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Post by dlectronic on Mar 17, 2010 3:37:01 GMT -5
www.youtube.com/watch?v=lobeX6ft6PAPerhaps we can get a discussion going regarding infinity. Sure the limit of 1/x is 0. I could put an infinite number of real numbers as the denominator, but I ask, can infinities exist in reality?
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Post by Patrick on Mar 17, 2010 13:35:05 GMT -5
They don't exist in physical reality per se, but they exist as an idea that can BEST solve many real world problems. For example if you start out with a square, then you add another side to make it a pentagon, then you keep adding an infinite amount of sides, you get a circle. We obviously cannot do this, but we can use the concept of infinity to approximate it.
For those of you who have experience in calculus or engineering, you know that we can use the concept of infinity to find areas and volumes of real world phenomena. One can imagine rectangles under the curve/graph that you want to find the area of, but these cannot find the true area unless you take the area of an infinite amount of them under the curve. And this is what integration does 100% accurately using the idea of infinity in just a few steps.
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Post by dlectronic on Mar 17, 2010 19:08:26 GMT -5
I am rather fascinated with the notion of infinity and its workings (seeing that it is so abstract to us)... For this I am bummed I never took advantage of the absolutely 1337 Calculus program my high school has.
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Post by Patrick on Mar 17, 2010 21:58:44 GMT -5
All the math in Calculus, Differential Equations, and most of Physics uses the concept of infinity to solve problems. What's interesting is that infinity itself is quite abstract, but its workings are not (they're extremely practical). It also seems interesting that no one but us is very interested in this thread. At least not until we start drawing similarities between the concept of infinity and God.  |
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Post by dlectronic on Mar 17, 2010 22:59:43 GMT -5
Yea haha... so maybe a new thing to discuss might: if infinities cannot occur in reality, how can God be, noting that He is infinite? Dr. William Lane Craig responds to this by stating the infinity that we deem impossible in actuality is quantitative. He claims God's infinitude is qualitative. www.youtube.com/watch?v=dXQ9Hc_rfdc&feature=relatedDiscussion starter hopefully... |
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Post by Patrick on Mar 18, 2010 0:01:44 GMT -5
Even though there is not an infinite amount of anything in nature, infinity exists as a rule. For example, if you want to measure the volume of an ocean wave, you must find an equation that graphically represents that wave and divide it into an infinite amount of rectangular prisms, find the volume of each of them (which one would expect to be zero), and add them all together.
So how could 0+0+0+0+..... (added infinite times) give you a non-zero number? Unforunately I haven't gotten that far in math yet, but the most important thing is that it does, and it gives you a correct number.
Just because we don't see God, and we cannot rationalize him, doesn't disprove His existence. Like infinity, all that matters is does a relationship with Him work. Does it do what the Bible claims that it can do. If it doesn't seem to work at first, am I looking at the solution wrong, or is the solution itself flawed (i.e. non-existant, different, or unimportant)?
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Post by Jeremy on Mar 18, 2010 21:59:53 GMT -5
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Post by Muffy on Mar 19, 2010 4:41:28 GMT -5
^Interesting doc.
I used to think about infinity alot at night... I almost drove myself insane too.
I have nothing to add to this discussion... I have thoughts about it, but I could never explain them in any kind of understandable form.
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Post by unicycletim on Sept 30, 2010 2:30:31 GMT -5
Sorry if this is a bit of a tangent, but it was the first thing that came to mind when a discussion regarding infinity was suggested. Something about infinity that boggled my mind is that there are different sorts of infinities. This was discovered by Georg Cantor in 1873. What I mean is that you can compare two infinite sets and say that one is bigger. Marcus du Sautoy describes it well in his book The music of the Primes (which I recommend- it's not too technical, even if the topic is slightly nerdy) To compare two infinites, imagine a tribe that has a counting system that goes 'one, two, three, lots'. They can still judge who is the richest member of the tribe, even though the exact numerical value of that wealth cannot be discerned. If chickens are the sign of a person's wealth, then two people just need to pair up each others chickens. Whoever runs out of chickens first is clearly the poorer of the two. They don't need to be able to count their chickens to see that one collection outstrips another.
Using this idea of pairing objects, Cantor showed that if you compare all the whole numbers against all the fractions (such as 1/3, 3/4, 5/101) the members of the two sets can be paired off exactly. This seems counterintuitive, since there would appear to be many more fractions than whole numbers. Yet Cantor found a way to establish a perfect match, with no fractions left without partners. He also produced a cunning argument to show that, in contrast, there was no way to match all fractions with all real numbers, which include irrational numbers such as pi and sqrt(2), and numbers with a non-repeating decimal expansion. Cantor showed that any attempt to pair the fractions with the real numbers would necessarily miss some number with an infinite decimal expansion. Here, then, were two infinite sets which Cantor could show were of different sizes.
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