The following is an adapted excerpt from the book What's the Use? It is reprinted with permission of the author and Hachette Book Group.
What is mathematics for?
What is it doing for us, in our daily lives?
Not so long ago, there were easy answers to these questions. The typical citizen used basic arithmetic all the time, if only to check the bill when shopping. Carpenters needed to know elementary geometry. Surveyors and navigators needed trigonometry as well. Engineering required expertise in calculus.
Today, things are different. The supermarket checkout totals the bill, sorts out the special meal deal, adds the sales tax. We listen to the beeps as the laser scans the barcodes, and as long as the beeps match the goods, we assume the electronic gizmos know what they are doing. Many professions still rely on extensive mathematical knowledge, but even there, we have outsourced most of the mathematics to electronic devices with built-in algorithms.
My subject is conspicuous by its absence. The elephant isn't even in the room.
It would be easy to conclude that mathematics has become outdated and obsolete, but that view is mistaken. Without mathematics, today's world would fall apart. As evidence, I am going to show you applications to politics, the law, kidney transplants, supermarket delivery schedules, Internet security, movie special effects, and making springs. We will see how mathematics plays an essential role in medical scanners, digital photography, fiber broadband, and satellite navigation. How it helps us predict the effects of climate change; how it can protect us against terrorists and Internet hackers.
Remarkably, many of these applications rely on mathematics that originated for totally different reasons, often just the sheer fascination of following your nose. While researching this book, I was repeatedly surprised when I came across uses of my subject that I had never dreamed existed. Often, they exploited topics that I would not have expected to have practical applications, like space-filling curves, quaternions, and topology.
Mathematics is a boundless, hugely creative system of ideas and methods. It lies just beneath the surface of the transformative technologies that are making the twenty-first century totally different from any previous era — video games, international air travel, satellite communications, computers, the Internet, mobile phones. Scratch an iPhone, and you will see the bright glint of mathematics.
Please don't take that literally.
There is a tendency to assume that computers, with their almost miraculous abilities, are making mathematicians, indeed mathematics itself, obsolete. But computers no more displace mathematicians than the microscope displaced biologists. Computers change the way we go about doing mathematics, but mostly they relieve us of the tedious bits. They give us time to think, they help us search for patterns, and they add a powerful new weapon to help advance the subject more rapidly and more effectively.
In fact, a major reason why mathematics is becoming ever more essential is the ubiquity of cheap, powerful computers. Their rise has opened up new opportunities to apply mathematics to real-world issues. Methods that were hitherto impractical, because they needed too many calculations, have now become routine. The greatest mathematicians of the pencil-and-paper era would have flung up their hands in despair at any method requiring a billion calculations. Today, we routinely use such methods, because we have technology that can do the sums in a split second. Mathematicians have long been at the forefront of the computer revolution — along with countless other professions, I hasten to add. Think of George Boole, who pioneered the symbolic logic that forms the basis of current computer architecture. Think of Alan Turing, and his universal Turing machine, a mathematical system that can compute anything that is computable. Think of Muhammad al-Khwarizmi, whose algebra text of 820 AD emphasized the role of systematic computational procedures, now named after him: algorithms.
Most of the algorithms that give computers their impressive abilities are firmly based on mathematics. Many of the techniques concerned have been taken "off the shelf" from the existing store of mathematical ideas, such as Google's PageRank algorithm, which quantifies how important a website is and founded a multi-billion-dollar industry. Even the snazziest deep learning algorithm in artificial intelligence uses tried and tested mathematical concepts such as matrices and weighted graphs. A task as prosaic as searching a document for a particular string of letters involves, in one common method at least, a mathematical gadget called a finite-state automaton.
The involvement of mathematics in these exciting developments tends to get lost. So next time the media propel some miraculous new ability of computers to center stage, bear in mind that hiding in the wings there will be a lot of mathematics, and a lot of engineering, physics, chemistry, and psychology as well, and that without the support of this hidden cast of helpers, the digital superstar would be unable to strut its stuff in the spotlight.
The importance of mathematics in today's world is easily underestimated because nearly all of it goes on behind the scenes. Walk along a city street, and you are overwhelmed by signs proclaiming the daily importance of banks, greengrocers, supermarkets, fashion outlets, car repairs, lawyers, fast food, antiques, charities, and a thousand other activities and professions. You do not find a brass plaque announcing the presence of a consulting mathematician. Supermarkets do not sell you mathematics in a can.
