Some time ago, I promised an explanation of how gravity works — in particular, how general relativity, Einstein's theory of gravity, works. Today I'm going to deliver. This one's a little mind bending, so definitely ask questions if you're confused. I like questions. Questions are cool.
In the beginning, there was Newton
To understand general relativity, we need to go back to one of Newton's laws — not Newton's law of gravity but rather Newton's first law: objects tend to travel at constant speed and in a constant direction (or remain at rest) unless some force acts on them. In simple terms, stuff that goes straight keeps going straight unless you push on it.
Believe it or not, I just explained gravity.
Newton may well have called me crazy. To him, gravity was a force, and it's easy to see why. Suppose we, your friends, hold you a hundred feet off the ground and then let go. You will fall, and then you will cry. In fact, we'll launch you sideways so you make a pretty arc as the earth careens toward you.
Now, if you buy Newton's First Law, there must be some force that acted on you. You went from stopped to falling — some force must have been behind that. So says Newton.
Silly Einstein's silly thought experiment
Let's probe deeper. Newton says that an object (namely, you) will stay on a straight line going at constant speed unless some force acts on it.
Well, when do you actually feel a force?
If we forget about wind resistance, you don't feel one while you're falling. You do feel a force before you're dropped — the force of us, your soon to be ex-friends, holding you up.
Catch that? In this way of thinking, you feel a force when your friends are holding you eight stories up about to drop you. If that's right, then Newton's laws say they're keeping you from going straight and at constant speed. Then when are you going straight and at constant speed? When you can't feel a force. In other words, when you're falling and making that pretty arc across the sky.
I'm glossing over some details, but this is Einstein's puzzling insight: falling is going straight. It's right there in Newton's laws. In other words, if can't feel a force but it doesn't look like you're going straight, you need to redefine what you mean by straight.
Long walks, curved spacetime, and gravity
It may seem like a contradiction to say you're going on a straight line at constant speed while making a pretty arc and accelerating toward the earth, but in fact it's not such an odd idea.
Consider starting at your house and walking due West. If you can manage to walk on water, you'll come back to where you started. You walked in a straight line, and yet you made a big circle.
We wouldn't infer from this that a force somehow bent your path. We'd infer that the surface of the earth is curved — which of course it is.
The same thing holds for astronauts orbiting the planet. They're floating up there, so they don't feel any forces acting on them. Yet orbiting the planet they make a great big circle in space. We don't infer that there's a force acting on the astronauts — after all, they can't feel one — so instead we infer that space and time are curved.
And that's what gravity is: curved spacetime. Explaining all the details — like exactly what it means to be going straight at constant speed while appearing to be doing the opposite — would take longer, but you've got the basic idea. No force? Go straight. No force, not going straight? It's not you that's not going straight. It's spacetime.
Tuesday, October 4, 2011
Though the past few decades have yielded a wealth of information about how the brain works, there is much that remains mysterious. It therefore came as a surprise to many a neuroscientist when the hallowed New York Times published an editorial by "marketing expert" Martin Lindstrom claiming that we loved our iPhones in much the same way we love our families and our dogs.
I'd leave it to my fellow neuroscientists to explain why there isn't a shred of evidence to support that claim, except that it exemplifies a logical error pops up everywhere from neuroscience to politics. In the interest of helping you be a better observer of both of those things — and because I like writing about them — here's the claim, the problem, and the broader lesson.
Lindstrom used a method called functional magnetic resonance imaging, or fMRI, to study what parts of the brain respond to smartphones. He had eight men and eight women aged 18 to 25 watch videos of iPhones and listen to their characteristic sounds. (If you've even been around an iPhone, you know the ones I mean.) His claim: iPhones activate the insula, a brain region he writes is "associated with feelings of love and compassion." Therefore, he goes on, we love our iPhones.
Let's break this down. First, what does fMRI do, and what does it mean that the insula is "associated with" love and compassion? FMRI is a brain scanning technique that measures how blood flows in the brain, and it's most often used to measure how different brain regions activate in response to everything from emotionally-charged images to trading in simulated financial markets. Then, to say the insula is associated with love and compassion is to say that evoking feelings of love and compassion activates the insula.
What inferences can we draw? Despite the connection to love and compassion, just because someone's insula responds doesn't imply that person is in a loving mood. The insula responds to a host of other things, among them disgust and the violation of social norms, and love activates other parts of the brain, including the caudate nucleus and the anterior cingulate cortex. Not only is it wrong to say that insula activation implies feelings of love, it's also wrong to say those feelings are somehow centered in the insula.
In fact, the most current viewpoint is that networks of brain regions are responsible for emotional responses, not to mention your capacity to do arithmetic and follow baseball. Your response to smartphones is not somehow "in" your insula — it's in a complex pattern of responses that extends across your entire brain.
Logic and the broader lesson
Lindstrom's argument illustrates a common logical error: the belief that the converse of a true statement is true.
Consider the statement, "if an animal is a person, it is also a mammal." Even though that's true, it's converse, "if an animal is a mammal, it is also a person," is obviously not. In Lindstrom's case, the underlying, reasonably well-supported claim is "something that evokes love activates the insula." Lindstrom infers that "something that activates the insula evokes love," but as the animal example illustrates, that doesn't necessarily follow.
If this kind of error seems harmless, it's not. Back in 1988, a political action committee that supported presidential candidate George H.W. Bush ran the now-infamous Willie Horton ad, focusing on a furloughed prisoner in Massachusetts who used his furlough weekend to escape and commit a series of crimes. Apart from the racist overtones and anti-Dukakis message of the ad, what the PAC wanted people to believe was that furloughed prisoners were going to rob your store and rape your women. See the flaw? One example, from which they hoped you'd generalize.
So when candidates start parading successful small business owners who were raised in a ditch or Canadians who've waited 28 years for a kidney transplant, ask yourself this: is this what always happens, or is this just one example?
Posted by Nathan Collins at 2:52 PM