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Mostly Mozart


Posted July 1, 2001

I think it was Aristotle who gave us the tradition of having five senses. Sight, hearing, touch, taste, and smell. Our experience of the world around us is determined entirely by what we see, hear, touch, taste, and smell.

For each of these senses, we have some special apparatus that translates information about the world into nerve impulses. For example, our eyes have lenses for focusing, and rods and cones for turning light waves into nerve impulses. There's also some specialized circuitry in the visual cortex, which interprets incoming pictures as patterns like straight lines, objects, and spaces. By the time the signals arrive at the conscious brain, they're pretty far removed from the actual pattern of photons arriving at the lens of the eye.

If you've ever had that experience called a head rush, you've noticed that you don't always see what's in front of your face. Sometimes you see mostly blackness, with something like the organic equivalent of TV snow. It doesn't have anything to do with the pattern of light arriving at your eyes. But it is what you see.

Even when your brain is working normally, it's easy to fool it. One way is to look at an Escher drawing. Everything fits together on a small scale, and everything looks fine on a large scale, but if you look at all the details in between, the small scale doesn't match up with the large scale. It usually takes a few seconds to figure out what's unrealistic about a given Escher drawing. Your brain is so accustomed to interpreting real objects that it rushes to a sensible conclusion about the Escher drawing without taking in all of the details.

You can have a similar experience just by reading a newspaper. Contemporary journalism standards dictate that all newspapers must have lots of typos and grammar errors. But you'll read through most of them without blinking, and you'll understand perfectly, because English is sufficiently redundant that you don't even need all the right words, let alone all the right letters. You can fill in a lot of blanks without even noticing.

But that's getting awfully close to the subject of language, which is not one of the five senses. If you couldn't hear, see, touch, taste, or smell, then the most romantic language in the world wouldn't do you much good.

And speaking of the number five, I wonder if you noticed that I have the list of senses wrong. If you didn't notice, well, neither did anyone else for a couple of thousand years. But then Ernst Mach noticed something about balance.

If you've ever been dizzy, you've had an encounter with the sixth sense. Dizziness definitely has something to do with the world around you, and you don't get that feeling by seeing, hearing, touching, tasting, or smelling anything. So where does it come from? If you swing your head around a bit -- being careful not to be so vigourous that it comes off -- you can get a bit dizzy. That means there's something in your head that tells you when to be dizzy.

And how about turning corners on your bicycle? You might have noticed as you lean into the turn that you have absolutely no trouble balancing. All of the visual cues are wrong -- the lines that should be vertical all look diagonal -- but you can feel that you're in the right position.

What I'm getting at is that you have a sense of balance. That's sense number 6. Even with your eyes shut, you can tell whether the car is going straight, turning a corner, or rolling onto its side. But we still speak of five special senses. I bet you can guess why one of the original five senses is not a "special sense": there's no special organ that gives you the sense of touch. It's just a property of various parts of the body that they report changes in heat and pressure by generating nerve impulses. So the five senses are now sight, hearing, smell, taste, and balance.

I mentioned that Ernst Mach was the one who figured out where the sense of balance comes from. If you knew that Mach 1 is the speed of sound, it probably comes as no big surprise that the sense of balance comes from some strange apparatus in your inner ear.

Inside each of your ears, there are three tubes with liquid in them. You need three because there are three spatial dimensions. Each tube reports to your brain how fast it's rotating, and that's usually enough to give you a sense of balance.

If you take a glass of water with some ice in it, and spin it around, you'll notice that the ice stays still at first, then gradually starts to catch up with the glass. If the ice lags behind, that means the water lags behind too. This is our old friend inertia, also known as momentum. If you lined the inside of the glass with little hairs, then the water would push all the hairs in the opposite direction to the way you're spinning the glass. Essentially, the liquid serves to amplify the inertia felt by the little hairs.

In your ear, these hairs send nerve impulses according to which way they're being pushed. When you turn your head, the container turns, but the liquid pulls the little hairs backwards.

Normally, when you're standing still, the liquid is also standing still, those little hairs aren't being pushed around, so you feel like you're standing still. But now you should take that glass of water, and keep spinning it around until the water and ice are spinning around at the same speed as the glass. Then stop. The water inside will take a while to slow down, and until it does, it's reporting inaccurate information. The water is still pushing those little hairs around, which is supposed to mean that the glass is spinning, but in fact the glass is not spinning. The glass is now dizzy.

If you spin yourself around a bunch of times, you'll get the same result. The liquid in your ears will catch up with the rotation of your head. Your sense of balance will indicate that you are not spinning, although your eyes will tell you that you most certainly are spinning. You'll notice the footwork getting more difficult, because your sense of balance isn't helping you any more.

If you suddenly stop spinning, the liquid will keep moving. Your sense of balance will indicate that you just started spinning all of a sudden. Your sense of vision will attempt to compensate for this fact by moving everything in your field of view in the opposite direction. Since everything in your field of view is stationary, this causes you to see a huge mess.

So how do dancers and ice skaters deal with this mess? The answer has to do with fluid dynamics and the difference between static and dynamic friction. In short, if you spin your glass of water really quickly, one whole turn at a time, and let it stand for a second between turns, then the water will take a lot longer to catch up. Dancers can move the rest of their bodies any which way without affecting their balance, but when they spin their heads around, they have to do it as quickly as possible, and let it rest for a second between turns. Which is OK artistically, because it looks like they're just keeping an eye on you at all times. And they also look a bit like owls.

Before I go, there's one more thing I'd like to mention about Mach. Mach 1, the speed of sound, is 330 m/s. That means it takes about 3 seconds for a sound to travel 1 km. The speed of light is almost a million times that. If you were to yell louder than anyone has yelled before, loud enough to be heard in Ottawa, it would take about 15000 seconds to get there. That's a little over 4 hours. And that's why telephones are so useful in a big country like Canada. So if you feel like smashing something, you should definitely smash your TV instead of your telephone.