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

Better for All the World by Harry Bruinius

The Drunkard’s Walk by Leonard Mlodinow

The Feud that Sparked the Renaissance by Paul Robert Walker

The Numerati by Stephen Baker

Rock Breaks Scissors by William Poundstone

The Unfinished Game by Keith Devlin

War Against the Weak by Edwin Black

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

Smarter Faster Better by Charles Duhigg

You may be like me in the sense of wanting to get more done and falling short. I realize I can’t do all the things I imagine I might do. There aren’t enough hours in life for it and I can let much of it go. However, there are some things that are important to me. It bothers me that I make so little progress on them.

Journalist Charles Duhigg considers this problem of productivity in Smarter Faster Better. Rather than turning to standard self-help fare, he sought out scientifically supported strategies.

For instance, there is a lots said in self-help books about motivation. Duhigg makes the interesting point that motivation can be learned. We can learn to push ourselves to make decisions and take action.

That is a neat concept. If you see motivation as a skill, you can quit beating yourself up and accept that you are not good at motivating yourself yet. Instead, you can focus on improving the skill. You can reward yourself for the effort—however imperfect—and seek lessons to do better next time.

You might start with Duhigg’s tip to think of what it feels like to be in control and how good it is. The memory, and the positive emotion attached to it, may be the boost that gets you moving. Also ask yourself why you are doing something; uncover why it is meaningful to you.

You can learn to pay attention to the right things at the right time, too. Productive people have good mental models that help them ignore the noise and see the details that make a difference. You can develop these models by telling yourself stories throughout the day about what you expect, why you expect it and how your experience matches or varies from the tale.

This imagination can help you make decisions. We can’t know the future, but if we accept uncertainty and imagine the possibilities—good and bad—we can make good guesses.

Another bit of advice from Duhigg is that when you learn something new, you should do something with it. In the last chapter of the book, he recaps by showing how he used the strategies to get his research and writing done.

Charles Duhigg also wrote The Power of Habit.

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

A Mind for Numbers by Barbara A. Oakley

The Big Thing by Phyllis Korkki

Future Bright by Martin E. Martinez

The Genius in All of Us by David Shenk

Get Smart! by Brian Tracy

Learn Better by Ulrich Boser

Level Up Your Life by Steve Kamb

Mindset by Carol S. Dweck

The Organized Mind by Daniel J. Levitin

The Procrastination Equation by Piers Steel

Rapt by Winifred Gallagher

Duhigg, Charles. Smarter Faster Better: The Secrets to Being Productive in Life and Business. New York: Random House, 2016.

Loserthink by Scott Adams

 America is awash in debate, but it seems there is very little actual discussion or argument happening. Many talk by each other and simply become more entrenched in their positions, or they adopt more extreme, outrageous or nonsensical views. It does not help that politicians and pundits engage in the same kind of thing and seem to encourage it in others. In addition, television and radio broadcasts are full of it, propagating the noise, perhaps emphasizing one side or the other, but rarely providing useful new facts or analysis.

I see this on social media a lot. I see a lot more people parroting or sharing a juicy tidbit that they seem to think carries a point (the point is not always clear and the facts are sometimes just wrong), but I rarely see someone address and issue with humility, reason or an admission of uncertainty.

Cartoonist Scott Adams noticed it in his social media interactions, too. He attributes some of this to the complexity of the world we live in and the issues we deal with; human beings are not very good and understating complexity. In addition, most people aren’t trained to think productively to produce reasonable solutions. As he put it in his book Loserthink, “Despite evidence to the contrary, we all use our brains. But most of us have never learned to think effectively.”

Loserthink is Adams’ term for unproductive, ineffective ways of thinking. He generously thinks that people are not stupid, they are just using unhelpful, unfruitful patterns of thinking.  You will get nowhere trying to shame people for stupidity, but you might get somewhere if you engage people in seeing how ridiculous is loserthink, and how it produces divisions that generally don’t benefit us (though it might benefit some).

Most of the book is devoted to identifying common types of loserthink an how to think more productively. He draws on ways of thinking from various professions and disciplines in which people are trained in thinking and problem solving: psychologists, artists, historians, engineers, leaders, entrepreneurs and economists.

Adams expresses some opinions about political and social issues that are likely to be controversial to some. Rather than take as evidence that you are right or that Adams is a dunce, take it as challenge to think things through for yourself. Test yourself to see if you might be engaging in loserthink. It might not change your mind, but it is likely to make you more modest about your certainty in some area, more confident in the workability of your solutions in others and generally more persuasive because you have check yourself for loserthink and you can gently help other address theirs.

