Category Archives: Science

Book Review: Steven Strogatz – Infinite Powers: How Calculus Reveals the Secrets of the Universe

Review of Steven Strogatz – Infinite Powers: How Calculus Reveals the Secrets of the Universe

This book is really, really good. It should be required supplemental reading for math teachers, who should assign relevant portions to their students. Most math pedagogy consists of memorizing procedures. It’s mostly how, with only a little bit of what or why. There is rarely much of any unifying theme that ties the separate problem-solving procedures together in a way that makes sense. Strogatz provides all that, and in a compelling way, complete with examples ranging from medicine to astronomy.

Strogatz also explains terminology, which is another common weak spot in classrooms. Why are calculus’ two main concepts called derivative and integrals? I didn’t learn that in undergrad. Nor in a high-quality graduate economics program. Instead, I learned it from Strogatz’s popular-level book in my late 30s.

Another fun bit of etymology is that the word “calculus” is derived some the world for rock. It shares a root with calcium, chalk, calcite, and other similar words. This is because in ancient times, people did their counting by sliding stones along an abacus’ strings.

The concept of infinity is key. Calculating the area of a circle is hard because of the curves. Slicing it into quarters, like a pizza, makes it a little easier. The wedges are kind of triangle-like, but there is still plenty of curved surface on the outside. Cutting into 8, 16, and 32 slices makes the curve progressively less important. Tending the number of slices towards infinity sends that tricky curved area towards zero. Long before infinity, it reaches deep decimal territory, where the accuracy of the calculation is good enough to satisfy even the most exacting engineers. Infinite parts are simpler than a complex whole. This view of infinity is the key to understanding calculus.

Differentiating is taking a complex whole, like a circle, and converting into many different parts, which are easier to calculate accurately. Derivatives are parts derived from a larger whole. Integrals take these differentiated parts and integrate them back together. Calculus is essentially the math of moving from a whole to its parts and back, as needed to accomplish the task at hand.

This is simple stuff that is so obvious to veteran instructors that they never bother to teach it to rookie students. This kind of larger context and purpose should be taught on day one of any course, and regularly reinforced as new material is introduced.

In high school, I spent months memorizing procedures for calculating sines and cosines, but never really learned much about their significance, or knew that they had anything to do with calculus. Moreover, why does it matter that the same curved shape is shifted horizontally? More than twenty years later, I finally learned why. The sine wave is interesting because of its continually changing slope. And a sine wave’s derivative is… it’s cosine. And now I have a greater appreciation of everything from the changing length of daylight during the seasons to how sound waves interact with each other. The rate of change in daylight as the calendar moves from solstice to equinox is a sine wave. The rate of change is slowest at the solstice (about 40 seconds), and fastest at the equinox (more than two minutes). Figuring out the rate of this change at any given point can be figuring out the derivative. In the special sine wave case, this is simple—just figure out the cosine.

Again, this is basic stuff that high schoolers deserve to know. GPAs would likely be measurably higher, and understanding measurably greater, by teaching a little bit more of this big-picture context and a little less rote memorization.

Needless to say, I will be reading Strogatz’s other books in short order. Infinite Powers would pair well with David Salsburg‘s The Lady Tasting Tea, which accomplishes a similar task with statistics.

Bill Bryson – A Short History of Nearly Everything

Bill Bryson – A Short History of Nearly Everything

A history of science that is accessible to nearly everyone. This would be an excellent gift for a bright middle schooler or high schooler who is interested in science, or for adults who enjoy trivia. Bryson covers all the main sub-disciplines, including cosmology, geology, chemistry, biology, archaeology, anthropology, and more. He also tells some stories about the scientists behind many major discoveries, but without overdoing it—ahem, Neil Degrasse Tyson. The breadth comes at the expense of depth, but that is not the worst of sins for a book like this. Interested readers can find plenty of additional reading for topics that spark their interest.

Bryson is a bit of a sensationalist, leaning heavily on apocalyptic scenarios wherever possible, from the odds of meteor strikes to catastrophic earthquakes or volcanic eruptions. This worst-first tendency harms his credibility as a narrator and gives off a bit of a boy crying wolf vibe, but one understands the strategy as a way to create excitement for younger people and scientific novices.

