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2D Puzzle Visualizations of Boolean Formulae
No full textIn the comparison between human and computational intelligence, often times the comparison is not straightforward because humans can possess domain knowledge inaccessible to the program they are competing with. To provide a level playing field, it is helpful to have humans and computers compete in a domain where both start with equal domain knowledge, and the domain is well understood
A Response to Clunn's Axioms of Morality
No full textThis is a brief critique of Clunn's foundationalism which grounds moral decision making in what he calls the three fundamental axioms of existence, consciousness, and identity. It shows how his precommitments create at least three incoherencies wherein a priori is a posteriori, individuality is an illusion, and objective morality is subjective. For Clunn's moral philosophy to offer practical value, these internal conflicts must be resolved
A Corollary of the Conant-Ashby Theorem Applied to Abiogenesis
No full textFrom the Conant-Ashby theorem about the "good regulator" is possible to derive a corollary about the origin of life (OOL). This corollary introduces the concept of "good constructor." Thenit is shown as nature, seen as a material system ruled by the laws of physics, cannot be a "good constructor" of the basic machinery necessary for a living cell. As a consequence OOL needs intelligent design
Solution of the Grazing Goat Problem: A Conflict between Beauty and Pragmatism
No full textWhat is the ideal solution of a problem in mathematics? It depends on your nerd ideology. Pure mathematicians worship the beauty of a mathematics result. Closed form solutions are particularly beautiful. Engineers and applied mathematicians, on the other hand, focus on the result independent of its beauty. If a solution exists and can be calculated, that's enough. The job is done. An example is solution of the grazing goat problem. A recent closed form solution in the form of a ratio of two contour integrals has been found for the grazing goat problem and its beauty has been admired by pure mathematicians. For the engineer and applied mathematician, numerical solution of the grazing goat problem comes from an easily derived transcendental equation. The transcendental equation, known for some time, was not considered a beautiful enough solution for the pure mathematician so they kept on looking until they found a closed form solution. The numerical evaluation of the transcendental equation is not as beautiful. It is not in closed form. But the accuracy of the solution can straightforwardly be evaluated to within any accuracy desired. To illustrate, we derive and solve the transcendental equation for a generalization of the grazing goat problem
The Products of Hyperreal Series and the Limitations of Cauchy Products
No full textCauchy products are used to take the products of convergent series. Here, we show the limitations of this approach in divergent series, including those that can be analyzed through the BGN method. Alternative approaches and formulas for divergent series are suggested, as well as their benefits and drawbacks
Is Information Content a Single, Static Quantity?
No full textBefore information may be measured it must first manifest as a specific kind of information, and that manifestation always occurs within a fixed context. If any critical element of the context is changed, the information that is manifested also changes. The implication of that is significant: information is \emph{not} a single, static entity but instead is a variable, dynamic entity that acquires fixed definition only within a context
Following the Science
No full textMore and more frequently we are hearing the words "follow the science" spoken by those who believe that they are right and are frustrated by those who disagree with them. To what degree is this a legitimate effort to avoid rehashing incorrect ideas compared to a way to stifle questions about weakly-supported concepts
PREPRINT: Proving the Derivative of sin(x) Using the Pythagorean Theorem and the Unit Circle
No full textThe oft-given proof for the derivative of sin(x) is difficult for students to understand, as it relies on the limit of sin(x)/x. Here, a proof of the derivative of the derivative of sin(x) is given which uses only the Pythagorean theorem, the unit circle, the definition of sine and cosine, the definition of the radian measure of an angle, the distance formula, and the power rule for derivatives.
(deposited 2020-11-15
How to Explain Behavior: Author Precis
Full text linkThis is an author precis of the book How to Explain Behavior: A Critical Review and a New Approach by Sam S. Rakover (2018, Lexington). The precis has two sections. The first, basic methodological origin-points, treats the fundamental ideas and premises concerning explanation and understanding. The second section outlines the book's arrangement, and summarizes the content of each chapter