supthos

The day strikes its first notes of blue as Joanne brews a few cups of her favorite coffee brand. With the click of a button the news start playing on the TV. Terrorists have bombed the Channel Tunnel that runs between London and France, killing thousands and causing an exorbitant amount of money in damages. The world is outraged and the only clue to who may have done it is a video left on a popular streaming website, from an anonymous account. In the video, an artificially generated voice over a completely black screen identifies itself as an anarchist military group called Enkidu and proudly announces they are responsible of the attack on the Channel Tunnel, claiming that civilization is the source of all human problems. They promise that this will not be the end—we should all be afraid. Very afraid. Joanne Bergson shrugs off the news. She’s got more important things to think about. Like what she’s going to wear tonight for her first webcam show, and how well would her friend Genevi...

Sadly, the arctangent function does not preserve a linear rate of growth, and I do not know if Riemann’s sphere retains this property. We want a transformation that, as you squish numbers together, their magnitude becomes proportionally smaller. Start with zero. The distance from zero to one is one. Zero has magnitude zero and one has magnitude one. But let’s squish in one to one half to allow for the number two to fit between zero and one. Then the number one will have magnitude one half, and the number two will have a magnitude of one. So, by mathematical induction, every time we squish in a number, we result in having each previous number divided by a magnitude of the newly squished in number. The question is what happens at infinity. In theory, no matter how many numbers we squish in, the slope of growth of the magnitude of our natural numbers will always be one. What we know for sure is that, at infinity, or at ω, the distance between each number is infinitesimal, and all the natu...