
- "A Minecraft YouTuber could beat CNN's numbers."
- "CNN has become more like a high-school production of a news show."

Not a few find fault with both channels, even if not always to the same degree:

- "That anybody considers either of those networks good news sources is troubling."
- "Both leave you understanding less rather than more."
- "This is what happens when you spout bullsh-- for two years straight. People find an alternative — even if it's just different bullsh--."
- "CNN is sh-- but it's nowhere close to the outright bullsh-- and baseless propaganda Fox News spews."

### "Old people learning to Google"

*Image: Google Trends*

CNN vs. Fox News search terms (200!-2018)

But what do the maps actually show? Created by SICResearch, they do show a huge evolution, but not of both cable news networks' audience size (i.e. Nielsen ratings). The dramatic shift is one in *Google search trends*. In other words, it shows how often people type in "CNN" or "Fox News" when surfing the web. And that does not necessarily reflect the relative popularity of both networks. As some commenters suggest:

- "I can't remember the last time that I've searched for a news channel on Google. Is it really that difficult for people to type 'cnn.com'?"
- "More than anything else, these maps show smart phone proliferation (among older people) more than anything else."
- "This is a map of how old people and rural areas have learned to use Google in the last decade."
- "This is basically a map of people who don't understand how the internet works, and it's no surprise that it leans conservative."

A visual image as strong as this map sequence looks designed to elicit a vehement response — and its lack of context offers viewers little new information to challenge their preconceptions. Like the news itself, cartography pretends to be objective, but always has an agenda of its own, even if just by the selection of its topics.

The trick is not to despair of maps (or news) but to get a good sense of the parameters that are in play. And, as is often the case (with both maps and news), what's left out is at least as significant as what's actually shown.

One important point: while Fox News is the sole major purveyor of news and opinion with a conservative/right-wing slant, CNN has more competition in the center/left part of the spectrum, notably from MSNBC.

Another: the average age of cable news viewers — whether they watch CNN or Fox News — is in the mid-60s. As a result of a shift in generational habits, TV viewing is down across the board. Younger people are more comfortable with a "cafeteria" approach to their news menu, selecting alternative and online sources for their information.

It should also be noted, however, that Fox News, according to Harvard's Nieman Lab, dominates Facebook when it comes to engagement among news outlets.

### CNN, Fox and MSNBC

*Image: Google Trends*

CNN vs. Fox (without the 'News'; may include searches for actual foxes). See MSNBC (in yellow) for comparison

For the record, here are the Nielsen ratings for average daily viewer total for the three main cable news networks, for 2018 (compared to 2017):

- Fox News: 1,425,000 (-5%)
- MSNBC: 994,000 (+12%)
- CNN: 706,000 (-9%)

And according to this recent overview, the top 50 of the most popular websites in the U.S. includes cnn.com in 28th place, and foxnews.com in... 27th place.

The top 5, in descending order, consists of google.com, youtube.com, facebook.com, amazon.com and yahoo.com — the latter being the highest-placed website in the News and Media category.## Mother bonobos, too, pressure their sons to have grandchildren

If you thought your mother was pushy in her pursuit of grandchildren, wait until you learn about bonobo mothers.

- Mother bonobos have been observed to help their sons find and copulate with mates.
- The mothers accomplish this by leading sons to mates, interfering with other males trying to copulate with females, and helping sons rise in the social hierarchy of the group.
- Why do mother bonobos do this? The "grandmother hypothesis" might hold part of the answer.

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