Showing posts sorted by date for query The Game. Sort by relevance Show all posts
Showing posts sorted by date for query The Game. Sort by relevance Show all posts

Wednesday, June 3, 2020

The Math Myth and Other STEM Delusions by Andrew Hacker

In the last decade or two, many have called for increased education in STEM fields (science, technology, engineering and math). As an engineer, I may hear more of it than others, or perhaps I am more attentive to it. Math, particularly algebra, trigonometry and geometry, has been seen as a foundation of STEM education with much support from the tech industry that has made it central to the Common Core curriculum used in the majority of states. However, this math requirement has become a stumbling block for many on the road to high school and college graduation. As when I was in school, students ask, “Am I ever going to need to use this?” The answer political scientist (and sometimes math professor) Andrew Hacker proposes in The Math Myth is no.

"This country has a problems. But more math is mathematics is not one of the solutions,” Andrew Hacker, The Math Myth and Other STEM Delusions

 One of the first myths that Hacker tackles is this issue of the usefulness of algebra and other higher math for STEM careers or adult life in general. Most people never need anything more advanced than arithmetic (addition, subtraction, multiplication and division), including most scientist, technicians and engineers. In the 25 years since I graduated from engineering school, I have never need to solve a differential equation. Easily 80 percent of the math I do is arithmetic—possibly more. The rest is basic algebra and basic statistics. On the rare occasion I’ve needed some more esoteric piece of math, I’ve learned or relearned it on the job.

 In spite of this, the move in the U.S. has been to require four years of high school math through Algebra II or beyond, plus a college level course in algebra or more advanced math. This applies even to students who plan to study liberal arts, humanities and other subjects that make practically no use of math. This requirement is the number one academic reason people do not complete high school or college (there are other reasons, of course, but they are not related to a required class or subject). Even youth form affluent families with educated parents can find algebra to be an insurmountable hill. Hacker wonders how much human potential goes undeveloped because educational opportunities are denied to people who do not need math beyond arithmetic, but must pass an algebra course to get their diploma or degree.

 Why is math, and especially algebra, a near universal requirement? Hacker points to college math professors and their influence on lower level curricula. They want prospective students to be prepared to move to the advanced subjects they study, though only on percent of undergraduates major in math, and that drops lower in graduate schools. These same professors almost never teach the entry level (and especially not remedial) math classes in their own colleges. For colleges generally, math can be a weed-out course. Even if most students don’t really need algebra, the requirement is a quick way to knock down the number of students. (As an engineering student, my fellows and I understood the sequence of calculus and math-heavy physics classes required of us as freshmen and sophomores was a way of persuading us to study something else—I almost did.)

 Tech companies also call for a math intensive education and lots of STEM graduates. Hacker points out that, in spite of the hype, there are actually not that many STEM jobs in the U.S., nor is there a lot of growth in these fields. A glut of STEM graduates, in addition to the foreign tech labor market opened up by H1-B visas, keeps wages low in the tech sector. If there was an actual shortage, employers would respond with increased wages. Computer programmers don’t use much math and great majority of them don’t earn high salaries. Sadly, the same is increasingly true in engineering. My advice to someone interested in an engineering career would be to pursue it if you find the work interesting, but don’t do it with the expectation that you’ll get a high salary or rise quickly because of the demand for your technical skills.

 I’d like to mention one more thing that Hacker brings up. Though the math people learn in school often has no practical utility in their work or daily life, people have a knack for math and often do complex mathematical things as part of their jobs. Hacker uses the example of a carpet layer, but I have seen it in machinists, carpenters and other skilled laborers. The use and shape materials in ways that require some complex math, but they don’t write out a page full of equations. They instead apply tools and methods they have learned on the job. I’m a little fascinated by some of this tool-based, mechanical math, and it seems to be just as effective and more understandable that school math, especially since very few of us aspire to study math for its own sake.

 If you’re interested in this book, you may also be interested in

The Numbers behind NUMB3RS by Keith Devlin & Gary Lorden

The Unfinished Game by Keith Devlin

 Hacker, Andrew. The Math Myth and Other STEM Delusions. New York: The New Press, 2016.

