Natural Science #12: Square-Cube Law

In 1638, Galileo Galilei described a simple law:

The ratio of two volumes is greater than the ratio of their surfaces.

To understand what Galileo was talking about, just imagine a cube. If you double the size of a cube, the surface area increases by the square of the length (2len2) and volume increases by the cube of the length (2len3). The surface area will be 4 times larger (22 = 4) and the volume will be 8 times larger (23 = 8). The ratio of volumes is greater than the ratio of surfaces.

The square-cube law says that as a shape grows in size, its volume grows faster than its surface area. This turns out to be a powerful idea for many scientific fields. For example, in mechanical engineering, it explains why a scale model engine won’t account for the heat loss of a full-scale engine, or why an airplane’s wings need to scale faster than the planes fuselage, or why building taller and taller skyscrapers is increasingly difficult.

Continue reading “Natural Science #12: Square-Cube Law”


History #15: Protestant Reformation

In the early 16th century, there was one church in Western Europe – the Roman Catholic Church. Then came Martin Luther and the protestant reformation. Like the name suggests, Luther spoke out against the church and sought change. Protest and reform.

Eventually, the Roman Catholic Church split, then split again, and again. Today, there are uncountable Protestant denominations – Baptist, Anabaptist, Methodist, Calvinist, Anglican, Quaker, Lutheran, Apostolic Lutheran, Reformed Lutheran, Free Lutheran, etc. But this idea of protest and reform wasn’t limited to the spiritual, much of the modern world has been shaped by it. The civil rights movement was primarily led by protestant clergy, including Martin Luther King Jr who was named after Martin Luther. The American revolution was a protest for individual rights. The scientific revolution was a protest for new ways of understanding the world. At each step in humanity’s progress, old ideas need to be reevaluated and reformed.

If we buy into this idea of progress, then we owe a lot to one man in the 1500s who broke a church’s 1000 year monopoly on politics and spirituality.

Continue reading “History #15: Protestant Reformation”

Human Nature #15: Attribution Error

Imagine you’re driving down a road, minding your own business, then suddenly¬†you’re cut-off by another driver. A natural response might be to assume the other driver is impatient, reckless, and probably a complete asshole.

Now flip the script. You are racing down the road to get to the hospital. Your wounded spouse sits in the back. You notice another car merging into your lane. It appears that they are going to hit you so you act quickly, swerving into another lane by cutting someone off. You don’t think twice about it. You don’t think you are impatient, reckless, or a complete asshole. A minute later someone cuts you off. You think to yourself “what a jerk”.

When dealing with other people, our tendency to place an undue emphasis on internal characteristics while downplaying external factors is known as the fundamental attribution error.

Continue reading “Human Nature #15: Attribution Error”

Numeracy #15: Male Population Puzzle

Question: Consider a country where every family wants to have a boy. Each family continues having babies until the arrival of a boy and then they stop reproducing. After years go by, what will be the proportion of boys to girls in the country? Assume that there is a 50% chance of having either a boy or a girl.

As always, try solving the problem yourself or keep reading for the solution.

Continue reading “Numeracy #15: Male Population Puzzle”

Economics #3: Comparative Advantage

In 1776, Adam Smith popularized the idea of specialization:

If a foreign country can supply us with a commodity cheaper than we ourselves can make it, better buy it of them with some part of the produce of our own industry employed in a way in which we have some advantage.

For example, if we are good at brain surgery and bad at making shoes, it makes sense to focus on brain surgery and trade for shoes. Same goes for legal work, accounting work, landscaping work, etc. If they guy down the street can do my taxes better than I can, I should ask him to do them. But what happens if we are better at everything? We can perform brain surgery, make shoes, practice law, file tax returns, and mow our lawn better than anyone else could. Do we just do everything ourselves?

In 1817, David Ricardo sought an answer to this question in the context of international trade. Why would a country that was better at producing everything, trade with a country that was worse at producing everything?

Continue reading “Economics #3: Comparative Advantage”

History #14: How WWI Started

On June 28, 1914, the Archduke Franz Ferdinand was assassinated while visiting a freshly annexed Bosnia-Herzegovina. A month later, on July 28, 1914, Austria declared war on Serbia. By August 4, 1914, a week later, Britain, France, Russia, Germany, Austria, and Serbia were at war.

In about the span of a month, what started as a localized terrorist attack in Southeastern Europe, grew into a continent-wide war that still resonates today. Looking back, it’s easy to connect the dots, but for the diplomats living at the time, the outcomes of their actions were anything but clear.

We study World War I to remember this. To remember that we are always one month away from possible catastrophe – one misunderstanding away from World War III. We do what we can to reduce the likelihood of that outcome.

Continue reading “History #14: How WWI Started”

Human Nature #14: Illusion of Control

Have you ever found yourself pressing an elevator button multiple times or with greater force? Have you ever found yourself blowing on a pair of dice or standing up for your team’s attempt at a winning play? In these examples, our actions have no effect on the outcome but we still feel like we have some influence on the situation.

In the 1970s, Ellen Langer ran a series of experiments showing that if you introduced some non-chance task into a random event, you could create an illusion of control. In one experiment, a subject and an actor took turns drawing from a fair deck of cards. The high card would win and the subjects could bet money on each turn. Subjects who were up against an awkwardly dressed actor would consistently bet more than subjects who were up against a professionally dressed actor.

Continue reading “Human Nature #14: Illusion of Control”

Numeracy #14: Probability of Car Passing By

Question: The probability of a car passing a certain intersection in a 30 minute window is 0.95. What is the probability of a car passing the intersection in a 10 minute window? Assume that the cars are randomly distributed.

Try solving the problem yourself or keep reading for the solution.

Continue reading “Numeracy #14: Probability of Car Passing By”

Investment Theory #13: Buffett’s 1968 Letter

In 1956, Warren Buffett concluded his work for Benjamin Graham and returned to Omaha, where he started an investment partnership. This partnership was formed with seven limited partners, made up of family and friends, contributing $105,000, and Warren Buffet contributing $100. It grew over time.

This post continues my series about that partnership. The goal is to gain some insight into one of the most successful investment vehicles in modern history.

Links to past years can be found here: 1957, 1958, 1959, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967

Continue reading “Investment Theory #13: Buffett’s 1968 Letter”

Economics #2: Financial Instability Hypothesis

On January 13, 2010, the chief executives of four top Wall Street institutions gathered together in Washington to testify on what went wrong in the years leading up to the great recession. Jamie Dimon, the CEO of JPMorgan Chase, noted that:

In mortgage underwriting, we somehow missed that home prices don’t go up forever.

Lloyd Blankfein, the CEO of Goldman Sachs, added:

Whatever we did, it didn’t work out well. We were going to bed every night with more risk than any responsible manager would want to have.

Continue reading “Economics #2: Financial Instability Hypothesis”