# data[].attributes.attachment_link.title
Max Hawkins: I let algorithms randomize my life for two years

# data[].attributes.attachment_link.description
What if everything in your life was randomized: from the food you ate to the things you did and the places you traveled? Computer scientist Max Hawkins created algorithms to make decisions like these for him -- and got hooked on the experience for two years.

# data[].attributes.attachment_link.readable_text
Please click here if you are not redirected within a few seconds.

Images
Big Data Applications - A manifestation of the hottest buzzword ...

data-flair.training

Images may be subject to copyright.

# data[].attributes.attachment_link.description
Please click here if you are not redirected within a few seconds. Images Big Data Applications - A manifestation of the hottest buzzword ... data-flair.training Images may be subject to copyright.

# data[].attributes.attachment_link.title
Kevin Slavin: How algorithms shape our world

# data[].attributes.attachment_link.description
We live in a world run by algorithms, computer programs that make decisions or solve problems for us. In this riveting, funny talk, Kevin Slavin shows how modern algorithms determine stock prices, espionage tactics, even the movies you watch. But, he asks: If we depend on complex algorithms to manage our daily decisions -- when do we start to lose control?

# data[].attributes.attachment_link.title
Sajan Saini: The hidden network that makes the internet possible

# data[].attributes.attachment_link.description
In 2012, a team of researchers set a world record, transmitting 1 petabit of data- that's 10,000 hours of high-def video- over a fifty-kilometer cable, in a second. This wasn't just any cable. It was a souped-up version of fiber optics, the hidden network that links our planet and makes the internet possible.

# data[].attributes.attachment_link.description
There is a mind-boggling amount of data floating around our society. Physicists at CERN have been pondering how to store and share their ever more massive data for decades- stimulating globalization of the internet along the way, whilst 'solving' their big data problem. Tim Smith plots CERN's involvement with big data from fifty years ago to today.

# data[].attributes.attachment_link.readable_text
What can be guessed about you from your online behavior? Two computer privacy experts - economist Alessandro Acquisti and computer scientist Jennifer Golbeck - on how little we know about how much others know.

The best indicator of high intelligence on Facebook is apparently liking a page for curly fries. At least, that's according to computer scientist Jennifer Golbeck (TED Talk: The curly fry conundrum), whose job is to figure out what we reveal about ourselves through what we say - and don't say - online. Of course, the lines between online and "real" are increasingly blurred, but as Golbeck and privacy economist Alessandro Acquisti (TED Talk: Why privacy matters) both agree, that's no reason to stop paying attention. TED got the two together to discuss what the web knows about you, and what we can do about the things we'd rather it forgot. An edited version of the conversation follows.
I hear so much conflicting information about what I should and shouldn't be posting online. It's confusing and unnerving not to know what I can do to protect myself. Can you both talk about that?
Alessandro Acquisti: My personal view is that individual responsibility is important, but we are at a stage where it is not sufficient. The problem is much larger than any one individual's ability to control their personal information, because there are so many new ways every week or every month in which we can be tracked or things can be inferred about us. It's absolutely unreasonable to expect consumers and citizens, who are all engaged in so many other activities, to also have the ability to continuously update their knowledge about what new tracking method the industry has discovered and to be able to fend it off. I think it's a larger problem that requires policy intervention.

Jennifer Golbeck: I agree with that. Even if you did have a person who wanted to be on top of this and was willing to dedicate themselves full-time to keeping track of what technology can do, and then try to make decisions about what they can post, they still actually don't have control.

Take language analysis, a really powerful tool where we look at the kinds of words that you use - not even necessarily obvious things like curse words, but things like function words: how often you use "I" versus "we," how often you use "the" versus "a," these little words that are natural in the way that you develop language and inherent to your personality. It turns out that those reveal all sorts of personal traits. There's a whole field of psycholinguistics in which people are doing deeper research into comparing the kinds of words you use and how often you use them with personal attributes, and that's not something you can understand or control.

AA: It's also difficult to predict how information you reveal now could be used five or ten years out, in the sense of new inferences that could be discovered. Researchers may find that a piece of information "A" combined with a piece of information "B" can lead to the prediction of something particularly sensitive - also in the sense of how this particularly sensitive information could be used. These are literally impossible to predict, because researchers every month come up with new ideas for using data. So we literally do not know how this will play out in the future.
What would a policy solution look like?
JG: Right now in the U.S. it's essentially the case that when you post information online, you give up control of it. So there are terms of service that regulate the sites you use, like on Facebook and Twitter and Pinterest - though those can change - but even within those, you're essentially handing control of your data over to the companies. And they can kind of do what they want with it, within reason. You don't have the legal right to request that data be deleted, to change it, to refuse to allow companies to use it. Some companies may give you that right, but you don't have a natural, legal right to control your personal data. So if a company decides they want to sell it or market it or release it or change your privacy settings, they can do that.

In Europe, users have more of a right to their data, and recently there was a decision in Spain where a man had sued Google because when people searched for him, it was coming up with information about financial problems that he had had a long time ago. He was basically arguing that he has a right to have this information forgotten about him. When we declare bankruptcy, for example, that stays on our credit report for seven years; it's not going to be there 30 years later. But a lot of this stuff on the Internet, including public-record stuff, does stick around well past the time that we would allow it to expire before, and users don't have control over that online.

So Europe is saying users have a right to own their data in a certain way, and in the U.S. we don't have that. That's one of the spaces where there are some clear and straightforward legal solutions that could hand control, at least in some part, back to the users.

"There are a number of ways in which transparency control can be bypassed or muted." Alessandro Acquisti

AA: If you go back to the 1970s, the Organization for Economic Cooperation and Development (OECD) - so not exactly an anti-business or anti-capitalist organization - came up with a number of principles related to handling personal data. These Fair Information Practices, or FIPs, were guidelines for what policymakers could do to make the handling of personal information fair.

