Saturday 25 February 2012

Two Infinity and beyond

   A few days back, a particularly relevant idea was presented to me by a good friend who tends to present me with relevant ideas. The topic at hand was infinity however the explanation was really quite simple. For the purposes of this discussion we will explore two ways of considering the idea of infinity.

     First, there is the idea with which we are most familiar. If there is a number line, it is simply moving forever in either the positive or negative direction. Conceivably, one never runs into a limit when counting in either direction, thus arriving at infinity or negative infinity.

      The second type of infinity is more like looking at the number line strictly between the numbers 0 and 1. Between 0 and 1, it's possible to make an infinite number of divisions, mathematically and theoretically speaking. For example you could divide the line at .01 or .011 or .0111 or .01111 or .011111. The point being, it is possible to add an additional 1 an infinite number of times, at any point between those two numbers. Each number refers to a slightly different point on the number line. When an additional 1 is added in the next decimal point to the right, we are zeroing in on a more specific spot, however it can always be made more specific by adding an additional 1 to the end.

     For me, the most relevant application of these two types of infinity is in the way a person's mind comes to  understand the world around them. For example, there are an infinite number of physical items that a person could know about including everything from rocks, water, trees, animals, tables, houses, computers, sports, artistic creations, cars, food, buildings, stars, planets, solar systems, galaxies and ultimately (I'm going to suggest) an infinite number of other things. There are also things that are less tangible and sometimes purely intellectual such as languages, mathematics, philosophy, opinions, dances, music, and other bodies of knowledge that could also be counted as things in this sense. Whether talking about psychical material items or ideas, the universe constantly produces more on its approach to infinity. This would be an application of the fist type of infinity.

    The second type can be understood in the way that there is an infinite amount of information to know about any one of those previously mentioned items. For example no matter how much a person cares about and wishes to learn about dogs, they can never truly know everything. The most knowledgable person in the world about dogs would still lack the knowledge of how many hairs their own dog presently possesses, how much blood, the number of breaths taken that day, or any number of other ridiculously precise pieces of information. Any item could be broken down in this fashion, but could never be completely understood because there is no limit of information in regards to any particular item.

     Lastly, there is almost a third type of infinity (which could actually fit in with the second type) that comes from those first two put together. With every additional thing that comes to exist, ideas or physical things, comes an additional relationship between that new thing and everything that already was. For example, when a new discovery in chemistry is made, it must then be observed how it relates, or doesn't, to all previous findings. This third type is sort of like adding an exponent of infinity to the number of things that were being counted.

     Hopefully this general take on infinity will help me explore other more specific topics later such as precision, learning, and awareness.

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