Wednesday, December 21, 2011

Gravity and the Curse of Knowledge

The problem with knowing something is that it makes it very hard to accurately put yourself in the shoes of someone who doesn't know it. Try as you might, it's very difficult to properly imagine the thought processes of someone who lacks knowledge. Things you know always seem obvious, even though they're not obvious at all when you don't know them. Psychologists call this the curse of knowledge.

When you suffer from the curse of knowledge, previous generations tend to look remarkably stupid. How can anyone believe the earth was flat? What morons they must have been!

But think about it - do you believe that humans now are genetically much smarter than people 500 years ago? Or are you just taking for granted the obviousness of the things that someone else told you, but you didn't have to figure out for yourself. I'd say you're safer to bet on the latter.

One case that always struck me was gravity. The earliest theories of gravity were from Aristotle's Physics. If you fired a cannonball, that cannonball would proceed in rectilinear motion, then fall straight back down to the earth. This was because it was made of the earth element, which wanted to be close to the earth.

So this predicts that if you fire a cannonball, it should look like this:

So here's the problem - clearly cannonballs don't actually fly like this! Now, admittedly it's hard to trace out the path of a rock in the air. But there's one very easy way for (male) physicists to check - just look at the path of your urine when you take a pee! Does it look like a triangle shape? No, not even close. It looks like a parabola. And that should immediately suggest a relationship of y = x^2 . 

It took until Newton, almost two millenia after Aristotle, to formalise a better theory of gravity. This theory actually predicted that the cannonball should follow a parabolic shape:

So why did people take so long to figure this out? Couldn't they see that the relationship was a parabolic  y = x^2, and figure out the rest from there?

Oh, you fools, cursed by knowledge! The first step is the known knowns - the curses you know you have. You know that you know about gravity, and thus your ancestors not knowing seems particularly idiotic.

But what about the unknown knowns - the curses that you don't even know you have?

Let's step back a second - when exactly in human history did people even have a clear idea of what a parabola was, and what y = x^2 meant?

When you draw a graph of y versus x for some function, the area you draw it on is known as a Cartesian Plane. This is named after Rene Descartes, who lived from 1596 until 1650.

In other words, even the idea of graphing y versus x (for anything, let alone being able to spot a parabola) dates all the way back to ... the 17th Century. 

Are you starting to see how much you're taking for granted when you look at modern science and think of how dumb people in the past were.

Rene Descartes was a muthaf***ing genius. And that's how smart you had to be to even come up with the idea of drawing a parabola on a graph, let alone understanding what that might have implied about a theory of gravity.

Understanding the curse of knowledge leads to a much greater humility about previous generations. The vast majority of your knowledge is unearned by you, and if you hadn't had it gifted to you by the accumulated wisdom of generations of men much smarter than you, it's highly doubtful that you would have figured it out on your own.

Just like your ancestors didn't.

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