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Innovation, confrontation, modelisation and parsimony
This writing gave me also the unexpected opportunity to a better understanding of some technical details of the fractal model of saccadic movements. In particular I completely changed my former interpretation of self-similarity. Instead of the "self-similar saccadic tree" I am ready to propose now the notion of "self-similarity of eye movements in time" based upon some computer simulations of my fractal model. Thus a specific fractal revival came out of a general essay about the cognitive process of scientific discoveries! This hybridization was totally unexpected when I started to write these pages. I think it is a new important fact to be analyzed as such. Thinking about a scientific endeavour had produced, in my case, some thinking upon a particular object of research and, what is really striking, engaged me to continue my elaboration of the old fractal model in greater detail up to the writing of a new version of it (the seventh!) after fifteen years.
Summing up, I think that I can end this story of a microdiscovery with a satisfactory view of all its properties, as stated at the beginning.
1. Innovation: the fractal nature of eye movements is an entirely new interpretation of some experimental facts already available.
2. Confrontation: the many versions of my scientific paper, the lectures and seminars, the personal discussion with the experts, the referees' criticisms, show the amount of interaction caused by my model. It is still open to discussion and confrontation.
3. Modelisation: the formal expression of the distribution of the amplitude of eye movements allows the mathematical calculation of the fractal dimension D. The equiprobability of the directions of sight during a long visual search can be now simulated along with the length of each saccade. The result is an effective computer model to be tested for different values of the temperature of sight 1/D.
3. Parsimony: The bulk of the theoretical research took place in only three months, although its roots (and leaves) expanded over 37 years! (from 1957 to 1994). The instruments were also restricted to standard equipment and simple calculations and programming.
I expect to show that the other scientific stories of this book will unfold within a similar pattern. If so I will have some ground to sustain my central hypothesis: Scientific research as a "mental enterprise" is quite the same in macro or in microdiscoveries.
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