The problem about the mirror, it's an old-fashioned, it's an old problem.
You look at a mirror, and let's say you part your hair on the right side, and you look in the mirror and the image has got its hair parted on the left side.
So the image is left to right mixed up.
It's not top and bottom mixed up because the top of the head of the image is up there at the top and the bottom of the feet are at the bottom.
And the question is, how does a mirror know to get the left and right mixed up and not the up and down?
You'll get a better idea of the problem if you think of lying down and looking at the mirror.
All right, your hair is still on the left side. And now the left and right was the up and down, whereas the up and down, which look okay, was the right and left before.
And the mirror somehow figured out what you're going to do when you're looking at it.
So what, to describe in a sort of symmetrical way what a mirror does, that it doesn't look lopsided and it takes left and mixes it up with right
and it doesn't do the same with up and down.
And after a lot of fiddling, you gradually read, I knew the an- we worked out the an-
answers to that one. You see, if you wave this hand, then the hand in the mirror that waves is right opposite it.
The hand on the East is the hand on the East, and the hand on the West is the hand on the West, and the head that's up is up and the feet that are down are down.
Everything's really all right.
But what's wrong is if this is North, your nose is to the North of the back of your head, but in the image, the nose is to the South of the back of the head.
So what happens really in the image is neither the right nor left mixes up nor the top and bottom, but the front and back have been reversed.
You see that? Which is, the nose on the thing is on the wrong side of the head, if you want it. All right?
Now ordinarily when we think of the image, we think of it as another person.
And we think of the normal way that a person would get into that condition over there. It's a psychological thing.
We don't think of the idea that the person has been squashed and pushed backwards, forwards with his nose and his head, because that's not what ordinarily happens to people.
A person gets to look like he looks in the mirror by walking around and facing you.
And because people when they walk around don't turn their head for their feet, we leave that part alone, but they get their right and left hand swung about, you see, when they turn around.
And so we say that it's left and right interchanged.
But really the symmetrical way, it's along the axis of the mirror that things get interchanged.
Well that's kind of an easy one.
A harder one, and very entertaining, was what keeps a train on the track?
And of course the answer is, as everyone thinks, the flanges on the wheels.
You know the wheels have some kind of flange on 'em. But that's not the answer.
Because those flanges are safety devices.
If the flanges rub against the track you hear a terrible squealing. They're just in case, they're not the real mechanism. It doesn't work.
There's another problem with trains that's connected to it.
People all know this about their automobile, that when you go around a corner, the outside wheels have to go further than the inside wheels.
And if the wheels were connected on a solid shaft, you couldn't do that. You can't turn the outside wheels further than the inside wheels.
And so the shaft is broken in the middle with a gear system which is called a differential.
Did you ever see the differential on a railroad train?
No, you look at those wheels under a freight car, and there are the two wheels and there's a solid steel rod going from one wheel to the other.
There's nothing, one turns the same as the other.
So now how does it go around a corner, a curve, when the outside wheel has to go further than the inside wheel?
And the answer is that the wheels are flanged like this. I mean not flanged, they're coned. This way.
That is, they're a little fatter closer to the train and a little thinner further out. If you look closely you'll see they got this beveled edge.
And it's all very simple. When they go around a curve, they slide out on the track a bit,
so that this wheel travels on a fatter part, of bigger diameter, and this on a smaller diameter.
So when they both turn one turn, this swings further than the other. And that's what keeps it on the track also the same way.
Suppose a train's running along on this thing, on the track, and the tracks here and here, and the two wheels are exactly balanced, and it's nice and even.
Suppose accidentally it gets a bump or something and slides out this way.
Then this wheel is on a bigger circumference than this one, but they're on a solid shaft.
So when it turns once around, it carries this wheel forward relative to the other and steers the train back on the track.
Of course if it gets too far off on the other side it goes back and forth and it stays on the track because the wheels are tapered.
And the flange is a safety.
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