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Introduction
"Ainsi lecteur, je suis moy-mesmes la matiere de mon livre: ce n'est pas raison que tu employes ton loisir en un subjet si frivole et si vain" . Michel de Montaigne, "Essais".
This is a psychological study of a scientific discovery of limited relevance and achieved in a short amount of time. It deals with my own mental itinerary in the mathematical and experimental pursuit of a psychophysical law about eye movements, that is given as an example. Thus the object of my research is a dual object. I will work with:
(1) the intimacies of a mathematical model (the fractal model) and some experimental applications of it (the saccadic eye movements) and
(2) a detailed psycho-historical account of the creation of that model based upon my documented recollections that were simultaneous to the scientific pursuit (1).
The reader will ressent the unstable equilibrium of two alternative focuses, like a person shifting from ground to figure in front of some drawing of Escher. But, most important, I have discovered during my writing that I used many levels of detail and depth in my comments and associations regarding my microdiscovery. The analogy with fractal objects is amazing, and perhaps this byproduct can be understood itself as a hint about "fractal scaling in memory". Benoît Mandelbrot's famous "How long is the coast of Britain (Science 1967, 155, 636-638) proves that you may increase without limit the length of the coast provide you take smaller and smaller units of measure. The same here. I am now afraid that my text will grow without limit if I take smaller and smaller details of my journey toward the discovery of a model for saccadic eye movements. Therefore I can use the capabilites of my computer to reduce the letter size by steps. The larger or first order text (this one of size14) will be used for central comments of the "first level of depth", the second one (size12) for secondary comments, and I will stop at the third level (size 10) for obvious cognitive and visual reasons, even if I could go further and further in depth.
The text will become a patchwork, the best static approximation I can conceive for a dynamic hypertext, and instead of mouse-navigation, clicks and buttons you will have only a visual pattern. (In the future, as an exercise, I hope to create a CD-Rom of this book, with texts, graphics, photos, videos and voice). Some readers may understand (1) as the "context of justification"and (2) as the "context of discovery" but this is not my personal understanding of the two settings, as I expect to show during the discussion. Also the different printing sizes could be interpreted as "scaling footnotes" of the main text of level 1. Thus level 2 gives new details about level 1 and level 3 makes "footnotes on footnotes", etc. My interpretation is different. I think that they belong to different levels of memory that are "self-similar" in the sense that each level can be unfolded as a complete story in itself. But it is not my aim to prove this hypothesis now. Also I must say that I very frequently use the opening of new windows, that lead to different chapters of this book. As in old novels I write "but this is another story" when I open a new window (as you do when you click a button in the hypertext to enter in a different realm). I will number the different stories (or chapters) with latin numbers. This fractal story is (I). Therefore "another story (II)" will jump to chapter II, and so on.
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