Algebra Without Equations, Engineering Without Diagrams?

March 23, 1999

GAINESVILLE — Imagine being able to solve an equation without doing the math.

That’s one application of a University of Florida professor’s efforts to create computer software that will enable people to describe and understand the world not through equations or scientific diagrams, but by manipulating a three-dimensional virtual world.

Paul Fishwick, a professor of computer and information science and engineering, says his software aims to bridge the gap between the real world and the abstract one that scientists, engineers or mathematicians use to describe and understand it. Written in Java and VRML, languages of the World Wide Web, he sees it as a part of a coming evolution of the Web into a place filled not only with images and text, but also with virtual objects. These objects represent both how real objects look and how they behave.

The idea of swapping equations or diagrams on paper for three-dimensional virtual objects can be difficult to grasp for adults, but young children understand it, Fishwick said.

“As kids, we played pretend all the time: You picked up a toothpick and you said that’s John,’ or you picked up a marble and you said that’s a fish,’” he said. “Modeling is a basic cognitive need. We need to get back to playing pretend.”

People traditionally represent natural or physical processes through symbols, icons or diagrams in equations or charts, Fishwick said. While this age-old paper tool kit clearly works, it requires education and the ability to grasp and manipulate abstractions.

So called “behavioral” 3-D graphics give people the opportunity to reason in more familiar territory — using models based on their own world, Fishwick said.

Where math students now move the terms of an equation around on paper, for example, they could one day move virtual chairs around in a virtual house. Instead of solving for the unknown term in an equation, they could open a series of doors to find the answer. Much more complex scientific and engineering tasks also can be modeled with 3-D images.

“For modeling dolphin population growth, for example, we can use a 3-D metaphor involving a water system, with marbles representing dolphins and water levels in tanks representing population sizes,” Fishwick said. “You enter and manipulate the model space as you might have when you were a child.”

Assisted by several graduate students, Fishwick is at work on creating simple behavioral models using Virtual Reality Modeling Language, or VRML, the three-dimensional equivalent of Hyper Text Mark Up Language, or HTML. The system is called “Rube,” after Rube Goldberg, who created fanciful cartoons of 3-D machinery. As one example of Fishwick’s work, he recently created a virtual teapot that models a “finite state machine,” a common conceptual model in engineering, through heating and cooling virtual water.

Such models can open conceptual doors, said Robert Cubert, who will earn his doctorate in computer and information science and engineering in August.

“Modeling based on the right metaphor empowers creative people to understand, explain, solve and build, both in simulation and software engineering and most branches of science and engineering,” Cubert said.

Fishwick said his 3-D behavioral graphics also have the potential for commercial use as virtual versions of real products. Plumbers today, he said, cruise the Web in search of a pipe with certain dimensions and flow capabilities. With pipe companies posting virtual pipes on web sites, plumbers one day could plug the pipe in to a virtual house to see if it’s the right one. “The same pipe found on the web by the plumber can be used by an ecologist who needs a pipe for building the dolphin population dynamics model,” Fishwick said.

The broad appeal of Fishwick’s research is obvious from the organizations contributing to it. The U.S. Department of Interior, one sponsor, has charged Fishwick with developing behavioral models useful in planning the massive Everglades cleanup. The U.S. Air Force and NASA Jet Propulsion Laboratories are the remaining contributors, with NASA seeking models that will help with the Cassini Orbiter’s planned deployment of a probe on Titan, Saturn’s largest moon. Combined, the organizations are contributing about $1 million for the research.