I’ve written about Aristotle’s four causes before (such as here and here). This also continues the discussion of observers and travelers, here. Forward kinematics refers to the use of the kinematic equations of a robot to compute the position of the end-effector (the device at the end of a robotic arm) from specified values for […]
The mathematical problem is this: given a curve with distance coordinates that are parametric functions of time (duration), find the reparametrization of the curve with duration (time) coordinates that are parametric functions of distance. Symbolically, given the regular curve α(t) = (a1(t), …, an(t)), find β(s) = (b1(s), …, bn(s)) such that bi(s) = t(ai)
The previous post in this series is here. The key to this middle way, if it is truly a middle way between extremes, is divine self-limitation—the idea that the God of the Bible is vulnerable because he makes himself so out of love. p.139 … the personal God of the Bible is revealed there as
This post continues from part 2, which is here. The following are more excerpts from Roger E. Olson’s The Essentials of Christian Thought. For [Emil] Brunner, and for me, natural theology means only (1) that the biblical-Christian worldview better answers life’s ultimate questions than its competitors and alternatives, and (2) that eyes of faith for
George Boole wrote on “the laws of thought,” now known as Boolean Algebra, and started the discipline known as Symbolic Logic. A different George, George Spencer Brown, wrote on “the laws of form,” which presented an arithmetic system underlying logic. Below are two symbolic logics equivalent to Boolean algebra that resemble ordinary arithmetic in some
This post continues from part 1, here. One characteristic of the book is that the “essentials” or “metaphysics” that Roger E. Olson elucidates are somewhat buried among the text dealing with the competing alternatives. What follows are excerpts that focus on the essentials of Christian/biblical thought itself. A basic presupposition of this book is that
The Essentials of Christian Thought: Seeing Reality Through the Biblical Story by Roger E. Olson was published by Zondervan in 2017. It’s 256 pages long in seven chapters with as many “Interludes” but no bibliography or index. The author gives a video introduction here. The intended audience for the book is those who accept the
The following is a continuation and revision of the previous post, here. Based on the differential geometry part of the book Shape Interrogation for Computer Aided Design and Manufacturing by Nicholas M. Patrikalakis and Takashi Maekawa of MIT. A pdf version in parallel is here. Let a three-dimensional curve be expressed in parametric form as
The following is slightly modified from the differential geometry part of the book Shape Interrogation for Computer Aided Design and Manufacturing by Nicholas M. Patrikalakis and Takashi Maekawa of MIT. A plane curve can be expressed in parametric form as x = x(t); y = y(t); where the coordinates of the point (x, y) of
I’ve written before about modernity here and parsimony here. An age begins by repudiating something essential about the previous age. The middle ages started with repudiating the ancient gods and myths (cf. St. Augustine’s City of God). The modern age began with the Reformation, which repudiated the history of the Church and the pagan past
