Musings on John McCarthy’s Death

Posted on October 25th, 2011 by

Although John McCarthy died only two days ago, enough words have already been written to render any more superfluous. Yet I can’t resist some personal musings.

The very name of this blog, MCS, is a good starting point: the blog of a department of “Mathematics and Computer Science.” Often I’ve been asked why computer science is combined with mathematics. There are lots of good answers, some of which I usually manage. But now I recognize one more: John McCarthy. He shaped the discipline of computer science in many ways, not least by positioning it as a mathematical science. Some of the obituaries note that he was a mathematician before becoming a computer scientist, but that misses the point. He stayed a mathematician all the while he was a computer scientist — not by dividing his attention, but by studying computation mathematically.

Two of his papers from the early 1960s still hit like bombshells when I read them in the 1980s: “A Basis for a Mathematical Theory of Computation” and “Towards a Mathematical Science of Computation.”  Although those papers were cornucopias stuffed with many interesting ideas, the two biggest ideas were right in the titles. First, computation could and should be studied mathematically. Second, a mathematical approach to computation didn’t flow inevitability from the mathematical nature of computation, but rather needed deliberate construction.

Computer science, despite its name, is more focused on computations than on computers. Even when we consider a computer, we often view it not as a physical construct of silicon and copper, but as a universal master computation: the “execute these instructions” computation that subsumes the “approximate this integral” computation, the “search these web pages” computation, and all the others. So the objects we study, computations, are inherently mathematical. Nonetheless, those computations can be studied in non-mathematical ways.  Which computations add value to an enterprise? Which methods of constructing computations minimize human labor? What notations for describing computations are easiest for humans to understand? None of those are mathematical questions.

McCarthy recognized that many other interesting and important questions were mathematical, and that the techniques mathematicians had traditionally used to reason about sets, functions, and propositions could be adapted for reasoning about computations.  That approach hasn’t displaced all others, but it has left a lasting impact on the nature of our field.

Another facet of McCarthy’s life that made a lasting impression on me was his engagement with world affairs.  He was known for his strongly held convictions and for his tireless efforts to persuade others.  He didn’t have much success with me, which won’t come as any surprise to those who know me. I suspect that it wouldn’t come as much surprise to those who knew McCarthy either; his failure to win me over can’t have been unusual.  I have a vague yet powerful memory of a conversation with him in his office.  Vague, because I can’t remember the topic.  But powerful because I recall how emotionally draining it was to clash with such an intellect.  He had earned his right to strong opinions, whereas I was just a cocky youngster.  I’m still a cocky youngster today.  In about 15 years, I’ll be the age he was then, though I’ll surely be nowhere near so accomplished. I hope that I will follow his example and retain my sense of engagement, not only with issues that matter to me, but with individuals who disagree with me. And I hope I will remember that the professional and the political shouldn’t be too rigorously segregated. For McCarthy, political questions ought to be examined from a scientific perspective, just as computational questions ought to be examined from a mathematical perspective.

For years, I’ve resisted the college bureaucracy’s idea that my title ought to be “Professor of Mathematics and Computer Science” to match the name of the department.  I keep crossing the title out and writing in “Professor of Computer Science.”  This semester, I’ve toyed with ending that battle and editing my personal web page to show the more inclusive title. In part, that’s because after 21 years in the joint department, I’m finally teaching my first math course — and enjoying it immensely.  But mostly its because of the dawning realization that I’ve been professing mathematics all these years, even when I teach computer science courses.  I should probably go ahead and edit my web page today, in honor of John McCarthy.


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