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(TAN.2) Why we crunch numbers

(TAN.2.A) Attending Plato's School

Almost everyone has learned something about the ancient Greek philosopher Plato. He was Aristotle's teacher and Socrates' student, and while much of his teaching sounds strange to modern Americans, his social philosophy served as a moral and philosophical foundation for Communism.

Figure 1—Greek Philosopher, Plato (424-348 BC)

Plato was wrong about communism (which he called a "Benevolent Dictatorship"), but he was right about one thing: we do not see the world as it really is, but instead form constructs of it in our mind. Plato believed there was one sphere of the universe where humans resided, and another sphere where the gods resided, and the world of gods was the true and perfect world. He explained this view using a metaphor of shadows in a cave. Humans can never see the true and perfect world of the gods, but we can see glimpses of it. It is like humans are raised in a cave with insufficient light to see outside the cave, Plato explained. Humans are chained to one another such that they cannot see the face of others—only their backs. A fire flickers though, and the shadow of humans created by that light gives us crude portraits of what people look like. We only see shadows of the true world, Plato thought.

Modern scientists are not so pessimistic as Plato about our ability to understand reality, but they do agree that we do not perceive the world exactly as it exists.

…we have no direct contact with reality. Our brain is always abstracting and interpreting the world around us. Even when we know the true nature of an illusion, this insight often does not change our experience. As far as the brain is concerned, if an event is an illusion, it might as well be real.
—Hood, Bruce. September/October, 2012. "Re-creating the Real World." Scientific American Mind. NY. Page 164.

There is a way to acquire a clearer picture of the true and perfect world, Plato thought. There is no such thing as a perfect triangle in the physical world of man, but man can conceive of a perfect triangle in his mind—through geometry. This is why Plato emphasized geometry so heavily, for he believed that the abstract nature of geometry helped humans learn to perceive things they cannot see.

Plato might have obsessed about geometry, but it wasn't because he thought geometry provided practical benefits—although algebra was an essential tool in the use of catapults, Plato was not a warrior. He was a social philosopher who cared more about the behavior of human societies than math itself.

While a young man Plato watched his society kill his beloved teacher Socrates, and it left him with a bitter taste for democracy. He wanted to establish a better society that would revere—not crucify—men like Socrates. Most of his philosophy was dedicated to creating a more peaceful, prosperous, fair, and loving society, yet he saw no such society anywhere save for his imagination. This better world could only be built by perceiving it first in the abstract, and geometry was the ideal exercise to prepare humans for such a task.

This is why Plato thought men should study geometry before they became involved in politics. Only once a benevolent dictator was imagined in the mind could it be established in a Greek city-state, and geometry is food for the imagination. For us in modern democracies, understanding the future consequence of a new policy first requires thinking about the policy in the abstract. Studying geometry prepares us for such abstract contemplation.

Let no one ignorant of geometry enter here.
—Motto written over the entrance to Plato’s academy. Patrick Grim. Lecture 9. Questions of Value. The Teaching Company.

Modern scholars agree with Plato—so do I. Math and geometry are taught throughout the educational system not only for its practical benefits, but because math makes us smarter in myriad ways. It has even been shown that an improved ability to think abstractly helps boost one's self-control, like committing to losing weight and achieving it.(F1) Indeed, any PhD economist will tell you that it is almost impossible to understand an economy without depicting it in geometrical or mathematical form.

This idea is not new, but is as old as science itself. The man who invented the word "mathematics" and "philosophy" was the person from whom Plato got his ideas about the importance of mathematics and geometry in becoming a champion thinker: Pythagorus.

Mathematics came first; not as the practical science that the Egyptians had made it, but as an abstract theory of quantities, and an ideal logical training in which thinking would be compelled to order and clarity by the test of figorous deducation and visible proof...each step...raised the student to a new platform, as the Pythagoreans put it, from which he might view more widely the secret structure of the world.
—Will Durant. 1939. The Story of Civilization Part II: The Life of Greece. Chapter 3: The Heroic Age. Page 162.

For the Jesuits, the purpose of mathematics was to construct the world as a fixed and eternally unchanging place, in which order and hierarchy could never be challenged. That is why each item in the world had to be carefully and rationally constructed and why any hint of contradictions and paradoxes could never be allowed to stand. It was a “top-down” mathematics, whose purpose was to bring rationality and order to an otherwise chaotic world.
—Alexander, Amir. April 2014. “The Secret Spiritual History of Calculus.” Scientific American magazine. Pages 82-85.

(TAN.2.B) Making the team

Even the NFL agrees that people who are better at math are also smarter in other ways. Every football player entering the NFL draft must take the Wonderlic intelligence test, which measures one's ability to solve math and logic problems. A higher score implies better math and logic skills. The teams know that players are not solving formal math problems on the field, but they assume quarterbacks who are smarter at answering math problems will make smarter passing decisions. The better a player's score, the more heavily a team will seek to draft him.

