We humans are castaways on an ocean of uncertainty. Since the beginnings of history, our ancestors sought knowledge and understanding about their lives, their relationship with the cosmos, and perhaps take a peek into their future. In such effort—long before the answers of science—earthlings developed a rich variety of divination practices and systems. Many forms of divination survive to this day, and can't be easily dismissed as irrational nonsense, or mere curiosities of a bygone age. On the contrary, divination seems to be essential to culture.
So much so, that perhaps our modern obsessions with predictive algorithms and numerical forecasts are best understood as a continuation of this ancient divinatory impulse. This is the provocative thesis of Alexander Boxer’s fascinating new book, A Scheme of Heaven: The History of Astrology and the Search for Our Destiny in Data.
A Scheme of Heaven
Astrology is indeed the most historically relevant of all divination practices, its aim having been nothing short of a systematic account linking the nature of the heavens to our own human nature. Across civilizations, human beings have proven to be superb stargazers. Entranced by heavenly patterns and periodicities—through sheer naked-eye observation—our ancestors were able to crack with uncanny precision the workings of the cosmos. Exact geometric relationships and precise mathematical elegance spoke of divine design and transcendent beauty.
For a long time, astronomy and astrology were one and the same magical “enterprise.” Alexander Boxer, a data scientist, whose eclectic erudition includes a PhD. in physics from MIT and degrees in the history of science and classics writes:
“Astrology was the ancient world’s most ambitious applied mathematics problem, a grand data-analysis enterprise sustained for centuries by some of history’s most brilliant minds, from Ptolemy to al-Kindi to Kepler.”
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I enjoyed learning about statistics, probability, zero, infinity, number sequences, and more in this heavily illustrated kids’ book called How to Be a Math Genius, by Mike Goldsmith. But would my then-11-year daughter like it as much? I handed it to her after school and she become absorbed in it until called for dinner. She took it to the dinner table and read it while we ate. The next day, she asked for the book so she could finish it. Loaded with fun exercises (like cutting a hole through a sheet of paper so you can walk through it), How to Be a Math Genius will show kids (and adults) that math is often complicated, but doesn’t need to be boring. Now my daughter is 16 and she devours math books. I'm not sure this is the book that kicked off her interest in math, but I'm sure it didn't hurt! Read the rest
The astonishingly prolific author/scientist Clifford Pickover is a math enthusiast with a talent for ferreting out fascinating anecdotes about math, and writing them in a way that inspires wonder.
Accompanied by beautiful illustrations, Pickover’s The Math Book about cicada-generated prime numbers, magic squares, the Golden Mean, Penrose Tiles, Xeno’s Paradox, and the butterfly effect just might turn you into a lover of math. It worked for me.
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YouTuber 3Blue1Brown has started a video series called "lockdown math." In his latest episode he goes over the fundamentals of trigonometry in a way that is accessible and enjoyable. Read the rest
You are probably familiar with these little tile slide puzzles with 15 tiles that slide around in a 4 x 4 grid. The object is to slide the tiles around so that the tiles marked 1 through 15 are arranged in numerical order. The card that comes with the puzzle shows a number of different ways to arrange the numbers, including arranging the tiles in reverse numerical order. In this episode of Numberphile we learned why this particular arrangement is impossible.
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Mathematician, artist, and engineer George W. Hart of "Möbius strip bagel" fame has recently been playing with a laser cutter to create head-spinning warped-grid jigsaw puzzles. He came up with an algorithm to generate the initial patterns but "the real fun is step 2," he says, "using a geometric transformation to warp things."
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Here's a good video that shows how the increase in the number of Covid-19 follows an exponential growth curve. Each day, says 3Blue1Brown, the number of coronavirus cases is "between 1.15 and 1.25 of the number of cases the previous day."
3Blue1Brown writes: "While this video uses COVID-19 (aka the Coronavirus) as a motivating example, the main goal is simply a math lesson on exponentials and logistic curves. If you're looking for a video more focused on COVID-19 itself, I'd recommend taking a look at this one from Osmosis:"
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On Vsauce2, Kevin Lieber explains the mathematical magic that enables mentalists to confound audiences by correctly guessing the number they've picked. Even though I know how it's done, it still confounds me.
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View this post on Instagram A post shared by Popular Mechanics Magazine (@popularmechanics) on Jan 29, 2020 at 12:14pm PST
Sure, you can count them. I did, and, er, I missed a few. Or you can take one of the approaches suggested by the mathematics professors that Andrew Daniels interviewed in Popular Mechanics:
“I would approach this just like one approaches any mathematical problem: reduce it and find structure,” says Sylvester Eriksson-Bique, Ph.D., a postdoctoral fellow with the University of California Los Angeles’s math department.
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This is the first use of AR/VR I have enjoyed.
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Jon Cog writes, "For Christmas, mathematician Donald Knuth shared some great geeky fun. He revealed how for the last 57 years, he's been incorporating the digits of pi into the exercises of his computer programming books -- a whopping 1,700 times. And before long his annual 'Christmas Tree' lecture 'had turned into a kind of intellectual funhouse,' sharing other mind-boggling pi-related miscellanies."
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There's a scene in my novel Homeland (the sequel to Little Brother) in which the first 1,000 digits of Pi are featured; when it came time to produce the audiobook edition, poor Wil Wheaton -- the narrator -- ended up reading out Pi for four solid minutes, with some entirely understandable difficulties. Nick Land set the reading to music, creating quite a delightful little tune!
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Nathan Davis writes, "When you shuffle a deck, it rearranges the order of the cards and I got wondering what that looked like. Read the rest
Are you the driver in the lot who parks in the first spot you see? Or do you circle around and around looking for a spot by the door? Physicists Paul Krapivsky of Boston University and Sidney Redner of the Santa Fe Institute explored the mathematics of parking. The research required different equations and simulations to model the benefits of the various parking approaches. From EurkeAlert!:
In their paper, Krapivsky and Redner map three simple parking strategies onto an idealized, single row parking lot. Drivers who grab the first space available follow what the authors call a "meek" strategy. They "waste no time looking for a parking spot," leaving spots near the entrance unfilled. Those who gamble on finding a space right next to the entrance are "optimistic." They drive all the way to the entrance, then backtrack to the closest vacancy. "Prudent" drivers take the middle path. They drive past the first available space, betting on the availability of at least one other space further in. When they find the closest space between cars, they take it. If no spaces exist between the furthest parked car and the entrance, prudent drivers backtrack to the space a meek driver would have claimed straightaway.
So which strategy is best? As the name suggests, the prudent strategy. Overall, it costs drivers the least amount of time, followed closely by the optimistic strategy. The meek strategy was "risibly inefficient," to quote the paper, as the many spaces it left empty created a lengthy walk to the entrance.
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From Toby's "Tibees" YouTube channel:
"A math lesson about logarithms inspired by the legendary painter Bob Ross."
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Making a solar hot-dog oven is a science fair standby, but JohnW539's CNC-milled Sundogger Instructable really digs into the classroom portion, drawing on the creator's experience as a physics/astronomy/computer science prof at Middle Tennessee State University.
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SL Huang got a degree in math from MIT, then became a martial artist, stuntwoman and weapons expert; her debut novel, Zero Sum Game, features an ass-kicking action hero called Cas Russell, who combines all of Huang's areas of expertise: Russell is a ninja-grade assassination/extraction contractor whose incredible math skills let her calculate the precise angles needed to shoot the bolts out of an armored window as she leaps towards it from an adjacent roof; to time a kick so that it breaks her opponent's jaw without breaking his neck, or to trace back the path of a sniper's bullet with eerie accuracy and return fire.
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