Day 34: Heart of Mathematics

1. Scales on graphs
2. Dimensions of content
3. The type of graphic: (we have choices, after all!)
   • Our authors propose pie charts: others argue against them

     Notice that pie charts use areas proportionally to the values represented (not heights or widths, as we saw in the doctor and dollar graphics above).

   • It is little known that Florence Nightingale, nurse extraordinaire, was also the creator of a sophisticated version of the pie chart. She is called "... a pioneer in the visual presentation of information and statistical graphics."

   • Here's an odd graphical technique for showing high-dimensional data: Chernoff Faces (local copy)

   • I just came across the following article in cnn.com this weekend, titled "Mapping out a new world order". These data maps use area effectively, counteracting the areal problem of the data map of the recent Presidential election (voting shifts)

     "Worldmapper" is the group that's doing this this important mapping.

4. "Emotional content" of a graphic:
   • We have to be careful to refrain from letting our statement or aesthetic issues get in the way of presenting the data. For example, this illustration of the disparity between the CEO and the average worker.
     • What's wrong with this graphic?
     • What's right about it?
     • Let's take a moment to ask ourselves why CEO salaries have been growing so rapidly. It's an example of what I call "bad social dynamics".

       Here's an example of "social dynamics" in an aphorism: "spare the rod, spoil the child."

       Can you think of an aphorism that explains why CEO salaries have been going through the roof?

   • Here's one that I think is done beautifully: U.S. Private Wealth in Perspective. This may be due in part to the change in the Tax Rates Over Time in the US.

• show the data
• induce the viewer to think about the substance rather than about methodology, graphic design, the technology of graphic production, or something else
• avoid distorting what the data have to say
• present many numbers in a small space
• make large data sets coherent
• encourage the eye to compare different pieces of data
• reveal the data at several levels of detail, from a broad overview to the fine structure
• serve a reasonably clear purpose: description, exploration, tabulation, or decoration
• be closely integrated with the statistical and verbal descriptions of a data set.

1. The representation of numbers, as physically measured on the surface of the graphic itself, should be directly proportional to the numerical quantities represented.
2. Clear, detailed, and thorough labeling should be used to defeat graphical distortion and ambiguity. Write out explanations of the data on the graphic itself. Label important events in the data.
3. Show data variation, not design variation.
4. In time-series displays of money, deflated and standardized units of monetary measurement are nearly always better than nominal units.
5. The number of information-carrying (variable) dimensions depicted should not exceed the number of dimensions in the data.
6. Graphics must not quote data out of context.

Here's our mascot for this unit:

Created by a very simple mathematical process

• a simple rule
• repeated over and over and over....

The pictures remind me of the "acres of dominoes" from Robert Graves's Warning to Children....

• fractals by subtraction

• After we're finished removing all that stuff, how much area is left in the triangle?

• The Chaos game - generating fractals using random movement! (p. 447)

  Once again, simple rules lead to complex objects. This time, however, we don't proceed methodically, but rather haphazardly - and yet we still produce the complex images!

  • with 10 points
  • with 100 points
  • with 500 points
  • with 1000 points
  • with an infinite number of points!

  • Here's a better version of that, that has more general options.

    From randomness comes order. From simple rules comes complicated objects.