Empirical Modelling, or Color Me Sudoku

When it comes to puzzles like Sudoku, I'm no Will Shortz, or even a Mark Nelson. Nor, for that matter, do I have a leg up on researchers at the University of Warwick’s Computer Science Department who've taken Sudoku puzzles to a new level.

Based on the work of Meurig Beynon and PhD student Antony Harfield, what they've developed is a color-based Sudoku puzzle to demonstrate the potential of "Empirical Modelling":

Empirical Modelling (EM) is about making artefacts to support human thinking. Interacting with such artefacts using computer technology enables us to think with computers, and is quite unlike conventional interaction with programs. The former is personal and cognitive, to do with exploring experience and meaning; the latter is impersonal and circumscribed, to do with achieving functionality and efficiency. EM proceeds by elaborating scripts to create interactive artefacts that are works of the imagination, reflecting experience and current understanding but open to many interpretations.

They go on to say that:

The term 'Empirical Modelling' supplanted the term 'Agent-oriented modelling' in 1992. The epithet 'empirical' was adopted in part because our modelling principles are based on observation and experiment, and in part to avoid confusion with the concept of 'agent-orientation' that became mainstream over the period 1987-92. The term 'modelling' is more appropriate than 'programming', since EM involves the construction of artefacts, and an accompanying identification of primitive patterns of interaction with artefacts, that may or may not lead to the type of functionally determined behaviour that is characteristic of a classical computer program.

Okay, but what does that have to do with Sudoku? Well, Colour Sudoku adds another dimension to solving the puzzle by assigning a color to each digit. Squares containing a digit are colored according to the digit's color. Empty squares are colored according to which digits are possible for that square taking account of all current entries in the square's row, column, and region. The empty square's color is the combination of the colors assigned to each possible digit. This gives players major clues as darker colored empty squares imply fewer number possibilities. Got that? An empty square that has the same color as a completed square must contain the same digit. If a black square is encountered, then a mistake has been made. Players also can gain additional clues by changing the color assigned to the each digit and watching the unfolding changes in the pattern of colors.

If you want to try this out for yourself, go to www.warwick.ac.uk/go/sudoku.

Steve Russ, another member of the Empirical Modelling group adds this explanation:

Traditional computer programs are best-suited for tasks that are so well-understood they can, without much loss, be expressed in a closed, mechanical form in which all interactions or changes are 'pre-planned'. Even in something so simple as a Sudoku puzzle humans use a mixture of perception, expectation, experience and logic that is just incompatible with the way a computer program would typically solve the puzzle. For safety-critical systems (such as railway management) it is literally a matter of life and death that we learn to use computers in ways that integrate smoothly with human perception, communication and action. This is our goal with Empirical Modelling.

The only part I have a problem with is the "something so simple as a Sudoku puzzle." Like I said, I'm no Will Shortz, Mark Nelson, or, for that matter, Steve Russ.

-- Jonathan Erickson
jerickson@ddj.com

Posted by Jon Erickson at 09:07 AM  Permalink