If you look at those principles, and then you look now at the state of policymaking in the United States when it comes to privacy, you see a significant difference. The policymaking effort in the U.S. focuses almost exclusively on control and transparency, i.e. telling users how their data is used and giving them some degree of control. And those are important things! However, they are not sufficient means of privacy protection, in that there are a number of ways in which transparency control can be bypassed or muted. What we are missing from the Fair Information Practices are other principles, such as purpose specification (the reason data is being gathered should be specified before or at the time of collection), use limitation (subsequent uses of data should be limited to specific purposes) and security safeguards.
Alessandro, in your talk you mentioned an experiment in which it took only 15 seconds for transparency - in this case, a privacy policy - to be rendered ineffective for users.
AA: Indeed. A very interesting aspect of that experiment is that people do remember what we told them about how we would use their data. But adding this delay between the time that we told them how their data would be used and the time where we actually started asking them to make choices about their data was enough to render that notice ineffective. That's probably because their minds started wandering.

JG: We are actually in the middle of a project where we've been showing people the Facebook privacy policy, and then alternatively having them watch this interactive video called "Take This Lollipop," which is one of my favorite privacy-oriented things online. It's an interactive personalized horror movie where this creepy stalker guy looks at your Facebook profile - which is generated because you click "Connect with Facebook" when you go to the website - and he looks at all your pictures and gets really angry and then kind of tracks you down.

When it first came out, I remember thinking, "Oh, I'm not going to bother trying this, because I'm one of the people in the world who knows the most about Facebook privacy settings. I have them cranked up so high; there's no way it could possibly see anything on my profile." A week later, I thought, "Well, you know, let's click on it and see," and it got all this data that I didn't think it could get. I remember thinking, if I don't understand what kind of data is being given to apps, how can anybody else understand?

We found that having people watch the video made them more informed and understand better what information was being shared than anything else. Now that doesn't necessarily mean it's the way that you want to convey a privacy policy, because it does show deep risk in some of this information being shared when it's not necessarily as risky as that video conveys, but I think this is an interesting point.

AA: To explain this phenomenon I borrow the term "rational ignorance." Rational ignorance has been used in other fields to refer to situations where people rationally decide to remain ignorant about a certain topic because they expect that the costs involved in making an effort will not be offset by the benefit of getting this information. Sometimes, in privacy, we may feel the same way. Sadly, sometimes correctly so: we may do everything to protect ourselves and do everything right, and still our data is being compromised or used in manners that we don't know about and don't want. And therefore, some of us may give up, and decide not even to start protecting ourselves.

"It's really important that people understand that there are computational techniques that will reveal all kinds of information about you that you're not aware that you're sharing." Jennifer Golbeck

JG: At the same time, the thing that I've had a hard time communicating in the years that I've been doing this work is for people to really understand that we can find things out computationally that they're not sharing explicitly. So you can "like" these pages, you can post these things about yourself, and then we can infer a completely unrelated trait about you based on a combination of likes or the type of words that you're using, or even what your friends are doing, even if you're not posting anything. It's things that are inherent in what you're sharing that reveal these other traits, which may be things you want to keep private and that you had no idea you were sharing.

So on the one hand, it's true that even if you know about all these computational techniques, you can't necessarily protect yourself. On the other hand, it's really important that people understand that there are computational techniques that will reveal all kinds of information about you that you're not aware that you're sharing.
How is what's happening on the Internet different from people analyzing the way I dress, cut my hair, where I work or where I live? I don't give people on the streets permission to judge those things, but they do it anyway.
AA: It's different on at least two grounds. One is scale. We are talking here about technologies that vastly increase the kind of abilities that you're describing. They make them more sophisticated. They allow many more entities - not just the friends you meet in your day-to-day life, but entities across the world - to make inferences about you. This data remains somewhere and could be used later to influence you.

The second is asymmetry. We all grow up developing the ability to modulate our public and private spheres, how much we want to reveal with friends, how much we want to protect. And we are pretty good at that. But when we go online, there is an element of asymmetry, because there are entities we don't even know exist, and they are gathering continuously information about us.

"The point is, we really don't know how this information will be used." Alessandro Acquisti

To be clear, I'm not suggesting that all this information will be used negatively, or that online disclosures are inherently negative. That's not at all the point. The point is, we really don't know how this information will be used. For instance, say I'm a merchant - once I get information about you, I can use this information to try to extract more economic surplus from the transaction. I can price-discriminate you, so that I can get more out of the transaction than you will.

That's why I'm interested in working in this area, not because disclosure is bad - human beings disclose all the time, it's an innate need as much as privacy is - but because we really don't know how this information will be used in the long run.

JG: You pick what clothes you wear, you pick the neighborhood you live in, you pick the job that you have - and in some way you know what that's saying about you. Say you're Catholic. Some people are going to associate one thing with you being Catholic, and some people are going to associate another. You have an easy way to understand what all the reactions will be.

But the kinds of things that we're talking about online aren't things that you can necessarily anticipate. One example of this is a pretty early project from a couple of undergrads at MIT called " Project Gaydar." They were able to infer people's sexual orientation by completely ignoring anything that the person had actually said and instead looked at the person's friends and what they had disclosed about themselves. So even if you're a person who wanted to keep their sexual orientation private, we can still find it out, and there's nothing you can do about it.

We have such a huge base of data - hundreds of millions of people, combinations of actions, likes and words. By themselves, it's a pile of traits that doesn't mean anything. Yet we can detect small patterns among these hundreds of millions of people to pretty accurately infer information that has basically no relationship to what they're choosing to disclose.
Once those algorithms are mapped out, how do you keep them from being used for evil? Do you worry your research could be used by less genuine entities?
JG: I sometimes tell people that I feel a bit like I'm working on the Manhattan Project. But I actually approach this from a scientific perspective. I'm interested in the science of it, and I think pretty universally, with very few exceptions, it's always worth doing the science. And in fact, what we're doing to infer these things can actually be used to teach people how to protect themselves. One of the things that we learned through this research is that the more data we have about people, the easier it is to make inferences about them. That has led me to be a regular purger of all my information online. That's a lesson that comes out of the science.

You're right that this stuff is going to get into the hands of companies, governments, and could potentially be used in evil ways. I don't think not doing the science is the solution to that. As Alessandro said earlier, the only solution is a legal one where people have control over how their data is used and there are limitations and real regulation on data brokers and other companies that have this data.

AA: I doubt that even the best researchers are able to give ideas to the industry that have not already come up or will not come up soon by themselves. In the best scenario, we are maybe one or two steps ahead of the game. And that would be important, because it's about raising awareness among individuals and among policy makers about things that are about to happen, or have started to happen.
Featured artwork by Dawn Kim.

