Let's move on to the implications for design related to separability. There are two main implications for design: The first one is that you should use integral dimensions when the effect that you want to obtain is holistic. What do we mean by holistic? Holistic means that you want your viewer to react to the graphics that you encode with two or more dimensions. Let's focus on two is easier. As one single unit, you don't want the viewer to think about one unit regardless without thinking about the other one. They are perceived as one single thing. I give you an example in a moment that is going to make this much clearer. What as you want to use separable dimensions, when you want the viewer to be able to focus on one single dimension at a time and then to the other. So, you want to be able to differentiate between the different channels that encode the different pieces of information. Let me give you a couple of examples that make this concept probably much much clearer. Here we have once again the same kind of plug that we used in previous examples. On the X-axis, we have sugar. On the Y-axis, we have calories, every single dot represents one food, and the foods are colored according to food categories. Now, if you think about it, what you can do with these graphics is that you can focus on the property of color and visually group all those elements that belong to a particular category. But you can also focus on position in trying to extract information about which objects, which items are in which position, and how they relate to the values that they represent. As we have seen before, position and color is highly separable, so it's very easy for you to focus either on one or the other without having any interference from one channel to the other. Now, let's move on to another example where we are using integral dimensions. Here we have a dataset that represents Body Mass. What is Body Mass? Body Mass is created as an equation of two parameters that are weight and height. Now, in these graphics, every single dot represents one person and it's represented through an ellipse, and the width and height of this ellipse are proportional to the weight and height of the person. Now, if I ask you to observe these graphics and tell me which individuals have a Body Mass that is proportioned between weight and height, which basically means which one is closer to circle, it's very easy for you to do it because you just have to look for objects of a specific shape. They are not elongated horizontally. They are not elongated vertically. You want to look for those that are as close as possible to the shape of a circle. But think about what you're doing here. The shape is actually given by the combination of two attributes. As we said, height and weight, but you are never really attending to one of these two attributes individually. You are perceiving them as one unit and that's what you want the graphics to communicate. So, this is an example where we are encoding two attributes through two integral dimensions. And because of that, the way we are perceiving this information is exactly the way we want it to be perceived as a unit, as we said before, holistically. So that's what it means to use integral dimensions in an appropriate way. Let me give you another example that is very very similar. Look at this map. So this is a map of the United States. And once again, we have information represented through an ellipse, and we have the width and the eye of the ellipse representing the amount of votes that go to Republicans and amount of votes that goes to Democrats. Now, once again, if I ask you to tell me what are the states where the two parties are balanced, you basically have to translate these into the visual query of looking for elements that are as close as possible to a circle. And that's another good example of using on purpose integral dimensions to perceive elements that are built through the combination of two attributes. This doesn't always work very well, so you have to be careful. Here is another example of a map where three quantitative values have been encoded as three different channels of color. Now, the problem here is that, in these original graphics, you should be able to identify areas where the three individual attributes one should be able to detect them independently from one to another. But this is impossible in this graphic because trying to discern for every single element, how much of each color is present is really really hard. Look at the legend on the left. There are four main colors in trying to figure out how much of each color there is in one area is extremely extremely hard. And by the way, it's also hard if you want to obtain the effect of an holistic view, it's really really hard to understand which areas have exactly the same combinations of the three colors. So, this doesn't always work and you have to be really really careful in the way you're using this technique. But the general idea is use separable channels when you want the viewer to be able to attend to one channel without the other, without the interference of the other, and use integral dimensions when you want the viewer to be able to perceive the combination of the attributes as one single thing.