Scott Adams also wrote

How to Fail at Almost Anything and Still Win Big

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

Bored and Brilliant by Manoush Zomorodi

The Checklist Manifesto by Atul Gawande

Choosing Civility by P. M. Forni

Freakonomics by Steven D. Levitt & Stephen J. Dubner

Histories and Fallacies by Carl R. Trueman

How Not to Be Wrong by Jordan Ellenberg

Range by David Epstein

Six Easy Pieces by Richard Feynman

The Thinking Life by P. M. Forni

Adams, Scott. Loserthink: How Untrained Brains are Ruining America. New York: Portfolio/Penguin, 2019.

Public Utility Depreciation by NARUC

I don’t usually read reference books, or textbooks, all the way through like I did with Public Utility Depreciation Practices. Because of my new job as a “depreciation engineer,” I undertook reading this guide from the National Association of Regulatory Utility Commissioners (NARUC).

The title describes the content of the book. It includes some historical and legal background, but the bulk of the book is aimed at the practicalities of determining depreciation expenses.

The main elements going into depreciation rate determination are depreciation base, service life, net salvage, and depreciation computation methods. Depreciation base is the starting point; it represents the initial investment of capital that is to be recovered as a cost through depreciation. Generally it is the book cost (original cost of the infrastructure including materials, equipment, labor and related costs).

Most methods of computing depreciation are referred to as age-life methods. These methods spread the cost of the expected life of a piece of infrastructure. The preferred method is straight line depreciation. To apply these methods, one will need to know or estimate the life of the infrastructure under consideration and the net salvage value. The depreciation rate is the difference between the base and the net salvage, divided by the life of the infrastructure. With the exception of unique pieces, like types of infrastructure are lumped together because they are expected to have a similar life (wooden poles, steel poles, copper wire, conduit, etc.).

Life expectancy can be estimated by several methods. Survivor curves are developed from statistical studies of the life of particular types of infrastructure, though other methods may be used depending on the type and quality of data available.

Net salvage is estimated based on experience. The gross salvage is the price received for the equipment or materials retired. The cost of removal is subtracted from this to calculate the net salvage. Sometimes it can cost more to remove infrastructure than the value of the retired equipment and materials, so net salvage can be negative.

Calculating depreciation is more art than science. Projections of future values are inherently tricky. Growth can cause infrastructure to become inadequate before it is expected, or slower than expected growth can extend the life infrastructure. New regulations can make infrastructure obsolete in an instant, as can new technologies. In addition, utilities are constantly adding and retiring infrastructure. Amidst this uncertainty, regulators must balance the level of service needed by utility customers with the returns needed by utility investors in a complex environment.

Admittedly, a book from 1968 may seem dated. However, many of the practices described are still in use. Government regulation of monopoly utility rates in the United States has been occurring for more than a century, and the practices to not change rapidly. Even so, some of the practices described were considered obsolete, or near obsolescence, at the time of publication, and are not likely to be encountered now unless you’re a financial historian combing through moldy account books.

National Association of Regulatory Utility Commissioners. Public Utility Depreciation Practices. 1968. Washington, DC: Author, 1974.

Chance by Amir Aczel

Aczel, Amir D. Chance: A Guide to Love, the Stock Market, and Just About Everything Else. New York: MJF Books, 2004.
ISBN-13: 978-1-56731-735-0
ISBN-10: 1-56731-735-9

Chance is an introduction to the basic principles of probability and how they can be applied to understanding real-life activities. The math is not difficult. Someone with a good foundation in arithmetic and algebra should be able to follow it. Where more advanced math might be needed, Aczel presents the gist and moves on.

One of the interesting issues brought up in the book is how probability can give rise to counterintuitive situations. What we sense may be the likelihood of something may be very different than the probability worked out mathematically—the math better fits reality. One of these examples is how random events can, and often do, result in unexpected aggregations. For example, a fair coin has equal chances of coming up heads or tails, but if you flip it enough times, you’ll find times when heads (or tails) may be repeated in hundreds or thousands of sequential flips. Unlike events can be surprisingly likely if given enough trials.

This may be why unlikely things sometimes happen in gambling, because it is so common. Aczel acknowledges the early history of probability as a way to understand gambling problems. He draws several examples from casino games, poker and horseracing. The mathematician’s admonition concerning casino gambling is don’t do it. Most betting games are good examples of probability because the potential risks and payoffs are known. Poker provides and example of dealing with uncertainty. For those who follow the ponies, an appendix by Brad Johnson provides an understandable description of how pari-mutuel betting works.


Not all the examples are drawn from gambling. Aczel also describes how probability relates to polling and polling errors, coincidences, and making choices in life and in games.

A drawback of the edition I read was typographical errors in some of the mathematical formulas and equations. Those familiar with the notation will quickly sort out what was intended, and others can follow the text. In one instance, the formula is made wrong by the typo, but the text describes it correctly.