In the category of things that I should have done at least a month ago, I’ve been wanting to find a moment to put down some thoughts on the plenary session presentation by Bill Buxton of Microsoft Research at the World Wide Web Conference last month in Banff.

Bill talked about a lot of things, but especially relevant to developers were his thoughts on the need for applications to do a better job with ideas about time. He presented a number of data sets, for example those involving different voyages of exploration in North America during the early 19th century: he showed that adding a time dimension, and displaying the location and progress of different voyages concurrently as time progressed, created a whole new way of seeing the accumulation of knowledge of the continent, as well as the coincidences of different parties nearly meeting up with each other but for accidents of weather or navigation.

I found myself thinking, as Bill spoke, about the interactive breakthroughs in Version 6 of Wolfram Research’s Mathematica. Only just released, on May 1, at the time of that conference in Banff, Mathematica 6 might have been designed to give Bill the toolkit he wants for adding new modes of interaction and presentation to our views of data or calculation. Merely wrapping an expression in a Manipulate[] command generates an interactive user interface that turns any result into a graphical widget enabling direct interaction.

I’ve followed the development of Mathematica for many years, and have often used it as an example of what computers can and should be made to do. Not only mathematical capabilities, but improvements such as Web services interfaces and "personal grid" computing are brought closer to developers for convenient (and therefore, perhaps, inspiring) exploration by Wolfram Research engineers.

And if you ever find yourself in a game of Risk with a tall, thin guy who seems to be consulting his laptop computer before every roll of the dice, find out if you’ve happened to run into my oldest son — who wrote himself a Mathematica function that simulates the successive rolls of the dice that take place during a Risk attack, and who therefore knows the precise probability (with a graphical display of the probability distribution) that a given number of attacking armies will overwhelm a given number of defenders assuming that each player uses the maximum available number of dice. Better decisions come from better information — although often not by obvious means — and tools like Mathematica can bring improved analytic power to many tasks.