Tuesday, March 31, 2020

Pascal's Wager by James A. Connor


Blaise Pascal had a great impact on mathematics. He laid the foundations of our mathematical understanding of probability. A computer programming language was named for him.

Pascal was also a deeply religious man and philosopher. His book Pensées is read as a devotional by many Christians. His argument that the belief in God is rational is widely known.

James A. Connor takes the name of that argument for the name of his biography of the man, Pascal’s Wager. Connor considers both Pascal’s life in science and math and his religious convictions.

For many, there is no conflict in scientific study and religious devotion, but there was for Pascal. He was a Jansenist, though somewhat at odds with the leaders of the movement because of his interests in science and philosophy. The Jansenists were deeply concerned with sin and living a life of penitence; to pursue anything else was to embrace worldliness. Pascal loved the discoveries he made by reason and experiment, but he also longed for a life of purity and closeness to God.

Pascal was seen as a bit of a mathematical prodigy, especially in his youth when his father led a secular life by the standards of the day. He published a pamphlet on conic sections when he was 16 years old. He invented a calculating machine, the Pascaline, when he was 19. He was still fairly young by modern standards when he developed a theory of probability in a series of letter he exchanged with Pierre Fermat.

He had a mystical experience in 1654 that changed his focus in life. He told know one about it, but wrote a note about it that he kept pinned in his coat to carry with him the rest of his life. The note was discovered by his nephew shortly after his death.

After his experience, he devoted more of his time to supporting Jansenism, which his entire family had come to follow, especially his sister, Jacqueline, a nun. Jansenists were in conflict with other Catholics over their views on original sin and election, especially with the Jesuits. Pascal became an apologist for Jansenism, and especially mocked the Jesuits in The Provincial Letters.

Politics and religion were deeply linked in 17th Century France, and the conflict between Pascal’s sect and the wider French Catholic church became a conflict with Louis XIV. He felt that the Jansenist leaders capitulated to the king and the Jesuits, which brought him into conflict with them as well.

Though religious debates had been part of his entire life, this heating up of the conflict to such a level occurred toward the end of his life. He expressed his devotion to God in self-imposed poverty and care for the poor; which in one case took the form of establishing the first public transportation system. He did not abandon math, though, and published a paper on the cycloid as well. He had been sick most of his life and passed away in 1662 at the age of 39.

Connor’s book is approachable for most readers. Though Pascal’s fame today probably rests more on his accomplishments as a mathematician, Connor shows how his life was shaped by his religion and both the religious and secular traditions of his time (Connor is a former Jesuit priest).

If you’re interested in this book, you may also be interested in

Connor, James A. Pascal’s Wager: The Man Who Played Dice with God. San Francisco: HarperSanFrancisco, 2006.

Saturday, April 6, 2019

Naked Statistics by Charles Wheelan


Statistics provides of us with a power set of tools for describing things in our world and making inferences about them. They can also rely on math and logic that seems counterintuitive and they are subject to other pitfalls. Economist Charles Wheelan provides and accessible introduction into how we can use, misuse and abuse statistics in Naked Statistics.

Data is everywhere. In my life time, the falling prices and increased interconnectivity of computers have massively increased the collection of data. It can be overwhelming. At the same time, my experience as an engineer and government employee have left me frustrated with lack of data on some issue and wonder what inferences I might draw and how much I can rely on them.  Statistics provides us tools for dealing with these issues.

For instance, statistics provides us a way to summarize lots of data with a simple number such as an average (many people are familiar with sports statistics that summarize a performance of a play or team over a game, season or even a whole career). Statistics can help us find trends and estimate how much various factors may be contributing toward those trends. Even in the case where there is little data, statistics can help us evaluate the reliability of your conclusions (statistics can’t prove something definitively, but it can quantify how likely you are to be wrong).

“Statistics cannot prove anything with certainty.”-Charles Wheelan, Naked Statistics

Though he doesn’t delve too deeply into the mathematics of statistics, he shows that the math is often the easy part. Getting good data, designing experiments, constructing reasonable hypotheses, and avoiding bias present many stumbling blocks that can turn statistics into nonsense.

