God's Equation by Amir Aczel

Amir Aczel wrote God’s Equation following the 1998 announcement of studies that indicated that we live in an open universe that will continue expanding without end. This is in contrast to theories that the universe might be closed, with gravity eventually pulling everything back in to a great collapse, or stable, with the universe continuing to expand at an ever slower rate. He attempts to show for a lay audience how these discoveries were built on the work of Albert Einstein and complex forms of geometry.

It is complex. Aczel does not dive too deep into the math. Most of his intended audience wouldn’t understand it—it is beyond any math I’ve mastered. It is rooted in Einstein’s general theory of relativity and his field equation, which describes it mathematically. Many people are familiar with E=mc². It is simple and it is fairly easy to understand what it is describing. The field equation may look fairly simple when written out, but behind it is very complex math that has complex ramifications.

I think a lay person could read this book and have no better understanding of the physics and math of our expanding universe than he did before. I’m not sure that understanding complex physics is the great value of the book anyway.

To me, the value of the book is the way it shows how science works. Aczel demythologizes the process, especially in relation to Einstein, without devaluing it or the accomplishments of leading scientists. For instance, the myth of Einstein is that he came up with the theory of relativity in an instant due to his extraordinary genius and it instantly revolutionized science.

The reality is that, even though Einstein was way ahead of his contemporaries, it took him years of effort and false starts to develop general relativity. He had help and input from other physicists and mathematicians. His work was met with skepticism. It took many years for Einstein and others to flesh out the ramifications of his theory, and for astronomers and other experimental scientist to confirm them.

Another bit of demythologizing is that Einstein wasn’t good at math. He simply wasn’t interested in math for its own sake, so he didn’t put in the effort as a student except to the degree he found it useful. Though Einstein came up with ideas with imagination that did not always depend on math, the fleshing out of his theories into sound physics required a lot of math. He applied himself diligently to mastering it, and it was quite advanced.

A physicist will seek more technical books on the subject of cosmology. Arguably a book that is nearly 20 year old may be a bit dated, too. However, I think it is still interesting history and how our understanding of the world is developed over time with imagination, diligence, debate, testing and the effort to many people.

Amir Aczel also wrote:

Chance

Descarte’s Secret Notebook

Why Science Does Not Disprove God

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

Copernicus’ Secret by Jack Repcheck

Einstein’s Clocks, Poincare’s Maps: Empires of Time by Peter Galison 

The Girls of Atomic City by Denise Kiernan

Planck by Brandon R. Brown

The Powerhouse by Steve Levine

Miss Leavitt's Stars by George Johnson

Aczel, Amir D. God’s Equation: Einstein, Relativity, and the Expanding Universe. New York: Four Walls Eight Windows, 1999.

STEM Books

I’ve reviewed 39 STEM-related books (and counting).  STEM is an acronym for science, technology, engineering, and mathematics.  As you may have seen in the news, there is a push to improve STEM education, interest students in STEM fields, and grow the number of workers in these fields.  The idea is that these will be the skills needed by workers of the future.  If you’re a STEM educator or a student considering a career in STEM fields, you might like to take a look at some of these books.

I’ll confess that I’m not an educator, but I think most of these books will be accessible to high school and college students, and a few to middle school students.  The list is also a reflection of my career and interests in engineering, public health, policy, and history.  Even with these biases, I think it is a good list for someone looking for STEM-related books.

How to Build an Android: The True Story of Philip K. Dick’s Robotic Resurrection by David F. Dufty

I was fascinated by robots as a kid.  I enjoyed reading Isaac Asimov’s robot stories.  I longed for the Omnibot 2000 in the Sears Wishbook.

Robots have come a long way.  In How to Build an Android, David F. Dufty describes the short strange life of a very complex robot made to look and talk like science fiction author Philip K. Dick.  The robot had a very sophisticated and lifelike head and complex artificial intelligence.  As with most complex things, it was the work of many people who had to solve a lot of problems.

If you’re interested in robotics, this is an interesting nontechnical book.  In addition, you’ll get introduced to some freaky sci-fi.  You may even get as (somewhat) legitimate reason to use the word “Dickhead” (capitalized, it refers to a fan of PKD, so don’t go using it on anyone).

The Big Roads: The Untold Story of the Engineers, Visionaries, and Trailblazers Who Created the American Superhighways by Earl Swift

The Interstate highway system in the United States is one of the most enormous structures built.  Some of the prospective STEM students who read this may actually be younger than the Intestate system, though in some sense it is never complete because it needs constant repair and maintenance.  The Interstates were completed in the 1990s, but the Federal-Aid Highways go back to 1916.