# data[].attributes.attachment_link.title
What are you revealing online? Much more than you think

# data[].attributes.attachment_link.description
The best indicator of high intelligence on Facebook is apparently liking a page for curly fries. At least, that's according to computer scientist Jennifer Golbeck (TED Talk: The curly fry conundrum), whose job is to figure out what we reveal about ourselves through what we say - and don't say - online.

# data[].attributes.attachment_link.title
Your social media “likes” expose more than you think

# data[].attributes.attachment_link.description
Do you like curly fries? Have you Liked them on Facebook? Watch this talk to find out the surprising things Facebook (and others) can guess about you from your random Likes and Shares. Computer scientist Jennifer Golbeck explains how this came about, how some applications of the technology are not so cute -- and why she thinks we should return the control of information to its rightful owners.

# data[].attributes.body
ONLINE MAGAZINE

# data[].attributes.attachment_link.description
Pure mathematics uses mathematics to explore abstract ideas, mathematics that does not necessarily describe a real physical system. This can include developing the fundamental tools used by mathematicians, such as algebra and calculus, describing multi-dimensional space, or better understanding the philosophical meaning of mathematics and numbers themselves.

# data[].attributes.attachment_link.title
Math in Nature: 5 Stunning Ways We See Math in the World

# data[].attributes.attachment_link.description
Do you notice math in the natural world? Do your kids? Learn about and explore the beauty of math in nature and then get outside to see it for yourself.

# data[].attributes.attachment_link.readable_text
Extremely well, as Einstein knew better than most, of course. In fact, most scientists would agree that, when it comes to teasing out the inherent secrets of the universe, nothing visual, verbal, or aural comes close to matching the accuracy and economy, the power and elegance, and the inescapable truth of the mathematical.

How is this so? Well, for the math-challenged, for that person who has avoided anything but the most basic arithmetic since high school, who feels a pit in his stomach when he sees an equation-that is, for myself-I will attempt to explain, with the help of some who do mathematics for a living. If you're math-phobic, too, I think you'll get a painless feel for why even that master of describing nature with words, Thoreau, would hold that "the most distinct and beautiful statements of any truth must take at last the mathematical form."

Ancient math

While many early civilizations, including Islamic, Indian, and Chinese, made important contributions to mathematics, it was the ancient Greeks who invented much of the math we're familiar with. Euclid fathered the geometry we named after him-all those radii and hypotenuses and parallel lines. Archimedes approximated pi. Ptolemy created a precise mathematical model that had all of the heavens wheeling around the Earth.

The Greeks' discoveries are timeless: Euclid's axioms are as unimpeachable today as when he devised them over 2,000 years ago. And some Greek proto-physicists did use their newfound skills to tackle mysteries of the natural world. With basic trigonometry, for example, the astronomer Eratosthenes estimated the diameter of the Earth with over 99 percent accuracy-in 228 B.C.

But while the Greeks believed that the universe was mathematically designed, they largely applied math only to static objects-measuring angles, calculating volumes of solid objects, and the like-as well as to philosophical purposes. Plato wouldn't let anyone through the front door of his acclaimed Academy who didn't know mathematics. "He is unworthy of the name of man," Plato sniffed, "who is ignorant of the fact that the diagonal of a square is incommensurable with its side." And so it remained for a millennium and a half.

Galileo strived to explain how objects fall rather than why, a modus operandi that set the stage for the advancement of science as we know it today.

The measure of all things

Galileo changed all that in the early 17th century. Eschewing the Greeks' attempts to explain why a pebble falls when you drop it, Galileo set out to determine how. The "great book" of the universe is written in the language of mathematics, he famously declared, and unless we understand the triangles, circles, and other geometrical figures that form its characters, he wrote, "it is humanly impossible to comprehend a single word of it [and] one wanders in vain through a dark labyrinth." (Wordsworth or Monet might take issue with that statement, but wait.)

Galileo sought characteristics of our world that he could measure-variable aspects like force and weight, time and space, velocity and acceleration. With such measurements, Galileo was able to construct those gems of scientific shorthand-mathematical formulas-which defined phenomena more concisely and more powerfully than had ever been possible before. (His contemporary, the German mathematician Johannes Kepler, did the same for the heavens, crafting mathematical laws that accurately describe the orbits of planets around the sun-and led to the scrapping of Ptolemy's Earth-centric model.)

A tidy sum

A classic example is the formula commonly shown as d = 16t2. (Hang in there, math-phobes. Your queasiness, which I share, should go away when you see how straightforward this is.) What Galileo discovered and ensconced in this simple equation, one of the most consequential in scientific history, is that, when air resistance is left out, the distance in feet, d, that an object falls is equal to 16 times the square of the time in seconds, t. Thus, if you drop a pebble off a cliff, in one second it will fall 16 feet, in two seconds 64 feet, in three seconds 144 feet, and so on.

Galileo's succinct formula neatly expresses the notion of acceleration of objects near the surface of the Earth, but that is just the start of its usefulness. First, just as with any value of t you can calculate d, for any value of d you can figure t. To get to t, simply divide both sides of the formula d = 16t2 by 16, then take the square root of both sides. This leaves a new formula:

This compact equation tells you the time needed for your pebble to fall a given distance-any distance. Say your cliff is 150 high. How long would the pebble take to reach the bottom? A quick calculation reveals just over three seconds. A thousand feet high? Just shy of eight seconds.

Broad strokes

What else can you do with a pithy formula like d = 16t2? Well, as hinted above, you can make calculations for an infinite number of different values for either d or t. In essence, this means that d = 16t2 contains an infinite amount of information. You can also substitute any object for your pebble-a pea, say, or a boulder-and the formula still holds up perfectly (under the conditions previously mentioned). Could a single poem or painting do as much?

And because the same mathematical law may govern multiple phenomena, a curious scientist can discover relationships between those phenomena that might have otherwise gone undetected. Trigonometric functions, for instance, apply to all wave motions-light, sound, and radio waves as well as waves in water, waves in gas, and many other types of wave motions. The person who "gets" these trig functions and their properties will ipso facto "get" all the phenomena that these functions govern.

