Toward a Mechanistic Interpretation of Probability

Kant on the "A priori" Toward an Interpretation

Bertrand’s Paradox Revisited: More Lessons about that Ambiguous Word, Random

The Bertrand paradox question is: “Consider a unit-radius circle for which the length of a side of an inscribed equilateral triangle equals 3 . Determine the probability that the length of a ‘random’ chord of a unit-radius circle has length greater than 3 .” Bertrand derived three different ‘correct’ answers, the correctness depending on interpretation of the word, random. Here we employ geomet...

Very low probability lung scan findings: A need for change

This study was conducted to determine the prevalence of PE in patients with V/Q scans interpreted as representing a very low probability (VLP) of PE (1-3 small segmental perfusion defects with a normal chest radiograph). An analysis of the entire data set obtained during the PIOPED study was performed. Of the total of 1,359 patients in whom the presence or absence of PE was confirmed, 80 ...

Intellectual Links between Mawlānā Jalāl ad-Dīn and Sultan Walad in the Realm of Hadith Interpretation: A Case Study of Masanvi Manavi and Sultan Walad’s Masnavies

Interpretations are of the most fundamental principles of mysticism (Sufis). Masters of taste with their scientific and intuitive power go beyond the surface structures and present real and unfathomable meanings of the Quran and Hadith in ways that may not cross the mind of ordinary people. Masnavi Manavi is one the works that has an interpretation look toward the Quran and Hadith. Delving into...

Mechanistic slumber vs. statistical insomnia: The early phase of Boltzmann’s H-theorem (1868-1877)

In 1872 Ludwig Boltzmann published a lengthy memoir containing two fundamental results: an integro-differential equation describing the time evolution of an ideal gas (Boltzmann equation) and a mathematical argument proving that such evolution must reach, sooner or later, the state of equilibrium described by the Maxwell distribution. The latter achievement, later called the H-theorem, expresse...