Not only that, people can take advantage of the weaknesses of statistics to provide persuasive support for wrong conclusions. Not everyone throwing around statistics intends to deceive, but a few do. A few just make mistakes, too. Wheelan describes many of the common mistakes people make while using statistics. This can help people new (or not new to statistics) avoid them. Possibly more important, it can help users of statistics recognize possible problems in how the statistics they use are developed or interpreted.

“Statistics cannot be any smarter than the people who use them.”-Charles Wheelan, Naked Statistics

This is not a statistics textbook. Wheelan does not delve into the details, but he does provide intuitive explanations of the concepts and simple examples. A student of statistics might find this book helpful in getting over some of the conceptual hurdles that may get in the way of understanding the rest of the material.

If you’re interested in this book, you may also be interested in

Wheelan, Charles. Naked Statistics: Stripping the Dread from Data. New York: W. W. Norton & Company, 2013.

Saturday, January 26, 2019

The Revenge of Analog by David Sax


The joke about visions of the future that never panned out is usually, “Where is my flying car?” The proliferation and promises of digital technology over the last two or three decade might prompt us to pose some other questions such as, “Where is my paperless office?”

In The Revenge of Analog, journalist David Sax discusses how analog technologies are sometimes thriving in the digital ages. Some are making comebacks. Some never went away. Some are growing more popular because of digital technology, not in spite of it.

Sax looks at a lot of analog technologies. This includes vinyl records, paper and pen, tabletop games, books and brick-and-mortar stores.

Some of these have very interesting histories in how they have fallen, risen and interacted with digital technology. What I found most interesting in the book is the reasons analog persists. It is usually because it brings something that digital technology leaves out.

For instance, analog technology appeals to the senses. I know a lot of bibliophiles who love the smell of books, though it would not seem to be a pertinent feature. The IRL space is simply much richer that even the most detailed virtual space.
 “There’s never going to be a virtual environment as completely engaging as the physical environment is,” computer game designer Bernie De Koven quoted in The Revenge of Analog

Analog is usually slow. Generally, a strength of digital is that it is almost always faster. We don’t always want fast. Sometime the slower pace, the pauses, helps us to take things in and savor them. For instance, when you listen to a vinyl record, you can’t skip songs at the touch of a button, you have to lift the needle and move it or even change records. You can’t listen to any songs you have in random order, but you have to listen to song on a single album in the order the artist or producer arranged them unless you introduce a lot of pauses as you interact with the discs and player.

Analog is limited. The digital world can be so rich with information and choices that it can be overwhelming. Paper and pen limits the size, colors and effects you can produce. These limitations help us hone in on the main issues quickly and get moving.

“People think limitations are bad things. But it moves the process forward, in a good way. You can easily get lost in the process. It’s easier to stick to a plan when you have limitations,” analog recording studio owner Chris Mara quoted in The Revenge of Analog

In the real realm of communication, analog is more intimate that digital. The ultimate analog communication is a face-to-face conversation, mediated by nothing but the air in between two people. We send off a lot of nonverbal signals when we speak, and we sense these signals from others, which gives us a more rich and nuanced understanding of what is said (and unsaid) than we can get from a text message or even over Skype or Facetime.

If you’re interested in this book, you may also be interested in

Sax, David. The Revenge of Analog: Real Things and Why They Matter. New York: PublicAffairs, 2016.

Sunday, September 23, 2018

How Not to Be Wrong by Jordan Ellenberg


When people complain about math being too hard or impractical, one might expect a college math professor to take up a defense, which Jordan Ellenberg does in How Not to Be Wrong. He manages to make is his argument without resorting to equations, and with very few numbers.

Math is not all about equations and numbers (though these are important objects in math). Ordinary people do math frequently in the form of thinking with a little more depth, rigor and structure than usual. This is the power of math to help us make better decisions. Though Ellenberg covers a lot of ground in math, science and history, the notion of better decision making through math runs through each chapter.

Along the way, he debunks some common uses of math, even those that are prevalently used among math-minded scientists. For instance, he takes on the notion of statistical significance, which sometimes bothers me, too. Statistical significance by itself is not an arbiter of the truth of something. It has a lot more to do with a particular way of framing arguments and the sensitivity of an experiment. If you have a large enough sample, you’re likely to have statistically significant results, even if those results are insignificantly small. You can “prove” ridiculous, plainly wrong things using an argument from statistical significance because improbable things happen sometimes (actually a lot).

