In this section, we're going to consider the perennial trade-off between simplicity and complexity. So we've already made reference to the world being a very complex place. Now, other things equal, we dislike uncertainty. If I asked you to describe the world, just considered a simple binary choice. Is the real world a, a, nice simple and easy or b, big, horrible and complicated? Well, clearly, it's the latter of being b. However, you'll be much nicer for us if it was nice, simple and easy, i.e, option a. So whenever we try to understand the real world around us, what we would like to try and do, is to simplify things as much as possible. Because there's an inherent appeal for simplicity over complexity. We like things to be as easy as possible for us to follow and to understand. So within a learning environment, we're not necessarily restricted to say statistics, we could extend this to mathematics, economics, finance, I know that I'm sure many qualitative disciplines as well. But our goal is to try and model the real world. So what is a model? Perhaps, many definitions we could offer here, but aversion I like is to say, a model is a deliberate simplification of reality. Such that we are trying to model some real world phenomenon, whereby a good model is one which captures the most important features of the real world and ignores some less important, some trivial details. So do keep in mind, that a model does not equal reality. However, a good model is one which is very close to reality. So the real world highly complex, we dislike it. So if we work with a model, we gain simplicity. So we reduce the complexity, improve the simplicity as we go from the real world to a model. But of course, that model is a departure from reality. So we do lose a little bit of realism. So the question is, is this trade-off acceptable and how to resort to resolve this trade-off? Well, ideally, we would like the benefit, I either gain in simplicity to be enough to off-set the slight loss of reality that we inevitably get with a model. So as an interesting example, I'll offer you the London Tube map. This is an iconic map, whether or not you visited London before, you may well have seen a snapshot of the world-famous Tube map. Now arguably, I could have chosen any metro system around the world for this example, they will all have similar maps which people use. But this is the University of London, so let's be London centric for a moment. So is this a good model? Well let's revisit my definition of a model. A deliberate simplification of reality. So is this a good model or a bad model? Well, arguably, the answer to this question is it, depends. It depends who we are and what we wish to use this model for. Now, if you are lets say a tourist visiting London, I offer this up as an excellent example of a model. So what do we see on the Tube map? Well, we see different colors representing the different London underground lines. Now, if your goal is simply to get from point a to point b and provided you're not colorblind and can read the station names, this Tube map is excellent for achieving that simple objective from point a to point b. Why? Because this map offers the need to know information for achieving that objective. It tells you the order of stations on a particular line, you have the different colors to distinguish the different lines, and it also shows the points of intersection where you would change from one London underground line to another. Frankly, if your goal is to get from point a to point b, that's the essential information you need to know. Now, show how familiar you are with the London Underground map, but there's different colors to represent different lines. Let's just pick one of them, the yellow line. Now, this is called the circle line. I'm sure you all know what a circle is, something like that. If you have a look at the London Underground map, you will see that the so-called circle line is in fact, a lie, because the line is not a true circle. It does go around in a bit of a loop, but it's not the exact geometric circle that you would have been familiar with from school maps. Nonetheless though, it is a simplification of what we observe in reality and you see that loop and circle seems a reasonable enough name. Perhaps, to pick another one, the red line. This is the central line passing through array, the main part of Central London, roughly from East to West. Now, if let's say you look at the center of the central line, you will see a straight red line on that London Underground map. You'll also see according to the map, that they stations are equi-distant from one another, the gap from one station to another it seems to be exactly the same. Well, if any of you have been on the London Underground line or any of those lines, I'm sure you can attest to these tunnels not being dead straight under the streets of London. They often have to hold onto the handrail as the train meanders through some curved tunnels under the streets. So the map does not clearly represent those features, that straight part of the red line there, the central line, is simply used to simplify reality. Frankly, if your goal is simply to go from point a to point b, do you really need to know exactly how that tunnel meanders underneath the streets? Clearly not. So at that map, for let's say, a tourist, someone just visiting London, is indeed fit for purpose. It tells you the essential information that you need to know. But of course, it is not a perfect representation of the real world. Indeed, we know those tunnels do move in curves and there are many bends along the way. Also, not represented on the map, would be the depth of those tunnels. Some indeed actually are on ground level, some of them very deep underlying. Indeed, they are the black line, the Northern line I believe is the deepest of the London Underground Lines. Now, depth is not presented on a map, but frankly, to get from point a to point b, you don't need to know that piece of information. On the other hand, if you were let's say an engineer, you're responsible for maintaining the tunnel network, maybe doing some repairs to the rails say. Then clearly, that geo-map would not be fit for purpose. You would need to know the exact distance between the stations, which is typically not equi-distant as the map seems to suggest. You will need to know where the actual access points are, you'll need to know exactly how that tunnel bends around under the streets, you'll need to know the depth information and other things as well. So depending on who you are and what you need that map for, you could argue it's a good model or it's a bad model. But of course, we know it does this world famous iconic map primarily for its use not by those engineers, but for the general public and tourists visiting London. So in that sense, I uphold this as a great example of a model. It retains the most important features that one needs for decision making, i.e, how to get from point a to point b and ignores less important details. However, it can be a little bit misleading. So you'll also find access through this MOOC course to what I call the the real London Underground map which is in fact, more geographically accurate. So perhaps as a takeaway exercise for yourselves, is for you to compare the familiar looking Tube map with those nice straight lines, very easy for people to interpret with the geographically accurate Tube map and see a comparison of the two. Now, both are examples of models. Even a geographically accurate one still omits some information. For example, the depth of those tunnels, you can't see those on that geographically accurate representation. Now, perhaps there's as a question, an open question to you to consider, is off those two maps, both the models, they're clearly different models. One geographically accurate, the other not. Which one of those is the better model? Well, given as an open-ended question, I would perhaps offer maybe a subjective answer here. Namely, it depends. There's clearly a trade-off between these two models. The geographically accurate one has the advantage of being geographically accurate. It's perhaps using that one, it's clearer to see their relative distances between your one and another and to perhaps decide on the optimal route in terms of the quickest route to undertake. Whereas, the more familiar looking Tube map is geographically inaccurate and can give very misleading indications as to the distance between stations, just as perhaps a simple example of that, if you compare say, edge-way road station with marble arch across these two maps and judge for yourselves what might be the optimal routes to take from one to the other. I'll give you the answer here. In fact, the quickest thing to do is to actually walk it. But these are both models. There is a trade-off. Geographically accurate is a good thing, but you might see you looking at it, it's a little bit more confusing to use than the more familiar form. So potentially, we could offer that up as an explanation for why transport for London, the transport authority here, for getting people from a to b through public transport opts for that more iconic map than the geographically accurate version. So I'm not saying these are academic models, but are familiar things, which really emphasize the point about what a good model should try and be, namely a deliberate simplification of reality.