Within the past year, I have been introduced to some of the ideas and concepts surrounding infinity. I was most intrigued by the work of Cantor and Hilbert. Cantor worried about the paradoxes when you start trying to work problems using infinity as if it were an integer, ie using "I" as infinity (I + I=2I??) How does that work?
One intriguing visualization from Hilbert is his infinite hotel or "Hilbert's Hotel". The hotel has infinite rooms and they are all occupied. Say, you show up, or you and all your friends, or you and an additional infinite friends show up and need a room. Hilbert would shift the guests so as to accommodate the new guests. This proposal of different kinds of infinity does not really make sense at least not to a finite creature as myself.
Now the way I have imagined it is that there is really the "single" infinity (whatever that means) and the infinite other infinities imagined in the Hilbert hotel are just part of that true infinity. One way to think of it might be a shape shifting object that is always changing into new forms of infinity but is really still the same object.
Now if that confuses you, if confuses me, too, but really if infinite buses showed up to the Hilbert Hotel with infinite passengers on each and the guests are moved to accommodate these new arrivals, really those guests were already there. I don't know how to explain this more clearly. It is kind of like travelling around a circle. No matter how far you travel around the circle, you end up in the same position. This makes sense to me but I may not be the best at explaining this concept. Let me just state one more time the continuing properties that Bob arriving at the hotel, can go to his room, but he himself has left that room to accommodate himself. Ok well, that may be even worse, so I will give it a rest for now and come back to it later. This is just one idea, and by no means my final thought on infinity.
I hope this gives you something to think about even if you feel that my train of thought is flawed.