Ellenberg discusses the related subject of probability, which any book like this should. Human beings are pretty bad at grasping probability; it requires deeper, rigorous, structured thinking that sometimes runs counter to our intuition.

Though math is sometimes misused or misunderstood, Ellenberg is bullish on the power of math to help us make better decisions and understand the world more deeply. Math itself is a pretty deep world, and mathematicians have discovered connections between things that seem to be unrelated. That is part of the power of math. Solutions in one are often lead to applications in many others.

Of course, math won’t eliminate uncertainty, though it can help you understand uncertainties better. I’ve spent most of my career in and around government and Ellenberg expresses some empathy for decision makers in the realm of policy, writing, “Maker of public policy do not have the luxury of uncertainty that scientist do. They have to for their best guesses and make decisions on the basis thereof.” This guesswork can be done with humility and honesty, as is fitting in a republic.

While Ellenberg eschews the pile of symbols many people think of as math, he does not avoid deep, challenging questions. It’s not the math you’ll find in journals, but it’s not fluff. He doesn’t call people to join the ranks of academic mathematicians (though don’t give up on the idea just because it seems hard at first), but he argues that people in all manner of professions could benefit from education in math. If you’re interested in becoming such person, How Not to Be Wrong is a good introduction to how mathematicians think about the world.

If you’re interested in this book, you may also be interested in

Ellenberg, Jordan. How Not to Be Wrong: The Power of Mathematical Thinking. New York: Penguin, 2014.

Sunday, February 25, 2018

The Numerati by Stephen Baker

Hari Seldon used mathematics to study psychology and society. He developed the science of psychohistory, which he would use to predict future social, economic and political trends. This was utter science fiction when I read Foundation in high school, and doubly so in the 1940s when Isaac Asimov was writing and publishing the stories that would eventually become the novel. (By the way, psychohistory now refers to the application of methods from psychoanalysis to the study of history and social sciences.)

We’ve come a long way. Computers are much more powerful and many of us carry a networked computer around in our pockets much of the day. The computers record a lot of information about us, especially how we use them, and are crunching the numbers so people can anticipate our wants and influence our behaviors.

Stephen Baker gives us a glimpse into that world in his book The Numerati. “Numerati” is Baker’s term for the mathematicians, computer scientists and other math-literate scientists and professionals who are trying to use numbers and equations to describe and predict human behavior.

This type of analysis has applications in many areas. As you might expect, stores, marketers and advertisers are using it to try to sell us stuff. Not only are they trying to persuade us, they are segmenting the market to try to get the highest prices they can for their products from each buyer (and spend less time dealing with die-hard bargain shoppers).

Similarly, politicians are using this type of analysis to reach swing voters. Companies are trying to get the most out of workers.  Health insurance companies are seeking to minimize exposures to risk. Law enforcement is getting all the information it can lay hands on to try to find the terrorist lurking in our midst (finding a needle in a haystack may be easier).

That sounds sinister, and Baker has reservations about the benefits of us sharing so much information, but there are opportunities for those of us who are not numerati, or can’t afford a staff of mathematicians to do our bidding. The numbers that show which workers are most productive could be turned around to help us show our value and potential win a raise or promotion. The numbers that show minute changes in our behavior might help us diagnose and treat diseases earlier and less expensively, or help us live more fully with chronic diseases. They might even match us with a soul mate.

Though science and technology have advanced in the decade since this book was published, the data sciences Baker described are still new. Some of the things we see being done with computers on television or film are still new concepts that don’t work nearly as quickly or accurately as depicted. However, people are working every day to make these technologies better.

If you’re interested in this book, you may also be interested in


Baker, Stephen. The Numerati. Boston: Houghton Mifflin, 2008.

Sunday, March 13, 2016

Level Up Your Life by Steve Kamb

Life is not a game, but you can learn from games to make your life more adventurous and fulfilling. Steve Kamb, a gaming enthusiast who turned his attention to physical fitness, used concepts of gamification to change his life. He describes the process in Level Up Your Life.