The teams care about much more than a player's ability to do math. After all, Vince Young performed horribly on the test, and so did Dan Marino. But the fact that they care even a little about a player's math skills attests to the value of learning math, whether one wishes to be an NFL Quarterback or a pesticide salesperson.(L1)

Video 1—The NFL and the Wonderlic Test

(TAN.2.C) Math has direct, practical benefits also

Math is also taught for its direct benefits. A future article discusses the importance of basic math in modern finance, and how the incorrect use of math helped cause the 2008 Financial Crisis. People selling car insurance provide customers with quotes given to them on a computer screen, and that quote is calculated by taking demographic information on the customer and crunching lots of numbers to determine the most profitable insurance premium. Farmers vary the rate of nitrogen fertilizer they spray based on statistics of the soil and fertilizer prices. Every time you charge money to your credit card a computer calculates the probability you will default on the credit card debt. I shouldn't have to give too many examples. You see mathematics everywhere, don't you?

Poor math skills can manifest itself in undesirable ways. Children sometimes suffer health problems from an improper dosage of medicine, and often these wrong dosages are caused by poor math skills on the parents' part.(L1)

In addition to personal decisions, social decisions are benefited by a citizenry adept at math. Measuring the carbon emissions from various pollution sources requires a overwhelming amount of number-crunching; so does the design of health care systems. Diagnosing health problems is increasingly out-sourced to computers,(A1) as they can sometimes make better decisions than doctors, like deciding who should receive an organ transplant.(J1)

(TAN.2.D) Helping the military kick ass

Our soldiers fighting abroad need timely and accurate information on when to expect insurgent activity. Mathematical simulation, using data from WikiLeaks, is actively used by the U.S. military in Afhanistan—with success.(E1)

(TAN.2.E) Public Health

Jenni McCarthy became famous not just for posing nude in Playboy, but for her crusade against the use of vaccinations in children. She believed that vaccinations caused her child to develop autism and began warning mothers not to have their child receive the shots. What a frightening thing, to have to decide whether to vaccinate your child or increase their risk of developing autism!

Fortunately, we do not need to make this decision anymore because statisticians have proven that vaccinations are not correlated with autism.(S1) Some damage was done though, as vaccination rates fell after McCarthy's crusade,(S2) leaving children at greater risk of disease. In 2012 an outbreak of Whooping cough in the U.S. was among the worst outbreaks in 50 years. Nine children died by August of 2012, and 18,000 contracted the sickness. All of these outbreaks were fueled by an unfounded fear that vaccinations posed serious health hazards.(B2) All were avoidable. A word of advice: don't take health advice from anyone who posed nude for a magazine!

It will take number-crunching to determine what exactly does cause autism, and though the results are far from settled, statistical analysis shows that pregnant women exposed to greater amounts of air pollution and pesticides are more likely to give birth to an autistic child.(W1)

Much of what we believe to be true about health is taken from statistical studies. Researchers often survey individuals about their eating and drinking habits, as well as any health problems they may have. This allows them to estimate the correlation between certain activities and health problems, and these "correlations" are statistics. For example, data from such surveys are incorporated into statistical models to determine the optimal alcohol consumption. Drinking alcohol obviously causes liver problems but provides benefits in the form or clearer arteries. The result? The average person is best served by drinking one-half of a typical drink per day.(N1) At this rate, the risk of heart problems is lowered without increasing the chance of liver problems.

Video 2—Simple Statistics To Battle Cholera in the 1850's and the Rise of Epidemiology(H3)
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(TAN.2.F) In business, math is everywhere

Every now and then I visit graduates and interns from our department at their workplace to see the kinds of tasks they perform. These visits have had a considerable influence on the topics I teach in this course. One thing you tend to see in business is that much of people's time is spent in Excel. Some perform most of their work in Excel. What they do in Excel isn't always fancy, but simple calculations and "what-if" thought experiments.

Employers expect college graduates to use Excel spreadsheets as a database, where information can be retrieved quickly using pivot-tables; create articulate graphs for meetings and presentations; critically analyze statistical reports, accounting budgets, and data collected by the business itself, and to communicate the results in writing; study data to determine the correlation between two variables over time; manage risk by projecting the businesses' profitability under various scenarios; create budgets to determine the break-even level of production, net present value, and set prices; use budgets and simulation to help manage the employees' retirement fund; mail-merge for sending one email to multiple people; and the like.

Those who rise to higher positions in business find themselves overseeing the collection, use, interpretation, and management of data. They might not do much number-crunching themselves, but they must understand what types of number-crunching can take place, and they must be the ones who implement data-intensive projects.

An example is The Cheesecake Factory, who decided it needed to use data and mathematical techniques to become more efficient. It consistently bought far more food ingredients than it needed, so much was wasted. To improve efficiency it decided to target a 97.5% efficiency rate in groceries, meaning they didn't want to throw away more than 2.5% of the groceries they purchased. Just imagine the difficulty of this. A restaurant obviously doesn't want to buy more groceries than it needs to feed the customers, but if they misjudge and run out of groceries—forcing them to turn away customers or inform them their preferred food of choice is not available—the lack of repeat business may hobble for restaurant for some time. Achieving a 97.5% efficiency requires superb judgment, one that is best achieved using data and math.