Earl Swift wrote an accessible history of the Interstates in The Big Roads.  If you interested in automobiles or transportation, it’s a good read.

Dreams of Iron and Steel by Deborah Cadbury

Deborah Cadbury describes seven wonders of engineering in Dreams of Iron and Steel.  It covers almost a century of history, but many of the events are concentrated in the Victorian Era.  That was a time of great technological innovation.

Though the book is history, many of the structures still stand.  Railways, the Brooklyn Bridge, the Suez and Panama Canals, and Hoover Dam stand testament to an age of big engineering.

The Physics of Superheroes by James Kakalios

Though the memory of Professor Wragg’s sneer prompts me to not make this confession, part of my interest in science and technology came from comic books.  Iron Man was cool.  Spider-Man’s web shooters were very cool.  Superhero comics are full of fantasy, admittedly, but the strange, unrealistic science and technology they depict have inspired many to study STEM in reality.

Physicist John Kakalios uses examples from comic books to explore real physics in The Physics of Supeheroes.  Sometimes comics get there science right.  Even when they get it wrong, it can be instructive.  If you know what people are talking about when they refer to the “New 52,” you may find this book to be a great introduction to physics.

1089 and All That: A Journey into Mathematics by David Acheson

Here is another confession: I’m not especially interested in math.  I endured a lot of math classes to study engineering.  Reading David Acheson’s 1089 and All That did not require such endurance.  For one reason, it is a short book.  For another, Acheson doesn’t expect his readers to be mathematicians; it is enough to follow the outline of the math he discusses.

I recommend this book because so many people have a fear of math.  1089 can be followed by many high school students and older folks with math phobias.  Just take a deep breath, relax, and follow along as well as you can.  You’ll see that math can be interesting, useful, and even beautiful in a way.

The Brooklyn Bridge: They Said it Couldn’t be Built by Judith St. George

Judith St. George’s The Brooklyn Bridge is a short history of and iconic bridge.  Written for the bridge’s 100^th anniversary, it is also the story of the engineers who sacrificed life and health to see it completed: John Roebling and his son Washington.  John Roebling was a German immigrant who built many suspension bridges and owed a wire-making business.  He gave his son and extraordinary education in bridge engineering for the time, and before beginning work on the Brooklyn Bridge he served as an officer in the Union Army during the Civil War.

Why should a cutting-edge STEM student read about a bridge that is almost 130 years old?  It’s because we still use and rely on very successful, centuries old technologies.  Improving and rebuilding our infrastructure will be an important part of our economy.  As recently as 2010, New York City and the federal government committed $500 million to repair and repaint the Brooklyn Bridge.

The Essential Engineer: Why Science Alone Will Not Solve Our Global Problems by Henry Petroski

STEM lumps together science, technology, engineering, and mathematics.  Is there a difference between science and engineering?  Is it important?

Henry Petroski, a professor of civil engineering and history and author of The Essential Engineer, believes there is an important difference.  At heart, science is about increasing knowledge.  Engineering is about invention.  Of course, new knowledge makes new invention possible.  Just as often, though, engineering runs ahead of science.  Sometimes science didn’t advance until someone invented the instruments to conduct new observations and experiments.  The invention of the microscope made possible the science of microbiology.  Steam engines were built and greatly improved before we had a modern scientific understanding of thermodynamics.  In fact, thermodynamics was to a large extent born out of desire to understand steam engines. In this sense, it is an engineering science (study of manmade things) as much as a natural science (study of natural things) or branch of physics.

Petroski’s focus in the book is the importance of engineering to policymaking, where it is often overshadowed by science.  Policy, science, and engineering play off of each other a lot.  Most of my career as an engineer has been related to government, policy, and regulatory compliance.

The Ghost Map: The Story of London’s Most Terrifying Epidemic—and How It Changed Science, Cities, and the Modern World by Steven Johnson

The Ghost Map by science writer Steven Johnson is the story of the birth of epidemiology.  Epidemiology is a medical science that uses statistics to help us understand how diseases operate in a population.  Using various statistical and geographic tools, long before we had computers and GIS, physician John Snow demonstrated that cholera, once a recurring plague that wiped out hundreds of thousands of people in some outbreaks, was a waterborne disease.  This understanding, initially met with much skepticism, allowed officials to intervene to prevent the spread of the disease.  For those who say of their math classes, “I’ll never us this,” here is a case where math (and science and policy) were used to make a great difference.

