## RESEARCH QUESTION--

Analysis of Dirty Pictures By-the-Numbers?

### Math for art's sake

Paint-by-numbers painting was a largely American phenomenon, in which planar maps were turned into paintings. The result: quantitative digital artworks that preceded the electronic digital revolution of the 1960s, 70s, and 80s. An exhibition of these paintings has been mounted at the Smithsonian Institution's National Museum of American History, in Washington DC.

(Mathematicians, of course, were familiar with such things long before the general public paid any notice. The four-color map problem bedeviled mathamaticians until it was solved in 1976 by Wolfgang Haken and Ken Appel at the University of Illinois.)

#### The Problems

But these pictures -- the ones on display in Washington -- are old, and collectively they present two problems: First, some of the pictures are incomplete. Second, some of the pictures are dirty.

#### The Likely Solutions

The solution to the first problem waa developed in 1931, by Kurt
Goedel, and is now famously knowns as **Goedel's
Incompleteness Theorem**

The solution to the second problem is more recent. Like Goedel's work, it can be found in almost any good science library:

"On the Statistical Analysis of Dirty Pictures," Julian Besag, Journal of the Royal Statistical

Society B, vol. 48, 1986, pp. 259-302.

The author, Julian Besag, is a professor in the statistics department of the University of Washington.

**NOTE:** If any reader succeeds in applying Besag's technique to dirty
paint-by-numbers pictures, it would be a courtesy to notify
Professor Besag and thank him for his still resounding contributions
to science and to art.

© Copyright 2001 Annals of Improbable Research (AIR)

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