May 3rd, 2012

## Galilean Relativity Theory

Galieleo’s relativity stated that an observer who moves uniformly with constant speed in a straight line, that is, who moves with constant velocity, is called an inertial observer.  The Galilean principle of relativity can be stated as follows: The mechanical laws of physics are the same for every inertial observer.  In other words, by observing the outcome of mechanical experiements, one cannot distinguish a state of rest apart from a state of constant velocity.

By Galileo’s definition, two inertial observers can disagree on whether or not two separate events occurred at the same position in space. Since no mechanical experiment can distinguish a state of rest from one of uniform velocity, Galileo effectively abolished the universality of the notion of an ‘observer at rest.’

November 22nd, 2011

## The Different Versions of Infinity and Cantorian Sets

When we think of infinity we usually think of the usual two categorical distinctions:  a potential infinite and an actual infinite.  A potential infinite suggests that infinity is only an idea or a concept but doesn’t actually exist in the Platonic sense or in the physical sense. In any set, one may always be added.  An actual infinite is the notion that there exists such a set, Platonic or physical, which is infinite.  A potential infinity may be symbolized by a lemniscate:  ∞.  An actual infinite can be depicted by the aleph-null or aleph-nought:  ℵ0 (The Hebrew letter aleph with a subscript zero).

First, let’s have a brief refresher on set theory.