A wealth of data

The power of a potent equation extends still further. Take Isaac Newton's universal law of gravitation, which brilliantly combines Galileo's laws of falling bodies with Kepler's laws of planetary motion. Many of us know gravity vaguely as that unseen force that keeps the pebble in your palm or your feet on the ground. Newton described it this way:

I won't go into this formula, but just know that from it you can calculate the gravitational tug between just about any two objects you can think of, from that between your coffee cup and the table it rests on, to that between one galaxy and another. Or, depending on which variables you know, you can nail down everything from the acceleration of any freely falling object near the Earth's surface (32 feet per second during every second of its fall) to the mass of our planet (about 6,000,000,000,000,000,000,000 tons).

"With a few symbols on a page, you can describe a wealth of physical phenomena," says astrophysicist Brian Greene, host of NOVA's series based on his book The Fabric of the Cosmos. "And that is, in some sense, what we mean by elegance-that the messy, complex world around us emanates from this very simple equation that you have written on a piece of paper."

And like Galileo's d = 16t2, Newton's formula is amazingly accurate. In 1997, University of Washington researchers determined that Newton's inverse-square law holds down to a distance of 56,000ths of a millimeter. It may hold further, but that's as precise as researchers have gotten at the moment.

Exact science

What amazes me most about Galileo and Newton's formulas is their exactitude. In Galileo's, the distance equals exactly the square of the time multiplied by 16; in Newton's, the force of attraction between any two objects is exactly the square of the distance between them. (That's the r2 in his equation.) Such exactness crops up regularly in mathematical descriptions of reality. Einstein found, for instance, that the energy bound up in, say, a pebble equals the pebble's mass times the square of the speed of light, or E = mc2.

Even things we can see and touch in nature flirt with mathematical proportions and patterns. Consider the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... Notice a pattern? After the first, every number is the sum of the previous two. The Fibonacci sequence has many interesting properties. One is that fractions formed by successive Fibonacci numbers-e.g., 3/2 and 5/3 and 8/5-get closer and closer to a particular value, which mathematicians know as the golden number. But what about this: Many plants adhere to Fibonacci numbers. The black-eyed susan has 13 petals. Asters have 21. Many daisies have 34, 55, or 89 petals, while sunflowers usually have 55, 89, or 144.

Is God a mathematician?

The apparent mathematical nature of Nature, from forces to flowers, has left many since the time of the Greeks wondering, as the mathematician Mario Livio does in his book of the same title, "Is God a mathematician?" Does the universe, that is, have an underlying mathematical structure? Many believe it does. "Just as music is auditory patterns that the human mind finds pleasant," says Stanford mathematician Keith Devlin, "mathematics captures patterns that the universe finds pleasant, if you like-patterns that are implicit in the way the universe works."

So did we humans invent mathematics, or was it already out there, limning the cosmos, awaiting the likes of Euclid to reveal it? In his book Mathematics in Western Culture, the mathematician Morris Kline chose to sidestep the philosophical and focus on the scientific: "The plan that mathematics either imposes on nature or reveals in nature replaces disorder with harmonious order. This is the essential contribution of Ptolemy, Copernicus, Newton, and Einstein."

Seeing the invisible

Formulas like Galileo's and Netwon's make the invisible visible. With d = 16t2, we can "see" the motion of falling objects. With Newton's equation on gravity, we can "see" the force that holds the moon in orbit around the Earth. With Einstein's equations, we can "see" atoms. "Einstein is famous for a lot of things, but one thing that is often overlooked is he's the first person who actually said how big an atom is," says Jim Gates, a physicist at the University of Maryland. "Einstein used mathematics to see a piece of the universe that no one had ever seen before."

Today, with advanced technology, we can observe individual atoms, but some natural phenomena defy any description but a mathematical one. "The only thing you can say about the reality of an electron is to cite its mathematical properties," noted the late mathematics writer Martin Gardner. "So there's a sense in which matter has completely dissolved and what is left is just a mathematical structure." Charles Darwin, who admitted to having found mathematics "repugnant" as a student, may have put it best when he wrote, "Mathematics seems to endow one with something like a new sense."

Fortune telling

Mathematics also endows one with an ability to predict, as Galileo's and Newton's formulas make clear. Such predictive capability often leads to new discoveries. In the mid-1990s, Kyoto University researchers realized to their surprise that equations originally devised by the mathematical genius Alan Turing predicted that the parallel yellow and purple stripes of the marine angelfish have to move over time. Stable, unmoving patterns didn't jive with the mathematics. To find out if this was true, the researchers photographed angelfish in an aquarium over several months. Sure enough, an angelfish's stripes do migrate across its body over time, and in just the way the equations had indicated. Math had revealed the secret.

"There really is a facing-the-music that math forces, and that's why it's a wonderful language for describing nature," Greene says. "It does make predictions for what should happen, and, when the math is accurately describing reality, those predictions are borne out by observation."

A math for all seasons

So much mathematics exists now-one scholar estimates that a million pages of new mathematical ideas are published each year-that when scientists face problems not solvable with math they know, they can often turn to another variety for help. When Einstein began work on his theory of general relativity, he needed a mathematics that could describe what he was proposing-that space is curved. He found it in the non-Euclidean geometry of 19th-century mathematician Georg F. B. Riemann, which provided just the tool he required: a geometry of curved spaces in any number of dimensions.

Or, if necessary, they invent new math. When the late mathematician Benoit Mandelbrot concluded that standard Euclidean geometry, which is all about smooth shapes, fell short when he tried to mathematically portray "rough" shapes like bushy trees or jagged coastlines, he invented a new mathematics called fractal geometry. "Math is our one and only strategy for understanding the complexity of nature," says Ralph Abraham, a mathematician at the University of California Santa Cruz, in NOVA's Hunting the Hidden Dimension. "Fractal geometry has given us a much larger vocabulary, and with a larger vocabulary we can read more of the book of nature." Galileo would be so proud.

Technological wonders

Galileo would also be proud of just how much his successors have achieved with his scientific method. Formulas from his own on falling bodies to Werner Heisenberg's on quantum mechanics have provided us the means to collect and interpret the most valuable knowledge we have ever attained about the workings of nature. Altogether, the most groundbreaking advances of modern science and technology, both theoretical and practical, have come about through the kind of descriptive, quantitative knowledge-gathering that Galileo pioneered and Newton refined.

