The Structural Theory of Probability: New Ideas from Computer Science on the Ancient Problem of Probability Interpretation

ISBN-13: 9780306474286 / Angielski / Twarda / 2003 / 162 str.

Paolo Rocchi

Opis

The Structural Theory of Probability addresses the interpretation of probability, often debated in the scientific community. This problem has been examined for centuries; perhaps no other mathematical calculation suffuses mankind's efforts at survival as amply as probability. In the dawn of the 20th century David Hilbert included the foundations of the probability calculus within the most vital mathematical problems; Dr. Rocchi's topical and ever-timely volume proposes a novel, exhaustive solution to this vibrant issue. Paolo Rocchi, a versatile IBM scientist, outlines a new philosophical and mathematical approach inspired by well-tested software techniques. Through the prism of computer technology he provides an innovative view on the theory of probability. Dr. Rocchi discusses in detail the mathematical tools used to clarify the meaning of probability, integrating with care numerous examples and case studies. The comprehensiveness and originality of its mathematical development make this volume an inspiring read for researchers and students alike. From a review by the Mathematical Association of America Online: " The author's] 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. ... 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

Recenzje

From the reviews:

"The structural theory of probability addresses the interpretation of probability, often debated in the scientific community. ... Rocchi's topical and ever-timely volume proposes a novel, exhaustive solution to this vibrant issue." (Rainer Beedgen, Zentralblatt MATH, Vol. 1069 (20), 2005)

"Probability theory from Pascal to Kolmogorov has focused on the events as sets of outcomes or results, and probablity 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 process would lead to a more fundamental understanding of the nature of probability. ... One hopes that in due course the author will develop his theories further and present overwhelmingly persuasive examples of the advantages of his approach." ---MAA reviews

Spis treści

Preface. 1. Cultural Roots. 2. Critical Remarks. 3. Events and Structures. 4. Notes on Structural Analysis. 5. Certainty and Uncertainty. 6. Probability. 7. Relative Frequency. 8. Objectivism and Subjectivism. 9. Probability Calculus. 10. Conditional Probability. 11. Stochastic Systems. 12. Distributions. 13. Bivalent and Multivalent Logic. 14. Two Applications. Appendix: History's Lessons. Bibliography. Index.