Related papers: MacLaurin and Morality
The Scientific Revolution sweeping through seventeenth-century Europe led to unprecedented intellectual and scientific insights and high-profile technological developments. Combined with a significant worldwide increase in naval commerce,…
In honor of Alan Turing's hundredth birthday, I unwisely set out some thoughts about one of Turing's obsessions throughout his life, the question of physics and free will. I focus relatively narrowly on a notion that I call "Knightian…
If Turing's groundbreaking paper in 1936 laid the foundation of the theory of computation (ToC), it is no exaggeration to say that Cook's paper in 1971, "The complexity of theorem proving procedures", [4] has pioneered the study of…
We pursue research leading towards the nature of causality in the universe. We establish the equation of the universe's evolution from the universe-state function and its series expansion, in which causes and effects connect together to…
I argue that European schools of thought on memory and memorization were critical in enabling the growth of the scientific method. After giving a historical overview of the development of the memory arts from ancient Greece through 17th…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
Various moral conundrums plague population ethics: the Non-Identity Problem, the Procreation Asymmetry, the Repugnant Conclusion, and more. I argue that the aforementioned moral conundrums have a structure neatly accounted for, and solved…
I employ an optimization-based inference methodology together with an Ising model, in an intentionally ineffectual manner, to get away with murdering an obstreperous scientific collaborator. The antics of this collaborator, hereafter "Conan…
In the first article in the series examining mathematics on coins, we discuss two great scientists who are not only featured on many coins, but also contributed to both theory and practice of coinage. The first one is Nicolaus Copernicus,…
This is a set of 288 questions written for a Moore-style course in Mathematical Logic. I have used these (or some variation) four times in a beginning graduate course. Topics covered are: propositional logic axioms of ZFC wellorderings and…
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…
The example of the calculus is used to explain how simple, practical math was made enormously complex by imposing on it the Western religiously-colored notion of mathematics as "perfect". We describe a pedagogical experiment to make math…
In a seminal paper of 2005, Nualart and Peccati discovered a surprising central limit theorem (called the "Fourth Moment Theorem" in the sequel) for sequences of multiple stochastic integrals of a fixed order: in this context, convergence…
Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…
Quantum Darwinism extends the traditional formalism of decoherence to explain the emergence of classicality in a quantum universe. A classical description emerges when the environment tends to redundantly acquire information about the…
A few remarks on how mathematics quests for freedom.
In this paper I address the difference between knowledge-inquiry and wisdom-inquiry (concepts introduced by N. Maxwell) in nuclear physics education, specifically in senior-level textbooks for first-degree physics students. Following on…
Newton's Principia, when it appeared in 1687, was received with the greatest admiration, not only by the foremost mathematicians and astronomers in Europe, but also by philosophers like Voltaire and Locke and by members of the educated…