Newton's law of gravity, for instance, has been critical in all our missions into space. "By understanding the mathematics or force of gravity between lots of different bodies, you get complete control and understanding, with very high precision, of exactly the best way to send a space probe to Mars or Jupiter or to put satellites in orbit-all of those things," says Ian Stewart, an emeritus professor of mathematics at the University of Warwick in England. "Without the math, you would not be able to do it. We can't send a thousand satellites up and hope one of them gets into the right place."

Mathematics underlies virtually all of our technology today. James Maxwell's four equations summarizing electromagnetism led directly to radio and all other forms of telecommunication. E = mc2 led directly to nuclear power and nuclear weapons. The equations of quantum mechanics made possible everything from transistors and semiconductors to electron microscopy and magnetic resonance imaging.

Indeed, many of the technologies you and I enjoy every day simply would not work without mathematics. When you do a Google search, you're relying on 19th-century algebra, on which the search engine's algorithms are based. When you watch a movie, you may well be seeing mountains and other natural features that, while appearing as real as rock, arise entirely from mathematical models. When you play your iPod, you're hearing a mathematical recreation of music that is stored digitally; your cell phone does the same in real time.

"When you listen to a mobile phone, you're not actually hearing the voice of the person speaking," Devlin told me. "You're hearing a mathematical recreation of that voice. That voice is reduced to mathematics."

Aftermath

And I'm reduced to conceding that math doesn't scare me so much anymore. How about you? If you still feel queasy, perhaps you can take solace from Einstein himself, who once reassured a junior high school student, "Do not worry about your difficulties in mathematics; I can assure you that mine are still greater."

Receive emails about upcoming NOVA programs and related content, as well as featured reporting about current events through a science lens.

# data[].attributes.attachment_link.description
Extremely well, as Einstein knew better than most, of course. In fact, most scientists would agree that, when it comes to teasing out the inherent secrets of the universe, nothing visual, verbal, or aural comes close to matching the accuracy and economy, the power and elegance, and the inescapable truth of the mathematical.

# data[].attributes.attachment_link.title
Math is the hidden secret to understanding the world | Roger Antonsen

# data[].attributes.attachment_link.readable_text
Singapore, like any modern city, faces a growing resource challenge. Who are Singapore's visionary thinkers and innovators? And how are we preparing for a brighter future through technology?
City of the Future: Singapore premiered on National Geographic on 18 Aug 2018

Singapore Prime Minister Lee Hsien Loong speaks exclusively with National Geographic about the island nation's future
Written by Mark Eggleton, National Geographic

When Singapore's Prime Minister Lee Hsien Loong talks about his country he does so with an enormous sense of warmth. A warmth for his people and importantly, his and the Government's role as stewards of the future. Rather than suggesting the Government owns the present, he emphasises the importance of taking care of Singapore right now and ensuring it's handed on in good condition to future generations. It's this genuine affection for his whole country which immediately strikes you.
In the days preceding the interview, Lee had invited a National Geographic photographer to tag along on his engagements - including a visit to a newly-opened pre-school, a stroll in the city's Botanic Gardens, a walk around his constituency's hawker market, and even the home of one of his constituents. What was surprising was how each visit quickly turned into something more. Reason being is unlike many politicians who can look awkward with their constituents, Lee revelled in simply being out and about. Generous with his time and happy to take endless smartphone selfies, he chatted and laughed with a range of people and families.
On the day we meet in his private office at Istana, Lee is dressed casually and keen for a relatively informal chat. Outside, the serenity of the property's vast pristine gardens is only broken by the low thrum of a lawnmower. A green sanctuary in the heart of the city, Istana is the official Presidential Palace as well as the Prime Minister's office, and its sense of peace had made its way inside where Lee is in an avuncular mood.
Sitting in his relatively austere office and responding to a remark that our interview might go slightly off-piste, Lee jokingly replies "we're not very good skiers" before outlining why he is excited for Singapore's future as a digital economy hub that continues to deliver outsize opportunities for its people. He is keen to point out that government is a team and while he can give orders nothing can happen "unless I've got teamwork", which includes Government ministers as well as the civil service and the private sector.
What excites him the most is while Singapore is still a young country of just over 50 years of age, "we have the resources, the people trained and the organisation, to plan our next 50 years, and remake Singapore substantially. Not all of it but step-by-step we can remake the economy, the whole (economic) landscape, the way we invest in our people and I hope our standing in the world. That's a big job. I'm 66 but my successors, they will have to carry it forward."
The Lion City is already well on its way to transforming itself into a thriving digital economy as it already has some of the most advanced digital infrastructure in the world. Government services are all migrating online and Lee says there is a huge focus on ensuring the whole population understands the opportunities afforded by the digital economy.

"The young ones, they call them digital natives whereas old ones like me, we're immigrants. There's a lot we can do to make the internet easy and convenient for old people to use and we have all sorts of classes for them," Lee says.
Ensuring every generation is catered for starts back in primary school classrooms where the first four years of schooling focus on English, mother tongue, maths and science and the nature of STEM (science, technology, engineering and mathematics) learning is given top priority. For Lee, who was the top mathematics undergraduate during his time at England's University of Cambridge, STEM skills are the key to the future and they're actively encouraged in tertiary education. GOING (DIGITAL) NATIVE
"You don't have to become a master programmer, but you must at least have an idea of how computers and programming works. Then it doesn't look like sheer magic to you and you will not be totally terrified by it when you are in a position of responsibility and you've got to make decisions."
Bearing in mind how the global economy is changing, Lee remains optimistic for the global economy and especially for Singapore, where he believes people will be able to adjust as automation and artificial intelligence fundamentally change the nature of work. He suggests Singapore's value proposition is its geography and it can do quite a lot of things well and perhaps sufficiently better than elsewhere, such as being a financial services and data hub for the region as well as providing a strong regulatory and legal framework for business.
"In medical services, we have patients who come here from all over the region as well as from longer distances such as Russia. I think if you are a first world-city with that concentration of talent, services and quality of life, people will want to live and work here."
As for Singapore's ever-evolving physical transformation, Lee speaks of moving the current military airbase at Paya Lebar in the central-eastern part of Singapore to Changi - freeing up an enormous amount of land for reuse and development.
"You can redevelop that land as a new township but most importantly all the surrounding areas, which is maybe one third of the island, has been developed in a height-constrained way. Take the airbase out and you have completely different possibilities."
Lee also spoke of the current process of moving the port at Tanjong Pagar to the Tuas mega-port on the western edge of Singapore, which will free up "really prime land right in the middle of the city. It's another opportunity for two-plus Marina Bays worth of redevelopment."

