Ah, that intro was a bit derivative, wasn’t it? No, not derivative, just unoriginal. But if it were derivative, it would be right on theme this week. And ‘derivative’ can mean a lot of things–at least three things–in the realm of math, finance, and art. So without further ado we’re going to hop to it.
A Mathematician Has Been Drinking at a Bar…
…and his friends dare him to solve for the slope of a curve. He sets some pen to paper and suddenly the bar explodes, killing everyone. This is, of course, a cautionary tale not to drink and derive.
That favorite joke of math teachers the world over is as good a lead-in as any to summarize a core principle of calculus: The Derivative. It’s basically the rate of change in a curve, the slope of a line at any given point, and it’s integral in how we understand mechanics and much of physics today. One of the most popular physics derivatives around is velocity. Because if you measure the change in something’s position, that’s its velocity. A car moving 60 mph is, over the course of an hour, changes its position by 60 miles.
If you want to find the rate of change of velocity, how fast you’re speeding up or slowing down, that’s acceleration. And we, as humans, can feel that acceleration as the sort of shoving into the seat when an airplane takes off or the whiplash and sharp pressure of a seatbelt when a car comes to an abrupt stop.
But you probably already know that, so what about the rate of change in acceleration? What’s the third derivative of position? I remember my math class asking a well-meaning Mrs. Breen that very question to which she replied that it was a quantity known as ‘jerk’. Okay, that makes sense, if acceleration is changing and you’re speeding up faster you might feel some jerkiness.
And the derivative of jerk? That’s called ‘snap’. But I’ll be honest, I’m not sure I can put a finger on the feeling of snap and say “that’s snap”. And if I could, I definitely wouldn’t be able to pinpoint the feeling of the derivative of snap, which is, of course, crackle. Whose derivative in turn is ‘pop’. Because mathematicians have the silliest sense of humor (for proof, see the ‘drink and derive’ joke from earlier).
And because it bears mentioning, calculus was invented in the late 1600s, simultaneously by Newton and his contemporary Leibniz (though Newton claimed his work dated to earlier in ~1666). In case you haven’t heard of him, Leibniz is the guy who did a lot of cool stuff including inventing binary (that would be used literally hundreds of years later in computing), and Newton was the guy who among his scientific contributions is widely believed to have died a virgin. So maybe giving him calculus seems fair.
Lock, Stock, and Two Under-costed Bushels of Corn
So that’s the concept of derivatives in math, but we’ve got some ground to cover yet. Financial derivatives are as complex as they are necessary to our way of life, so let’s take a quick jaunt into the world of Wall Street.
You’re probably familiar with stocks, right? One can buy a piece of a company for a share price and then you share in the company’s profits and losses. Derivatives work a bit like that, but like their math equivalent, they’re a step (or more) removed from the action. A sample derivative might be what’s called a ‘put option’ that gives the owner the right (but not obligation) to sell a commodity at a certain price at a designated time in the future. This option is also called a ‘future’ for obvious reasons.
So you could buy a ‘put’ which in turn would let you then sell the underlying stock (or whatever) at a certain price. Why is this important? Let’s go back to farming. In the late 1800s farmers were terrified that they’d plant and grow and harvest their crops all season long and maybe they’d be a surplus in the market and the price they’d be able to fetch per bushel of corn (or whatever) would be too low to cover their costs and support their families. So they would by put options and if when they wanted to sell the market price was higher than the put’s ‘strike price’, they just threw away the put and sold it in the market. If it was below the strike price, they could force the person who sold them the put option to buy their crops at the agreed-upon price.
Effectively, this is farmer insurance, which is how we can spread around risk for a market and guarantee that people keep growing food. And there are many more (like call options, CDOs, etc), but this was first sold in standardized fashion in Chicago in 1864, almost exactly 200 years after the invention of calculus.
But some other people realized that through some funky math and a little bit of gambling, one could buy or sell these derivatives and without actually giving a shit about corn or pork bellies, one could make a fair bit of money speculating on these markets. And then decades and decades later people are using derivatives and similar financial instruments to completely tank the economy (multiple times). But I digress.
(How Art) Ch-ch-changes
This is getting long and I’m effectively out of whiskey, so let’s wrap this one up.
The last kind of derivative I care to reference is that of art. Any art that takes something already made and changes enough to make it different, that’s a derivative artwork. Remixes, covers, these are all derivatives.
One popular cover is Smash Mouth’s I’m a Believer, which you may just know as ‘that other Smash Mouth song from Shrek‘. However, the original song was by a band called The Monkees in 1966, almost exactly 300 years after Newton claims he invented calculus. Coincidence? Almost certainly.
But if you’re looking for coincidence: both the lead singer of The Monkees and the famed David Bowie were born ‘David Jones’. The Monkees frontman had the first mover advantage of ‘Davy Jones’, so the one we know as Ziggy Stardust decided to use the stage name of David Bowie. And the rest was history.
Look, it’s late, I’m not sure if I should add more footnotes, I’m told people like them², but I’m just gonna call it here.\
And here’s a gif I couldn’t fit anywhere else in the article but wanted to include!
Until next week, something-something optimistic-encouragement-referencing-derivatives!
¹ If you’re unfamiliar with the Robin Williams 1987 movie Good Morning, Vietnam, I would highly recommend it.
² Maybe they’re just being nice.
Fun Fact Friday 