dominator2010's Journal: ad infinitum

As a consequence of the book of paradoxes I picked up, I've been thinking about certain aspects of the world and science. It would seem to me because of infinity that measurements are arbitrary. Take such an example:

If there is an infinite set of numbers, then you could measure a single point forever.

To further the example and get more specific, you could measure a length onto infinity. Say you wanted to measure the distance of a room. Because a measurement can be broken down, you could keep measuring even though there was a boundary. You could take one inch and it would keep getting broke down into infinity. One inch into one centimeter, one centimeter into one millimeter, one millimeter into one element, one element into one atom, and you could measure that one atom into more miniscule proportions. What then? The atom doesn't go on forever, but with fractions of the measurement it would because each fraction would never lead to a whole.

The point being that any measurement is meaningless and only given to bring about a definition or terms for explaining something. Time is another measurement that I believe to be insignificant. Time isn't anything you can see, but it gives humans a way to measure that which is not there. I can't say that I believe time really exists, but that is not to say I don't find it helpful. It's a way for people to sync with each other.

I'm going to limit my thoughts at this point, otherwise this journal entry would go on forever. Be careful when playing with infinity.

funny

[stoolpigeon]

i was just thinking about this the other day. we discussed this topic in a programming class i took in high school. the teacher was asking how an arrow ever reaches it's target, if you can continue splitting the distance into infinity. the thing is, while there are an infinite number of ways to measure the distance, the distance itself is finite. there aren't an infinite number of meters between the archer and target. there aren't an infinite number of centimeters or millimeters either. so while the w

Re:

[arb]

The trick is in understanding limiting series. With the archer, each step is half the distance of the previous one and the time taken for the arrow to travel that distance is half the previous step. If you sum the limiting series you will see that it does actually approach a finite total. Now if the time taken for the arrow to travel each distance remains constant, then you've got a more interesting problem.

Re:

[dominator2010]

Your description is the same as that of the paradox of Achilles and the Tortoise. This is of course because each interval as it gets smaller is passed more quickly than the intervals before it. As what you stated last, if the time taken to travel each distance was constant, then Achilles would have never caught the tortoise.

Maybe I should write a few of these out. It's interesting to think about, especially being able to see the development of thought. Today we have answers to most of these questions, or