Can you See Infinity in the Bathroom?
So we have come really far. Alice Liddel herself, the Cheshire cat smilingly asked her, really, and he asked have you heard of the word infinity? And of course Alice had heard it as everybody else had but she never really understood it just like nobody else did. And the cat smilingly said, “Do you want to see infinity?” or “Have you seen infinity?”, and she said “No”, and you could see the glow and curiosity in Alice’s eyes as he mentioned the word “Do you want to see infinity?”. And even more naughtily he said, do you know that you have already seen infinity. And she said “Really? I don’t know.” Now she was beginning to get even more curious and now he showed her some time ago I put these two mirrors so that they were facing each other and as you saw across, what did you see? And she recollected that she had seen many, many, many images of her. He asked her how many? She said I don’t know. As far as I could see. And he asked could you count that? Could you tell me where exactly it stops? And as she began to see that again, she realized that no matter how many hours or days or years she counted there would still be one more. She realized that she could spend an entire lifetime counting each of the images that she saw that were getting smaller and smaller and smaller but no matter how many she counted there was going to be just one more. And then she realized what the cat was trying to get at. When you place two mirrors on each side, when you look across you’re actually staring at the depths of infinity from wherever you are. And if that doesn’t fascinate you, the cat said, nothing will. Because right here there is infinity. Somewhere between two mirrors. Nobody knows where but there is an infinity. And even more surprising is that he said what is the formula you, you kind of wrote down in that paper. She said, I, I had understood that you know you take a circle and divide it by the number of the angle and subtract one, you will get the number of images. And he said great. So 360 divided by (Θ – 1). Now what happens if I placed these two mirrors parallely? What would that Θ become? And she thought about it and she thought, okay if that is 90 then if you bring the two together, it must be zero degrees between each other. Now but how do we divide by zero? 360. O then she felt really bad because what she had just made up doesn’t work. And he smiled and said you are right, it doesn’t work but we can do a little cheating here. We can cheat a little bit and then we can see what happens. And he said what if it’s not exactly zero but something very, very, very, very, very close to zero? And when he asked that she said yeah maybe, maybe I can make it .00000001 degrees. Then what happens? You can divide by that number. And she said oh my god that looks like a very, very, very large number. And he said how large? Well if we make it .00000000000 and so many zeroes and 1, that number is going to be that much and that much larger. Right. So 360 by Θ is going to be a very, very, very large number. But exactly what you see right. Now what if you make that angle so close to zero, that number becomes extremely close to what we call infinity because the closer and closer that angle becomes to zero, the closer and closer, in one sense of the word, that number becomes infinity. And infinity minus 1, ha, you can’t count it. Anyways, it’s as far as you can see that minus 1 is also going to be as far as you can see. So when you place two mirrors facing each other you get infinitely large images. Again following the exact formula that we derived. Even though it might not appear to be following it at first. So now Alice was in a much, much, much better position to understand little things about life that she always thought she understood. And in that moment it dawned on them and as it dawned on them, literally, and just before they thought it can’t get any crazier, as she began to look at the light, and turned around, just before she thought this is as crazy as it can get, the cat had arranged two mirrors at 60 degrees to each other and she thought, hah, this is not going to be a challenge for me. She knows that if she stands inside, she will see 5 images of herself on each of those sides. She knew that. But what happened after that was that the cat closed the other side as well, as you can see. And when that happened all of a sudden there was a riot. Things were happening crazily and now because the number of images that were happe.. that were being generated was so much, right. One image from the reflection of this, the reflection of that, and so on and so on and so forth so every single point generated so many images till whatever anybody from outside could see, so the cat was enjoying this site where from inside he was able to see something similar to what you’re seeing right now. Artists, the cat said, use this to be able to get creative ideas about what designs to create. Because the moment you take something like this, you have 3 mirrors, you make a little setup with this, put as many colors as possible inside, things that reflect light, shake them apart, and then put it out, you keep getting patterns that keep changing one after another after another, almost so unique that you shake it once and see it again you will not see something that you’ve seen before. Crazy right. A lit.. this little device, it’s usually this small, you, you need not make it that big as show, as we showed it, as the cat did it for Alice. You can do it really, really small. Somewhere over here and as you see it here, right, if you take a little glass and put it on one side, take 3 mirrors, put little broken glass bangle pieces inside, and look. You’ll begin to start seeing a crazy amount of patterns. It’s called a kaleidoscope and it’s been a very, very, very famous toy for a long time. Now even though Alice played with one that was huge and you can find such huge things in certain museums, what you can have within your hand can still be as fascinating as you can think of.