(Things I think about when I should be sleeping)
Say I have a line segment that starts at 0 and ends at 1.
How many numbers are between 0 and 1? Infinity, right? But how can infinity not include the number two? In fact, there are infinite numbers NOT included in the infinity between 0 and 1. How can these completely different sets both be infinity? Or even worse, if there are infinte numbers between 0 and 1, there must also be infinite numbers between 1 and 2. And between 2 and 3....etc. There infinite sets of infinity! And none of them have the same numbers!
Now look at a ruler. How much space is really between the end of the ruler and the 1 inch line? If I were to start at 0 and travel towards 1, visiting every point between, I would have to visit infinite points, and would never get to 1.
But obviously we do get to 1 in our everyday lives. In fact, we can even go to 2 and beyond! But how? Do we somehow skip over the infinite space? We obviously hit some points between 0 and 1. 0.5 is even marked on the ruler, I must at least hit that point. But just as obviously we cannot hit every point. How does our body know which points to skip?
If we can go to 2, how far can we go? That's right, we could go forever! The space we live in, right now, our entire universe, is within an infinite space. But our infinite space could be like the infinite space between 0 and 1, bounded. Maybe all of existence is expanding towards a 1 that we can never reach.
Fuck it, I'm done. I'm going to sleep, to dream of impossible 2's...
9 comments:
Are you treating infinity like a number, or a set of numbers? We have to remember than infinity is not a number, but rather a concept.
For example, there are an infinite amount of numbers between 0 and 1. Not every number on a number line, but an infinite amount.
Am I misinterpreting you here?
I know that infinity is not a number. I was just remarking that it is amazing, (to me at least) that there are infinite numbers between 0 and 1, and none of them are 2.
I have a hard time even understanding infinity and its implications. So I have an even harder time trying to communicate my (admittedly disjointed) thoughts about it.
"How can these completely different sets both be infinity?" Because infinity cannot be defined as a particular set of numbers. And you are right, there are infinite sets of infinite numbers! I really think your confusion stems from trying to assign value to infinity.
I had a hard time explaining infinity to my 6th graders this year...I don't think they really truely understand it because I don't truely understand it. Like your example of skipping over an infinite space...do we really do that? Is that even possible? You could apply your example of distance to time as well. Are there infinite measures of time? Are we "time traveling" as we speak?
You got me curious...and I started to do a little research on the internet today, and what I found out was that people don't know.
Hope that helps =).
After rereading my comment, I am TRULY upset with how I spelled 'truly'. It is bothering me right now.
"How can these completely different sets both be infinity?"
Re-reading that, I see that it sounds like I think that infinity has a set value. That was a poor choice of words.
I was trying to describe my awe, and also that infinity can be counter-intuitive. Perhaps what I should have said was, "I'm amazed that two infinte sets can exist without overlapping"
Do we really skip over infinite space?
I don't know. To me, it seems like we do. That's really all I have. I don't know why, or how, or even if it actually happens.
I don't even have a concrete idea of what I mean by infinite space...
Infinity and time is a whole other post.
"Are we time traveling right now?" is a whole other post too, even without infinity. (Because we definitely are. Theory of relativity and such...)
Infinity and time travel together? That just blew my mind...I never really thought about the implications of that. I'll have to think about that one for a while. (Needless to say that it needs its own post as well)
Can you do a time travel post first?
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