If I can’t picture it, I can’t understand it

June 23rd, 2014


“If I can’t picture it, I can’t understand it.” – Albert Einstein


Along the same lines

“It is impossible to even think without a mental picture.” – Aristotle:

“Man’s mind cannot understand thoughts without images of them.” – Thomas Aqunias:

“The evolution of images is a kind of intermediate between that of the perceptions and that of the intelligence.” – Jean Piaget:


“Mathematics is cognitive process-thinking-that requires the dual coding of imagery and language. Imagery is fundamental to the process of thinking with numbers. Albert Einstein, whose theories of relativity helped explain our universe, used imagery as the base for his mental processing and problem solving. Perhaps he summarized the importance of imagery best when he said, ‘If I can’t picture it, I can’t understand it.’ “– NANCI BELL AND KIMBERLY TULEY


One of my favorite examples of the power of graphics to easily, quickly and powerful display quantitative information is Anscombe’s Quartet.

From  http://en.wikipedia.org/wiki/Anscombe’s_quartet

Anscombe’s Quartet
I II III IV
x y x y x y x y
10.0 8.04 10.0 9.14 10.0 7.46 8.0 6.58
8.0 6.95 8.0 8.14 8.0 6.77 8.0 5.76
13.0 7.58 13.0 8.74 13.0 12.74 8.0 7.71
9.0 8.81 9.0 8.77 9.0 7.11 8.0 8.84
11.0 8.33 11.0 9.26 11.0 7.81 8.0 8.47
14.0 9.96 14.0 8.10 14.0 8.84 8.0 7.04
6.0 7.24 6.0 6.13 6.0 6.08 8.0 5.25
4.0 4.26 4.0 3.10 4.0 5.39 19.0 12.50
12.0 10.84 12.0 9.13 12.0 8.15 8.0 5.56
7.0 4.82 7.0 7.26 7.0 6.42 8.0 7.91
5.0 5.68 5.0 4.74 5.0 5.73 8.0 6.89

 


Edward Tufte uses this example from Anscombe to show 4 datasets of x and y that have the same mean, standard deviation, and regression line, but which are qualitatively different.

 

 


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  2. June 23rd, 2014 at 17:54 | #1

    Kyle,

    Excellent point. Too often data is “lost” when not adequately visualized. And when data is put in the correct context, it reveals a lot about the collected information.

    Cheers,
    Maaz


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