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Critical Mass, Length, Temperature Many systems and processes—whether in nature or society—can appear unchanging until they reach a certain transition point, after which their behavior shifts dramatically. Think of disease outbreaks, the spread of information in a network, or battery failures in electric vehicles. Let’s go through some examples. Disease Outbreaks Consider a disease outbreak such as COVID-19 in 2020. The goal of many governments was not just to reduce infections slightly, but to bring the average number of new infections per case—known as the reproduction number, or \(R_0\) —below the critical threshold of 1. When \(R_0 < 1\) , each infected person, on average, transmits the disease to fewer than one other person, and the outbreak dies out. However, if \(R_0 > 1\) even by a small margin, the number of infections can grow exponentially. ...

Do you trust your calculations? This book review is about The Los Alamos Primer, the first lectures on how to build an atomic bomb, by Robert Serber. The review focuses on the basic calculations and physics knowledge of the Manhattan Project scientists. Since the Primer is a collection of 1943 lecture notes combined with Serber’s hindsight commentary, it corrects some of the original calculations and measurements by comparing them with modern values. This makes it fascinating to see how close—or off—the physicists were at the time. For anyone interested in the topic, I highly recommend reading both the Primer and The Making of the Atomic Bomb by Richard Rhodes, one of my all-time favorite books. ...

The Mystery of Inequality Why are some countries rich and stable while their neighbors are poor and chaotic? In their 2012 book Why Nations Fail, Daron Acemoglu and James A. Robinson argue that the answer isn’t geography, culture, or luck. It comes down to one thing: institutions. The authors open with a perfect real-world experiment: the city of Nogales. A fence cuts the city in half. North (Arizona, USA): Residents have property rights, a functioning legal system, and can vote people out of office. They are relatively wealthy and healthy. South (Sonora, Mexico): Just a few feet away, residents face corruption, unreliable laws, and economic instability. They earn a fraction of what their northern neighbors do. Both sides share the same geography, the same climate, and the same culture. The only difference is the system they live in. ...

What is it? Why is it interesting? Consider a toy example of a gamble. Someone offers you a game where a fair coin will be tossed: you will win 70% of the money you bet when heads comes up and lose 60% of the money you bet when tails comes up. Furthermore, you are offered the opportunity to play this game many times, although not arbitrarily often, say just once a day. Intuitively, this gamble seems favorable, especially when you are allowed to play it repeatedly. However, it becomes trickier when you ask yourself questions like, “How much of my total wealth should I bet?” and “What is the best strategy to maximize my long-term wealth, say over 10 years?” The Kelly Criterion provides the answer to these questions! ...