Considering the Nature of Infinity
Infinity is not something that should be examined by the weak of mind. In a general sense, we all know what it is. That is to say, we know that it is something without end but that is a grossly simple description. When one begins to ponder it's nature, the concept and, possibly, the reality infinity can cause our most solid of logical principals to break down. Trying to reconcile our limited ability to understand the endless can become an obsession. However, coming to terms with what "forever" or "endless" really means may be valuable and capable of significantly altering the way that we experience our lives and the world that we inhabit.
One may think that the infinite is a simple thing to grasp but is this the case? Consider this for a moment: Some infinities may be larger than others. Imagine that you have an infinite number of marbles that have an equal chance of being one of three colors. This means that you have an infinite number of each color but you must also have more of colors one and two combined than you have of color three alone. Logic seems to stop functioning here. How can a thing without end be smaller than another thing? People who are better at math than you or I struggle with this problem and it is not the only one that arises when we start to dive into the concept of the infinite.
Can an infinity exist within something that is finite? Logic would say no but there is reason to believe that the answer may be yes. A number can be divided and divided again. One may continue dividing on into infinity but he or she will always end up with a new, smaller fraction of the original number. The difference between one and two, for example, is decidedly finite but, somehow, an infinite number of fractions can exists between them. Again, we are left with a concept in which logic seems to be inadequate.
There may be dangers in thinking too deeply about infinity but there are also potential rewards. Some maintain that the mathematician George Cantor was driven mad by his meditations on infinity (and when one considers the subject, this seems like a possibility) but that claim is disputed. Whither pondering infinity actual drove Cantor crazy is irreverent because it is no secrete that we can obsess over ideas when they can't be made to conform to our logical principals and that obsession can be very unhealthy. However, an obsession with infinity may be worth risk. We will die and, as far as we know, that is a infinite state of affairs. Coming to terms with the eternity that we will all face can alter the way we live our lives leading up to our demise because we will more greatly appreciate the limited time that we have. Understanding that the finite moments that we exist in may be far "longer" than we understand, can change our perception of them and allow us to draw them out and better savor them. I believe that it is to our advantage to spend some time thinking about the infinite even if we do risk becoming obsessed and, potentially, unhinged in the process.
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