Throughout much of his childhood and into his early adult years, Kamb spent much of his free time playing video games. It was an escape for a life he didn’t always like. On the down side, these nearly addictive games were not helping him achieve a life he really wanted. He began to look for what made games so satisfying and how that could be adapted to making life more satisfying.

It is surprisingly simple. Our brains enjoy making progress, and it triggers our internal reward centers when we get feedback that lets us know we’ve progressed. Designers build incremental progress and associated rewards into the structures of most video games.

Much of the middle part of the book deals with goal setting. It is not much different from the advice you might find in other self-help or popular psychology books, except for the gamification spin. Imagine your idea life (Kamb calls it your “Level 50” life). Choose some challenging, inspiring, big goals (quests). Break them down into smaller, doable goals (specific timelines help). Create systems of accountability and rewards to encourage yourself to stick to it. Find a group, or groups, of people who can help and encourage you along the way.

In the final chapters, he deals with supporting concepts about overcoming fear, supporting your goals with good health and fitness, stirring up you sense of adventure, travel tips, and making the sacrifices you may need to make to live the life you desire and respond to a higher calling. He takes inspiration from fictional heroes of popular culture: Bruce Wayne (Batman), Jason Bourne, Indiana Jones, and Katniss Everdeen. He also lists several resources, both web sites and other books. If you’re inspired by adventure stories (in games, books, film or other media), you may find in Kamb’s book a framework for building the life you want.

I like that Kamb emphasizes that life, like a game, should be enjoyed. We should enjoy the process as well as the achievement. We should be flexible and open to the adventures we may discover along the way; they can enhance our lives and may prove useful to our quest in surprising ways.

If you’re interested in this book, you may also be interested in


Kamb, Steve. Level Up Your Life: How to Unlock Adventure and Happiness by Becoming the Hero of Your Own Story. New York: Rodale, 2016.

Saturday, October 31, 2015

Rock Breaks Scissors by William Poundstone

People are terrible at producing randomness. We are very bad at recognizing it, too. In his book Rock Breaks Scissors, William Poundstone describes the ways we misunderstand randomness. In addition, he shows how knowledge of this blind spot can help us to make better decisions, or at least help us to avoid being duped by fraudster or our own minds.

The early chapters of the book describe how researchers have come to identify our biases related to randomness perception, even if we do not wholly understand it. Poundstone avoids the textbook psychology and pulls examples from interesting sources such as mass experiments in parapsychology (designed to sell radios) and a machine that beats people at a child’s outguessing game using a simple algorithm.

These experiments reveal two important things about our perceptions for randomness. First, we are almost incapable of intuitively recognizing true randomness and prone to identify as random things that aren’t. In addition, we have all manner of unconscious preferences that show themselves when we try to be random, though we’re unaware of their appearing.

The book takes its title from another child’s outguessing game: rock-paper-scissor. I risk angry comments with this description, because some people take the game very seriously. Serious players have strategies for playing the game. These strategies probably provide little advantage over advanced players, but may give you an edge over ordinary players. My own impromptu experiment seemed to confirm it. (This is another trap we fall into: seeing patterns and drawing conclusions from small data sets that may be random.)

Another way our inability to be random is used is in detecting fraud. We can expect certain sets of number to occur in certain distributions of frequency. For instance, Benford’s law describes the frequency of first digits in numbers. The most common first digit is one, and the frequency declines for each digit to nine (leading zeros are ignored for the first digit). If the distribution of first digits is different, and especially if there are thresholds that may be associated with incentives, then there may be some fudging of the number. In other cases, you might expect the frequency of occurrence to be equal, such as the last two digits of numbers. People will avoid digit pairs that don’t seem random and unconsciously favor certain pairs. An uneven distribution of these pairs could be another sign of fraud. Keep this in mind when you’re preparing your taxes.

The utility of Poundstone’s strategies varies widely. The outcome of rock-paper-scissors means little to most of us (I would not risk something I care greatly about on it). On the other hand, a patient, long-term investor might gain an edge on the market that could amount to a lot of money over time. The chapter for homebuyers might also save you a lot of money by helping you avoid an overpriced market. Use caution, though. Poundstone is pointing out how you might outguess people, because people have trouble with randomness. You’re not going to outguess the lottery because truly random things can’t be outguessed.

