The Fifth Dimension
Visualizing beyond the edge of the universe and the place of non-space
Infinity has never been a number — it’s an idea. One that’s difficult enough as it is for the mind to grasp. Yet there can be infinities of different sizes, just as Galileo imagined the problem of points along two circles. A larger circle and a smaller circle will both contain an infinite number of points and yet the larger circle, according to logic, must somehow contain more points than the smaller one. In the theory of transfinite numbers, infinities can be added to one another just as 3 and 3 can be added. They may also be subtracted and even give way to ever larger infinities beyond the smaller ones. A set of integers (1, 2, 3, 4,…) is infinite but is not as large as a set of transcendental numbers (numbers like π or e).
To be trans-finite is to be beyond a boundary. The term is meant to distinguish between different levels of infinity. While the theory of transfinite numbers and set theory — both created by Russian mathematician Georg Cantor around the end of the 19th century — are used throughout the branches of mathematics and are seen as fundamental to our modern insights, the theories weren’t welcome when they were first introduced. In fact, Cantor felt humiliated by his peers who had gone as far as to call the theories a “disease”. His former professor…