Fortunately for The Cheesecake Factory, a small industry has emerged to satisfy this need, where computer programs are written to engage in "guest-forecasting." This involves using forecasting models to anaylze historical data on the number of customers who visited the restaurant in the past. The computer then tells them how many customers to expect next week, giving them the predictions needed to buy enough groceries to feed their customers but little more.

These models seem to do a good job, allowing the restaurant to know in advance the amount of groceries it will need to purchase. It even adjusts the predicted number of customers to account for the weather and sports games.(G2)

Achieving successful guest-forecasting requires one to either study the topics in this class or learn them on the job.

(TAN.2.G) In business, skills in math, computers, and abstract thinking are highly valued

There are undeniable benefits of earning a college degree. Though not all of the value of a degree can be attributed to college graduates' proficiency with math, computers, and abstract thinking, college is certainly the place where most of these skills are learned. The workplace has undergone a revolution, where skills with machines, computers, math, and writing have increased in value and simple labor requiring no intellectual skills have fallen in value. Employers like to hire college graduates because they know graduates will already have computer and quantitative skills, but more importantly, can learn how to operate other machines quickly.

    Guest: Absolutely. So when you sort of say: Why is it different now than in the past? The theory that I think has some merit for this is the fact that highly educated people can make very productive use of new, cheap, sophisticated capital equipment such as information technologies. So, you give a college graduate, fax machines and cell phones and personal computers with advanced software—it makes them incredibly productive. A lot of those machines and technologies are taking the place of—
    Russ: lower skilled—
    Guest: Yeah. My favorite story for this is you look at say the ports of New York and New Jersey. In 1950, I think about roughly 10,000 guys—longshoremen. Big strong guys. Guys with strong backs worked there. Pick up a box, put it on the ship; take a box and take it off the ship. That was the technology for offloading.
    Russ: Today no person touches anything, except who operates the crane.
    Guest: Yeah.
    Russ: Forklift.
    Guest: Today, I think about maybe under 1000 people. So there's been a drop of a factor of 10 drop in employment. They are all college grads operating [the cranes]. These union guys, the 6'1", 250 pound guys who could pick up anything, they are not around anymore. Unskilled labor lost that job to capital goods [college graduates and machines].
—Roberts, Russell [host] and Lee Ohanian [guest]. August 20, 2012. “Ohanian on the Great Recession and the Labor Market [podcast].” EconTalk. Library of Economics and Liberty: econlib.org.

Video 3—Employers Are Desperate for Employees Who Can Do Math

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Except in rare cases (e.g., Mark Zuckergerg) acquiring a college degree is the smartest investment one can make, even if the student must pay all the costs themselves. It increases the salary one makes by about 8% their entire life,(F3) and college graduates have a lower unemployment rate than their counterparts. The more education one earns, the better their prospects. Not for everyone, but for most people.

Figure 2—Unemployment Rates and Earnings Corresponding to Various Education Levels(T1)

Periodically The Wall Street Journal will make a list of the top occupations in the U.S., based on the occupations' average salaries, stress on the job, happiness on the job, degree of autonomy on the job, ability to move locations and change jobs easily, and the like. It is in this list where the benefits of obtaining quantitative skills becomes especially clear.(N2)

Best ten ways to make a living in the U.S.

  1. Mathematician
  2. Actuary (a statistician who specializes in things like insurance)
  3. Statistician
  4. Biologist
  5. Software Engineer
  6. Computer Systems Analyst
  7. Historian
  8. Sociologist
  9. Industrial Designer
  10. Accountant

Now consider the top ten worst jobs.

Worst ten ways to make a living in the U.S.

  1. Lumberjack
  2. Dairy Farmer
  3. Taxi Driver
  4. Seaman
  5. Emergency Medical Technician
  6. Roofer Garbage Collector
  7. Welder
  8. Roustabout (Oil Worker)
  9. Ironworker

There will be some people who simply don't like working with numbers and computers, and hate to think at an abstract level. In these cases there is nothing wrong with refusing to acquire these skills, for they should pursue happiness, not wealth. If the reader just happens to enjoy math, computers, and abstract thinking, then lucky for you, because you can pursue wealth and happiness through the same job!

(TAN.2.H) The quantitatively skilled are happy workers

Most of your time awake will be spent at work, so if you are not happy there, you are not happy in life. What kinds of jobs do people find particularly happy? People tend to think of their work either as a (1) job (2) career or (3) a calling. The people who consider their work a job are generally unsatisfied at the workplace because the only benefit they obtain from work is the money they earn.

When work is seen as a career people are happier on the job because they acquire some of their meaning in life at the workplace. When we think of careers we think of a steady progression towards higher positions with more responsibility and higher pay. These promotions are a life-objective to a person, and when they are obtained the person feels a sense of meaning in life—a belief that they are special and are respected by others.

