So when we visualize data we usually want to make a decision based on that data. That means we need to reason about the data. And so we need to learn the different ways that the human cognitive system reasons. So what we'll learn is how does a human observer understand a visualization? And how does a human observer respond to a visualization? What are they thinking about when they see this data presented to them visually? So we use the model human processor, but we're going to focus on the cognitive processor, and the information provided to it through the visual image store and visual perception, and how we reason about that information. And there's three kind of reasoning that we'll look at, deductive reasoning, inductive reasoning, and abductive reasoning. Deductive reasoning is basically drawing a conclusion based on the data. It's based on logic, if A then B so, if you see A then you can conclude that B is going to exist. And if B doesn't exist you might conclude that A doesn't exist, because if A happened then B would've happened. So these are all valid logical conclusions based on visual data. Sherlock Holmes used to say, when you have eliminated the impossible, whatever remains, however improbably, must be the truth. And that's basically just the process of elimination, which is again a deductive reasoning method for drawing a conclusion. And so, for example, these reasoning examples, I'm going to use this life expectancy data. This is average data for all countries in the world. And our life expectancy has grown in the 1960s from an average of 54 years, to an average of about 71 years in 2012. And so based on this data, I might deduce that I'm one of the members of one of the countries that was used to create this data. I might expect that my life expectancy has similarly increased over the past few decades. And that would be a logical conclusion based on the information from this graph. Also you can see a correlation here anytime you have a graph that's increasing this way. It's showing a correlation between time and between life expectancy, and so we're deducing, we are concluding that life expectancy is increasing over time. And so people nowadays are living longer than they were a few decades ago, and that's a reasonable deduction. We have to be careful that this is showing correlation and not causation. And that we're not showing that because people are growing older, time is passing necessarily. There are many other cases where two items are correlated, but one does not necessarily cause the other. Or you get the causation in the wrong direction. There's also inductive reasoning, which basically says if something is true for x then it's true for x +1, and you know that's it's true for x, so in that case it's true for all x. If it's true for one specific case, it's true for all of the cases. And these are generalizations. We can use this to extrapolate data, for example, life expectancy. I can look at this shape and I might expect that life expectancy is going to continue to grow at the rate of about ten years every decade and a half. And so eventually we'll live to be 200 years old. And so some generalizations are helpful, some generalizations aren't helpful, and we have to be careful with those kinds of extrapolations. Also interpolation, I've got this data yearly, but I'm drawing this as a smooth line which is an inductive reasoning prediction that says that this is varying smoothly in between the data items, it's interpolated. And it's not varying widely between an individual year and the next year. So inductive reasoning allows us to infer missing data. It allows us to extrapolate data, either before or after the graph, but it's less reliable than deductive reasoning, but still can be helpful. And finally, abductive reasoning. This is based on sort of the human need for meaning, to ask why. And so given this data that life expectancy on average has been increasing over the past few decades, we might start to ask why is that the case, and we might create models. And so in this case the graph is increasing almost like a straight line, and so you can do regression. You can fit a line to this data and create a model for this data. And you can use that model to replace the data, and in our minds we might not think of every single detail of this data. And we might think in general, the data is growing at the rate of our life expectancies, growing at the rate of ten years every decade and a half. And those models are good but they create a problem. For example, cognitive dissonance, it's our ability to entertain simultaneous contradictory opinions at the same time. So it may be difficult for us to think of two things, two opposite models at the same time, even though we don't know which model is correct, and so we tend to take sides. And if our evidence disagrees with our model, sometimes the model is so powerful in our minds, that we tend to disregard the evidence, and that can be dangerous. And so as we go about with visualization, we have sort of the baggage of our models, our expectations of the way the world works, and our abductive reasoning is trying to fit this data to those models. So there are three different kinds of reasoning. There's deduction, where we draw a conclusion. There's induction, where we make a generalization. And then there's abduction, where we try to predict how an event happened. And all three of those are at play when we're understanding the data that we're seeing in a visualization. [MUSIC] [SOUND]