Dig a little deeper, however, and the importance of mathematics quickly becomes apparent. The mathematical equations of aerodynamics are vital to aircraft design. Navigation depends on trigonometry. The way we use it today is different from how Christopher Columbus used it, because we embody the mathematics in electronic devices instead of pen, ink, and navigation tables, but the underlying principles are much the same. The development of new medicines relies on statistics to make sure the drugs are safe and effective. Satellite communications depend on a deep understanding of orbital dynamics. Weather forecasting requires the solution of equations for how the atmosphere moves, how much moisture it contains, how warm or cold it is, and how all of those features interact. There are thousands of other examples. We do not notice they involve mathematics, because we do not need to know that to benefit from the results.
David Schmidt, a geology professor at Westminster College, had just arrived in the South Dakota Badlands in summer 2019 with a group of students for a fossil dig when he received a call from the National Forest Service. A nearby rancher had discovered a strange object poking out of the ground. They wanted Schmidt to take a look.
"One of the very first bones that we saw in the rock was this long cylindrical bone," Schmidt told St. Louis Public Radio. "The first thing that came out of our mouths was, 'That kind of looks like the horn of a triceratops.'"
After authorities gave the go-ahead, Schmidt and a small group of students returned this summer and spent nearly every day of June and July excavating the skull.
Credit: David Schmidt / Westminster College
"We had to be really careful," Schmidt told St. Louis Public Radio. "We couldn't disturb anything at all, because at that point, it was under law enforcement investigation. They were telling us, 'Don't even make footprints,' and I was thinking, 'How are we supposed to do that?'"
Another difficulty was the mammoth size of the skull: about 7 feet long and more than 3,000 pounds. (For context, the largest triceratops skull ever unearthed was about 8.2 feet long.) The skull of Schmidt's dinosaur was likely a Triceratops prorsus, one of two species of triceratops that roamed what's now North America about 66 million years ago.
Credit: David Schmidt / Westminster College
The triceratops was an herbivore, but it was also a favorite meal of the Tyrannosaurus rex. That probably explains why the Dakotas contain many scattered triceratops bone fragments, and, less commonly, complete bones and skulls. In summer 2019, for example, a separate team on a dig in North Dakota made headlines after unearthing a complete triceratops skull that measured five feet in length.
Michael Kjelland, a biology professor who participated in that excavation, said digging up the dinosaur was like completing a "multi-piece, 3-D jigsaw puzzle" that required "engineering that rivaled SpaceX," he jokingly told the New York Times.
Morrison Formation in Colorado
James St. John via Flickr
The Badlands aren't the only spot in North America where paleontologists have found dinosaurs. In the 1870s, Colorado and Wyoming became the first sites of dinosaur discoveries in the U.S., ushering in an era of public fascination with the prehistoric creatures — and a competitive rush to unearth them.
Since, dinosaur bones have been found in 35 states. One of the most fruitful locations for paleontologists has been the Morrison formation, a sequence of Upper Jurassic sedimentary rock that stretches under the Western part of the country. Discovered here were species like Camarasaurus, Diplodocus, Apatosaurus, Stegosaurus, and Allosaurus, to name a few.
Triceratops illustration
| Credit: Nobu Tamura/Wikimedia Commons |
As for "Shady" (the nickname of the South Dakota triceratops), Schmidt and his team have safely transported it to the Westminster campus. They hope to raise funds for restoration, and to return to South Dakota in search of more bones that once belonged to the triceratops.
Studying dinosaurs helps scientists gain a more complete understanding of our evolution, illuminating a through-line that extends from "deep time" to present day. For scientists like Schmidt, there's also the simple joy of coming to face-to-face with a lost world.
"You dream about these kinds of moments when you're a kid," Schmidt told St. Louis Public Radio. "You don't ever think that these things will ever happen."
- YouTube www.youtube.com
The human brain is a pretty lazy organ. Although it's capable of remarkable ingenuity, it's also responsible for nudging us into bad behavioral patterns, such as being impulsive or avoiding difficult but important decisions. These kinds of short-sighted behaviors can hurt our finances.
However, they don't hurt the video game industry. In 2020, video games generated more than $179 billion in revenue, making the industry more valuable than sports and movies combined. A 2021 report from Limelight Network found that gamers worldwide spend an average of 8 hours and 27 minutes per week playing video games.
Good at gaming, bad at saving
It's not necessarily bad that Americans spend millions of dollars and hours on video games. But consider another set of statistics: 25 percent of Americans have no retirement savings at all, while roughly half are either living "on the edge" or "paycheck to paycheck," according to a recent report on the Financial Resilience of Americans from the FINRA Education Foundation. Meanwhile, experts predict that Social Security funds could dry up by 2035.