For the fortunate workers who consider their occupation a calling, they are the happiest, for when they work the feel a sense of flow, where time passes quickly in a continual state of cheerfulness and meaning. These individuals feel like they were put on this earth to perform their job, and so they obtain the greatest amount of satisfaction with what they are doing in life and what they are accomplishing. A good measure of how much people like their job is the frequency in which they look at the clock, anticipating quitting time. Those who consider their work a job find themselves looking at the clock every five minutes. Those who consider their job a calling are surprised when quitting time is announced, for they are so cheerfully involved in their work they don't think to look at the clock.(H2)

Put this discussion in the context of Maslow's Hierarchy of Needs, where the first need (physiological needs) are the most important and are pursued first, before one begins seeking the other needs, and where self-actualization is only sought after the first four needs are obtained.(M1)

Maslow's Hierarchy of Needs

  1. Physiological Needs (food, water)
  2. Safety Needs (shelter, protection from disease)
  3. Love Needs (loving relationship with parents, community, spouse, children, and God)
  4. Esteem Needs (achievement, respect from others)
  5. Self-Actualization (personal interests and skills being applied to some activity, an activity valued by oneself and others)

For people who consider work to be a job, career, or a calling, the first two needs are easily provided by the income the work provides.

When work is considered only a job, the love, esteem, and self-actualization needs are difficult to obtain because the person does not have a personal interest in the work. Remember, when work is a job, the only benefit from working is the money, and while physiological and safety needs can be purchased the other three needs cannot.

Conversely, when work becomes a career / calling it provides benefits in addition to money. The workplace becomes a community, where love and esteem needs can be found, and esteem is acquired in greater amounts as one moves to higher positions within their career. When work is a calling it provides people with a sense of identity, allowing the person to discover a source of self-actualization. It should be also noted that because higher incomes can be earned when work is a career or a calling, the first two needs can be purchased in greater amounts.

Achieving actualization needs and respect from others usually requires you to have autonomy on the job. Without autonomy you are a wage-slave just following directions—where is the glory in that? With autonomy you see your hard work and your decisions manifested in success; you feel like you play an important role in the world and that others value you. Generally speaking, one will not be given autonomy at work unless they have a solid education and number-crunching skills.

If the reader truly wants to be happy in life, they must find a way to achieve all five needs at the workplace. I argue one strategy is to acquire skills highly valued by employers: quantitative, computer, and abstract-thinking skills are three possibilities.

(TAN.2.I) Abstraction and the rise of intelligent man

The movie Idiocracy was about a world where only the dumbest Americans hav lots of children, and so over time the average intelligence of humans steadily declined. While the movie is hilarious, its premise is false. We aren't getting dumber over time. Instead, average IQ scores steadily rise each year. Every year for the last thirty years, we get smarter.

This may surprise those readers who believe our education system is "failing us." In some ways it is, but the explicit topics you learn in school like vocabulary and math have nothing to do with our rising IQ. The parts of IQ tests that measure math and vocabulary knowledge are showing roughly the same scores every year. The part responsible for our rising IQs have to do with our ability to think in the abstract.

"If you don't classify abstractions, if you're not used to using logic, you can't really master the modern world," Flynn says. "Alexander Luria, a Soviet psychologist, did some wonderful interviews with peasants in rural Russia in the 1920s. He would say to them, 'Where there is always snow, bears are always white. There is always snow at the North Pole. What color are the bears there?' They would say they had never seen anything but brown bears. They didn't think of a hypothetical question as meaningful."
—Folger, Tim. September, 2012. "Can We Keep Getting Smarter?" Scientific American.

An example of abstract thinking on IQ tests have to do with "similarities." The person taking the test is presented questions like, "How are an apple and an orange alike?" Answers like "They're both edible," receive a low answer while answers like "They're both fruit," receives high scores because it requires people think beyond the obvious qualities of both items, and to consider how the two items are placed into abstract groups with vague descriptions.

Figure 3—Rising IQ Scores Over Time Due To Improved Abstract Thinking(S4)

Our enhanced ability to think in the abstract isn't solely due to our formal education. Technology may be the most important factor. My daughter is a toddler, and one of her favorite things to do is to watch videos of herself on my iPhone. Though only one year old, she is able to understand that the person she sees on the iPhone is her from the past. That is an abstract conception of oneself, and should help her think better in the abstract than an ancient Sumerian who could only see their reflection in a calm pond.

Videos games, television, and toys that speak (my daughters have a kitchen that talks to them as they cook!) require children to imagine entities which do not really exist. It is not surprising my daughters could answer the question about bears (my five-year-old could; I asked her) while Russian peasants could not.

