## Simplifying Mathematics: Introducing Vectors and Vector Addition

[caption id="attachment_23153" align="alignright" width="480"] Magnetic vector force field[/caption] We all know how to add, subtract, multiply and divide ordinary numbers, even if basic units are attached to them such as gallons, apples, feet, tons, and so forth. 4+3 = 7 5 lbs x 3.2 = 16 lbs These two examples illustrate pure numbers in the first instance, and simple quantities in the second instance. Introducing Vectors: What About Direction? What if we toss in direction? Imagine a huge square, 5 miles on a side. We have to travel along the perimeter to travel from Point A to Point B, and then on to our destination, Point C (see the image). We thus travel 10 miles to reach Point C. If we could travel "as the crow flies", we would only…

## Edge Effects for the Universe?

[caption id="attachment_7377" align="alignright" width="480"] Introducing the universe.[/caption] A strange thought crossed my mind. I was in that twilight state between awareness and sleep. What about the edges of the universe? Does the universe experience edge effects? Materials all have their own properties. Metals, for instance, have a melting point. They have conductivity, density, malleability, and ductility. Liquids, gases, and plasmas have properties as well. A material or an object can act differently at its interior, than at its edge. Consider some objects interacting with electromagnetic radiation. Magnets and Capacitors Capacitors exhibit so called Casimir edge effects. The electrical field between capacitor plates behaves differently at the edges, than between the centers. The same is true of the edges of magnets. Frequency Skin Effect Electrical engineers understand the high frequency skin…