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[MUSIC]. 
In the last lecture, we provided a set of 

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three exercises on mapping data types to 
visual attributes. 

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In this lecture, we are going to give 
more examples of data combinations and 

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the mapping of data to visual attributes. 
And we'll talk about the effects of 

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dimensionality on the visual display. 
So, if you have a single variable to 

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display or univariate data, you have a 
plethora of choices for visualizations. 

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Dot plots, line plots, bar graphs, or 
Tukey box plots are but a few of the 

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examples. 
For bivariate quantitative data, the 

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scatter plot is the most common choice. 
So, here we have two quantitative 

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variables, and the scatter plot describes 
the information quite clearly. 

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Moving up to three dimensions, now it's 
getting a bit more challenging. 

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So, we can try a 3D scatter plot, but, 
what are some of the problems? 

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Let's look at the 3D scatter plot on the 
right with blue cubes. 

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Where, exactly, are E and F in relation 
to each other? 

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It's a bit of a problem trying to 
represent 3-dimensional information on a 

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2-dimensional surface. 
A better choice might be to use a 

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2-dimensional scatter plot, with a third 
dimension represented by some other 

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attribute. 
Here we use area for the red circles for 

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the third quantitative dimension. 
Area's not perceived as accurately as 

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position, so you want to put the most 
important dimensions on the x and y axes. 

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And save the least important or perhaps 
the most easily distinguished for the 

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third. 
Since we already discussed what are the 

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issues in trying to map three variables 
to a third spatial dimension. 

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Let's look at other ways to deal with 
mapping three variables to a 

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visualization. 
So, we know that two variables on the x 

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and y axis can map to points. 
So, we have scatter plots, maps, et 

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cetera. 
Now the third variable must use something 

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like color, size or shape. 
And as you can imagine, we have a very 

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large design space. 
So, finding the optimal mapping becomes 

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more challenging as the number of 
dimensions increases. 

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You can always use shape or different 
types of marks, to represent nominal or 

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categorical data. 
Now, moving up to multidimensional data, 

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how many variables can be depicted in an 
image? 

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We've talked about one, two, and three 
dimensions. 

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But what about more? 
Is there some perceptual limit? 

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Starting in 1967 Bertin and others asked 
this question. 

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And Bertin stated, with up to three rows, 
a data table can be constructed directly 

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as a single image. 
However, an image has only three 

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dimensions. 
And that barrier is impassible. 

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We'll look into answering this question 
in the next lecture.