For many students the most frustrating part about college is when professors force them to think conceptually, in the abstract. It is often difficult for students to even understand what the professor is asking, much less be able to answer their question. The answers to abstract questions are sometimes nebulous, and a student can submit an answer believing it to be correct, only to lose all points on the question because they didn't answer it exactly how the professor wanted (oh, they get so mad when this happens!). It is students' dislike of abstract thinking, and the power they can possess on student evaluations, that make teachers give multiple choice questions that have only one answer, and requires simple memorization or calculation. Students may like the class, but it serves them little good.

While it may frustrate students, they are best served when the teacher asks them to think in the abstract—to not only ponder what the teacher is asking but the many different answers one could give, and how the "correct" answer may depend on a person's background. Successful people owe their achievements to their ability to work with others and communicate well, but also their abstract thinking skills. CEO's must establish new strategies for their company, where they imagine how the company's units must change and how the product is altered and marketed to different customers. This new vision exists solely in the abstract, before implemented in reality. A politician must understand the perspectives of those with varying political affiliations, and think deeply about how their message will resonate among voters. When George W. Bush started speaking of "compassionate conservative", it was because it seemed like a good phrase in the abstract. Name any position worthy of admiration, and I can point to an important role for abstract thinking in most of them.

(TAN.2.J) Math as a signal

It must be acknowledged that math is often taught not just because of its practical benefits but as a way to signal work-ethic and intelligence. Passing mathematics courses is a way of advertising your ability to learn and your innate intelligence. Even if you will never use the math you learn, employers want proof you can learn on your own before offering you certain opportunities, and they look to your performance in quantitative courses, the number of quantitative courses you took, your major, and your familiarity with software for this proof.(B1,H1)

(TAN.2.K) Math, computers, and a more powerful mind

There are many things the human mind can do better than today's supercomputers. However powerful computers are, they are not near as efficient as the brain.(G1) We provide more intelligence for every watt of power used. There are some tasks where we are superior to computers, and one of these is the visual search.(F2) The act of looking for your lost car keys and finding them is simple to us but surprisingly difficult for a computer. Our ability to recognize certain visual patterns, like facial recognition, exceeds that of computers though. We are creative in ways computers are not, and of course, we know how people think, something which is important when dealing with customers.

Computers beat us at many things though, and two of these are memory and math. We have trouble remembering numbers with more than seven digits, so we have outsourced most of our memory tasks to computers. Not only do computers remember numbers better than us, they can crunch numbers better. Most of the math performed today is done in spreadsheets, where we decide what numbers will be crunched and how, and Microsoft Excel does the crunching. Math and computers are now inseparable.

As you take courses involving the use of math within spreadsheets, view the computer as an accessory to your brain. It does all the tasks you have trouble with, but all it can do is crunch numbers. Most of the work involving visualization and creativity remains your domain. Do not think for a second that the field of number-crunching is dominating by those who are superior in math. The "nerds" are important, but computation is something anyone can do with computers.

No, the quantitative world is dominated by those with the creativity to imagine the important questions which need solving, such as where a new Wal-Mart distribution center should be located, and how the mathematical structure of corn's DNA can be altered to provide immunity against pests.

There are many questions to be asked in this class: whether math is important is not one of them.

(TAN.2.L) Human creativity and emotion, coded in data

Computers married with quantitative tools are still performing their traditional role by preserving data and calculating numbers, but are expanding to other areas many thought improbable. Nothing is so human as the composing and listening to music. Only the human mind can appreciate a song, we believe. To a some extent this is true, but it is also true that by converting songs to numbers computers know what songs we like. We can then ask computers what songs people might like, to help us decide what songs to promote and what songs would make a bad investment.

If you have heard Ben Novak's song Turn Your Car Around you have a computer algorithm to thank. This algorithm analyzed a large database of popular songs, detecting the various mathematical patterns many of the songs possessed, and when the algorithm heard Turn Your Car Around, (i.e., when it read the numbers describing the song) it concluded the song shared similarities to other successful songs. The owner of the algorithm helped Mr. Novak find a label, something he never would have done if the algorithm didn't assure him of the song's potential. This and other algorithms have helped over 5,000 artists acquire record deals, all based on the mathematical patterns their songs possess.

Using similar methods, mathematical algorithms (all algorithms are mathematical) are now grading student essays just as effectively as human graders, but at a much lower cost.

Less than a second after a football team has won, an algorithm used by the Big Ten Network has written and posted an article about the game. The algorithm was constructed by evaluating articles written by humans and statistics about the game, thereby learning tips such as: if a team posts more offensive yards, it should write something like, "the OSU offensive dominated the game, overwhelming any defense the Sooners presented."

When you call a company and a recorded voice tells you your call will be handled in the order it arrives, the computer may also ask you several questions, and based on your answers and the tone of your voice, helps the company ensure your call is ended satisfactory. It even categorizes your personality as you talk, so that when a "real" person does pick up the phone they know if they are dealing with an asshole!(S3)

The point of this article is not to imply that everyone should become math majors or that you should become a computer programmer. The people who use math for the greatest good are not the "quants" or the "computer nerds". The real heroes are the visionaries who dream of new frontiers for math and computers, are able to convince investors to back their dream, and are able to implement that vision on a practical, affordable scale. Mark Zuckerberg has triumphed not because he is a remarkable computer coder (though I'm sure he is) but because he recognized the value in a social network like Facebook, even when there were already networks like MySpace.

