Study Hacks Blog

Today is March 14th, which to us math nerds is also known as Pi Day, in reference to the first three significant digits of the mathematical constant pi (3.14).

Part of what makes pi interesting is that it’s one of the most famous irrational numbers, meaning that it cannot be expressed as the fraction of two whole values (though 22/7 comes pretty close). In honor of Pi Day, I thought I would learn more about the history of irrational numbers, so I turned to one of my bookshelf favorites, The World of Mathematics: a four-volume history of math, edited by James R. Newman, and published in a handsome faux-leather box set in 1956. (I picked up my copy at a used book sale five years ago.)

The first volume contains an extended essay (originally a short book) titled “The Great Mathematicians,” written by Herbert Western Turnbull, the late Scottish algebraist. Turnbull dedicates much of the essay to great innovations from ancient Greek mathematics. It was Pythagoras (570 – 495 BC), he notes, who is most often credited for discovering that irrational numbers exist.

We know something of the proof that Pythagoras used due to a later account by Aristotle. The proof is elementary by modern standards (indeed, it’s a common example in undergraduate-level discrete mathematics courses). It goes something like this…

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Last week, I wrote about a paper appearing in the American Economic Review that conducted a randomized trial to measure the personal impact of deactivating Facebook. A few days later, a different study was published, this one appearing in the journal Computers in Human Behavior, that also deployed a randomized trial to measure the impact of reduced Facebook use.

The authors of this new paper, a group of psychologists from Ruhr-Universität Bochum, in Germany, randomly split a group of roughly three hundred volunteers into an experiment and control group. The participants in the experiment group were asked to reduce their daily Facebook use, while the control group made no changes.

Personal impacts were measured with online surveys administered at regular intervals. To summarize the paper’s main findings:

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In the most recent issue of the prestigious American Economic Review, a group of well-known economists published a paper titled “The Welfare Effects of Social Media.” It presents the results of one of the largest randomized trials ever conducted to directly measure the personal impact of deactivating Facebook.

The experimental design is straightforward. Using Facebook ads, the researchers recruited 2,743 users who were willing to leave Facebook for one month in exchange for a cash reward. They then randomly divided these users into a Treatment group, that followed through with the deactivation, and a Control group, that was asked to keep using the platform. 

The researchers deployed surveys, emails, text messages, and monitoring software to measure both the subjective well-being and behavior of both groups, both during and after the experiment. 

Here are some highlights of what they found:

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Sir William Osler is one of the most important figures in the founding of modern medicine. In 1910, he published a book titled Aequanimitas: With Other Addresses to Medical Students, Nurses and Practitioners of Medicine. It builds on a farewell address he gave at the Pennsylvania School of Medicine in 1889, and details his thoughts on what it takes to thrive in an intellectually demanding medical field.

As one of my readers helpfully pointed out recently, chapter 18 of this book contains the following prescriptive gem about how to succeed in an endeavor that requires you to create value with your mind:

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I recently finished Edmund Morris’s epic new Thomas Edison biography. It took me a while to get used to his reverse chronology structure (he works backwards from Edison’s later years to his earlier years), but once I did, I found it riveting.

One thing that caught my attention from the book was the degree to which early 20th century Americans were exposed to rapid technological change. We think the arrival of the internet and smartphones were a big deal, but these innovations were trivial in magnitude compared to the arrival of electricity.

Constraints that had been constant throughout all of human history — the darkness of night, the slow pace of information dissemination — were obliterated in just a few decades.

Edison was born in an age of horses and sailing ships. His death was broadcast worldwide via radio waves, and whole cities — their streets clogged with cars and their skies blotted with steel-girded buildings — temporarily powered down their ubiquitous electric lights to honor his passing.

These changes naturally led to some reactionary technophobia (though, as I argued in a recent op-ed for WIRED, there wasn’t as much of this resistance as popular commentators like to imply). I’m interested in this historical moment of technophobia, as skeptical technology commentators such as myself, or Tristan Harris, Jaron Lanier, and Douglas Rushkoff, are sometimes associated with this tradition by our detractors.

But does this analogy hold up?

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It’s been about a month since I proposed the Analog January Challenge. Accordingly, I’ve begun to receive reports from those who’ve made it through a full four weeks of enhanced analog activity.

I thought it would be interesting to share one of these case studies…

One of the first reports I received was from Edward (not his real name), a young man living in London, who ended up traveling to Florida to visit family during the month.

Edward claimed that jet lag complicated the READ piece of the challenge, but he still managed to finish two biographies, a non-fiction book on psychology, and Gone With the Wind. He also started Little Women, as he figured it was probably smart to have read the book before going to see the Greta Gerwig film.

As for the MOVE piece, Edward noted that “London really does save my butt on this one.” While in the city, he found it both easy and enjoyable to walk its historic streets, observing his surroundings and allowing his own thoughts to keep him company. When the “crazy city noise” got overwhelming, he’d find refuge in Hyde Park.

Edward’s time in Florida, on the other hand, was a different story. As he explained, unless you live in one of the Sunshine State’s big cities, “the incentive to move for any reason is severely curtailed.”

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