Giulia Enders – Gut: The Inside Story of Our Body’s Most Underrated Organ

Giulia Enders – Gut: The Inside Story of Our Body’s Most Underrated Organ

A good popular-science book about the digestive system. Enders offers insights about the digestive process, the human microbiome, how the body extracts nutrients from food, and more. One fun nugget is that the stomach “knows” how long to work on different types of food before passing it along to the intestines. Liquids can pass through in as little as ten minutes, whereas tougher-to-digest foods that need substantial breaking down can linger for several hours. Enders doesn’t offer anything groundbreaking here, nor is she offering s controversial new thesis. It’s just an enjoyable, if at times a little gross, way to learn some biology.

Simon Winchester – The Perfectionists: How Precision Engineers Created the Modern World

Simon Winchester – The Perfectionists: How Precision Engineers Created the Modern World

After a brief appreciation of the notion of precision and how it differs from accuracy, Winchester begins with the story of longitude and John Harrison’s precision clocks. The general organizational theme of the book is chronological, with engineers’ precision capabilities increasing over time.

Winchester is at his best in the lengthier middle chapters. In one, he compares two different kinds of precision—those espoused by Henry Ford and by Rolls Royce. In a Ford assembly line, workers needed almost no skill to fit the precision-made interchangeable parts together in mass quantity on the precisely designed assembly line. The handmade Rolls Royce instead emphasized that every aspect of the car must be hand-made to the most exacting precision by the world’s most skilled craftsmen, to the point that its factory could muster just two cars per day, compared to a new Model T every 40 seconds at Ford’s factory.

His chapter about the birth of the jet engine and the mind-boggling precision needed for its fan blades and other parts is similarly excellent. And the chapter on optics, beginning with how lenses are made and climaxing with the story of the Hubble Space Telescope, its initial blurry pictures due an almost unthinkably small mistake, and its 1993 repair done in space, is also a tour de force.

From there, Winchester goes into the history of the transistor, which nowadays requires atomic precision. Before too long, quantum computers may bring precision requirements down to the quantum realm. The book ends by returning to timekeeping. John Harrison’s famous H-4 clock has since been surpassed by atomic clocks and time-based GPS systems so precise they must take the theory of relativity into account.

Kim Stanley Robinson – Blue Mars

Kim Stanley Robinson – Blue Mars (Mars Trilogy, Book 3)

The conclusion to the trilogy. With Mars now politically independent and boasting a population of about 12 million, Robinson devotes substantial time to constitutional design and how to design a political system from scratch. Politics and economics are clearly not his expertise, but just going through the exercise with him and his characters is a lot of fun. About a quarter of the way through, some of the characters take a trip to Earth for diplomatic purposes. A few of them are among the Earth-born First Hundred to go Mars, and they don’t feel as though they’ve returned home. Nirgal, a second-generation Martian, has his own troubles adapting to Earth’s gravity and open atmosphere.

Robinson also devotes a lot of time to aging. Most of the characters take longevity treatments, and members of the First Hundred are a good 140-150 years old at the beginning of the book, with their apparent physiological ages topping out at about 70. Some of them make it well past 200. But there are tradeoffs to longevity that affect their memories, both short-term and long-term, as well as a number of sudden deaths.

There are also points where beauty and science mix. Descriptions of imported and genetically engineered Earth and plant wildlife are surprising and comforting at the same time. As far as sunsets go, Mars’ atmosphere extends much higher than Earth’s due to low gravity, and has lots of light-reflecting dust. Combined with atmospheric thickening from terraforming, and the characters get to admire sunsets that linger far longer than they do on Earth.

Timothy Ferris – The Science of Liberty: Democracy, Reason, and the Laws of Nature

Timothy Ferris – The Science of Liberty: Democracy, Reason, and the Laws of Nature

Ferris has an easy-reading prose style, a refreshing optimism, and an emphasis on reason and science as important ingredients in modern freedom and prosperity. At the same time, he oversells his case. This book is more for a general audience, and doesn’t need to delve as deeply as roughly similar-minded academics such as Joel Mokyr or Deirdre McCloskey. But there are points where Ferris is either painting with too broad a brush, or seems to not know his source material very well.