Undaunted Courage: Meriwether Lewis, Thomas Jefferson, and the Opening of the American West by Stephen Ambrose

It is not much publicized today that the Lewis and Clark expedition of 1804 to 1806 had a partly scientific mission.  Captains Lewis and Clark were charges with bringing back samples of the flora, fauna, and culture of the western territories.  It was also hoped that they would find a water passage to the Pacific Ocean.  In Undaunted Courage, Stephen Ambrose writes about the scientific mission as well as the policy, diplomacy, and commercial hopes the expedition carried.

Of course, what attracts most people to the Lewis and Clark expedition is that it was a great adventure.  There is a place in STEM fields for thoughtful adventurers and explorers. 

Buried Alive: The Terrifying History of Our Most Primal Fear by Jan Bondeson

A list like this deserves something strange, creepy, and more fun than you care to admit.  Right now, thousands of very young future STEM workers are catching bugs and snakes, breaking their toys to see what is inside, or staring into space with a weird expression of vacancy and concentration.

Jan Bondeson’s Buried Alive is not a morbid book.  It is sometimes humorous, especially in consideration of topic.  From a STEM point of view, Bondeson shows how knowledge accumulates over time.  The fears and activities of our forefathers may seem strange to us, but they sometimes made sense in light of what they knew.  Buried Alive doesn’t simply play off our fascination with the grotesque and death, though the book might not have been written if we lacked that fascination, I think it reminds us to approach our ancestors with a touch of grace and humility.  Maybe our progeny will show us the same courtesy.

If you’re looking for something for a younger student, check out this post→ from Joanne Loves Science or these recommendations→ from STEM Friday.  By the way, I also write about engineering, infrastructure and the environment at Infrastructure Watch.

Google

The Checklist Manifesto by Atul Gawande

Gawande, Atul. The Checklist Manifesto: How to Get Things Right. New York: Picador, 2009.

Many of the things in our modern world are very complex. Little things done are not done, especially by the experts who undertake some of the most complex tasks, can have significant results. Surgeon Atul Gawande suggests a solution for managing this complexity and making sure that those important, little things aren’t overlooked. His solution is the checklist.

The thread through his book, The Checklist Manifesto, is the development by the World Health Organization (WHO) of a surgical checklist. WHO wanted to reduce surgical complications, especially in the third world. The team they put together, including Dr. Gawande, eventually settled on a checklist.

It was met with much skepticism, even on the part of those who developed it. The results changed minds. Use of the checklist cut serious complications from surgery almost in half. Dr. Gawande recounts his own experiences using the checklist and how it helped him prevent and solve surgical problems.

The checklist isn’t purely a matter for medicine. A very successful user of checklists is the aviation industry.

Aviators were once like surgeons, seen as virtuosos who drew upon skill, daring and intelligence to perform their jobs. Airplanes eventually became to complex for pilots, as the book illustrates in the case of a once experimental military craft. The pilots who took on the new airplane looked for ways to succeed, and survive, where their successors hadn’t. Rather than more training or expertise, the fallback of many professionals, they looked to the checklist. Use of checklists have become standard in aviation, where it checklist making has been much refined.


An interesting chapter deals with the landing of US Airways Flight 1549 in the Hudson River a few years ago. Dr. Gawande praises the skill of the pilot and crew. He also points out, as the crew of the flight always have, the importance of the procedures they used, and especially the checklists that helped them to implement those procedures.

Through several examples, the outline of what make a good checklist and the cases where they work best are show. There isn’t yet and exact science to making checklists, but there is a well-developed art, which includes testing and revision.

It takes a dose of humility to accept that checklists can help highly trained professionals do their jobs better. Dr. Gawande seems to hope his fellow surgeons can show some the humility shown by pilots and allow checklist to become a tool for improving their work.

I come from a background in engineering and this makes sense to me. A procedure is designed much like anything else. If there are critical elements in anything, it is wise to reinforce them in ways that ensure their performance. The human mind is capable of amazing things, but can’t necessarily be relied on to remember to turn off the lights or stove or do any number of other little things.

I’ve also worked in the regulatory field, and seen thoughtless, narrow adherence to rules bring about undesirable results, sometime contrary to what the rules intended. This is not at all in the spirit of The Checklist Manifesto. A good checklist ensures consistency and quality while at the same time freeing the minds of its users to creative deal with the complexities of their task.

If you’re interested in this book, you may also be interested in
Awakening the Entrepreneur Within by Michael Gerber

Outliers by Malcolm Gladwell

Prior to reading Malcolm Gladwell’s book Outliers, I had seen it referenced by others in relation to the so-called “10,000-hour rule.” This is the concept that mastery of a complex skill takes about 10,000 hours of practice. This idea is not original to Gladwell, but his book popularized the concept.

