August 1, 2010
A look into the Infinite: How it works Conceptually and In Reality
Well I’m both a little surprised and impressed with the reception my last post received and am glad to continue with a topic with many similarities with the last one. This post will look at the concept of the infinite by looking at a couple of paradox’s and in the end it will show how and idea can work in theory, and in reality. Now as a forewarning I am firstly a philosopher and only further down the line a mathematician/physicist, but I’m going to play those roles for this post. If there are any mistakes or clarifications that are needed, feel free to post the information in the comments and I’ll make the corrections as soon as time permits.
First, I’ll just introduce the subject matter through an illuminating argument I had with a former professor a few years ago. He brought up the topic of the infinite and how it worked as a mathematical concept, and in doing so he pointed out that in math you could have a number that was infinite ( Z for example) and also a number that was double that infinite (2Z). Fair enough it does make sense within the framework of mathematics, but a problem arose when I was asked to define what the infinite meant.
Now when asked I said that the infinite is really a concept that is irrational when applied to the world around us (Look back that may be going a bit to far, but it points out how much the meaning changes when applied to real world issues). The infinite really breaks down and can’t be used in real applications, except as a concept that doesn’t exist in reality. Take for instance the simple equation above, and try to put that into an example that makes sense.
There is an infinite number of apples, but there are twice as many oranges as apples. Try to prove that statement is true. It makes sense as an idea when the sentence is read, but to really prove it all the apples and oranges would have to be counted, which cannot be done. Yet there is also a problem with being double the infinite of another infinite, because as soon as you hit infinity you’ve reached the limit, there can no longer be anything more. It is the equivalent of saying that something is more unique than another unique item. Unique means one of a kind, and once you’ve hit the status of one of a kind there can no longer be anything more unique. If there was something more unique it wouldn’t exist.
So, what if someone is running on a circled track and there is another person running twice as fast as the other person. Couldn’t it be said that the one person is traveling twice the distance of the other, while they are both in an infinite loop? Well I think that would be a fair but inaccurate description of that is going on. The relative speed is the important part, while noting the infinite distance, just implies that it isn’t known when or if they will stop. It doesn’t add any information.
Now this seems to be an example of the infinite, and in a way it is. The problem comes with trying to find a home for the infinite within out observable universe, without there being a loop. The earth, due to it having a curved surface, has no endpoint. A person could fly around the earth and end up in the exact same spot they were in, but it wouldn’t be fair to characterize the earth as having a surface of infinite size.
This brings up how the infinite is a supernatural answer to some questions. How far can the universe expand? How long will space/time exist? How dense is a black hole? If the answer to those questions was given as infinite, it just means that the answer really isn’t known, but there is no reason to think that there is an upward limit.
The infinite is a placeholder when used to talk about most real things, and an effective tool when used conceptually.
Sorry I didn’t get to some of the interesting paradoxes, but I will in my next post.
Thanks for reading
-the moral skeptic