For example, possibly in his eagerness to link science and liberalism, Ferris claims Isaac Newton as a classical liberal. True, many of Newton’s achievements indeed furthered causes such as reason and empiricism. And Newton did much to raise scientists’ social status. His funeral stunned a young Voltaire, who “marveled at a society where a scientist was buried with the honors of a king.” But Newton was also something of a mystic who dabbled not just in alchemy, but maintained an active interest in millenarianism and the occult, which Ferris does not mention. Newton also had no known liberal political or economic philosophy.

At the other end of the spectrum, Ferris is a little too eager to draw a straight line from Rousseau to Napoleon to Hitler. Again, right impulse, but far too much of an oversimplification.

While I favor a big tent, Ferris’ definition of “liberal” seems to know few bounds, to the point of drawing more than one chuckle as I read. Despite this and other reservations, Ferris has the right spirit, and this book would be good for an interested undergrad or general reader, with the proviso that Mokyr or especially Deirdre are deeper, and more accurate thinkers.

Another quibble—he identifies F.A. Hayek as a Chicago school economist. Hayek did teach at the University of Chicago for several years, but not in the economics department. By that stage of his career, he had mostly moved on from technical economics and was exploring other disciplines such as political philosophy and law. Hayek is more a product of the Austrian liberal tradition of Menger, Mises, and Bohm-Bawerk, and a reaction against the German Historical School. Hayek was also influenced by earlier figures in the study of spontaneous orders such as David Hume, Adam Smith, Bernard Mandeville, and Adam Ferguson. This was a very different set of thinkers than the more concrete and empirical Chicago school, exemplified by thinkers such as Stigler, Peltzman, Gary Becker, Posner, Friedman, etc. If one were to draw a Venn diagram of the two schools’ intellectual roots, there would be some overlap. They still have distinct philosophical and methodological approaches.

Ferris also argues on page 169 that Thomas Carlyle coined the term “dismal science” in response to Thomas Malthus’ pessimism. This is inaccurate. Economic historian David Levy tells the full story in his book How the Dismal Science Got its Name (free PDF courtesy of the University of Michigan Press). Carlyle, a hardcore racist even by the standards of Victorian England, was frustrated with economists’ consistent abolitionism and defense of racial equality. He coined “dismal science” as an angry ad hominem. Malthus had nothing to do with it.

Ferris’ distinction between Bacon and Descartes is similarly broad-brush, but also a useful shorthand he returns to throughout the book. Bacon preferred hands-on experiments, just as liberal democracy is a constant process of trial and, often, error. Contrast this with Descartes, who preferred abstract deductive reasoning. Descartes’ approach to science that has parallels with top-down political orders based on intelligent design rather than messy emergent orders.

Ferris takes this framework through the Scientific Revolution, the Enlightenment, the American Revolution, the French Revolution, and up to today. While he oversells his case and needs to be a little more rigorous in his factual research, this is a good introduction to a powerful thesis: positive cultural attitudes towards science, reason, and progress are important ingredients in making possible the mass modern prosperity we enjoy today.

Rose George – Nine Pints: A Journey Through the Money, Medicine, and Mysteries of Blood

Rose George – Nine Pints: A Journey Through the Money, Medicine, and Mysteries of Blood

I was expecting a science-oriented book that would also touch on history and culture. Instead, George offers mostly ideology. Different chapters go through blood donations, leech treatment, the author’s work with HIV patients in South Africa, hemophilia, plasma, and other blood -related issues. The science, history, and culture of all these has the potential to be fascinating; perhaps I’ll find a book someday that does them justice.

In some cases, George’s strident ideology is for the good. HIV/AIDS patients do not deserve the social stigma they receive. The global hush-hush attitude towards menstruation, and the awful treatment of menstruating women in the world’s more illiberal regions, are blatantly unjust. George’s attempt to shed some light on the matters and move social norms in the right direction is needed and welcome.