Beyond Singapore, Lee speaks of the country's role as ASEAN Chair this year and the two ideas chosen as themes for the chairmanship - Resilience and Innovation. Both underline the opportunities and challenges countries in the region need to confront in a globalised digital economy. Lee says resilience means dealing with shocks and problems and dangers, while innovation means looking for new opportunities to work together and to grow.
"On resilience, we're talking about things like disaster relief and cybersecurity cooperation while on innovation, we're talking about a smart cities network. We have 26 smart cities signed up and we hope we can work together. We are chairman for a year, it's a rotating chairmanship. It doesn't mean we are the commander-in-chief, we are just the co-ordinator for this year. What it means is we have to work together to make ASEAN relevant in the world. Work together economically and work together when it comes to political and strategic issues."
Lee is a great believer in a networked future where nations work collaboratively and he envisions a world where talent connects globally.
"There are any number of cities in Asia which have three or four million people in them; probably dozens, many dozens. Why are we different? It's because of the way we have been able to make our people work together and to make the system work. It doesn't mean we're smarter than other people, I think we work as hard as others but we work together more effectively and so you produce something special." CHALLENGE AND OPPORTUNITY

# data[].attributes.attachment_link.title
City of the Future: Singapore on National Geographic

# data[].attributes.attachment_link.description
Singapore , like any modern city, faces a growing resource challenge. Who are Singapore's visionary thinkers and innovators? And how are we preparing for a brighter future through technology?

# data[].attributes.attachment_link.title
David Christian: The history of our world in 18 minutes

# data[].attributes.attachment_link.description
Backed by stunning illustrations, David Christian narrates a complete history of the universe, from the Big Bang to the Internet, in a riveting 18 minutes. This is "Big History": an enlightening, wide-angle look at complexity, life and humanity, set against our slim share of the cosmic timeline.

# data[].attributes.attachment_link.title
City of the Future: Singapore – Full Episode | National Geographic

# data[].attributes.attachment_link.title
Neil MacGregor on the Cyrus Cylinder: A great moment for the Middle East

# data[].attributes.attachment_link.title
Jean-Baptiste Michel: The mathematics of history

# data[].attributes.attachment_link.description
In the vast sweep of history, even an empire can be forgotten. In this wide-ranging talk, Gus Casely-Hayford shares origin stories of Africa that are too often unwritten, lost, unshared. Travel to Great Zimbabwe, the ancient city whose mysterious origins and advanced architecture continue to confoun…

# data[].attributes.attachment_link.readable_text
One of the joys of studying history is the intellectual curiosity of fellow historians. On her first day at university, the undergraduate historian will meet a wide range of people, fellow students and tutors, all of whom share a thirst for knowledge about the past. She will meet people who also want to know more about propaganda in Soviet Russia or tactics at the Battle of Agincourt. Why should we worry about what this knowledge is and the purposes it serves when sheer contemplation of such exotic human diversity is wonderful in itself? This wonder can become a lifelong passion. The new history undergraduate's excitement will be shared by those who have been studying history for much longer - the more the historian knows about the past, the more she wants to know.

In Durham, the historian's passion for knowledge of the past is intensified by the fact that this passion has been felt by historians in the city for nearly a thousand years. As long ago as the late eleventh century, the Norman monk Symeon used archival records belonging to the community guarding the body of St Cuthbert to write a history of the origins of that community. Symeon's successors remained obsessed with the past, gathering information and writing new histories of Durham. On the way to her lectures, the new history undergraduate might choose to walk round the cloisters in which her monastic predecessors discussed their historical interests many centuries before. The effect of this sense of a shared interest in the past is spine-tingling and makes our knowledge of distant periods and peoples very real.

As historians, though, we must take care. Historical knowledge can bring wonder and joy - but there is much more to it than that. We must remember that creating historical knowledge is not like digging up buried treasure. Understanding the past is not simply a matter of accumulating information: historical work will never be 'finished'. This is because, without historical questions to guide us, knowledge means nothing. I am reminded of the hero of one of Borges' stories 'Funes the Memorious'. Funes has had a head injury which means he remembers everything he sees: he describes shifting cloud formations minute by minute; he learns every word in a language by simply reading a dictionary. Such prodigious knowledge acquisition had the effect of rendering him incapable of thought: his mind is constantly acquiring information and this makes it impossible for him to sift, to analyse, to select. As historians, we must bear Funes in mind because, until the historian understands the questions she is asking, she will not be able to understand the past.

When the Durham monks carried out historical research, they wanted to understand the relationship between the earthly community in which they lived and St Cuthbert, a heavenly figure who was a daily part of their earthly lives. In other words, they needed to understand the past in order to make sense of the present - and their understanding of the present was very different from ours. For the medieval historian and the twenty-first-century historian alike, then, knowledge must have a purpose. This is something which is easy to forget for those engaged in historical study. This may sound rather ominous, but it is no exaggeration to say that historical knowledge can be dangerous. Let us turn, for a moment, to the dictatorship of General Franco in Spain in the mid-twentieth century. Franco was responsible for the murder of hundreds of thousands of Spaniards and for the misery of millions more. He was also celebrated by many of his contemporaries as the hero who delivered Spain from chaos. Franco's power to convince people of the legitimacy of his rule depended on historical 'knowledge': it depended on a glorious interpretation of Spain's distant past and a bleak version of its transition into modernity.The reasons for the longevity of Franco's brutal regime are complex, but it depended in part upon a particular body of historical 'knowledge'. Much of this 'knowledge' had been assembled by historians in the nineteenth and early twentieth centuries, unaware of its potential as a justification for murder and torture.

