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"Falling" (1967) by James Dickey (1923-1997, author of "Deliverance") At the end of this post, you'll be able to answer these questions nearly instantly, and you'll remember how to do it for the rest of your life. What I'm about to tell you is no more advanced than what a middle-school child learns in science class (and forgets the moment the test is over). We all know the names Pythagoras and Galileo. Pythagoras (c570BC - c495BC) is most famous for the Pythagorean Theorem (which has nothing to do with this). He was a Greek scholar, philosopher, and mathematician, and was clever enough to devise the following mathematical formula. Don't stop here - this is *easy*! Note that the drawing is a "square." The numbers on top are just 1, 2, 3 .... The numbers on the left are the number of dots in that section (count them and see). You should be able to clearly see that this drawing can be extended to infinity. But what does it represent? Let's take the number 3. Count up all the dots in sections 1-3, and you'll get 9 dots, or, 3-squared. With the number 4, count up all the dots in sections 1-4, and you'll get 16 dots, or 4-squared. This is all very easy to see, and intuitive as a graph; unfortunately, it needs to be represented as a formula. Don't leave! Skip the following line if you need to because it's not that important: For any number (call it "X"), it's square is equal to the first "X" odd numbers, added up. Don't leave! With the number 4, it's square is equal to the sum of the first 4 odd numbers: 1 + 3 + 5 + 7 = 16. Hi-Fi was rumored to be a square as well: [Exit Pythagoras] [Enter Galileo] Galileo (1564-1642) is one of absolute most famous scientists in history, and his accomplishments are so vast that listing them here would be pointless. There really isn't any "one thing" he's most famous for; he's a lot like Leonardo da Vinci - just a total Renaissance man, and you'd have to put him on any Top 10 list of "Scientific Contributions To Mankind" for his lifetime achievements. Galileo was fascinated by Pythagoras, and one of the things he did was take this formula by Pythagoras - purely mathematical - and apply it to the real world. In other words, he took pure Math, and applied it to Physics. Galileo figured out that the above figure corresponded almost exactly to how fast objects fell. This is what he figured out. Don't leave! This is just as easy. Here are a few details that you can skip because for the purposes of understanding this, you don't need to know them; just be aware that they exist: SKIP ME - SKIP ME - SKIP ME - SKIP ME - SKIP ME - SKIP ME - SKIP ME - SKIP ME - SKIP ME 1. In reality, this applies only to objects falling in a vacuum. Things like drag (stick your arm out the window of a moving car) and buoyancy (a cork floating on water) are important to scientists, but not for us. 2. All things - no matter what their weight, mass, or density - fall with the same acceleration and speeds. This has been proven, and you can count on it being true: in a vacuum, a feather will fall exactly as fast as a brick, and they'll hit bottom at the exact same time. 3. There is an upper-bound called terminal velocity which happens when the forces of drag + buoyancy cancel out the force of gravity. Since you've made it this far, you are hereby rewarded by the trailer of the 1994 film with the same name: SKIP ME - SKIP ME - SKIP ME - SKIP ME - SKIP ME - SKIP ME - SKIP ME - SKIP ME - SKIP ME Are you still here? Okay, we're almost done. Don't leave! Here is what Galileo figured out, using what Pythagoras did as a basis (note that the metric system was not introduced until 1668, after Galileo's death): For every 1/4-second increment spent falling, you cover the distance shown by adding up the numbers on the left side of the above figure. Examples: 1/4-second: You fall 1 foot. 1/2 second: You fall 1 + 3 feet. 3/4 second: You fall 1 + 3 + 5 feet. So for every 1/4-second interval that something falls, just add up the odd numbers. That's it! Now, ask yourselves: how far do you fall in one second? Two seconds? Hint: one second is four 1/4-second intervals; two seconds is eight 1/4-second intervals. (The answers are 16 feet (1+3+5+7) and 64 feet (1+3+5+7+9+11+13+15), respectively.) As a shortcut which makes it even easier, you can just take the square of the number of 1/4-second intervals (for one second, it's 4-squared; for two seconds, it's 8-squared; for 5 seconds, it's 20-squared which is greater than the length of a football field). You are now free to live the rest of your life knowing that if you fall for much longer than one second, you're pretty much fucked. PS - the sheriff at the end of Deliverance was James Dickey himself: Does anyone know why Dickey gets in and drives off in the passenger's side of the car? Is this some weird mirror-image thing? Or was this filmed in England?