This class is only partly concerned with the mathematics of modern data analysis. It is more concerned with understanding what data analysis has accomplished, so that you can better envision what hasn't but could be achieved.

(TAN.2.M) Statistics matter in policy debates

Around 2011-2012 there were fierce policy debates about whether the government should borrow more money to help the unemployed or if more borrowing would create excessive harms to the economy. A number of conservative politicians, including the 2012 Vice-President candidate Paul Ryan, cited an economic study by the economists Rogoff and Reinhart which showed that countries whose debt divided by their GDP exceeded 90% sufferred particularly low growth (or no growth at all). Because the U.S. was approaching this threshold the study was taken very seriously.

This threshold was discovered by examining the growth rates of various countries around the world, observing how countries whose debt divided by GDP was greater than and less than 90% varied in their rate of economic growth.

Then the threshold was shown to be in error. In fact, it was the result of a simple mistake in Excel where the authors unintentionally left out five countries when they calculated an average. The error was discovered by a graduate student who recreated Rogoff and Reinhart's error as part of a class assignment. No mistake in data analysis probably received as much attention as this. It even made it onto The Colbert Report, as shown below.

Figure 4—The Rogoff-Reinhart Excel Error (the economists intended to select all the countries but accidentally excluded the bottom five)

Video 4—How statistics can drive policy debates, from The Colbert Report
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TAN.2.N—Using data to monitor employee performance

Though this video is from the fictional HBO series Enlightened it provides a realistic description of how data and computer systems are being used to monitor the efficience of all aspects of a business, including labor.

Video 5—Monitoring Employee Efficiency in HBO's Enlightened (Season 1, Episode 8)

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TAN.2.O—Fighting Crime

Britain is known for their sophisticated use of surveillance to fight crime, but less known is the increasing value they place on number-crunching. A crime-prediction program called PredPol takes large amounts of data on past crimes to predict where future crimes may happen.  The software provides maps where pink boxes indicate where crimes are likely to be committed. By matching past crimes with information like the road network computers can infer where other crimes might take place; for instance, criminals like stealing in areas where a quick getaway is possible, so a location's proximity to other highways matters. Also, muggers don't like working in the rain, so PredPol will account for the weather in predicting the likelihood of a crime.

PredPol allows officers to patrol the areas surrounding pink boxes between calls, and in the process crime in those areas has fallen. In contests, these pink boxes provide better predictions than expert judgment.(E2)

TAN.2.P—Understanding Crime Rates And Good Parenting

Video 6—Steven Levitt Interview On The Daily Show

If you have trouble seeing the video click here.

TAN.2.Q—Manage Personal Finances

Before the 2008 Financial Crisis many people made foolish house purchasing decisions. They bought houses they could not afford and paid for them with loans they could not understand. Why did so many people make such poor decisions, when buying a house is the most important decision a family can make? A 2013 study suggests that a major reason was simply poor math skills. This study questioned over 300 individuals who were subprime borrowers (meaning they had a poor financial record) and asked them questions to measure their ability to do math, including the calculation of percentages and the understanding of compound interest.

Perhaps not surprisingly, those with poorer math skills were more behind on their mortgage payments and more likely to default on their mortgage.(S5) We learn how to crunch numbers in school so that when we really need the skills they will not fail us.

(TAN.2.R) Who is the worst farter: women or men?

This is a question that demands an answer, and after compiling statistics we now have it!

Video 7—The Farting of Women and Men

(TAN.2.S) Playing Poker

Poker is less about bluffing and more about explicit mathematics. A 2013 Wall Street Journal article was titled The New Science of Poker: Bluffing still matters, but the best players now depend on math theory. These new, best players rely heavily on statistics, to the extent that bluffing is now only a small part of the game.

Poker theoriest David Sklansky once wrote that you should consider yourself a winner as long as you had the higher probability of winning the hand when all the money went into the pot. This attitude is consistent with the underlying mathematical reality of poker, and it can smooth out your emotional reactions to losses and wins.
—Chabris, Christopher. July 27-28, 2013. "The New Science of Poker." The Wall Street Journal. C3.

For an entertaining and enlightening story of how poker has changed, please listen to the Radiolab podcast below.(R1)

For a spreadsheet of Texas Holdem Odds Charts, click here.

(TAN.2.T) Operating a catapault in the ancient world

Most people don't realize the prominent role mathematics played in ancient war. Sure, war was mostly uneducated males killing each other, but the military has always been among the most receptive audiences to new technology. It is easy to think that only modern militaries need math, but algebra was used in war before Alexander the Great conquered the world. The catapault was invented by the engineers who worked for the ancient city of Syracuse (in Sicily) in the fourth century BC.(D1) Catapults may seem like blunt, unreliable weapons, but in fact much thought went into calibrating catapults to ensure their precision, and algebra was part of this thought process.

