[MUSIC] So at this point I think it's good to basically do an overview of the different kinds of visualization that there are. For example, there's mathematical visualization. This is the visualization of data generated from a mathematical equation that's readily available just by running a computer program to generate the data. A good example of this is the Mandelbrot set here, this black object. This is basically a shape that's in the complex plane, these are all complex numbers, and you get this shape basically by starting with zero in the complex plane, zero-zero, and you take that and you multiply it times itself and add a constant, and then multiply that result times itself and add the same constant. Then keep multiplying it times itself adding a constant. Depending on which constant you have corresponds to a point in the complex plane. And if you start at zero and keep adding that constant, squaring and adding that constant. If that goes off to infinity, you're out in this purplish region. If that sticks around, you're in the black region. Now mathematicians knew that these dynamics were interesting in the early 1900s, but they did know how interesting the dynamics were or what was going on. And it wasn't until plotted this. Using data visualization to plot the results of these points, to find that the dynamics were very interesting. You got all this great structure. You could zoom into a little section here, and see even more, and more detail, and that was something we just hadn't encountered before in mathematics, and so visualization kind of revolutionized this area of mathematics in our understanding of this area of mathematics by basically getting the data out of this mathematical equation and through our visual perception into a cognitive process so we could better understand it. So, if If you pick a point inside this and you start to look at the dynamics, you get what's called a Julia set. And this plotted in the complex plane. And one of the things I worked on with this was to take this complex Julia set and look what's going on in the quaternions. And again, data visualization is really helpful because you get these whorl patterns. That are basically connecting different parts of this Julia set to other parts of this Julia set through these additional dimensions, and you couldn't understand that very well without actually being able to visualize how those connections are being made. There's also scientific visualization. And this is the visualization of scientific data. And that data tends to either be measured from real world scientific devices or it. Comes as the result of a lengthy expensive supercomputer simulation. In here visualization can be really useful because if you have supercomputer simulation, you can use the visualization as the simulation is being generated to determine if there's problems with the simulation or if you want to steer the simulation in a more productive direction. This tends to be coordinate data, spatial coordinates, XYZ coordinates, time. It measures things like temperature and pressure and other physical quantities, and this is an example from my own work where we're visualizing sort of the fronts of the blood flow as it's coming through a lower aorta that happens to be has an aneurysm here. It's bulging. And the actual calculation of these fronts requires a tremendous amount of computer time. Work in this area has recently taken as long as a month to compute these fronts. But we're able to visualize it very quickly and interactively so we can see what's going on to better understand the complicated nature of this flow which is resulting from millions of simulation steps. And finally there's information visualization. This is the visualization of more abstract, non-coordinate data. For example, what we'll look at in our Data Visualization Course will be, for example, relationship data. And this happens to be a visualization that my students and I worked on a few years ago, these are basically connections between different flicker users on the flicker photo sharing website. And there's 7 million of these connections and so it's far to many to be able to understand by looking at just an ordinary. Graph, but by coloring and clustering and laying things out, we can start to see certain people are more popular and certain photo collections are gaining more attention and we can provide an overview of all of t hat data that you can then investigate in more detail. And so it relies more heavily on this information visualization. It relies more heavily on the ability to process the data from its abstract form into something geometric, something concrete that we can then transmit to our brain from our visual channels. But that conversion becomes more challenging with information visualization, then perhaps it is with scientific or mathematical visualization. And there's a variety of different domains that visualization is used in. It's used in medical imaging. For example taking CT Scans and being able to reconstruct three dimensional shapes from that so you can get a better context of where you are spaciouly and the patient data. Being able to take business intelligence information marketing results and being able to present those in a way that makes it easier to make a business decision. Educational visualization, this is a visualization of how quaternions multiply, that I made a few years ago that helps the user understand geometrically what's going on with an otherwise abstract four dimensional number system. Or geographic information systems, taking data that's geographic in nature, and being able to plot that in ways that helps you reason about your region, or about the world as a whole. And finally, there's some modes of visualization, and these are important to understand for data visualization in general. There's three that we'll go over., the first is interactive visualization and this is the kind of visualization that's used for discovery. Basically, a single investigator would use this. Maybe one or two collaborators might join in, but its basically a single investigator in front of a computer. And, plotting data to try to understand what's going on with the data. You've got full control of the data and you can change what data sets and how it's displayed on the fly in order to help understand what you're looking at. And that's different than, for example, presentation visualization. Presentation visualization is the kind of visualization that we use for communication. Its a kind of visualization that you would see in a video or in a slide presentation and its intended for a large group or mass audience to basically communicate some aspect of data to that mass audience. And the difference between presentation visualization and interactive visualization, mainly, is that presentation visualization doesn't support user input. So you're just sitting there and observing, but you can't really interact with the data. You're just sort of getting the data packaged in a way that helps you understand it, without the interaction. In between here, there's the Internet has basically enabled this third mode of visualization that has been called interactive storytelling. And these are presentation visualizations, but they are presented via interactive web pages. And so they allow the viewer to interact with the data in some limited fashions. The viewer can't change the dataset. But they can sort of investigate a little bit further and there's more information that can be presented all at once, as it would be with a presentation visualization. And so another way of describing these differences is to visualize the modes of visualization, and so I've laid them out in a table. We can compare them in terms of user interaction. Interactive visualization, the user controls everything including what data set you're looking at. In presentation visualization the user is only observing, there is no interaction. In interactive storytelling there's a presentation, but the user can still filter the data, or inspect details of the data, but can't necessarily change the data set that they're looking at. There's different graphics rendering methods. You would use real-time rendering. Anytime you're supporting interaction as you make changes, your display needs to respond to those changes so you need real time graphics to do that. Where as presentation visualization, the rendering is precomputed and stores, say on video or images in a slide show. The target audiences are different. For presentation visualization, you're targeting a mass audience, your colleagues or everybody that goes to your webpage, whereas the target for interactive visualization is an individual investigator or maybe a small group of. Collaborators that are working on understanding some data. And finally, the medium is different. When you're running interactive visualization, you're running software and the Internet can enable some software to be run, but it's basically running a software program on a computer. In order to display the data. When you're doing interactive storytelling, you're working mostly on the Internet or some other information kiosk that can support a mass audience. When you're working on presentation visualization, you're working on slide shows, or video, or some other format that allows you to prerecord the visuals, and then present them to a mass audience. [MUSIC]