Review: Humble Pi

Humble Pi: When Math Goes Wrong in the Real World, Matt Parker. New York: Riverhead Books, 2020

Summary: An exploration of all the ways we use (and misuse) math in the real world, and the ways our calculations can go badly wrong.

Were you among those who wondered how on earth you would ever use that math you learned in high school? The truth is that even if you do not, there are others using that math in just about every aspect of our physical world from our bridges to our medical hardware to our buildings. The amazing thing is how we can describe and predict how things will work through our calculations. And sometimes, if we make a mistake, or a wrong assumption, those calculations can go badly wrong. Some of those mistakes are just amusing or complete nonsense. But some can be deadly…

Matt Parker explores many of the ways math goes wrong in the real world, citing dozens of real world examples for the different classes of math errors he discusses. He starts with how we lose track of time, particularly with our timekeeping rollover features on our computers. Usually, it’s no problem because they start counting each time we turn them on. But leave it running long enough for the time to roll over, and the world can come to a grinding halt, a real problem if it occurs mid-flight.

He discusses engineering problems, like the failure to calculate resonance effects on bridges and engineer to compensate for them. One of the most famous, and tragic, was the collapse of the Kansas City Hyatt Regency Walkways when the design of how sections of box beams were supported by nuts was changed without recalculating load limits. Then there are the errors that can creep into spreadsheet formulas and calculations that can produce misleading information on which businesses make decisions.

We often make counting mistakes with intervals. Like how many posts do you need to support a five section fence? (Six). We make geometry mistakes, like the example of the diagram of a soccer ball with all the sections, white and black, being hexagonal. This is not possible on a spherical ball which is why the white sections are hexagons and the black ones are pentagons. Shapes are important. Deformations on rocket boosters combined with cold circular O-rings spelled disaster on a space shuttle. Some are the minor difference in precisely engineered parts that are outside tolerances or times when conventions of measurement vary among those on the same project.

Many of the mistakes concern the peculiarities of computer calculations, including rounding errors and supposed randomization programs and errors of even a single line of code in an algorithm. Another math problem is what “average” means and what you do with that where most people aren’t “average.” So often, math and computer code are part of complex systems, that when changed, involve recalculating or reviewing every part. Often the things overlooked create problems.

Parker explains all of this in language even this non-mathematician can understand and includes many images and illustrations, making this an enjoyable read (while reminding us the acts of faith involved in everything from spreadsheets to suspension bridges to airplane flights). We assume talented people have made, checked, and rechecked calculations and code for accuracy. And most of the time, things work…except when they don’t.

He also alerts us to fallacies that we may encounter with statistics or so-called random numbers or even in how we count. What seems common sense is not in every case.

There’s one other interesting quirk in this book, and that is in the pagination, which is in reverse order, from 313 to zero, and then a roll over number, 4,294,967,294. I kind of liked it personally. How many times have you wondered, “how many pages left in this book?” In this case, the page number you are on is the answer! This feature may give you a sense of the light touch this author takes in a book dealing with ostensibly serious matters making it such a good read.

Review: The Artist and the Mathematician

The Artist and the Mathematician, Amir D. Aczel. New York: Thunder’s Mouth Press, 2006.

Summary: The story of the Bourbaki, named after the greatest mathematician who never existed, who led a revolution in the emergence of the “new math,” introducing a new rigor into the field.

When I was in middle school, we were introduced to “the new math.” One of the things I was always curious about was why the first thing we did was learn about sets. I was reminded of this when I read this book, which explained why sets were foundational to the approach.

This is the story of Nicolas Bourbaki, who convened a group of mostly French mathematicians around him, creating a tremendously productive group that in its day revolutionized the practice and teaching of math. Aczel introduces us to the key figures in this group–Andre Weil (brother of philosopher Simone Weil, not to be confused, as I did, with Andrew Wiles, who solved Fermat’s Last Theorem), Laurent Swartz, Henri Cartan, Claude Chevally, Jean Delsarte and Jean Dieudonne. We are also introduced to Alexandre Grothendieck, perhaps the most brilliant and also eccentric of them.

