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