My first memory of bumping into the idea of infinity is from a geometry class in grade school where we were learning about lines and rays. Teacher took us through the idea of lines and rays, explaining that a line continues without end in both directions, while a ray, of course, is fixed at one end and continues without end in the other direction.
Then Teacher asked us which was longer.
I still puzzle over how infinity can be so simple and so irrational at the same time.
Bro Jim left a copy of The Elegant Universe at the house after being here for the Big Game, and I've enjoyed browsing through it and reading the progression of unification theories vying to resolve the sibling rivalry between relativity and quantum mechanics. The book focuses on String theory, with the author's awesome descriptions of messenger particles, 11-dimensional supergravity, and the myserious M-theory. The book is over a decade old, and I would assume a lot of progress has been made in pushing the envelope of human understanding of the physics that describe the makeup and behavior of the universe since it was first published. The progressive march of human understanding of the world carries on impressively, although I wonder sometimes how far along the infinite path to total enlightenment we have really gotten.
Admiring the view of the full moon setting in the western sky during my drive in to work this morning I was reminded of another childhood brush with the infinite in the form of a rambling, drunken, and apparently brilliant math professor who lived down the street from us. We grew up in a small college town in Alabama, and although this was normally a pretty quiet southern town you never really knew who or what you may see on the street at any given time because the college attracted such a wide range of characters. One of those characters was our neighborhood math prof who would routinely be seen wobbling down the sidewalk, beer in hand, a number of dogs and kids trailing behind, mumbling mathematical expressions all the while. He inspired a mix of awe and pure terror in the neighborhood kids, but pretty much just pure disgust in the neighborhood moms.
Relativity in action, huh?
I wonder sometimes if he behaved as crazy as he did because his mind was blown-out trying to get a good grip on infinity and failing, or if he had actually gotten a glimpse of what infinity really is and it was way more than his head could handle.
Anyway, getting back to purpose of this post, I was looking for information online this evening regarding the Goseck Circle, and wandered down a rabbit hole of science and astronomy websites. Along the way, I found this little video that shows how adding all of the natural numbers from one to infinity equals -1/12
Who would have guessed?