# Color Sudoku game adds twist to computing

An interactive Sudoku game that features shifting color patterns is adding a new twist to the popular puzzle, a novelty its creators hope will spur wider recognition for a rather unorthodox way of thinking about computing.

Designed by Antony Harfield, a doctoral student in the Department of Computer Science at the University of Warwick in the United Kingdom, the online game is one of many programs designed by the department’s researchers to explore the interplay between logic and perception as humans interact with computers.

The theme is central to what the scientists call Empirical Modelling, a 25-year-old approach that has yet to be widely embraced by the larger field of computer science. Nevertheless, its backers believe the unique take on programming could be harnessed for creative applications in artificial intelligence, computer graphics, automation and educational technology.

“It’s really, we believe, quite a radical alternative to computation,” said Steve Russ, a lecturer in computer science at the university. “It’s not replacing it — it’s just saying there’s an awful lot more that we need computers for than just algorithms.”

The human factor
Empirical Modelling, he said, pays more attention to what humans take into account and provides a practical means to explore problems that aren’t so cut and dry. Our thought processes include reasoning, of course, but Russ said we’re always on the lookout for rumors, body language and other signs of potential deception that get built into our experience. Plus, we often learn from our mistakes.

For Sudoku, understanding can emerge through a mix of perception, expectation, experience and logic — a combination Russ said is a far cry from how traditional computer programs would try to solve the puzzle. Color adds yet another dimension to the human problem-solving repertoire, in this case for a game normally associated with numbers.

In regular Sudoku, players try to correctly arrange the numerals 1 through 9 within a partially completed grid of 81 boxes.

The new version has assigned a unique color to each numeral: 1 may be matched with red, for example, while 2 equals brown and 3 a forest green. Squares with numbers already in place on the game board are colored accordingly, while each empty square assumes a blend of colors representing the possible digits that could go there. As a player fills in more numbers, the open squares change colors to reflect the new limitations — with a blend of red, brown and forest green perhaps serving as a shorthand note that either 1, 2 or 3 must belong in the square.

An empty square colored the same as a completed square must contain the same digit, whereas a black square means the player has made a mistake. The game’s interactive element allows players to change the colors assigned to each digit and even brighten them during a game to see how the Sudoku board’s pattern changes accordingly, providing even more clues toward the solution. Sudoku fans can try the game here. (Requires a Flash 9 download.)

Deconstructing a train accident
Deciphering Empirical Modelling’s core principles can be daunting for those unaccustomed to its jargon, reliance on definitions or unique programming language, though its backers believe its spreadsheet-like framework translates well to real-world applications.

One favorite example is the famous Clayton Tunnel railway accident near Brighton, England, in 1861. By all accounts, the interactions between personnel and the telegraph and signal-based system used to control tunnel access went badly wrong, leading to the collision of two trains and the deaths of 23 passengers.

Reports after the accident centered on whether one train driver approaching the tunnel had seen the signalman wave his red flag as a signal to stop. He apparently had, despite the signalman’s doubts, and stopped the train after entering the tunnel. A subsequent telegraph miscommunication led the signalman to wave the following train into the tunnel, leading to the catastrophic pile-up.

For their Clayton Tunnel project, Warwick researchers created a computer-assisted environment that explores the roles of the drivers, signalmen and other railway personnel leading up to the accident. Two graduate students designed a role-playing tool that lets schoolchildren on six different workstations see unique vantages of the scene and its components, such as the controls or the warning flag.

“The point would be that we are including those experiences, the view of the red flag on the screen, within our thinking about computation,” Russ said.  “It’s not that it’s just a spin-off or side-effect of the program. That’s going to be included in what we’re calling computation.”

New visual tools
Although not designed to yield definitive answers, the Clayton Tunnel exercise has nonetheless suggested that systemic problems may have arisen from the introduction of new technology and that the accident’s cause was not limited to human error alone. Likewise, Russ said, the integrative approach of Empirical Modelling recommends itself for improving the safety of modern systems that require human involvement and as a platform for more imaginative pursuits.

Among the dozens of departmental student projects available for downloading from the research group’s site, one simulates the buildup of traffic behind three traffic lights at a T junction. Another offers a simulated environment for practicing how to park a car, complete with steering wheel and pedal. And a third attempts to realistically model how ants navigate, focusing in particular on their visual cues and use of landmarks.

Using the same approach, project leader Meurig Beynon has created a kind of visual map for Franz Schubert’s musical adaptation of a dramatic poem called “Erlkönig,” challenging conventional associations between mathematics and music in the process. With one color-coded band, Beynon marked out different characters’ actions within the song, while a second symbolized the changing musical keys and harmonies. Traditional mathematical-based representations of a song often link its cycle of keys to a color wheel, with the ends of spokes corresponding to different keys.

Empirical Modelling, by contrast, allowed Beynon to create a flexible version of the wheel that could be distorted to accommodate Schubert’s unusual tendency to blend incongruous keys such as C major and C minor — keys normally kept far apart. The resulting visual display can be synched to a performance of the song, presenting a blend of the computer’s automatic associations and Beynon’s subjective choices — and perhaps, offering a new tool to gauge how people perceive music.

Redefining computer science
The open and exploratory nature of Empirical Modelling can have its downside. “We find it very hard, on the whole, to communicate with traditional computer scientists,” Russ said. “They want everything to be very formal and are suspicious when we say that we haven’t got a formal notation for something.”

Willard McCarty, a professor at the Centre for Computing in the Humanities at King’s College in London, said part of the miscommunication may stem from the lack of a common language among the widely disparate arms of computer science. And unlike its academic cousins, he said, Empirical Modelling is far more improvisational, with no pre-determined idea of what might happen. “You’re creating something that doesn’t yet exist, for which there are no plans or models,” he said.

Although McCarty hailed the Warwick group for breaking the mold, he conceded that such admiration has been far from universal. “They have existed in a semi-hostile environment for many years,” he said. “What they’re trying to do is redefine computer science to venture into the area of creative activity, and that’s a very risky thing to do.”

Ultimately, he believes the gambit will pay off, with the potential to benefit research delving into open-ended questions in fields such as childhood learning and developmental psychology. The history of invention, after all, is filled with “people who really didn’t know what they were going to find; they were just fiddling with materials,” McCarty said.

What they did have, he said, was a good medium for channeling their creativity — something that Empirical Modelling may yet become.