The most striking thing we learn is that the group formed around a mathematical joke upon which Weil built. Nicolas Bourbaki never existed except as a made up identity that reflected the collective effort of this group to rehabilitate and revolutionize mathematics in France that had fallen into the backwaters of German mathematics and science. These mathematicians met regularly and forged a consensus on how math would be practiced and taught in France that resulted in the prolific production of texts, revolutionized not only math education throughout the world, but touched a variety of other disciplines. Their approach was founded on set theory. They emphasized math in the abstract, focusing on mathematical proofs and rigor.

They were trying to articulate the structure of mathematics and this led to interesting interactions with pioneering anthropologist Claude Levi-Strauss, child psychologist Jean Piaget, linguistic theorists, and even writers including Italo Calvino. Aczel traces how structuralism for a time replaced existentialism in philosophy until the turn to the post-modern.

During the war Weil fled to America and stayed there, and gradually, his influence in Bourbaki waned. In the early 1950’s Alexandre Grothendieck joined for a time. His brilliance both stimulated the work of the Bourbaki and led to his departure as he recognized the weakness of set theory as a basis for Bourbaki, trying and failing to convince them of the idea of categories. Grothendieck differed from the Bourbaki, preferring to work alone.

The parting spelled a turning point for both. While Bourbaki continued to have a spreading influence for a time, it was more on the basis of past work. Grothendieck went on to do innovative work for a time, and directing students into significant problems. He held a position at the IHES, a French version of the Institute for Advance Study. Then he became more engaged in political and environmental causes, and when his efforts failed in these areas, he retreated to the Pyrenees, where his whereabouts remained unknown. After this work was published, he died in 2014 in Saint-Girons, Ariège.

The title of this work is a bit of a puzzle. Apart from a chapter on cubism, Braque, and Picasso, and its connections to antecedents to the Bourbaki, this is not a book about artists, unless this is a contrasting reference to Grothendieck and Weil, which was opaque to this reader. I found the organization of the book a bit labyrinthine. Nevertheless, it was an intriguing account of a movement in mathematics I’d never heard of. It was fascinating to see how productive this group was for a period and yet how significant the human factors were in the ultimate fate of Bourbaki.

Review: Mathematics for Human Flourishing

0569e4e1b4786e93a5b457eb58f2bb99 (1)

Mathematics for Human FlourishingFrancis Su, with reflections by Christopher Jackson. New Haven: Yale University Press, 2019.

Summary: An argument for the value of mathematics in all of our lives through meeting our deep desires and cultivating virtues helping us and others to flourish.

I have to admit approaching this book with both fascination, and a bit of trepidation. I was curious for how the author would demonstrate that math fosters human flourishing. And I was afraid that the book would reveal the deficit in my rusty math skills, that it would be a discussion of inside baseball, with me on the outside, as it were.

Francis Su sets us at ease from the earliest pages. He introduces us to a correspondent friend, Christopher Jackson and to Simone Weil. Jackson is in prison for armed robbery, connected with drug addiction, who won’t be released until 2033 at the earliest. Simone Weil was the younger sister of famed number theorist, André Weil. Simone Weil once said “Every being cries out to be read differently.” As it turns out, Jackson runs circles around most of us in his knowledge of advanced subjects in mathematics, and Weil loved mathematics, and more than held her own with her brother’s circle of friends.

Su’s appeal in this book is that we read others, and perhaps ourselves differently when we think of mathematics. For too long, he contends, we have left math to the whiz kids who can solve problems quickly and the eccentrics. For many of us, math is either irrelevant or a memory of shame. He contends we are all mathematicians, and all teachers of math and invites us to read ourselves, others, and the practice of mathematics differently.

His contention is that mathematics fosters human flourishing. We flourish as we develop certain virtues, and our pursuit of virtues is aroused by basic desires or longings. Longings like that of exploration, such as how to explain the gaps in the rings of Saturn. Or the longing for meaning, such as the stories we may use to make sense of the Pythagorean theorem. There is play, particularly as we explore the interesting patterns we find in math, engaging in inductive inquiry, and deductive reasoning to explain what we find. We come up with shortcuts, and try to figure out why they work. We long for beauty, and discover it in the sensory beauty of a fractal, the wondrous beauty of an elegant equation, the insightful beauty of the dualities in math (multiplication and division, sine and cosine), and the transcendent beauty when we realize that math can explain the world. We long for permanence and truth and find these in mathematical ideas that do not change.

