How Humans Achieved Flourishing Societies George Angwin, 12 July 2022 The energy we use to power our civilization has two sources: solar radiation and radioactive decay. In turn, some of the solar radiation is converted into glucose by photosynthesis. The glucose is stored in plants and in their parasites and symbiotes. Animals, includ...

George Angwin, 16 March 2022 Many news reports compare electricity rates in different parts of the United States and other countries. I find these comparisons suspicious because of the ambiguities in the term "electricity rates". My February electricity bill illustrates these ambiguities. The table shows the break out of charges. The t...

George Angwin, 17 February 2022 Meredith sent me the following image of an electricity bill. Why is this funny? In 1957, the teacher of my English Composition course brought up the question of what constitutes comedy. After some discussion, this was the University of Chicago, he offered his opinion. Comedy is the contradiction of expec...

George Angwin, 28 January 2022 Yesterday’s Wall Street Journal had several articles about the unfolding drama along the eastern border of Ukraine. There were two themes: President Biden threatened vague responses if Russia’s Vladimir Putin continued his pressure to force Ukraine back into the Russian Empire, and Germany is continuing t...

What is the probability that a random chord of a given circle is longer than the side of an inscribed equilateral triangle? The previous post on this subject, "Magic Chords", made two attempts to solve this problem that ended in confusion. Those attempts were based on analyzing sets of chords. I now believe that approach is too complic...

I was daydreaming over my morning coffee, thinking about how many different cultures my family came from. By my family I mean the immediate family: 1. Me. • Mother’s parents – barely middle class from Worcester, England • Father’s parents – Cornish miners 1. My wife. • Mother’s parents – Jewish peddlers and seamstresses from Ukraine in...

George Angwin, 2 January 2022 James Tanton (of G’day Math fame) proposes an elementary problem in probability in his course Geometry: An Interactive Journey to Mastery: What is the probability that a randomly chosen chord of a circle will be longer than the side of an inscribed equilateral triangle? A chord is a straight line segment j...

From an article about the Texas grid in the New York Times, 23 December 2021: “Extreme weather events will be mitigated tremendously by our winterization requirements that are now in place,” and by operating the grid with “an abundance of caution,” said Peter Lake, the chair of the state’s Public Utility Commission, which regulates the...

Ian Stewart wrote a popular book, In Pursuit of the Unknown: 17 Equations That Changed the World, published by Basic Books in 2013. Stewart is one of the 20th century’s most well‑known and creative mathematicians, so I am a bit arrogant to go up against him. However, the more I thought about his list, helped by a glass of wine, I decid...

A few years ago, I wrote this letter to the editor of my local paper, the Valley News, but never submitted it. I was probably too shy to contradict one of their regular columnists. ===================== I was amazed at Steve Nelson’s column on January 21, 2018. He states that he was an officer, and that “military training is in many wa...

I recently ran across this provocative note: And when I gave up on archaeology, it was theatre that was there waiting for me. It was the first time I consciously made a decision based on autobiography. Instead of examining my feelings (which change hourly anyway) or making those ridiculous pro-and-con lists that always look so rational...