People I exchange e-mail with sometimes ask me about my educational background, so I am putting up this web page to help explain it. Another page on my academic interests covers some of the same territory from a different perspective.
To begin with, I will tell again the story I hand out whenever someone asks me what I majored in at university. It is the story of a search for fundamentals. I must admit that it’s is a very whitewashed story, one that omits the all the nervous breakdowns and mentions only the academic disciplines I passed through.
To better begin the story, it helps to start with a subject that I have occasionally studied didn’t formally enroll in after one (grade 11) course I took high school — biology. (The teacher offered to give me an A in the course if I agreed not to take his grade 12 course the next year, and rather foolishly I let myself be bought off with the A rather than pursuing this interesting subject a bit further.)
Fundamental to all biology is the biology of the the cell, since biological organisms are made up of cells. I have on my bookshelves a very good book called “Molecular Cell Biology”, but one cannot read it without a very good knowlege of chemistry, and almost every page deals with chemical reactions.
It seems that the fundamental basis of the discipline of biology is to be found in another discipline, chemistry. I did study chemistry at university, for a few semesters, and one of the best books I used was one called “Valency and Molecular Structure”, which addressed the fundamentals of chemistry: the bonds that join molecules. But just as “Molecular Cell Biology” seemed to talk about chemistry on every page, “Valency and Molecular Structure” talked about physics on almost every page.
So it seems that the fundamental basis of chemistry is to be found in another discipline, physics, which I also studied for a few semesters. But again, books on physics seem to devote almost all of their space to the discussion of a more fundamental discipline, one that every physics student is required to study: mathematics.
Mathematics is not a well-unified discipline, but seems to be sharply divided into pure and applied mathematics. For physics, one need only study applied mathematics, and I was required to devote quite a bit of time and effort to learning that side of the discipline. But, as one might expect, applied mathematics is not at all a self-contained discipline — it is heavily dependent on pure mathematics.
Although pure mathematicians often take a perverse pride in the uselessness of their discipline, it is in fact used to establish the fundamental validity of the methods taught as applied mathematics.
I have always been very interested in the applications of whatever I was learning, but when I realized that applied mathematics was but a part of a much larger and much more fundamental discipline, I found that I could not resist turning in that direction.
At this point I encountered a real problem. Some pure mathematicians seemed to believe that pure mathematics provided its own foundations, and did not rest on any more fundamental discipline, while others believed that the foundations of mathematics depended on something separate called formal logic. And indeed, most of the pure mathematics books begin with an introduction to logic.
Although there are formal logic courses given in mathematics departments, at the univerity I attended the most thorough study of formal logic was in the philosophy department. But once I began taking these courses, I soon discovered that the professors invoked other branches of philosophy to justify their approach. In particular, they repeated referred to the philosophy of language, and treated logic as an artificial language.
But when I took courses on the philosophy of language, it quickly became apparent that other disciplines were ahead of me. The philosophy of language made many references to the science of language, linguistics, and even though most philosophers knew little about actual human languages, it soon became clear to me that such knowledge was essential. So I turned to linguistics and ended up taking almost all the undergraduate linguistics courses and some graduate ones.
But again I found that the discipline I was studying was becoming increasingly dependent on some other discipline. Linguistics, the study of natural languages, was increasingly dependent on a new discipline called computer science, and formal models of natural language were now usually described by the methods used to define the new artificial languages used to program computers.
I began graduate studies intending to study human language using a computer, and ended up learning more about computers and their languages than about human language.
One might expect that my studies of computer science would again lead me to a new discipline, and indeed the foundations of computing are in another discipline. But here my path looped back on itself, because the fundamental basis of computer science is in the discipline that is wrongly called pure mathematics, something I had already studied.
Copyright © 1998 Douglas P. Wilson