Kris Carlson

Just another weblog

Wolfram on the history and future of computable knowledge

This is absolutely fascinating. The history is superb, and what he leads up to is his hope and intention that Alpha will be the culmination of it all. Of course, Google, IBM, and others are vying for that privilege, too.

Mathematica, imho, is one of the great achievements of our age. Further, imagine creating a powerful scientific instrument to explore the universe, and pioneering its use yourself. See A New Kind of Science.

“In Mathematica, for example, my goal has been to create a framework for doing every possible form of formal computation. Mathematica is in a sense a generalization of the usual idea of a computer language. In a sense, whatMathematica tries to do is to imagine all possible computations that people might want to do. And then to try to identify repeated structures—repeated lumps of computational work—that exist across all those computations. And then the role of the Mathematica language is to give names to those structures—those lumps of computational work. And to implement them as the built-in functions of the system.

I wanted Mathematica to be a very general system. Not a system that could just handle things like numbers, or strings, or even formulas. But a system that could handle any structure that one might want to build. So to do that I in effect went back to thinking about the foundations of computation. And ended up defining what one can call unified symbolic programming. One starts by representing absolutely everything in a single unified way: as a symbolic expression. And then one introduces primitives that represent in a unified way what can be done with those expressions.

In building Mathematica over the past 23 years one of the big ideas has been to include in it as much—in a sense formal—knowledge as possible. The methods, the algorithms, the structures that have emerged throughout the fields of mathematics and computation.

Well, one of the reasons I wanted to build Mathematica in the first place was that I wanted to use it myself. To explore just what the broad implications are of the fundamental idea of computation. You see, while computation has been of great practical importance—even in science—there’s a lot more to explore about its implications for the foundations of science and other things. If we’re going to be able to do science—or in general to make knowledge systematic—we kind of have to imagine that there are ultimately theories for how things work. But the question is: what are the primitives, what’s the raw material, for those theories?”

Ultimately it’s not that you can’t build complexity from mathematical primitives and so on. But what’s happened is that the exact sciences have tended to just define themselves to be about cases where that doesn’t happen. We haven’t studied the full computational universe of possibilities, only a thin set that we’ve historically found to be tractable.

Well, this has many implications. It gives us a “new kind of science”—as I pointed out in the title of the big book I wrote about all this. A kind of science that in a sense generalizes what we’ve had before. That uses a much broader set of primitives to describe the world.”

June 21, 2010 - Posted by | Uncategorized

No comments yet.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: