The author mentions two interpretations of probability, the frequentist and the bayesian one. With both interpretations, a negative probability does not make se

The author mentions two interpretations of probability, the frequentist and the bayesian one. With both interpretations, a negative probability does not make sense. The frequentist thinks of the ratio number of occurences in the limit of an infinite number of experiments. Negative probabilities would imply negative numbers of occurences (which does not really make sense). In the bayesian interpretation, probabilities are somewhat of a generalization of boolean logic. Based on the assumption that there is True (1) and a False (0), probabilities represent the degree of reasonable believe that a proposition is true. I.e. probabilities are bound in (0, 1). While in math it often turns out that one should not dismiss a certain extension of a calculus (complex numbers are the textbook example, they are not immediately recognizable as "natural" but they work flawlessly and give interesting insights), I really do not get the point here, why would we need negative probabilities? What could we gain from using them? The example brings up an example from the theory of interest, it seems that he identifies an expectancy value-like equation with negative probabilities. I wonder if this could be interpreted as a quasi-discrete case of probability-densities, which can be indeed negative.