Chapter 35: Phi (ϕ)

Phi, the magic number was discovered by the Greeks, by Pythagoras or his followers, as best as we can tell. Originally, it was described as a ratio of line segments described by the following situation. For a line segment composed of two components, a and b, the ratio of the length of a/b is the…

Chapter 34: The Vortex

Wow! This is just stunning, don’t you think? Here we have two phenomena, orders and orders of magnitude apart with respect to size, and yet, their characteristics, their flow patterns and their overall forms are just the same. The galaxy shown extends about 50,000 light years in every direction from the center (each light year…

Chapter 32: The Linear Dimension

As humans, we are inextricably caught between the large and the small. We are much too small to capture the wonder and size of the cosmos. Oh sure, we have developed powerful telescopes that we can use with clever techniques to get keyhole sized views of the universe in the distant past. Because the speed…

Chapter 31: The Three Accelerations and Einstein’s Elevator

The fundamental assumption for Dr. Einstein’s  triumphal paper on General Relativity regards the equivalence of gravitational mass and inertial mass. It is so basic, so fundamental that it has come to be regarded as one of the basic building blocks of all Science and reason, and has become one of the most stalwart principles in…

Chapter 30: New and Improved! The Three Dimensions

I remember the moment very clearly. It was in the fall, in the Great Lakes region of Ohio. The leaves were starting to turn, making the wooded area surrounding our porch into a mad palate of varied colors and hues. Fall is a particularly beautiful season in the upper Midwest, and this one was no…

Chapter 29: What is a Dimension, Anyway?

Webster says: “Dimension (in the general sense): an element represented in an equation by a symbol that functions analogously to symbols representing the three spatial dimensions and regarded as a constituent of a geometric space” Whew! That’s a mouthful. To be truthful, I thought that I’d try to come up with a definition of my…