This article is in part a celebration of the sheer wonder of historical knowledge - the dizzying sense of excitement the historian feels in learning about the past. This article is also a warning. Historians have great responsibility in their exploration of knowledge: we must try to understand where the knowledge comes from, why we are exploring it and the uses to which it might be put. What is more, we must encourage others to treat historical knowledge in the same way.

# data[].attributes.attachment_link.title
What is the nature of historical knowledge? by Ben Dodds

# data[].attributes.attachment_link.description
One of the joys of studying history is the intellectual curiosity of fellow historians. On her first day at university, the undergraduate historian will meet a wide range of people, fellow students and tutors, all of whom share a thirst for knowledge about the past.

# data[].attributes.body
EYE WITNESS TESTIMONY

# data[].attributes.attachment_link.readable_text
The events of the 1960s are fading into history, but John Lewis believes eyewitness accounts are key to continued progress.

Reuters

ASPEN, Colo.-What makes John Lewis such an important link to the crucial period of the civil-rights period isn't just that he was there. It's that he can conjure dates, faces, and details from those experiences with such impressive command.

The longtime Georgia Democratic member of Congress demonstrated a little of that Wednesday at the Aspen Ideas Festival, which is hosted by The Atlantic and the Aspen Institute.

He spoke about the powerful feeling he got the first time he met Martin Luther King, when Lewis was still a teenager: "To be in his presence, to be able to talk with him, just made me feel stronger and more daring."

He remembered exactly what was said in the moments before Alabama State Troopers attacked the peaceful marchers on the Edmund Pettus Bridge in Selma: Hosea Williams asked Officer John Cloud for a moment to pray, but the mass of troopers attacked instead. (Lewis's skull was fractured by a nightstick that day.)

Dispatches from the Aspen Ideas Festival. Full coverage.
See more fromAtlanticLIVE.

He remembered the meal he ate with fellow Freedom Riders the day before they boarded buses in Washington, D.C., headed south. It was the first time he'd ever had Chinese food. "Someone said, 'You should eat well, because this might be your last meal,'" Lewis recalled.

He remembered being tipped off that he was going to be arrested one day and going to a used-clothing store the day before to buy a suit for $5. (He wishes he still had the suit, though he doesn't imagine he'd still fit in it. But he's going to wear one just like it to attend Comic-Con this year, where he's promoting a graphic memoir.)

# data[].attributes.attachment_link.title
The Power of Memory in the Civil-Rights Movement

# data[].attributes.attachment_link.description
The events of the 1960s are fading into history, but John Lewis believes eyewitness accounts are key to continued progress. ASPEN, Colo.-What makes John Lewis such an important link to the crucial period of the civil-rights period isn't just that he was there.

# data[].attributes.attachment_link.title
History is not what happened - TOK RESOURCE.ORG

# data[].attributes.attachment_link.description
Continue in similar vein with two new volunteers readings of the following pair of official distillations of the nature of history from the International Baccalaureate Organization itself. Ask the class to reflect on how much these lofty descriptions have aligned with their actual experience in school history classes.

# data[].attributes.attachment_link.title
Mikhail Zygar: What the Russian Revolution would have looked like on social media

# data[].attributes.attachment_link.description
History is written by the victors, as the saying goes -- but what would it look like if it was written by everyone? Journalist and TED Fellow Mikhail Zygar is on a mission to show us with Project1917, a "social network for dead people" that posts the real diaries and letters of more than 3,000 people who lived during the Russian Revolution.

# data[].attributes.attachment_link.title
Kelly Richmond Pope: How whistle-blowers shape history

# data[].attributes.attachment_link.description
Fraud researcher and documentary filmmaker Kelly Richmond Pope shares lessons from some of the most high-profile whistle-blowers of the past, explaining how they've shared information that has shaped society -- and why they need our trust and protection.

# data[].attributes.attachment_link.title
Ron Eglash: The fractals at the heart of African designs

# data[].attributes.attachment_link.description
'I am a mathematician, and I would like to stand on your roof.' That is how Ron Eglash greeted many African families he met while researching the fractal patterns he'd noticed in villages across the continent.

# data[].attributes.attachment_link.readable_text
Mathematics is the science that deals with the logic of shape, quantity and arrangement. Math is all around us, in everything we do. It is the building block for everything in our daily lives, including mobile devices, computers, software, architecture (ancient and modern), art, money, engineering and even sports.

Since the beginning of recorded history, mathematical discovery has been at the forefront of every civilized society, and math has been used by even the most primitive and earliest cultures. The need for math arose because of the increasingly complex demands from societies around the world, which required more advanced mathematical solutions, as outlined by mathematician Raymond L. Wilder in his book "Evolution of Mathematical Concepts" (Dover Publications, 2013).

The more complex a society, the more complex the mathematical needs. Primitive tribes needed little more than the ability to count, but also used math to calculate the position of the sun and the physics of hunting. "All the records - anthropological and historical - show that counting and, ultimately, numeral systems as a device for counting form the inception of the mathematical element in all cultures," Wilder wrote in 1968.

Who invented mathematics?

Several civilizations - in China, India, , Central America and Mesopotamia - contributed to mathematics as we know it today. The Sumerians, who lived in the region that is now southern Iraq, were the first people to develop a counting system with a base 60 system, according to Wilder.

This was based on using the bones in the fingers to count and then use as sets, according to Georges Ifrah in his book "The Universal History Of Numbers" (John Wiley & Sons, 2000). From these systems we have the basis of arithmetic, which includes basic operations of addition, multiplication, division, fractions and square roots. Wilder explained that the Sumerians' system passed through the Akkadian Empire to the Babylonians around 300 B.C. Six hundred years later, in Central America, the developed elaborate calendar systems and were skilled astronomers. About this time, the concept of zero was developed in India.

As civilizations developed, mathematicians began to work with geometry, which computes areas, volumes and angles, and has many practical applications. Geometry is used in everything from home construction to fashion and interior design. As Richard J. Gillings wrote in his book "Mathematics in the Time of the Pharaohs" (Dover Publications, 1982), the pyramids of Giza in Egypt are stunning examples of ancient civilizations' advanced use of geometry.

