How “Mathematical Notation for Law Representation” Came To Be

For three years beginning in 1983, I was enrolled in the doctoral program at the School of Urban and Public Affairs (SUPA -- since renamed The Heinz School) at Carnegie-Mellon University, in Pittsburgh, PA. Mathematical Notation for Law Representation was written in fulfillment of a Ph.D. program requirement to produce original, scholarly research of publishable quality. It was presented orally to an open hearing of faculty and students in 1986.

Although the faculty eventually voted to approve the paper, reaching that stage required a prolonged series of demeaning audiences with faculty members, in which my mentors would help extend the boundaries of knowledge by, for example, directing me to change occurrences of “he” to “he or she.” My advisor at the time once characterized the position of a Ph.D. student in the program quite accurately by remarking to me: “you are a supplicant in all your relations to the university.”

The problem with this paper was that it was indeed original, and perhaps quixotic, in that it was unrelated to the research activities of SUPA faculty members. By contrast, a piece of academic gibberish I had produced the year before (published in the March, 1987 issue of the National Tax Journal, with my advisor as co-author) received swift faculty approval because it was conventional and meshed directly with my advisor’s research.

In a healthier academic climate I would have extended my paper into a Ph.D. dissertation. Under the circumstances, I opted to forgo the lengthy exercise of sycophancy (estimated at one year) that gaining a Ph.D. would have necessitated. I left the program on gaining “all but dissertation” status and returned to work in the software industry. I was later granted a Master’s degree in recognition of the work I’d completed in the doctoral program.

One of the positive aspects of the SUPA program was that it provided almost complete freedom to pursue coursework outside the school. I enrolled in doctoral-level courses in the department of mathematics, in the business school, and even outside CMU, at the nearby University of Pittsburgh School of Law, where I enrolled in three courses (as the only non-law student). One of those courses was Bill Brown’s stimulating and enjoyable Corporate Taxation. Prof. Brown provided generous advice in the research leading to this paper.

I believe my reaction to these law courses, my first exposure to the legal discipline, was a very natural one for anyone who has studied math and grasped its intellectual elegance, or who has learned to appreciate the established principles of sound software development. I was struck by the primitivity of the intellectual apparatus used in law to analyze and articulate complicated, intricate ideas. One can hardly express what was missing more aptly than the mathematician, Alfred North Whitehead:

By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race.

Once I began the research for this paper, I was surprised to discover that the practice of math itself had once been hampered by the same deficiency. I found mathematicians, 400 years ago, urging the benefits of symbolic notation on skeptical colleagues, since this was -- 400 years ago -- a novelty. Math, as everyone knows, embraced this advance, while somehow law has persisted to modern times without it.

My research also led me to The Language of the Law, a blistering, book-length criticism of the legal discipline by UCLA Law Professor David Mellinkoff. “One look at any digest of cases,” states one passage, “a study of the litigation that has turned repeatedly (and in many directions) on the interpretation not of layman’s words but of law words, brings a conviction of imprecision or incompetency, or of both.”

Not one of the 15 reviews of Mellinkoff’s book referenced by the Index of Legal Periodicals seriously challenges Mellinkoff’s charges of imprecision. One reviewer states: “Directed against a profession which is so innately involved in the business of communication, this is a critical and serious indictment. The charge is supported by devastating scholarship and thoroughness.”

From the outset of my study of law, my outlook was congenial to this critical perspective. I was there as a student of public policy rather than for professional training. With my math background, I had direct knowledge of the overarching benefits of symbolic notation. From my training and working experience in computer science, I had concrete familiarity with a far more potent approach than what I saw in the legal discipline for designing structures of rules to produce desired effects. I was, moreover, among the enthusiasts of APL, a little-known programming language expressly created by Harvard mathematician Ken Iverson as “a tool for thought” to take the potential of notation to new heights.

The impetus for this research project came in Prof. Brown’s Corporate Taxation course, where I found myself rendering parts of the Internal Revenue Code in symbolic notation simply as a practical means to cope with the course. Doing so exposed the kind of flaws, ambiguities, and pointless complication that could generally be obviated, if the legal discipline would accept modern intellectual technology.