Greek and Roman catapults were designed using the cubic equation [y = ax3 + bx2 + cx + d] in order to calculate the torsion necessary, so that when you released the pressure the catapult threw the rock...
—Goldman, Steven L. 2007. "Algebra, Calculus, and Probability." Great Scientific Ideas That Changed the World. The Teaching Company.

Figure 5—A Catapult

(TAN.2.U) Winning at Golf

Phil Mickelson is one of the best golfers of all time, and he does so partly by crunching numbers. He keeps detailed statistics on his shots. For instance, he knows that he makes 99% of puts at three feet from the hole, 88% at four feet, 75% at five feet, and so on. He so that when he plays for the big dollars he can concentrate on making the shots where he has the greatest probability of success.(M2) For more, listen to an excerpt of the July 26, 2013 edition of the Science Friday(S6) podcast below.

Video 8—Golfer Phil Mickelson Talks With Science Friday.

(TAN.2.V) Information Technology on the Farm

Farmers used to drive their tractors. Now some tractors drive themselves. Farmers used to apply the same amount of fertilizer throughout a field. Now computers have yield maps which allow the automatically-driven tractors to apply different rates of fertilizer within the same field. In addition to yield maps, data on more sophisticated soil tests and aerial photography allows farmers to apply more fertilizers and pesticides to the parts of the field where it will have the biggest impact.

This is no fad. Two-thirds of farmers responding to a survey used autosteering tractors and/or yield maps. The corporation Monsanto is developing a new service where algorithms crunch numbers on a field's soil, topography, and the like so that it can plant different seeds at different parts of the field.

Much of the future innovation in agriculture may not come from new inventions but better ways to collect data on a field and use that data to help the farmer adjust his input usage between fields, and every square foot within a field.(B3)

Video 9—Green-Seeker Technology for Fertilizer Applications

(TAN.2.W) Other examples

  • The hit show Mad Men no longer depicts the advertising industry. Instead relying on creative individuals for successful promotion, the role of computer programmers and data analysts are becoming the most valued. The reason has to do with digital advertising, where analysts study what type of person consumes each media type (like, what demographic gets their music from Spotify and what demographic relies on The Huffington Post for news instead of a traditional newspaper?). By discovering what digital media the targeted demographic visits, advertising agencies then develop clever interactive advertisements to reach them. The industry has changed fast. After a mother took two years off to have a child she tried to return to the advertising industry only to find out her skills were now in little demand.(V1)
  • When you go to buy car insurance they will first ask you a number of questions, like your age and gender. What they are really trying to do is to guage how risky of a driver you are so that they can charge riskier people higher premiums (it is more expensive to insure a risky driver, after all). Now companies are going to even greater lengths to use data to determine your riskiness. Some insurance companies are allowing drivers to volunteer for a program whereby electronic devices are installed in their car, gathering data on how fast they tend to drive relative to the speed limit, how abruptly they brake, and how fast they accelerate. If the company analyzes the data and concludes the person is a safe driver, then they are rewarded with a discount on their insurance premium.(S7)
  • The National Basketball Association (NBA) has decided to install SportVu video cameras which can collect all sorts of data during each basketball game. At every 30th of a second it can measure each player's speed, separation from other players, who has the ball, every dribble, every rebound, ...almost anything one can imagine. The data will be made available to all teams and perhaps to the public at-large. You can bet coaches and their statisticians will be studying these data to help them design strategies, and to help identify the value of each player, just like such data have revolutionized baseball.(B4)
  • Fantasy sports has become a big deal. Some even make decent money playing it, and those that do often create large spreadsheets where they compile and analyze statistics to help them choose who they should put on their team. There is even insurance on fantasy players now, where if you draft Tom Brady but Brady gets hurt the insurance company pays you an indemnity.(P1)

References

(A1) Ayres, Ian. 2007. SuperCrunchers. Bantam Books: NY, NY.

(B1) Briggeman, Brian and F. Bailey Norwood. 2011. “Employer Assessment of the College Graduate: What Advisors Need To Know.” Natural Resources and Life Sciences Education. 40:19-28.

(B2) Bailey, Ronald. November, 2012. "Big Whoop." Reason magazine. Page 13.

(B3) Beiser, Vince. September/October 2013. "Field & DataStream." Pacific Standard. Page 23.

(B4) Beck, Howard. September 5, 2013. "Sophisticated Cameras to Begin Tracking Every N.B.A. Play." The New York Times. Accessed September 14, 2013 at http://www.nytimes.com/2013/09/06/sports/basketball/sophisticated-cameras-to-begin-tracking-every-nba-play.html?ref=basketball&_r=1&.

(D1) Durant, Will. 1939. History of Civilization. Part 2: The Life of Greece.

(E1) Ehrenberg, Rachel. August 11, 2012. "Simulation helps forecast fighting in Afghanistan." Science News.

