Last December, me and my fellow Nobel Laureates were asked by a journalist if there was one thing that we could teach the world, what would it be? And to my surprise, two economists, two biologists, a chemist, and three physicists gave the same answer. And that answer was about uncertainty. So I’m going to talk to you today about uncertainty.
To understand anything, you must understand its uncertainty. Uncertainty is at the heart of the fabric of the Universe. I’m going to illustrate this with a laser. A laser puts out a small, but not infinitesimally small point of light. You might think that if I go through and I try to make that point of light smaller by, for example, bringing two jars of a slit together, that I could make that point as small as I want. I just want to make those slits closer and closer.
So let’s see what happens when I do this for real. My friends at Mount Stromlo gave a call and made up a nice little invent, a little here. By essentially adjusting the laser, the slit – we’re going to go through and we are going to see what happens when I close the jaws of the slit. The more I close it, instead of getting smaller, the laser gets spread out. So it works exactly the opposite of what I was expecting. And that’s due to something known as Heisenberg’s Uncertainty Principle.
Heisenberg’s Uncertainty Principle states that you can’t know exactly where something is and know its momentum at the same time. Light’s momentum is really its direction. So, as I bring those slits closer and closer together, I actually constrain where the light is. But the quantum world says you can’t do that. The light then has an uncertain direction.
So instead of being a smaller point, the light has a randomness put out to it, which is that pattern that we saw. Many things in life you can think of as a series of little decisions. For example, if I start at a point, and I can go left or right, well, I do it, let’s say, 50% of the time I can go left or right.
Let’s say I have another decision tree down below that. I can go left, I can go right, or I can go to the middle. Because I’ve had two chances to go to the middle from above, I would do that 50% of the time. I only go one quarter to the left and one quarter all the way to the right. And you can build up such a decision tree, and Pascal did this. It’s called Pascal’s triangle. You get a probability of where you are going to end up. I brought something like this with me today. It’s this machine right here. This is a machine you can put balls into and you can randomly see what happens.
So, for example, if I put a ball in here, it’ll bounce down and it’ll end up somewhere. It’s essentially an enactment of Pascal’s triangle. I need two people from the audience to help me, and I think I am going to have Sly and Jon right there come up and help me if that’s okay. You know who you are. What they are going to do is they are going to, as fast as they can – faster than they are going right now, because I only have 18 minutes – put balls through this machine, and we’re going to see what happens. This machine counts things where they end. So you guys have to go through as fast as you can. Work together, and during the rest of my talk, you are going to build up this. And the more you do, the better it is, okay? So go for it, and I’ll keep on going.
All right. It turns out that if you have a series of random events in life, you end up with something called a Bell Shaped Curve, which we also call a Normal Distribution or Gaussian Distribution. So, for example, if you have just a few random events, you don’t get something that really looks like that. But if you do more and more, they add up to give you this very characteristic pattern which Gauss famously wrote down mathematically. It turns out that in most cases a series of random events gives you this bell-shaped curve. It doesn’t really matter what it is. For example, if I were going to go out and have a million scales across Australia measure my weight.
Well, there’s some randomness to that, and you’ll get a bell-shaped curve of what my weight actually is. If I were instead to go through and ask a million Australian males what their weight is, and actually measure it, I would also get a bell-shaped curve, because that is also made up of a series of random events which determine people’s weight. So the way a bell-shaped curve is characterized is by its mean – that’s the most likely value – and its width, which we call a standard deviation. This is a very important concept because the width and how close you are to the mean you can characterize, so the likelihood of things is occurring.
So it turns out if you are within one standard deviation, that happens 68.3% of the time. I’m going to illustrate how this works for work example in just a second. If you have two standard deviations, that happens 95.4% of the time; you’re within two. 99.73% within three standard deviations. This is a very powerful way for us to describe things in the world. So, it turns out this means that I can go out and make a measurement of, for example, how much I weigh, and if I use more and more scales in Australia, I will get a better and better answer, provided they are good scales.