That is not at all the point of Outliers. Instead, Gladwell takes on myths of success, especially the myths of genius and the self-made man. Certainly people of extraordinary achievement are intelligent and hard-working, but Gladwell shows that they also the beneficiaries of opportunities provided by their culture, sometimes very unique opportunities.

To start, Gladwell tackles our enchantment with intelligence (or talent). He describes research that shows that intelligence matters very little after it reaches some threshold. Once someone has enough intelligence to succeed at something, whether he succeeds for the degree of his achievement is not determined by intelligence. Other things are more important.

One of those other things is the amount of work someone puts into improving a skill (going back to the 10,000-hour rule). Even for a very motivated person, it is hard to put 10,000 hours into learning and improving any complex skill, especially while relatively young. Drawing from many cases (including Bill Gates and Mozart), high-achievers were enabled by opportunities provided by the culture (family, economic situation, law, technological development, etc.). In addition, they gained their mastery at a time when those abilities were highly valued (another cultural contribution that is often time-limited).

After establishing this foundation, Gladwell looks at other aspects of culture and success. Culture can contribute to success and hinder it. Cultures are persistent, yet some have found ways, at least in certain contexts, of overcoming limits to opportunities and opening the doors to success.

Culture matters. We like stories of the lone genius or plucky rag-to-riches go-getter. Without discounting their talent or effort, Gladwell shows that these stories typically veil the many opportunities and lucky breaks that were available to these successful people that very often were not available to others.

The implication is that we rely on luck to produced highly successful people, and luck doesn’t strike often. We could create cultures that provide more opportunities for more people. There are plenty of smart-enough people. Many of them are willing to work hard at something meaningful (itself something that is a cultural heritage). We might have many more successful people, and even more of those extraordinary performers, if we got serious about providing opportunities for everyone.

Malcolm Gladwell also wrote

Blink

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

The First 20 Hours by Josh Kaufman

The Genius in All of Us by David Shenk

Mindset by Carol S. Dweck

The Organized Mind by Daniel J. Levitin

Rapt by Winifred Gallagher

Succeed by Heidi Grant Halvorson

Your Intelligence Makeover by Edward F. Droge, Jr.

Gladwell, Malcolm. Outliers: The Story of Success. New York: Little, Brown and Company, 2008.

Technology in World Civilization by Arnold Pacey

For those looking for a brief survey of technological history around the world, Technology in World Civilization by Arnold Pacey would be a good start. With just a little preface to introduce ideas about how civilizations interact in relation to technology, Pacey dives into a historical narrative of the development of major technologies. He starts in A.D. 700 and continues almost to the time the book was published in 1990.

Throughout the book, Pacey describes the interactions between civilizations as a dialogue. Straightforward, direct transfer of technology from one civilization to another is rare in his view. The success and development of a technology that originated in a foreign culture depends a lot on the customs, organization, government, economy, and technology of the receiving culture. Very often, the adoption of a foreign technology spurs adaptions, improvements and even new inventions among the adopters. Even the rumor of a foreign technology can spur people invent, or independently reinvent, solutions to a problem. Pacey is keen to recognize this stimulus effect in cross-cultural dialogue related to technology.

In addition to recognizing the inventiveness found in many cultures, Pacey is careful not to overemphasize mechanical inventions, which might tend to put the focus on the West. He points out that the development of more efficient and productive crops and agricultural practices in Asia were also important technologies.

Another important technological improvement centered on organization and abstraction. As technologies became larger and more complex, they exhausted what could be experienced directly by craftsmen. Improvement depended on developing new ways of thinking about materials and work. Scale drawing and model-making became a way to deal with complex construction. New principles of organization were applied to work, such as specialization and division of labor, especially as people began to work with powered machinery. Some technological improvements even required a new way of understanding materials, spurring interest in the development of sciences, especially chemistry.

Pacey follows this progression through guns and railroads and into the 20^th century with computers, nuclear power, and flights to the moon. He doesn’t stop there. Instead, he takes a look, seemingly “back,” to survival technologies. Technologies related to agriculture, sanitation and environmental health in the 20^th century have a huge impact on the way we live today. In the decades since this book was published, the Internet has revolutionized the way we think about computing and communications, but in many ways our health, wellbeing and lifestyles depend on technologies that are centuries old and we cannot neglect them. Perhaps in an ongoing cross-cultural dialogue about technology, new and old, we can find solutions to current and future problems (climate change, water shortages, clean energy, food security and more) that are adaptable to the various needs, scales and organizations of cultures around the world.

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

Dreams of Iron and Steel by Deborah Cadbury

Pacey, Arnold. Technology in World Civilization: A Thousand-Year History. Cambridge, MA: The MIT Press, 1990.

