We are never finished learning and relearning math

“Astronomer Copernicus, conversation with God” by Jan Matejko (1872). Image from Wikimedia Commons

In school, you learned that the Earth was the center of the universe. At least, you learned that people used to think that. Your science teacher then explained to you that actually, the Earth revolves around the sun instead. A man named Nicolaus Copernicus proved it during the Renaissance, and set off a scientific revolution.

If a teacher just wanted to teach you about orbits and the solar system, there would be no point in telling you that people used to be wrong about the sun and the Earth. There would be no point mentioning Copernicus, or Kepler, or Galileo…


Explaining and Simulating Binomial Distributions in R

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Cheating is as old as humanity itself. It manages to creep into every corner of life, even into something as simple as a coin flip.

Suppose your friend Dave has a coin, and he makes you a bet: if he flips the coin and it lands on tails, you win $5, but if it lands on heads, you lose $5. You take the bet. The coin lands on heads. Dave wins. You take the bet again. It lands on heads again. You keep taking the bet a dozen times, and you get really suspicious of the coin. The coin doesn’t…


“This pill will make you 20% happier”

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You know when you go to a doctor and they try to push specific medications onto you?

I remember going to a specialist doctor a few years ago (I’ll call him Dr. P), and he really, really wanted me to buy this medication, which I’ll just call Dolusol. He told me that Dolusol would not only help me with my problem, it would also increase my quality of life and decrease anxiety. He proclaimed that people on Dolusol “reported 20% more happiness! They reported 35% more calmness!” Then he gave me a snazzy bar graph and like 30 pages of…


A little moment that changed my life

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I usually didn’t study for math tests in college. It wasn’t because I was a savant who could get every question right without studying. It was because the night before a test, I would usually tell myself “I’ll start studying at 9pm” and then I would “start” around 1am and then sleep at 2am. I slacked off. Also, I majored in math in college, so I pretty much only took math tests.

In my second year, I had yet another midterm where I didn’t study much and got most of the questions wrong. We had to write proofs of geometry…


Too much gamified learning will hold you back

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Deep down, we all know that you don’t get fluent in a language from only Duolingo. Same goes if you’re only using Rosetta Stone, or any other gamified language-learning app. They supplement your learning, for sure, and they can be good for certain things like vocabulary. But we all understand that clicking buttons and regurgitating the word for “apple” thousands of times will not, on its own, teach you Vietnamese.

The barrier to entry for a foreign language is fear. That’s really it. Everyone is capable enough to memorize words, to understand grammar, to speak in full sentences. We already…


Flour mills, McDonald’s, and cars that drive themselves

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Self-driving cars will take over the world of long-distance delivery, and it makes sense once you consider, of all things, automatic flour mills and McDonald’s. These 3 products all seem unrelated, but they all adhere to a simple principle: high volume, low labor costs. Automatic flour mills and McDonald’s became unstoppable for their respective industries. Self-driving cars, or really self-driving 18-wheeler trucks, will likely become unstoppable too.

The Mill Man

In 1785, Oliver Evans changed flour milling forever. Back in his day, flour was milled by hand. To get flour, a farmer would grow wheat on their own farm, take the wheat to…


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Eventually, we will go back to eating at restaurants. Yet the modern restaurant may never be the same, and we can only wonder what restaurants of the future will look like.

Restaurants change the way we eat food, often drastically. Even putting the pandemic aside, a young man or woman in 1921 would be stunned to learn that today we have Doordash, Instagrammable food, fast food, drive-thru windows, and modern chain restaurants that long for the nostalgia of the 1950s, the 1930s, even the 1430s.

Did you know that there’s a restaurant where you can eat a balloon? People in…


A quick example of a common mistake we make with percentages

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One reason the 2016 U.S. Presidential election was… erm, remarkable?… was that it was the first election where both major-party candidates had an unfavorability rating of over 50% (more accurately, “first election” as in the first held after pollsters started recording unfavorability).

The other day someone told me this: “It was the first election where a majority of Americans disliked both candidates.”

No. No! That’s not what this statistic means. It could be the case that a majority of Americans disliked both candidates, but it’s much more likely that most Americans disliked one candidate and had a neutral/favorable rating of…


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The man who got me into reading books never once told me to read a book. When I was 18, I went to therapy through my college. The therapist I met with was the catalyst who inspired my reading habit, a habit that has since changed my life.

Growing up, I mostly kept my distance from books. You could count on one hand the books I had read in the first 18 years of my life. …


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I believe that a good book changes the way you view something forever. It doesn’t always change your mind, but it changes your view. A great book from any genre does this, from self-help to journalism to fiction. The Steve Jobs biography changes your view of Steve Jobs. A good novel, like Little Fires Everywhere, changes your view of family values, adoption, etc.

In 2020, I finished 40 books. To be honest though, if you read one great book in a year, I think you’re doing well. The exact number does not really matter. One great book that changes something…

Mike Beneschan

Math Tutor | Orange County, CA | If you want to reach out beneschan@gmail.com

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