Math cultivates virtue as we struggle. Su gives the lie to the whiz kid who comes up with the quick solution. Real creativity in math involves struggle, the failed solutions that lead to a novel way of seeing the problem that yields the solution. Math’s power may be coercive or creative. The creative use of power multiplies math’s power in the lives of others rather than showing oneself to be powerful. Math can be used to include or exclude and may be a source of either justice or injustice. Math can be a source of freedom–particularly if it is coupled with justice and extend welcome to all. When this happens, mathematics creates good communities, not ones that exclude those who don’t “measure up.” Math sees everyone as capable of discovery in math. Suddenly, you have a group of people engaged in joyous discovery.

Above all, Su believes that love is the ultimate virtue in math as in all things. This is not merely the love of math, but the love of people that believes “that you and every person in your life can flourish in mathematics.” One of the beauties of this book is that Su models this in the respectful way he engages Christopher’s questions and desire to learn math. It is evident that he sought Christopher’s advice on the book, and includes in each chapter one of Christopher’s reflections. At the end of the epilogue, an interaction between the author and Christopher, Su mentions that Christopher will share in the book’s royalties.

When you read this book, I suspect you will agree that Francis Su is the math teacher we all wish we had. He reminded me of one high school teacher, Mr. Erickson, who made math fun, and was not above engaging in dialogues with his invisible friend Harvey during class. Su helps us to discover the fun in math by including math puzzles in each chapter. He offers hints or solutions to each in the back, but I was reminded of the math puzzles I used to delight solving in Mr. Erickson’s class, and as a kid. I found myself wanting to find some math books and brush up my math. He got me curious about the mathematical realities I could do well to pay more attention to, like trying to make sense out of the analytics on a website and what the patterns mean, or the correlation between voting percentages and incarceration patterns.

I wonder if others will have this reaction and if in fact that is the author’s intent. Even teachers can lose their “first love” of math, and lose touch with the desires that math aroused in their lives. Might renewal come with remembering, remembering ourselves as we consider the student before us,  allowing that remembering to shape how we teach? Su does us a valuable service in awakening us to the ways we flourish through math, motivating us to share with others the abundance we have discovered, even as Christopher now teaches other inmates the math he has learned, flourishing even more as he does so.


Disclosure of Material Connection: I received a complimentary review copy of this book from the publisher. The opinions I have expressed are my own.

Review: Faith Across the Multiverse

faith across the multiverse

Faith Across the Multiverse: Parables from Modern Science, Andy Walsh. Peabody, MA: Hendrickson Publishers, 2018.

Summary: Explores how science, particularly math, physics, biology, and computer science, might illuminate one’s understanding of the Bible and the God of the Bible.

In his parables, Jesus spoke of various natural phenomenon to help us understand the kingdom of God–seeds, birds of the air, lilies of the fields, yeast, sheep, and more. God invites Abraham to count the stars and questions Job about the creation. In Faith Across the Multiverse, Andy Walsh asks the question of how various observable phenomenon and theories in science might illuminate our understanding of God, the Bible and spiritual realities. He focuses his inquiry in the fields of math, physics, biology, and computer science, reflecting his background in several of these fields. His day job is Chief Science Officer at Health Monitoring Systems where he develops statistical methods for public health surveillance. His doctoral and post-doctoral work was in fields of molecular biology and immunology and computational biology. He writes a weekly science column for InterVarsity’s Emerging Scholars Network blog.  It is also important to know that Andy is a fan of super-hero comics, particularly X-Men and he mixes these characters and stories, along with popular science fiction into his discussion of science and faith.

In the realm of mathematics, he explores faith as a choice of axioms, sin in terms of mathematical optimization and choosing an objective function to maximize. Most fascinating for me was his use of chaos dynamics as a possible way to understand sovereign grace in which various paths might lead to the same outcome, as is the case with “strange attractors.”

In the realm of physics, he follows John Polkinghorne in discussions of how the dual wave/particle character of light might give us insight into the incarnation of Jesus. He also explores how entropy might help us understand sin and death, and the transformative work of dying to oneself in Christ.