But her hostility to paid blood donations is literally killing people. This is an inhumane stance she should immediately take back. She should at the very least listen to Georgetown University ethical philosopher Peter Jaworski‘s arguments. George’s virtue signaling contributes to easily-solved blood shortages that deny patients life-saving care for no good reason.

There is some good content in Nine Pints, just not enough. And George deserves praise for her advocacy on behalf of HIV/AIDS patients and women’s rights. But her amount and intensity of ideological posturing off-putting, and her anti-paid donation stance hurts sick and injured people around the world.

Stanley Kim Robinson – Green Mars (Mars Trilogy, Book Two)

Kim Stanley Robinson – Green Mars

The second volume of Robinson’s Mars trilogy, and more enjoyable than the first. The characters, style, setting, main plot points, and stylistic conventions were established in the first book, so this book can get to the point more quickly. Red Mars began with a barren, untouched planet with its first hundred colonists just getting started in 2026 (the series came out in the 1990s). By the end, 35 years of active terraforming and immigration were making a noticeable difference in habitability, and Mars even had its first political revolution in 2061. Green Mars starts several decades after that revolution.

Political stability and ongoing terraforming lead to Mars being able to sustain first lichens, and then plants in its thickening atmosphere and warming climate. Robinson shines as he describes the various terraforming methods they try, ranging from solar arrays in space that increase Mars’ solar gain to inducing volcanism to release greenhouse gases. By the end of the book, Mars has warmed enough to have some liquid surface water here and there—hence the third book’s title, Blue Mars. The atmosphere has also thickened and warmed enough for humans to breathe with only the aid of a breathing mask and some warm clothing. This comes in handy, as the book ends with another revolution and Mars declaring its independence from Earth.

Sabine Hossenfelder – Lost in Math: How Beauty Leads Physics Astray

Sabine Hossenfelder – Lost in Math: How Beauty Leads Physics Astray

Hossenfelder brilliantly covers the intersection of philosophy, hard science, and social science. She has a lot of wisdom about certainty, error, doubt, and why quantitative analysis is important and useful, but also prone to abuse. Her thesis is that a scientist’s proper goal is to understand the natural world. In that pursuit, many scientists get a little too caught up in constructing elegant mathematical models. Models and equations are useful when they add to understanding, which they often do. In fact, they are often vital to it. But models are a means, not an end.

To Hossenfelder, it is disconcerting how often scientists describe their models and equations as elegant. The word is everywhere. It appears constantly in scientific papers and conferences, in the classroom, and in popular-level books, magazine articles, and documentaries. Scientists sometimes even judge their theories and experimental results to be true or false based on whether they are viewed as beautiful or elegant. Even Einstein fell into this trap with his famous “God does not play dice” remark to express his unease with the Heisenberg uncertainty principle.

This is a problem because the universe does not care if people think it is beautiful or not. f=ma is either true, or it isn’t. Ptolemy’s laws, or Keplers, or Newton’s, or Einstein’s, or the string theorists’ ideas, are each either true or false. The answers do not depend on whether someone thinks they are elegant. Rather than chasing elegant ghosts, a scientist’s goal should be to get as close to objective understanding as possible, given human limitations.

Hossenfelder is a deep enough thinker to realize that our aesthetic sense likely evolved in response to our universe; causality runs both ways. It is not a coincidence that our eyes are most sensitive to the very E-M frequencies the sun sends our way, or that our ears respond precisely to the most common sound frequencies around us. In addition to our sensory organs’ capabilities being determined by evolutionary processes, so too did the way we interpret those sensory inputs.

Aesthetically, people tend to find beauty and elegance in evolutionary success, and ugliness in threats or failures to reproductive success. it is not a coincidence that signs of beauty are almost universally signs of youth, health, and fertility. Most people consider symmetrical faces more beautiful because symmetry correlates with good health, and with good genes. We prefer cleanliness over filth because bacteria and disease are bad for survival and reproductive success. So it makes sense that scientists, as humans who evolved in just this way, both have the aesthetic sense that they do, and that they feel compelled to find it in physics and other sciences.

