 So the next topic we're going to talk about is mechanics, which is just the rules by which everything moves. And this is one of the most foundational elements of modern physics, in fact. Before that, people thought that everything had its own rules, and after the laws and mechanics were discovered, people realized that everything in the entire universe seemed to follow the same rules. Rather than rocks being different to planets or stars, it was realized that they actually follow the same universal principles. Now, if everything follows the same physical principles, then you'd imagine that we'd be able to figure out what they were fairly quickly, because everything would be reasonably simple. So why did it take literally thousands of years to figure out the laws and mechanics? Well, there's two main reasons. The first is that a rock and a waterfall and a feather and a fire and a star all behave extremely differently. And the main reason for that is that even though they follow the same rules, they're composed of very different things and they have very different environments, which means that when they follow those rules, they do very different things. And the second is the underlying rules are quite different to the apparent behavior of all the things we see around us. For almost 2,000 years, the dominant ideas of how things move came from Aristotle. And he described two kinds of motion. He described natural motion and violent motion. Now, the natural motion of something was what it would do if it was left to its own devices. And there were five kinds of things in the universe according to the Aristotleian point of view. So the idea was that everything below the moon was made up of the four elements, earth, air, fire and water. And they all had a natural motion that was at rest, just still, and on the ground. So the earth would be in the bottom, then the water, then fire, then air. And the idea was that the ether made up everything that was in the night sky. So stars, planets, the sun, all those kinds of things. And then natural motion was to move and stay in the sky. And then violent motion was everything that you would do to make something behave against its natural motion. So for example, if you throw a rock, which is mainly made of earth, the natural motion is for it to be at rest and on the ground, and you have to apply some force to it in order to make it move. Now I don't want to go into enormous detail about Aristotleian physics, because all of it is wrong. But it doesn't look so wrong at first glance. So for example, it's hard to know whether things are made up of earth, air, fire and water, or atoms, because we haven't seen either of those things. And it's hard to know whether things weigh up in the night sky are made of something else, because we haven't been there. And also this idea of things having a natural motion at rest and on the ground, that's incredibly intuitive. It's intuitive because all the things I see when I look out my window are at rest and on the ground, with the possible exception of a fountain of water, and that water is dripping down because it was pumped up there. So someone imparted some violent motion to get it up there, and then pretty shortly afterwards it's at rest and down in that pool. Look around the room now, you probably see a large number of objects, and they're probably at rest and sitting on things or on the ground. And so in other words, this is a very strong intuition that we have, that that is normal. And so all of this was so convincing and reasonable sounding that over the next thousand years it became accepted knowledge. People were taught it, educated people were taught it, would teach other people. It became Christian church dogma. And really over the next thousand years, the only things that happened is that various people worked on trying to improve the details of this idea of violent motion. So if you pick up a brick and you throw it, once you've given it that force, you can make it move and make it not be on the ground. But once you let go, why does it keep moving for a while? Why doesn't it just stop and be on the ground at the same time suddenly? And how do you get through the details of that? And people invented ideas of things called impetus, which is the set of ideas that try and describe from an Aristotleian point of view how something that's been thrown keeps moving even once you let go of it. And this was invented by a Greek philosopher and subsequently refined and analyzed by Persian philosophers and then eventually Western philosophers until finally it came to Galileo Galilei. Who, after a large number of careful experiments and measurements and a lot of thought, came to the conclusion that the problem wasn't in an insufficiently detailed model of impetus but rather with Aristotle's fundamental idea of natural and violent motion. And instead Galileo said that rather than requiring a force to make something move, if you don't apply a force to something, then it will keep moving exactly the way it was moving. So if something was at rest, then with no force it will stay at rest. But if something is moving, then if you don't apply a force, then it will keep moving. So something has the same speed in the same direction. That means it has the same velocity. So velocity is the vector that has the speed and the direction of that speed. And so that's a nice statement of Galileo's discovery. It is now typically called the law of inertia or most commonly Newton's first law. Newton came along much later and used Galileo's work as the basis on which he built his laws and mechanics. And Newton's laws and mechanics enabled him to quantify exactly what happens when you do have forces. So in the Aristotelian worldview, a book sliding across a desk comes to rest because that's what books do. Books like everything else on earth should be at rest. In the Galilean Newtonian point of view, a book sliding across a table stops because there's friction. And if the book falls off the edge of the desk and falls toward the ground, there are two explanations for that. In the Aristotelian worldview, the book is mainly made of earth which means it wants to be as close to the earth as possible and so it goes down. And in the Galilean Newtonian point of view, it experiences a force called gravity. And the reason that the Galilean and Newtonian point of view really supplanted all those old ideas is that the force of gravity also explains why the moon acts the way it does and why the moons of Jupiter act the way they do and the celestial bodies. So we have this common theory that describes everything that we see on earth in terms of gravitation and everything in the sky. And so the fact that the Newtonian laws were both universal and quantitative enabled people to explain everything that they used to be able to explain and more meant that those ideas supplanted the old ones rapidly.