(Image credit: Konstik)

Geometry went hand in hand with algebra. Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī authored the earliest recorded work on algebra called "The Compendious Book on Calculation by Completion and Balancing" around 820 A.D., according to Philip K. Hitti, a history professor at Princeton and Harvard University. Al-Khwārizmī also developed quick methods for multiplying and dividing numbers, which are known as algorithms - a corruption of his name, which in Latin was translated to Algorithmi.

Algebra offered civilizations a way to divide inheritances and allocate resources. The study of algebra meant mathematicians could solve linear equations and systems, as well as quadratics, and delve into positive and negative solutions. Mathematicians in ancient times also began to look at number theory, which "deals with properties of the whole numbers, 1, 2, 3, 4, 5, ...," Tom M. Apostol, a professor at the California Institute of Technology, wrote in "Introduction to Analytic Number Theory" (Springer, 1976). With origins in the construction of shape, number theory looks at figurate numbers, the characterization of numbers, and theorems.

Mathematics in ancient Greece

The word mathematics comes from the ancient Greeks and is derived from the word máthēma, meaning "that which is learnt," according to Douglas R. Harper, author of the " Online Etymology Dictionary." The ancient Greeks built on other ancient civilizations' mathematical studies, and they developed the model of abstract mathematics through geometry.

Greek mathematicians were divided into several schools, as outlined by G. Donald Allen, professor of Mathematics at Texas A&M University in his paper, "The Origins of Greek Mathematics":

In addition to the Greek mathematicians listed above, a number of other ancient Greeks made an indelible mark on the history of mathematics, including Archimedes, most famous for the Archimedes' principle around the buoyant force; Apollonius, who did important work with ; Diophantus, the first Greek mathematician to recognize fractions as numbers; Pappus, known for his hexagon theorem; and Euclid, who first described the golden ratio.

(Image credit: Shutterstock)

During this time, mathematicians began working with trigonometry, which studies relationships between the sides and angles of triangles and computes trigonometric functions, including sine, cosine, tangent and their reciprocals. Trigonometry relies on the synthetic geometry developed by Greek mathematicians like Euclid. In past cultures, trigonometry was applied to astronomy and the computation of angles in the celestial sphere.

The development of mathematics was taken on by the Islamic empires, then concurrently in Europe and China, according to Wilder. Leonardo Fibonacci was a medieval European mathematician and was famous for his theories on arithmetic, algebra and geometry. The Renaissance led to advances that included decimal fractions, logarithms and projective geometry. Number theory was greatly expanded upon, and theories like probability and analytic geometry ushered in a new age of mathematics, with calculus at the forefront.

Development of calculus

In the 17th century, Isaac Newton in England and Gottfried Leibniz in Germany independently developed the foundations for calculus, Carl B. Boyer, a science historian, explained in "The History of the Calculus and Its Conceptual Development" (Dover Publications, 1959). Calculus development went through three periods: anticipation, development and rigorization.

In the anticipation stage, mathematicians attempted to use techniques that involved infinite processes to find areas under curves or maximize certain qualities. In the development stage, Newton and Leibniz brought these techniques together through the derivative (the curve of mathematical function) and integral (the area under the curve). Though their methods were not always logically sound, mathematicians in the 18th century took on the rigorization stage and were able to justify their methods and create the final stage of calculus. Today, we define the derivative and integral in terms of limits.

In contrast to calculus, which is a type of continuous mathematics (dealing with real numbers), other mathematicians have taken a more theoretical approach. Discrete mathematics is the branch of math that deals with objects that can assume only distinct, separated value, as mathematician and computer scientist Richard Johnsonbaugh explained in "Discrete Mathematics" (Pearson, 2017). Discrete objects can be characterized by integers, rather than real numbers. Discrete mathematics is the mathematical language of computer science, as it includes the study of algorithms. Fields of discrete mathematics include combinatorics, graph theory and the theory of computation.

(Image credit: Anton Belitskiy/Getty)

Why mathematics is important

It's not uncommon for people to wonder what relevance mathematics serves in their daily lives. In the modern world, math such as applied mathematics is not only relevant, it's crucial. Applied mathematics covers the branches that study the physical, biological or sociological world.

"The goal of applied mathematics is to establish the connections between separate academic fields," wrote Alain Goriely in "Applied Mathematics: A Very Short Introduction" (Oxford University Press, 2018). Modern areas of applied math include mathematical physics, mathematical biology, control theory, aerospace engineering and math finance. Not only does applied math solve problems, but it also discovers new problems or develops new engineering disciplines, Goriely added. The common approach in applied math is to build a mathematical model of a phenomenon, solve the model and develop recommendations for performance improvement.

While not necessarily an opposite to applied mathematics, pure mathematics is driven by abstract problems, rather than real-world problems. Much of the subjects that are pursued by pure mathematicians have their roots in concrete physical problems, but a deeper understanding of these phenomena brings about problems and technicalities.

These abstract problems and technicalities are what pure mathematics attempts to solve, and these attempts have led to major discoveries for humankind, including the universal Turing machine, theorized by Alan Turing in 1937. This machine, which began as an abstract idea, later laid the groundwork for the development of modern computers. Pure mathematics is abstract and based in theory, and is thus not constrained by the limitations of the physical world.

According to Goriely, "Applied mathematics is to pure mathematics, what pop music is to classical music." Pure and applied are not mutually exclusive, but they are rooted in different areas of math and problem solving. Though the complex math involved in pure and applied mathematics is beyond the understanding of most people, the solutions developed from the processes have affected and improved the lives of many.

Originally published on Live Science.

# data[].attributes.attachment_link.description
Mathematics is the science that deals with the logic of shape, quantity and arrangement. It's all around us.

# data[].attributes.attachment_link.title
An introduction to mathematical theorems - Scott Kennedy

# data[].attributes.attachment_link.description
View full lesson here: http://ed.ted.com/lessons/scott-kennedy-how-to-prove-a-mathematical-theory Euclid of Alexandria revolutionized the way that mathematics is written, presented or thought about, and introduced the concept of mathematical proofs. Discover what it takes to move from a loose theory or idea to a universally convincing proof. Lesson by Scott Kennedy, animation by Karrot Animation.

# data[].attributes.attachment_link.description
Finding the right mate is no cakewalk -- but is it even mathematically likely? In a charming talk, mathematician Hannah Fry shows patterns in how we look for love, and gives her top three tips (verified by math!) for finding that special someone.