An Unexpected Correspondence

Enter any expression and it’ll get evaluated:

And internally—say in the Wolfram Language—what’s going on is that the expression is progressively being transformed using all available rules until no more rules apply. Here the process can be represented like this:

We can think of the yellow boxes in this picture as corresponding to “evaluation events” that transform one “state of the expression” (represented by a blue box) to another, eventually reaching the “fixed point” 12.

And so far this may all seem very simple. But actually there are many surprisingly complicated and deep issues and questions. For example, to what extent can the evaluation events be applied in different orders, or in parallel? Does one always get the same answer? What about non-terminating sequences of events? And so on. Continue reading

Logic, Math and AI

In many ways the great quest of Doug Lenat’s life was an attempt to follow on directly from the work of Aristotle and Leibniz. For what Doug was fundamentally trying to do over the forty years he spent developing his CYC system was to use the framework of logic—in more or less the same form that Aristotle and Leibniz had it—to capture what happens in the world. It was a noble effort and an impressive example of long-term intellectual tenacity. And while I never managed to actually use CYC myself, I consider it a magnificent experiment—that if nothing else ultimately served to demonstrate the importance of building frameworks beyond logic alone in usefully representing and reasoning about the world. Continue reading