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.
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