So, why don't people save more? After all, the benefits of compounding interest aren't exactly a secret: Investing a few hundred bucks every month would make most people millionaires by retirement if they start in their twenties. However, the recent FINRA report found that many Americans have alarmingly low levels of financial literacy, a topic that's not taught in most public schools.
Even for the financially literate, saving money is psychologically difficult
But what if we could infuse the instant gratification of video games into our long-term financial habits? In other words, what if finance looked less like an Excel spreadsheet and more like your favorite video game?
A growing number of finance applications are making that a reality. By using the same strategies video game designers have been optimizing for decades, gamifying personal finance could be one of the most efficient ways to help people save for the future while reaping instant psychological rewards. But it doesn't come without risks.
What is gamification?
In simple terms, gamification takes the motivating power of video games and applies it to other areas of life. The global research company Gartner offers a slightly more technical definition of gamification: "the use of game mechanics and experience design to digitally engage and motivate people to achieve their goals."
The odds are you have encountered gamification already. It's utilized by many popular apps, websites, and devices. For example, LinkedIn displays progress bars representing how much profile information you have filled out. The Apple Watch has a "Close Your Rings" feature that shows how many steps you need to walk to meet your daily goal.
Brands have used gamification to boost customer engagement for decades. For example, McDonald's launched its Monopoly game in 1987, which essentially attached lottery tickets to menu items, while M&M's gained consumer attention with Eye-Spy Pretzel, an online scavenger hunt game that went viral in 2010.
In addition to marketing, gamification is used in social media, fitness, education, crowdfunding, military recruitment, and employee training, just to name a few applications. The Chinese government has even gamified aspects of its Social Credit System, in which citizens perform or refrain from various activities to earn points that represent trustworthiness.
Finance is arguably one of the best-suited fields for gamification. One reason is that financial data can be easily measured and graphed. Perhaps more importantly, financial decisions occur in the background of almost everything we do in modern life, from deciding what we eat for lunch to where we are going to spend our lives.
Gamification doesn't just make boring stuff fun; it's also an effective way to change our behavior. Used properly, it can also disrupt our habits.
The nature of habits
It's tempting to think that we make our way through life by thoughtfully considering the information before us and making sensible choices. That's not really the case. Research suggests that about 40 percent of our daily activities are performed out of habit, a term the American Journal of Psychology defines as a "more or less fixed way of thinking, willing, or feeling acquired through previous repetition of a mental experience."
In other words, we spend much of our lives on autopilot. From an evolutionary perspective, it makes sense that we rely on habits: our brains require a lot of energy, especially when we're faced with tough decisions and complex problems, like financial planning. It's relatively easy to rely on learned behavioral patterns that provide a quick, reliable solution. However, those patterns don't always serve our long-term interests.
Saving money is a good example. Imagine you have $500 with which to do whatever you want. You could invest it. Or you could go on a shopping spree. Unfortunately, the brain doesn't process these two options the same way; in fact, it actually processes the investing option as something like a pain stimulus.
Why gamification works
Saving is painful. But can't people simply choose to be more financially responsible? In short: Yes, but it takes a lot of effort. After all, when it comes to changing behavior, willpower is only part of the equation.
Some psychologists think willpower is a finite resource, or that it's like an emotion whose motivational power ebbs and flows based on what's happening around us. For example, you might establish a monthly budget and stick to it for a couple weeks. But then you get stressed. The next time you're out shopping, you might find it harder to resist making an impulsive purchase in your stressed-out state.
Pixel Art Lootvlasdv via Adobe Stock
"A growing body of research shows that resisting repeated temptations takes a mental toll," the American Psychological Association writes. "Some experts liken willpower to a muscle that can get fatigued from overuse." In the terminology of psychology, this is called ego depletion.
Gamification offers a way to outsource your willpower. That's because games offer psychological rewards that can motivate us to perform certain actions that might otherwise have seemed too boring, taxing, or emotionally draining. What's more, gamifying parts of your life is less of a change of mind and more of a change of environment.
A 2017 study published in Computers in Human Behavior noted that "enriching the environment with game design elements, as gamification does by definition, directly modifies that environment, thereby potentially affecting motivational and psychological user experiences."
The study argued that games are most motivational when they address three key psychological needs: competence, autonomy, and social relatedness. It's easy to imagine how games can tap into these categories. For competence, games can feature badges and performance graphs. For autonomy, games can offer customizable avatars. And for social relatedness, games can feature compelling storylines and multiplayer gameplay.
Gamification and the brain
Games can motivate us by satisfying our psychological needs and giving us a sense of reward. From a neurological perspective, this occurs through the release of "feel-good" neurotransmitters, namely dopamine and oxytocin.
