Paolo Rocchi's The Structural Theory of Probability addresses the question: " What IS probability?" from an angle that, as the author explains, is based on his background in the culture and ideas of software programming. His basis thesis is this: Probability theory from Pascal to Kolmogorov and onwards has focused on events as sets of outcomes or results, and probability as a measure attached to these sets. But this ignores the structure of the processes which lead to the outcomes, and the author explores how taking into account the details of the processes would lead to a more fundamental understanding of the nature of probability.
This is an interesting idea, and the author makes it clear that at present this is a work in process and not yet a finished product, for he says that he has tried to give "an impulse in the right direction" with his theory. Though the concluding chapter gives two examples intended to show how "the structural calculus has a competitive edge over today's calculations," these do not seem to establish the author's points quite as definitively as one would like them to. One hopes that in due course the author will develop his theories further and present overwhelmingly persuasive examples of the advantages of his approach.
Ramachandran Bharath is visiting professor of mathematics at Colby College.