## In Simple Terms: The Heisenberg Uncertainty Principle

[caption id="attachment_26306" align="alignright" width="480"] L to R: Niels Bohr, Werner Heisenberg, Wolfgang Pauli[/caption]Werner Heisenberg (1901-1976) was yet another bright German physicist. He was a "founder" of quantum mechanics, the physics of the subatomic. As with astrophysics, behavior at this level appears to vary from the physics of the everyday world. A Brief Description The velocity of an auto of mass m can be measured accurately. If its velocity remains constant, its location over time is predictable. This is the norm according to ordinary human experience. Yet, at submicroscopic levels, physicists experienced something different. For certain measurements, various pairs of variables could not both be accurately known simultaneously. Simultaneous measurement is only precise to a point. These pairs of variables are termed conjugate variables. The Standard Example The simplest example is…

## Discrete Mathematics: What is a Point and What a Line?

[caption id="attachment_7234" align="alignright" width="440"] Discrete points? An abstract.[/caption] Most technically minded people will probably take me to task over what I am going to say in this article. That is OK, though. I’m used to it. Not only are my writings quirky—I am quirky. Hey! This is QuirkyScience. I want to talk about points and lines in the real world—in other words, discrete mathematics. What is Reality, What Fantasy? To a mathematician, the point may be a dimensionless object in 3D space, a mathematical object with an x, y, z coordinate in Euclidean space. A line would be a collection of such dimensionless points lined up all in a row. But that is in the world of the mathematician. In the real world, there can be no such thing. Rather,…