"Two core things have to happen in the brain to influence your decision-making," Paul Zak, a neuroscientist and professor of economic sciences at Claremont Graduate University, told Big Think. "The first is you have to attend to that information. That's driven by the brain's production of dopamine. The second thing, you've got to get my lazy brain to care about the outcomes. And that caring is driven by emotional resonance. And that's associated with the brain's production of oxytocin."
Cheerful Father And Son Competing In Video Games At HomeProstock-studio via Adobe Stock
When released simultaneously, these neurotransmitters can put us into a state that Zak calls "neurologic immersion." In this state, our everyday habits have less control over our behavior, and we're better able to take deliberate action. It's an idea Zak and his colleagues developed over two decades of using brain-imaging technology to study the nature of extraordinary experiences.
As he wrote in an article published by the World Experience Organization, neurologic immersion can occur when experiences, including video games, are unexpected, emotionally charged, narrowing one's focus to the experience itself, easy to remember, and provoking actions.
"The components of the extraordinary come as a package, not in isolation from each other," Zak wrote. "It's the 'action' part that is key to finding immersion. Extraordinary experiences cause people to take an action, whether it's donating to charity, buying a product, posting on social media, or returning to enjoy an experience again."
Games can invoke these types of immersive experiences.. But how exactly are financial organizations using gamification to help people "level up" their financial futures?
Gamifying personal finance
Banks and financial companies have been using gamification for years. What started with simple concepts, like PNC Bank's "Punch the Pig" savings feature, has evolved into a diverse field of games that are helping people stick to budgets, save money, and pay off debt.
What's surprising about the gamification of personal finance is that some of the most successful apps are redirecting destructive financial behaviors, like buying lottery tickets, toward positive outcomes. One example is an app called Long Game, which uses an approach called "lottery savings."
"People actually really love the lottery," Lindsay Holden, co-founder and CEO of Long Game, told Big Think. "The lottery today is a $70-billion-dollar industry in the U.S., and the people that are buying lotto tickets are the people that least should be buying lotto tickets. And so how can we redirect that spend into something that's helping them in their lives?"
Long Game's answer is to encourage users to make automatic or one-time investments into a prize-linked savings account. As users make investments, they earn coins that can be used to play games, some of which offer cash prizes. But unlike the real lottery, the prize money comes from banks that are partnered with Long Game, meaning users can't lose their principal investment.
Blast is a savings app aimed at traditional gamers. The platform lets users connect a savings account to their video game accounts. Users then set performance goals in the video games, such as killing a certain number of enemies. Accomplishing these goals triggers a pre-selected investment into the savings accounts. In addition to earning interest, users can also win prize money by accomplishing certain missions or placing high on public leaderboards.
"Gamers tell us they feel better with the time they spend gaming when they know they are micro-saving or micro-earning in the background," Blast co-founder and CEO Walter Cruttenden said in a statement.
Young gamer playing a video game wearing headphones.sezer66 via Adobe Stock
Fortune City takes a different approach to gamified finance. The app encourages users to track their spending habits, which are represented by visually appealing graphs. As users log expenses, they're able to build buildings in their own virtual city. The expense categories match the types of buildings users can construct; for example, buying food lets users construct a restaurant. It's like "SimCity" meets certified public accountant.
The risks of gamification
Gamifying your finances might help you save money, but it doesn't come without risks. After all, receiving extrinsic rewards when we perform a behavior can affect our intrinsic motivation to repeat that behavior both positively and negatively. It's a phenomenon called the overjustification effect.
In addition, gamified finance apps can also be addictive and encourage risky financial behavior. Robinhood, for example, uses visually appealing performance metrics and lottery-like game elements to incentivize the trading of stocks and cryptocurrencies. But while investing in these assets might be a good financial decision for some people, Robinhood arguably encourages its users to be "players" in the difficult world of trading, not necessarily rational investors.
What's more, gamification doesn't seem to work for everyone.
"From social psychology and behavioural economics, we know that the most likely [result of] gamification [is that you] will motivate some people, will demotivate other people, and for a third group there'll be no effect at all," noted a 2017 study on gamification and mobile banking published in Internet Research.
But given that 14.1 million Americans are unbanked, and millions more struggle with financial literacy, it's reasonable to think that gamified finance apps could help many people work toward financial independence.
"One of the most interesting things we've found is that people want help when it comes to making difficult decisions," Zak told Big Think. "In my view, any app that helps you be a more effective saver is probably a good app. But I think we have to do a lot more work to really understand the underlying neuroscience of gamification. And so we need to continue to design games that teach you more about how to 'level up in life,' not just level up in the game."
