[MUSIC] So far you've learned how to develop a mathematical model to capture the critical details of a given disease. In the next few lectures, we will start working with actual data. And we'll discuss ways of making sure that your model can capture real world data. But before that, it's worth taking a step back to think about the relationship between models and data in general. This is a relationship that you'll find in many different fields from climate science to financial engineering, and many of the core concepts are shared across these disciplines. For this lecture, we're going to look at our understanding of the solar system, and how this understanding has changed over thousands of years. As you'll see the story has some important insights that are helpful to keep in mind when confronting any kind of modeling with real world data. Our ancestors would have seen the sun, moon, and stars and would have noticed a certain regularity to the way these bodies move across the sky. If we have a good model for the motion of these bodies, then we can predict where they will be at any given point in future. This used to be important not only for astrological predictions but also for any form of navigation requiring observation of the heavenly bodies. So let's go back to ancient Greece over 2,000 years ago where the prevailing view was that the sun, moon and stars all revolve around the Earth. And not only that, the ancient Greeks place great value on the harmony of perfect geometry. And so they believed that all the heavenly bodies orbit to the earth on a surface of perfect spheres. This seemed to work reasonably well but only up to a point. The problem was that several planet seem to behave in pretty quirky ways. Planets were known to change their brightness as they orbited. And even more alarmingly, Mars will sometimes appear to stop and reverse in motion. To get around these problems the ancient Greeks proposed the existence of epicycles which means the planets were not fixed a perfect spheres, but rather they had circular orbits around points on those spheres. If you like, orbits around orbits. And notice here how an existing model was tweaked and made slightly more complicated. This occurred to accommodate data that the original model could not explain. In fact, the Greeks went a step further to propose epicycles upon epicycles. The model was getting more complicated. However, it wasn't until the Copernican revolution in the 16th century that we started to think of the Earth and planets as revolving around the sun. Of course, this was a fundamental shift in the way we had been thinking of ourselves and our place in the cosmos. And Copernicus was motivated by two observations. Although the model of the ancient Greeks didn't perform too badly in their time, it had small errors that got worse and worse over the centuries. And also, the system of cycles and epicycles had gotten really complicated. Copernicus knew that a sun centered model could explain the facts in a simpler way. However, he's still stuck with circular orbits, and so his model still needed epicycles. We now have to jump forward another hundred years to the time of Johannes Kepler who realized that planetary motions around the sun we are not perfect spheres, but instead we are ellipses like a square circle. And just like that it was possible to get rid of epicycles. Isaac Newton then explained by a very simple rule of gravitation that depended on the mass of two bodies and the distance between them, how elliptical orbits could exist. And that's amazing progress over the last thousand years. However, there was still some nagging behavior that couldn't be explained. The planet Mercury is the closest to the sun, and very strangely, its orbit around the sun tends to shift over time. The existing models couldn't explain why. Again, we need to jump forward over 200 years to the time of Albert Einstein and the Theory of General Relativity. Although Newton's laws were a good approximation in most of space, Einstein's theory showed how they tend to break down new highly massive objects like the sun. And those environment space and time get distorted and Einstein's equations could explain why these distortions have such an effect on Mercury's orbit. They could also explain many other astronomical phenomena. Now, I skipped over contributions from towering figures like Tycho Brahe and Galileo, who critical and providing a detailed astronomical observations that people like Kepler could use to develop new theories of the solar system. But the important thing is to notice how we've moved from the model of the solar system based on perfect sphere centered around the Earth to ellipses with a focus on the sun, all the way to the present day ideas of how gravity distorts space time. The general trend is that models become improved as we strive to make sure that they remain faithful to the data. And sometimes this means that models should be made more complex as in the development of general relativity. But sometimes this means that existing models should be simplified. For example by considering the sun, not the Earth as the center of the solar system. So let's bring our minds back to infectious diseases here on Earth. In the next few lectures and activities, you're going to start comparing your models with data. As such, I'd like you to keep the same things in mind. Am I happy with the way my model is explaining the data? Is my model doing so in the simplest possible way, or do I have unnecessary complications? On the other hand, are there critical features that my model is missing? All of these are important questions to keep in mind when confronting models with data. [MUSIC]