Blog Archives

A Miniature Introduction To Infinity

Infinity is a topic that has for ages caused a great deal of both fascination and confusion among students. It is a mathematical abstraction that unlike other abstractions seems hard to make concrete. The fact there is more than one type of infinity and that infinity is often treated like a number but is not an element of what we know as the real numbers adds to the confusion. The charming little video below from the Open University takes a sixty second look at Hilbert’s paradox of the Grand Hotel, a comic, yet mathematically serious example of how to think about infinity. The name is a bit of a misnomer as it’s not really a paradox, but simply a question with a somewhat counterintuitive answer. The animation does not explore all aspects of Hilbert’s thought experiment, but it is a good start that will pique anyone’s curiosity.

The Scale of the Universe and How We Measure It

Students often ask about the existence of the largest, smallest, or most distance objects that exist. These questions undeniably provide intellectual entertainment, especially when we can visualize the answers with ease. Take a look at this beautiful interactive animation created by Cary and Michael Huang to get a sense of the the kinds of distances and sizes that exist in the universe, and then look at the Royal Museums Greenwich animation that introduces the physics of measuring distances to macroscopic objects in the Universe. The video skips the details of how some of the distances are calculated but is a good starting point for further geometrical explorations that are not beyond the school curriculum.