How to graph 5 or more variables at once?

[Munfred]

Hi there

For quite some time now, I've been wondering if/how it would be possible to plot 5 or more variables on a single graph. If we have 2 variables we can make a simple 2D graph, if we have 3 variables we can make a 3D graph and if we have 4 variables we can make a 3D graph that changes in time (a video). Now, what if we want to plot 5 variables? As I understand it, each variable requires a whole dimension, and since we only have 4 dimensions at our disposal (3 spatial and one temporal) it looks to me that we can't have 5 variables plotted at once, due to the limitation of the number of dimensions of the universe we live, unless we made infinite animated graphs, each one to illustrate one value of our 5th variable.

So, how do we solve this problem? Or will we have to accept that we can't possibly plot all possible values for 5 variables at once?

Thanks in advance

 

[nicksauce]

How about using the Hue and Saturation of the graph to represent another variable or two? (For example, see any plot of the CMB fluctuations)

 

[Munfred]

Well, yeah, like in a ternary graph we can in fact represent 3 variables in a 2D space, but that's because they have to sum up to 100%

Suppose a equation with 5 variables, how could we possibly graph it, showing all values that al variables can assume?

 

[HallsofIvy]

Sometimes called "the best statistical graph ever drawn", Charles Minard's graph shows the position, and direction of Napolean's army advancing on and retreating from Moscow in 1812 as a function of time and gives the air temperature at each time. Counting position as two variables, that is a total of 5 variables on one map.

http://www.edwardtufte.com/tufte/posters