If a symmetrical face is elegant and beautiful, so is a scientific equation that exactly has a given symmetry, or exactly fits a certain exponent. e=mc2 is much more appealing than, say, e=mc2.1. Some laws, such as this exchange rate between matter and energy, do have this elegant precision. This is fortunate, otherwise humans might never have discovered them! Other phenomena that are just as true are less elegant, such as entropy, the probabilism of quantum mechanics, or the way friction coefficients, alloys, and engineering tolerances all defy perfect precision in practice.

Our search for elegance in scientific research is a longstanding natural impulse redirected in a new and foreign direction. Humans have been a species for perhaps 200,000 years, and proper scientists for just a few hundred years–just a thousandth or two of that time. Our 200,000 years is in turn perhaps a touch more than one three thousandth of the animal kingdom’s existence. Our evolved aesthetic sense is very, very old. As such, it will be some time before evolution is able to adapt to our new social environment and address Hossenfelder’s concerns. Until then, the least we should do is be aware of our elegance problem.

While reading the book, I kept thinking it had just the sort of message that my former economics professor Russ Roberts would enjoy. One of the hallmarks of his approach is a conscious avoidance of certainty, and keeping in mind the difference between good and bad uses of statistics (Russ is also a keen and humble philosophical thinker). As it turns out, Russ had an excellent conversation with Hossenfelder on his EconTalk podcast. It’s worth a listen, especially for those who don’t have time to read the whole book.

Though Hossenfelder’s home is in physics, in several points during the book she acknowledges how her thinking applies to the social sciences. She’s right. Economists in particular would do well to consider her arguments. Her arguments about the parallel uses and abuses of mathematical modeling has some intersection with Jerry Z. Muller’s recent book The Tyranny of Metrics, though Hossenfelder’s arguments are more nuanced and broader-ranging, and have a deeper philosophical foundation.

Lost in Math also reminded me of F.A. Hayek’s The Counter-Revolution in Science, which distinguishes between science and scientism. As Hayek defines the terms, science is the process of learning about the universe and the beings who live in it. Scientism is more about method-worship, valuing mathematical rigor and elegance as its own end. When taken too far, scientism can color results and potentially stunt entire research programs and lines of inquiry.

This has happened in economics. Crudely, science and scientism can be personified as Adam Smith vs. Paul Samuelson–though again, very crudely. Peter Boettke contrasts mainline vs. mainstream economics to make a similar point. Smithian mainline economists are interested in the human condition; mainstream Samuelsonians are a little too interested in technical proficiency and elegant modeling. They would do well to focus a little less on Homo economicus, and a little more on the admirable and real, though admittedly less elegant, Homo sapiens.

Richard Panek – The Trouble with Gravity: Solving the Mystery Beneath Our Feet

Richard Panek – The Trouble with Gravity: Solving the Mystery Beneath Our Feet

More philosophical than I expected. Panek gives an excellent history of gravity, from Aristotle on down through Philoponus, Galileo, Newton, and on down the line. Philoponus, an Egypt-born 6th century Byzantine philosopher, was someone I was unfamiliar with, and it was a treat learning about a new figure in the history of science. He figures prominently early in the story, and more or less came up with the modern understanding of inertia, which he called impetus.

Unusually for his time, Philoponus was not content to rely on Aristotle and Plato’s works as settled fact. He preferred some measure of empiricism. He did not go as far as Francis Bacon’s audaciously titled New Organon (intended to replace Aristotle’s Organon, which was all but an eternal sacred text), but Philoponus’ empiricism was still controversial.

While Panek ably explains the science of gravity at a popular level, he is clearly more interested in the philosophy surrounding it. In particular, if you ask a scientist not what gravity is, but why it exists, they have no choice but to tell you they do not know. That, more than anything, is what interests Panek, and what drove him to write this book.

A good scientist has no problem admitting they do not know something, of course. A lifetime of study and experiment tells even the most brilliant scientist nothing about why, only about the what. Maybe someday we’ll gain that level of knowledge. But after so many attempts from Aristotle to Philoponus through today’s sophisticated experiments, Panek is not optimistic.