Tuesday, February 22, 2011

How Long Should My Thesis Be?

Perhaps understandably, it's a question that I get asked by students all of the time: "How long does my thesis (dissertation) have to be?" I say, "understandably" because writing such a document is a grueling task, no matter how excited you are about the new results that you’ve discovered. My stock answer has always been that it's the content, not the length of the thesis, that’s the important issue. I'm sure that, deep down, students know this already and so perhaps my response is not as helpful as it might be!

I'm talking here about theses in theoretical or applied econometrics, but much of what I have to say will apply to other areas of Economics. As well as being a central component of any Ph.D. program, a thesis or dissertation (I'll use the terms interchangeably) is often required to complete a Masters degree, or an undergraduate "Honours" degree. It may even be possible to choose between different types of theses, and trade off a "more substantial" type for less course work. That’s the case, for example, for M.A. students in my own department right now. I'm not going to get into the pros and cons associated with such choices – perhaps another day. However, the fact that questions arise regarding the appropriate length of the tome is even more understandable when students can choose between a "minor thesis" and a "major thesis".

Of course, in some academic institutions and departments there are guidelines dealing with the number of words or pages that a thesis-writer should target or adhere to. This is fine, but unless such guidelines are very detailed they still miss the point. Content is paramount. Clarity of expression and the balance of the presentation of the material are crucial.  Depending on the subject mater of the research, the novelty of the methodology that has been used, and the form in which the results have to be conveyed (e.g., by means of charts or tables), there can be substantial variations in the “appropriate” length of a thesis. And then, are we talking about the main body of the thesis, or are we also counting appendices that contain supplementary results, computer code, and the like?

Recently, when the dreaded question has arisen, I’ve given my standard response. I guess that old habits die hard! However, I've also gone on to give an example of how length and content need not be positively correlated. The example actually relates to a journal article rather than a thesis, but I think that it makes the point rather well.

It’s about a famous mathematician (now retired) who happened to be Chair of the Department of Mathematics at the University of Canterbury in New Zealand when I was a member of their Department of Economics. His name is Roy Kerr, and if you want to find out more about him and his work, you can do so on Wikipedia under Roy Kerr or Kerr metric. In 1963, Kerr published a paper titled, "Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics", in the journal Physical Review Letters (ranked number 3 among Physics journals for the period 1999-2004, by Science Watch® ).

Roy Kerr’s paper gave rise to what is referred to as "the Kerr metric", or the "Kerr vacuum". The Kerr metric provides an exact solution of the ten equations that summarize Einstein's general theory of relativity. Because these equations are highly non-linear, there is no guarantee that an exact solution exists, and it's extremely difficult to find it (or them, if there is more than one solution). But Kerr succeeded! In a nutshell, the Kerr metric enables physicists to describe the behaviour of rotating black holes. Oh yes - among other things his metric allows for the existence of a type of "time travel". Heady stuff!

Fittingly, Roy Kerr has received many honours. In January of this year he was made a Companion of the New Zealand Order of Merit, “for services to astrophysics”. His other major awards include The Royal Society of New Zealand’s Hector Medal in 1982, and their Rutherford Medal in 1993. Most notably, The Royal Society of London awarded the prestigious Hughes Medal to Roy Kerr in 1984, with the following citation:

"The Hughes Medal is awarded to Professor R. P. Kerr in recognition of his distinguished work on relativity, especially for his discovery of the so-called Kerr black hole. In the early 1960s Professor Kerr discovered a specific solution to Einstein’s field equations which describes a structure now termed a Kerr black hole. Not only was the solution especially complex, lacking symmetry of previous solutions, but it became apparent that any stationary black hole can be described by Kerr’s solution. His work is therefore of particular importance to general relativistic astrophysics, and all subsequent detailed work on black holes has depended fundamentally on it. Professor Kerr has made other significant contributions to general relativity theory, but the discovery of the Kerr black hole was so remarkable as to compare with the discovery in physics of a new elementary particle."

If you take the time to check the list of recipients of the Hughes Medal, you’ll find some rather familiar names, including: Niels Bohr (1921), Enrico Fermi (1942), and Stephen Hawking (1976). To get some idea of where Roy Kerr and his work are placed in this Hall of Fame, consider what Subramanyan Chandrasekhar, the 1983 Physics Nobel laureate, had to say:

"In my entire scientific life, extending over forty-five years, the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity, discovered by the New Zealand mathematician, Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the universe. This shuddering before the beautiful, this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound."  Chandrasekhar (1975).
                                                                                                                                                                                                     
So, what does all of this have to do with a student's question about how long their thesis should be? Well, I recall that for some time the actual Hughes Medal that was awarded to Roy Kerr was on display in a glass box in the Sciences Library at the University of Canterbury. Next to it was a copy of the 1963 paper that he published in Physical Review Letters – the one that got everyone so excited. The glass box was unassumingly small – but then, the paper is less than one and a half pages long (including footnotes)!

Postscript:
            
The Hughes Medal is named after David Edward Hughes (1831 – 1900), inventor of the  carbon microphone, which was essential to the development of the telephone. The Royal Society awards the Hughes Medal “in recognition of an original discovery in the physical  sciences, particularly electricity and magnetism or their applications”.


References

Chandrasekhar, S. (1975). "Shakespeare, Newton, and Beethoven", Ryerson Lecture,  University of Chicago. Reprinted in S. Chandrasekhar, Truth and BeautyUniversity of Chicago Press, Chicago, 1987.

Hawking, S. W. (1988). A Brief History of Time: From the Big Bang to Black HolesBantom, New York.

Kerr, R. P. (1963). "Gravitational Field of a Spinning Mass as an Example of  Algebraically Special Metrics". Physical Review Letters, 11 (5), 237-238.

Melia, F. (2009). Cracking the Einstein Code. Relativity and the Birth of Black Hole Physics. University of Chicago Press, Chicago.

Wiltshire, D. L., M. Visser and S. M. Scott (eds.) (2009). The Kerr Spacetime. Rotating Black Holes in General Relativity. Cambridge University Press, Cambridge.




© 2011, David E. Giles

2 comments:

  1. Let's see if I can post this in the right place.

    Your tale also reminds me of John Nash. His dissertation was 28 pages long and his paper "Equilibrium points in n-person games" was merely 1 page (http://www.pnas.org/content/36/1/48.full.pdf+html).

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