Back to Humble Pi. I actually think Innumeracy: Mathematical Illiteracy and its Consequences did a better job at being a book about math. Humble Pi was a lot about design and engineering omissions. But it also did a good job summarizing how we can avoid mistakes and drawing trends through the faults that have decreased our time, money, and safety throughout history.
One running theme of the book is that human brains are just bad at thinking about large numbers. A meme going around a long time ago asked a question about Obamacare expenses... if the affordable care act was going to cost us $340 million dollars, and the US population is 330 million people, why not just give everybody one million dollars? 340/330 is about one, and the unit is "millions", right? Except that's not how units work, and we'd all get a dollar, and no healthcare.
We are also bad at making judgements about how much memory a computer could possibly need, how many bits will be needed to store a date (this'll work for decades, surely we'll be using all new technology by then!). We think an object is precise enough or easy to figure out or fool-proof, and we are wrong. Errors tend to stack up. The book talks a lot about the "swiss cheese" model of failures - it takes several mistakes to cause the worst.
And the sad part is, we don't look at each other's mistakes much or learn from other industries because mistakes are shameful and we are secretive about it. We are afraid of exposing weakness.
So it's the big obvious failures we end up reading about. Crumbling bridges, space shuttle explosions, exits that don't let people escape, unit conversion failures, memory allocation bugs, compatibility conflicts.
One of the errors he talked about, I just DID. So I'll fess up to it. I scheduled a meeting for team members around the world to call in to. I set it to 9am. Most of Europe didn't call in. I just figured I wasn't popular - but nope. The issue was that we went to daylight savings time on March 8, but Europe doesn't go until March 29th. They were all an hour late and missed the call. Oops. The book has a whole chapter about calendars and how incredibly long it took us to all agree on how months, days, years and hours should work... we're still not there!
I think the author would sympathize with my experiences in pregnancy communities trying to convert weeks to months. He's never been pregnant, so he can't understand my struggle, but it was real.
So good luck, designers. Check your math.