(E2) The Economist. July 20, 2013. "Predictive policing: Don't even think about it." Pages 24-25.

(F1) Fujita, K. and J. J. Carnevale. 2012. "Transcending Temptation Through Abstraction: The Role of Construal Level in Self-Control." Current Directions in Psychological Science. 21(4):248. DOI:10.1177/0963721412449169.

(F2) Fischetti, Mark. November, 2011. "Computers vs. Brains." Scientific American.

(F3) Freakonomics Radio. August 20, 2012. "Freakonomics Goes To College: Part 2 [podcast]." National Public Radio. Accessed August 22, 2012 at http://www.freakonomics.com/2012/08/16/freakonomics-goes-to-college-part-2-a-new-freakonomics-radio-podcast/

(G1) Guo, Fei, Tim J. Preston, Koel Das, Barry Giesbrecht, and Miguel P. Eckstein. 2012. "Feature-Independent Neural Coding of Target Detection during Search of Natural Scenes." Journal of Neuroscience. 2012. 32(28):9499-9510. DOI: 10.1523/JNEUROSCI.5876-11.2012

(G2) Gawande, Atul. August 13 & 20, 2012. "Big Med." The New Yorker.

(H1) Hacker, Andrew. July 28, 2012. "Is Algebra Necessary?" The New York Times.

(H2) Haidt, Jonathan. 2006. The Happiness Hypothesis. Basic Books: NY, NY.

(H3) History Channel. 2012. Mankind. Revolution

(J1) Joffe-Walt, Chana. May 30, 2012. "What Air Traffic Can Teach Us About Kidney Transplants." Planet Money Podcast. National Public Radio.

(L1) Lehrer, Jonah. 2009. How We Decide. Houghton Mifflin Harcount Publishing Company: NY, NY.

(M1) Maslow, Abraham H. 1943. Hierarchy of Needs: A Theory of Human Motivation. www.all-about-psychology.com [publisher].

(M2) McGurn, William. July 20, 2010. "Phil Mickelson's Science Project." The Wall Street Journal.

(N1) M. Nichols, P. Scarborough, S. Allender, M. Rayner. What is the optimal level of population alcohol consumption for chronic disease prevention in England? Modelling the impact of changes in average consumption levels. BMJ Open, 2012; 2 (3): e000957 DOI: 10.1136/bmjopen-2012-000957.

(N2) Needleman, Sarah E. January 6, 2009. "Doing the Math to Find the Good Jobs." The Wall Street Journal. D2.

(P1) Planet Money. October 11, 2013. "Episode 490: The Real Economy of Fantasy Sports." National Public Radio. Accessed October 17, 2013 at http://www.npr.org/blogs/money/2013/10/11/232162006/episode-490-the-real-economy-of-fantasy-sports.

(R1) Radiolab [podcast]. Season 11, Episode 5. "Are You Sure?" Abumrad, Jad and Robert Krulwich [hosts]. National Public Radio.

(S1) Infectious Diseases Society of America (2009, February 1). Vaccines And Autism: Many Hypotheses, But No Correlation Found. ScienceDaily. Retrieved August 7, 2012, from http://www.sciencedaily.com­ /releases/2009/01/090130093407.htm.

(S2) University of Cincinnati (2012, June 4). Vaccinations of US children declined after publication of now-refuted autism risk. ScienceDaily. Retrieved August 7, 2012, from http://www.sciencedaily.com­ /releases/2012/06/120604142726.htm.

(S3) Steiner, Christopher. August 18-19, 2012. "Automatons Get Creative." The Wall Street Journal. C3.

(S4) Folger, Tim. September, 2012. "Can We Keep Getting Smarter?" Scientific American.

(S5) Sanghani, Radhika. June 25, 2013. "Poor maths skills linked to mortgage defaults." The Telegraph. Accessed July 23, 2013 at http://www.telegraph.co.uk/finance/personalfinance/borrowing/mortgages/10140287/Poor-maths-skills-linked-to-mortgage-defaults.html.

(S6) Science Friday [podcast]. July 26, 2013. "Phil Mickelson Takes a Swing at Science." Flatow, Ira [host]. Intagliata, Christopher [Associate Senior Producer]. National Public Ratio.

(S7)Scism, Leslie. August 5, 2013. "State Farm Is There: As You Drive." The Wall Street Journal. C1.

(T1) Thompson, Derek. September 27, 2011. "The Value of College is: (a) Growing (b) Flat (c) Falling (d) All of the Above." The Atlantic. Accessed August 21, 2012 at http://www.theatlantic.com/business/archive/2011/09/the-value-of-college-is-a-growing-b-flat-c-falling-d-all-of-the-above/245746/

Vranica, Suzanne and Christopher S. Stewart. August 5, 2013. "Old-School Ad Execs Sweat As Data Geeks Flex Muscle." The Wall Street Journal. B1.

(W1) Wang, Shirley S. May 4-5, 2013. "Autism Linked to Environmental Factors." The Wall Street Journal. A3.

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