music
Max Cooper - Aleph 2
In collaboration with Martin Krzywinski, Max Cooper set out to explore Georg Cantor’s ground-breaking ideas on different sizes of infinity. What you see is an authentic numerical rendering of Cantor’s work, and if you’re willing to spend the time reading about what each part shows it should provide real insight into some exotic ideas. The video begins by counting the natural numbers 1, 2, 3, and so on. This list continues forever, but can be thought of as a single entity: the infinite “set” of natural numbers. We next look at the set of integers (whole numbers including negative numbers), and pair naturals off with integers.This process is called a bijection. Two sets with a bijection have the same size, or “cardinality”. A set with a bijection to the naturals is considered “countable”. Even though the cardinalities of the naturals and integers are infinite, they’re the same “kind” of infinity.