Rescaled range analysis and the fractal dimension of pi

P. Vanouplines

University Library, Free University Brussels,
Pleinlaan 2, 1050 Brussels, Belgium

Once upon a time ...

... I decided to prepare a PhD dissertation. In Belgium, when one was close to the completion of the dissertation, it used to be "good" practice to:

and then to present it, together with the main thesis, as a so-called additional or secondary thesis. In the best case it was advised to write a text about the subject in the form of a paper that was ready to be published.

This practice stems from the idea, formulated many years ago by a few wise men, that the young doctorandus had to prove that he (in those times often not yet she ...) was able to work scientifically on a subject quiet different from the subject that was elaborated during three or four years for the main thesis. Only then the doctorandus could succesfully undergo further examinations to obtain a full Philosophical Doctor title, and become part of the small, erudite club of respectable scientists.

No joking now. I wanted to present such and old-fashioned secundary thesis ... While my basic formation was that of a geographer (which is in Belgium quiet different from "British geography" -- we study a sound mixture of human, economical, and physical geography), my primary thesis discussed surface water hydrology, remote sensing and computer sciences. That was indeed a multidisciplinary approach, which I very much loved (and still love).

A such, I had to search for something which was even more exotic for me. So, I made several excursions in science. I came accross Hofstadter. I met fractals. I was fascinated by prime numbers, and the number pi. Adoring multidisciplinary work, I played with the idea to tackle a combination of these. All this might look a "tour de force", but after all, while looking back at the hours I spent to this, the effort was worth the result. More important than the work behind this, I gained a deep appreciation for the wise men, forcing young researchers to open their mind for more than the narrow field of their specialist thesis.

And then, at the moment of the submission of my almost completed dissertation, both texts of the main and secundary thesis, for a final revision by my promotors, I was told that it was no longer necessary to prepare such an additional thesis ...

Accept, dear reader, this text from a non-mathematician, so that this work may eventually find its proper way.


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Last updated on Wednesday 7 February 1996.
©Patrick Vanouplines.