The biology of the genome, our immune systems, and even the constitution of ant colonies may shed light on the relational dynamics and nature of the church. The world of computer science, in which simple rules, procedures, and inputs may result in complex outcomes suggest how a single book, the Bible might be able to address the complexities of human existence throughout our history.

The book has the feel of being written for “science nerds,” kind of like the characters one encounters on The Big Bang Theory, who geek out on in-depth discussions of scientific theory, punctuated by excursions to the comic book store and debates over Star Trek versus Star Wars. Walsh writes, “One feature of the world that pains me and I believe pains God is the fact that so many feel they need to choose between science and belief in the God of the Bible.” I’ve worked with “science nerds” in graduate student ministry, and I can vouch that there many who think science and faith are mutually exclusive. Walsh’s careful explanation of scientific theories and phenomenon, which may be off-putting for some, establishes for the scientifically literate grounds for drawing the connections or “parables” of science and Christian belief. The effect of his discussion is both to suggest a consonance between science and Christian beliefs for the skeptic, and to shed fresh light from science on Christian belief for those who do believe. The frequent references to comic superheroes makes this all the more fun.

I suspect this book was not written for a social science-liberal arts-theology nerd like me. I’ll confess that I haven’t solved a math equation since college, and while I enjoy general science writing, the depth of explanations was a stretch for me, that made me flex some under-used mental muscles. I suspect my math geek, computer scientist son would love this book, particularly the portions on fractals and chaos mathematics. There are significant numbers like him out there, and many question whether there is even room for Christian belief in a world shaped by science and technology. Andy Walsh writes as one of them who hopes to remove the barriers between science and belief by sharing the ways his own research and other science reading has enriched his understanding of and love for God.


Disclosure of Material Connection: I received a complimentary review copy of this book from the publisher in exchange for an honest review. The opinions I have expressed are my own.

What Mr. Erickson Knew


Julian Fractal, By GARDEN [Public domain], via Wikimedia Commons

One of my favorite high school teachers was Mr. Erickson. He taught math, and also an introductory computer science class in the early days of computers. I did pretty well in math, even though it wasn’t a favorite subject. Mostly, I enjoyed Mr. Erickson because he enjoyed math (and some corny jokes)–it wasn’t just numbers and equations and laws to him, but rather something beautiful that could describe the order of the world and translate “the music of the spheres” into an equation.

I haven’t thought about Mr. Erickson for a long time. But two occurrences in my life recently have brought him to mind. One is that my son, a software engineer for a local company spent his vacation at a conference in Waterloo, Canada exploring the intersection of math and art. Back in elementary school, he had a teacher kind of like Mr. Erickson, who introduced him to fractals. He has never lost his fascination with this geometric patterns that often look like objects in the natural world (and sometimes not) that can be described in mathematical equations and produce repeating patterns at smaller and smaller scales. He has a shelf of graduate level texts at home on fractals (guess what is on his Christmas wish list!) and even has several fractal-related publications (as well as a work of fiction) you can purchase. The conference brought mathematicians and artists together to explore the connection between these two seemingly unrelated aspects of life–in visual art, music, and even opera and poetry from what I’m told.

The other occurrence is reading Stratford Caldecott’s Beauty for Truth’s SakeCaldecott argues that one of the great deficits in our modern educational program is the divorce of the liberal arts from math and the sciences.  This reflects a loss of vision for the unity and interconnectedness of all truth, and perhaps belief in the One in whom they are connected. In a chapter on math, he explores numbers and their expressions geometrically, their significance in a variety of areas of life (musical chords, the use of numerical and geometric properties by visual artists, recurring numbers in the Bible, and the ways mathematics maps onto the world, and more). Somehow, numbers and equations connect to imagination, and reflect beauty. Why is that?

Math and beauty? What Caldecott, Mr. Erickson, and my son all seem to get that I think I’ve lost sight of is the beauty that lies hidden in the equations. In my world, math gets reduced to spreadsheets, financial reports, columns of figures, raw data. Perhaps I’ve bought into that divorce between math and the world of the imagination and the beauty of the world. Perhaps it is time to recall the joy Mr. Erickson had when he explained the beauty in the equations. Perhaps…