Math as we practice it today turns out not to be the only way to map reality.
One of the summers most controversial books was Stephen Wolframs "A New Kind of Science," which has sold a remarkable number of copies for a 1,200-page tome full of mathematical diagrams and expressions. If every equation in a book really does cut its sales in half, as someone once warned physicist Stephen Hawking, then the printing of Wolframs book might have consumed every forest in the world if he had confined himself to words and pictures.
But Wolframs message requires equations because hes presenting a view of both the natural and the abstract world as being tied together by underlying principles that we finally have the tools to explore. The implications are huge for domains such as medicine and biotechnology, where largely trial-and-error methods could give way to more systematic searching of the space of possible solutionsif we can understand the di- mensions of that space and plan our journey through it.
I met with Wolfram last month at Comdex, the day before his keynote speechprobably the most cerebral event that the show has ever seen. I left with a much-improved understanding of what hes actually accomplished, compared with the buzz of comment on his book that (for the most part) loudly misses the point.
Wolfram has been said to claim that because simple rules can produce complex behaviors, it must follow that all behaviorsfrom the shapes of seashells to the composition of musicwill ultimately be traced to simple rules. No, thats not what he said, he assured me during our hour together.
"Models are a high-judgment business," he explained. "Calculus was one sort of raw material for making models of things; Im trying to provide another.
"The main difference," he continued, "is that in calculus there are a limited set of primitivesderivatives, integrals, things like thatbut Im interested in the arbitrarily general primitives that can be represented in programs." Math as we practice it today, he asserted, turns out not to be the only way to map reality onto sets of symbols and operations; "whats been explored is a tiny fraction of what there is."
Theres untold value in that unknown territory.
Peter Coffee is Director of Platform Research at salesforce.com, where he serves as a liaison with the developer community to define the opportunity and clarify developers' technical requirements on the company's evolving Apex Platform. Peter previously spent 18 years with eWEEK (formerly PC Week), the national news magazine of enterprise technology practice, where he reviewed software development tools and methods and wrote regular columns on emerging technologies and professional community issues.Before he began writing full-time in 1989, Peter spent eleven years in technical and management positions at Exxon and The Aerospace Corporation, including management of the latter company's first desktop computing planning team and applied research in applications of artificial intelligence techniques. He holds an engineering degree from MIT and an MBA from Pepperdine University, he has held teaching appointments in computer science, business analytics and information systems management at Pepperdine, UCLA, and Chapman College.