William Poundstone also wrote Fortune’s Formula.  If you’re interested in this book, you may also be interested in


Poundstone, William. Rock Breaks Scissors: A Practical Guide to Outguessing and Outwitting Almost Everybody. New York: Little, Brown and Company, 2014.

Sunday, August 23, 2015

Freakonomics by Steven D. Levitt & Stephen J. Dubner

Economist Steven D. Levitt and journalist Stephen J. Dubner look into the unexpected relationships between aspects of our society in their book Freakonomics. They not particularly interested in the things you might expect economists to write about such as business, markets or investment. Instead, they look at cheating, crime, expertise and parenting.

There is no particular theme of the book, except possibly that common explanations and expectations are often off the mark. Levitt and Dubner are skeptical of conventional wisdom and expertise. They are interested in data and what questions can properly be put to that data.

They sometimes come to conclusions that some might find disturbing or troubling. For instance, they trace the drop in crime rates in the 1990s to the legalization of abortion in the 1970s. Many of the women who had abortions in the wake of Roe vs. Wade were poor, had low education, or very young. All of these traits in the parents tend to produce worse outcomes for children, including a higher likelihood of committing crime. As the first post-Roe cohort of children reached their teen years in the 1990s, there were fewer who had been raised in those conditions that may have pushed them into crime, and therefore fewer budding criminals and a decline in crime rates.

Reading this made me think of the arguments of eugenicists. They believed that a host of social ills, including crime, could be mitigated by keeping the unfit people from reproducing. To the eugenicists, unfit was essentially equivalent to nonwhite, though it also extended to the feebleminded (a disease a eugenically-minded psychiatrist or psychologist might have found in any poor, uneducated person). The eugenicists saw intelligence, criminality, poverty and host of other features as fixed and hereditary. Limiting the reproduction of the unfit through abortion or sterilization would reduce and eventually eliminate poverty and crime.

Of course, Levitt and Dubner are not eugenicists. Nor do they propose abortion as means to reduce crime. Crime does not have its roots in race or intelligence. It is strongly tied to poverty and low education. Charles Dickens chilling portrayed Ignorance and Want in A Christmas Carol, and they are still a threat to all of us.

Each chapter reveals an interesting twist on some subject, though few are as potentially charged as that on crime. In another chapter, the authors show that crime does not pay, except for those at the top, on unlike in a corporation. In spite of faddish thoughts on the issue, parents matter, though maybe not in the ways we’d like to think.

My previous reading has inclined me to focus on the darkest part of the book, but the overall tone is conversational and light, though the authors are not flippant about serous subjects. They are not technical either. Their use of statistics is straightforward. They do not delve deep into theory, though they focus much on the central theory of economics that people respond to incentives.

If you’re interested in this book, you may also be interested in


Levitt, Steven D., & Stephen J. Dubner. Freakonomics: A Rogue Economist Explores the Hidden Side of Everything. New York: William Morrow, 2005.

Saturday, November 15, 2014

The Peerless Peer by Philip Jose Farmer

I usually review nonfiction books on this blog (a likely cause of no one reading it). Sometimes I read a fiction book that I enjoy so much, I comment on it anyway.

The Peerless Peer is such a book. Philip Jose Farmer brings together Sherlock Holmes and Tarzan in the heart of Africa. Holmes and Watson are on a mission to retrieve a formula that could change the course of World War I by destroying all the fish and chips. Along the way, Holmes sorts out certain points of the Greystoke family history that are “wrong” in the sensational jungle king novels of Edgar Rice Burroughs.

Farmer throws in cameos and name-dropping of a host of popular and pulp heroes. On their first two, back-to-back airplane flights, Holmes and Watson have the mixed blessings of being piloted by G-8 (possibly The Spider) and The Shadow. They obviously meet Tarzan, and unexpectedly meet the daughter of Allan Quatermain. Along the way, they interact with Henry Merrivale and Gideon Fell. As a player of The Game, Farmer describes how Watson’s previously unpublished manuscript came to him through a chain of provenance that included Lord Peter Wimsey.

If you’re looking for a short, fun, pulpy, nostalgic novel, this will do. It is fun.

If you’re interested in this book, you may also be interested in