Canals and Their Architecture by Robert Harris

Harris, Robert. Canals and Their Architecture. New York: Frederick A. Praeger, 1969.

Water has always been an important part of human life. Drinking water is a necessity, but that is only the beginning of our uses of it. Water is also an element in agriculture, industry, transportation and commerce.

It is water’s role in transportation and commerce that Robert Harris focused on in Canals and Their Architecture. At times, artificial or modified waterways have been major means of transporting products in bulk.

Harris mentions canals from continental Europe and North America, especially the United States, but his book is mainly about the canals of Britain. This is an appropriate focus because the canal boom in Britain both fed and was fed by the Industrial Revolution that started there.

The boom began with the Duke of Bridgewater’s famous canal, construction of which began in 1760. The duke owned coalmines and wanted a cheaper way get coal to the mills and factories in Manchester. The canal was by no means an easy or inexpensive project, but it was greatly successful and the wealth put into it was regains many times over.

Bridgewater recognized the talents of millwright James Brindley, who went on to become the most prominent canal engineer of his day. Harris discussed the works of several British engineers who were successors of Brindley including Thomas Telford, John Rennie, and William Edwards.

As the title of the book suggests, it is organized mainly by the types of structures found on canals. In addition to the canal cut, Harris wrote about bridges and auqueducts, locks , tunnels, boats, buildings and unique ways of handling elevation changes on a canal route. Early canals followed the contours of the land to avoid the use of expensive and complex equipment and, where needed, were crossed by utilitarian bridges of wood or brick. As canals became straighter, and more lucrative, they added locks and other mechanisms for raising and lowering boats. The materials became more varied and complex, including stone and iron. Spectacular aqueducts carried canals over low lands. Tunnels were well-made features of canals early on because the technology for building them was readily adapted from mining.

The older canals are impressive in that so much was done with manpower and simple tools. As canals aided other industries, the improvements those industries spawned, especially in iron construction and railroads, returned to canals and the way they were made. The construction of modern canals is the work of enormous equipment.



Canals and Their Architecture includes many illustrations and photographs. These are very helpful for the laymen to see the types of structures discussed in the text, though even an engineer familiar with the terms will likely appreciate the images.

If you’re interested in this book, you may also be interested in
The Ancient Engineers by L. Sprague de Camp
Dreams of Iron and Steel by Deborah Cadbury
Water by Marq de Villiers

Range by David Epstein

Specialization is king. It has become seen as the road to success. Since Malcolm Gladwell popularized the 10,000-hour Rule a few years ago (perhaps unintentionally), I’ve seen a lot of people using it to justify and spell out the road to specialization: focus and start early. However, specialization can hurt when we face problems that cross boundaries and pull us out of our niche; we can be lost and ill equipped outside of our specialization. Journalist David Epstein explored the issue in his book, Range.

 Epstein starts out by showing the limitations of specialization. It works well in an arena where repeating patterns prevail, and we can learn to recognize those patterns from exposure. When there are no repeating patterns, or they are complex and obscure, a high degree of specialized knowledge can lead to wrong conclusions and false confidence. We can have a few good tools that we trust, but if they are the wrong tools for the job we may be doing the wrong thing without realizing it. Complex environments and problems require us to reason conceptually, connect ideas from different contexts and solve problems without direct prior knowledge of what we are facing. We need breadth.

 Though it is not as popular a narrative, Epstein provides several examples of how people with broad and diverse knowledge have become high achievers. Creativity is, to a great extent, finding relationships between seemingly unrelated things. One must be equipped with a variety of experience to be able to make these leaps.

 I can see how the generalist’s path can seem unappealing. It may not seem like a path at all. Deep learning is slow and effortful. It is a way of errors, false starts and diversions that can seem like a waste of time. Developing range is messy and uncertain; by comparison, specialization seems like a sure thing.

 Epstein’s book contains ways to develop range. Analogies allow us to apply knowledge from one area to another, and seeing where analogies fall apart can lead to new ideas. Take an outsider’s cooler, distant and critical view and save yourself from the pitfall of taking a rosy view of familiar things. Pay attention to things that don’t fit the model. Don’t plan too far ahead, but be open to exploration an experimentation. There is a time for mastering particular knowledge and procedure, but the overall approach to learning should be to make connections and gain perspective.

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

The Checklist Manifesto by Atul Gawande

The First 20 Hours by Josh Kaufman

Freakonomics by Steven D. Levitt & Stephen J. Dubner

The Genius in All of Us by David Shenk

Learn Better by Ulrich Boser

Outliers by Malcolm Gladwell

 Epstein, David. Range: Why Generalists Triumph in a Specialized World. New York: Riverhead Books, 2019.

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.