Archives for posts with tag: math

There are few people who would argue with the statement that math is at the heart for most of our modern world. What is less well understood is what happens when that math goes wrong. And it does. All the time!

Mr. Parker’s highly amusing and thought-provoking book is about math and computers, but what becomes clearer as the book goes on is that this is also a book about systems and how and why systems can fail. There are lots of examples of people adding up numbers incorrectly or trying to take shortcuts to make the math simpler, which in turn leads to devastating and sometimes lethal consequences. However, it the subtler applications of mathematics where “Humble Pi” really scores.

For example, looking at 30- or 40-year-old kitchen appliance, still in use, is often accompanied by a phrase such as “they don’t make things today like they used to.” While this might seem obvious at first glance given that we are talking about an appliance working well beyond its expected lifespan, this is actually an example of “Survivor Bias.” If we looked at how many of the appliances had been manufactured, and then looked at how many were still in daily use, the chances are that we would recognize that this surviving appliance is an outlier and that the vast majority of the appliances have actually long been replaced or broken down. It is only the existence of this surviving outlier that prompts the idea even though we would likely not comment on its existence were more of the appliances in existence. The appliance’s rarity generates a false narrative that can only be understood by understanding the underlying math of the number of appliances produced.

For managers there is much to take away from Humble Pi. Mr. Parker encourages us to look at systems like layers of sliced Swiss cheese. All systems should be made of multiple layers – the checks and balances of any good system. But it is important to understand that there are possibilities for mistakes in every layer of a system – the holes in the cheese. The challenge as designers of systems is to ensure that the holes in each layer do not align. The author uses the example of two different nurses in a hospital performing a complicated drug calculation the same way and both making the same math mistake leading to a medical error.

Related to this idea of errors being a natural part of a system is the impact of a lack of tolerance for errors on new employee training. If managers terminate employees for making mistakes, the people who are left to train new employees are those who are must less likely to make mistakes. These are probably the worst people to train new employees who are obviously more prone to making mistakes. If instead, we teach employees to work a system that can detect mistakes and provide feedback, a system where the holes do not line up, then we will overall have far less mistakes – even when people are new. As the books says, humans can be very resourceful in finding ways to make mistakes.

This is not just a book about rounding errors, and why you should turn your computer off regularly. It is a book about what it means to be human in a world that relies and is built on mathematics, which humans are inherently not very good at. It is a fun and interesting read that will stay with you long after you put it down.

(Clicking on the image above will take you to Amazon where a tiny percentage goes to help my movie and book buying habit.)


Statistics, standardized testing, crime prediction, Google, Facebook, “Moneyballing,” insurance risk analysis, and mathematical models all have one thing in common; they can all fall into the catch all term of “big data.”

There are very few parts of modern life that are not impacted by big data; for better or for worse. The mathematical models that harness vast amounts of data are used for everything:  to determine who should receive a bank loan, which teachers should be fired, whether to hire a particular worker, where police should patrol, which colleges are the best to apply to, which students should offered a place in a college, how sports are played, and even the sentences that convicted criminals should receive.

Some of these mathematical models are transparent.  The model featured in the book and movie “Moneyball” (you can read my review of the movie here) would be an example of a transparent model. The data and the rules that lead to the model’s conclusions are open and available for everyone to see. However, more and more, the models are opaque and it is these models that Ms. O’Neil goes after with devastating logic and passion.

The fundamental issue with these opaque models, other than a lack of openness and therefore the impossibility to challenge their assumptions, is that they can suffer from a lack of feedback or create self-reinforcing feedback loops. Because the models are opaque, many people may not even realize that are in a mathematical model, or that the model is partially or wholly responsible for their circumstance.

As Ms. O’Neil states in her introduction: “Without feedback; however, a statistical engine can continue spinning out faulty and damaging analysis while never learning from its mistakes. Many of the W.M.D’s (Weapons of Math Destruction) I’ll be discussing in this book … behave like that. They define their own reality and use it to justify their results. This type of model is self-perpetuating, highly destructive, and very common.”

Ms. O’Neil does go to some great lengths to stress that a lot of these models have been built with the intention of being fairer. The idea being that removing flawed human beings from decisions that could be made by mathematical models would remove their biases and faulty logic from the progress. However, it is these same flawed humans that are creating the models and without proper feedback, monitoring, and proper understanding of statistics, the models themselves can cause far worse problems than the ones they are supposed to solve.

Written for the layperson, about a subject that would cause most peoples eyes to glaze over unless written by Ms. O’Neil, this is a great and important book and one that I feel will become only more important as mathematical models become even more entwined in our lives. This is also an important book for those is position to make use of mathematical models in their business as there can be significant pressure to accept the word of a program when we should be asking some pretty hard and detailed questions; not only to ensure that what we are getting is correct, but also to ensure that we are not contributing to the Weapons of Math Destruction problem.

Garbage in – Garbage out, has never been more apt.  

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