  According to classical tradition, Thales of Miletus predicted the total solar
eclipse that took place on 28 May 585 BCE. Even if some authors have flatly
denied the possibility of such a prediction, others have struggled to find
cycles which would justify the achievement of the philosopher. Some of the
proposed cycles have already been refuted, but two of them, namely those of
Willy Hartner and Dirk Couprie, remain unchallenged. This paper presents some
important objections to these two possibilities, based on the fact that these
authors do not list all the eclipses potentially visible by their criteria. In
addition, any explanation based on cycles will need to face the complex problem
of visibility (smallest observable eclipse, weather...). The present article
also includes a statistical study on the predictability of solar eclipses for a
variety of periods, similar to that performed by Willy Hartner for lunar
eclipses, resulting in lower probabilities in the solar case (and percentages
depend on the chosen magnitude limit). The conclusion is that none of the
cycles proposed so far provides a satisfactory explanation of the prediction,
and, on statistical grounds, none of the periods studied leads to a significant
probability of success with solar eclipse cycles.
