But again, infinity is greater than all real numbers so if you actually did try cutting something up into X pieces, you could never just round it off, it will always be quantifiable Between any two real numbers, no matter how small the difference, there is an infinate number of numbers. there is an infinite amount of numbers from 1 x 10^-100 and 1.1 x 10^-100 However, there is no way to ever reach infinity because it isnt real, you cant count to infinity because the real number line never ends. for example you can calculate Sigma(X+1) for you entire life, then your children can too, and you will have a HUGE number, but unless you do this for an infinite time you will never get an infinite number. So just to clarify your example of cutting something up, the idea holds in theory, but not reality
The more we discuss the idea of "infinity" the more it becomes clear that its far more complicated than I originally thought. I'm going to try and explain why I somewhat disagree with Skywalkers definition of infinity. Keep in mind, im a bit fried and the whole idea of what we are talking about goes much deeper than I had first imagined. Anyway, here goes.... Lets take a line segment as an example: [__________] - Lets say that this line segment is an inch long. Using skywalkers logic, infinity lies within this one inch segment. As he explained it, it seemed to make sense how it might be possible. In theory, this segment could be divided and divided and seemingly the divisions could possibly be endless...thus making the space within this segment infinite. However, doesnt that seem like a contradiction? The space within something being infinite? Infinity cant be bound within a certain amount of space, otherwise it wouldnt be infinite....right? Heres another example: Lets say this cube represents our Universe... If this "space" were used to represent our Universe, clearly it wouldnt be infinite. Even though the space inside could be broken down into parts so small that we may never fully understand them, this certain space clearly has its limitations....in other words, its not truly infinite.....I think. But this line of thought got me thinking even more... Lets say skywalkers idea was right: that you can break down the space within something an infinite amount of times. Lets say that although there are limitations to how big you can get within a certain space, there are no limitations to how small you can get. Things can just become smaller and smaller and smaller. Wouldnt that suggest infinity within a limited space is possible? Can infinity be possible in only one direction (in relation to space)? Can infinity be limited to how big it can become, but not to how small it can become? In other words, if something can be broken down into smaller pieces an infinite number of times...that to me would suggest that it is possible to have an infinite space within a clearly defined area....which really blows my mind all together. What do you think?
well, while attempting to dodge the temporal limitation inherent to the question... yes. it can be created. autopoiesis.
Again, you can divide an inch (or foot, or mile, or picometer) into infinately small pices, however this does not mean that original measurement is infinite what all this is really saying, is that infinity is larger than all real numbers. thats what it comes down to. its always possible to add an extra 0 to your number.. if you divide an inch into a billion pieces, you will always be able to divide it into a billion plus 1 pieces. As long as you keep dividing, you will always be encountering more real numbers and never reach infinity. Infinity does not lie within a discreet space, rather, that discrete space can be divided into infinitesimally small spaces. if you add all these slivers, you will again end up with 1 inch (or w/e your original measurment)
Well it's complicated LOL but the space is finite and the number of times you can divide it is the infinite part. Space cannot be infinite, space is another word for finite. Concepts or principles can be infinite because there is no way to measure them in terms of space. You can just keep applying the concept (in this case, division) over and over again because it doesn't have any dimensions or limitations. So he's right in a way, there is infinity in that concept but you are confused because the infinity is NOT in that space. It is in division. yes, but not in space- in the amount of times you can divide it. Infinity can be limited in any way but it will instantly become finite. That's the trick behind reality in my understanding. Infinity doesn't sit inside the boundaries of logic and reason and therefore exhibts some very odd 'behavior' LOL I still wonder why things are the way they are, knowing that there is a chance that what made this all possible is completely irrational and not logic-based in the least bit! (infinity) I guess I should understand why so many things don't make sense... Yet, I still wonder what the fuck is going on sometimes... Oh well, life goes on-
See, it sounds like your contradicting yourself. In my opinion, it certainly means that the original measurement is infinite...because the measurement itself is pointless if we are thinking in terms of true infinty. Measurements dont apply to infinity if you accept infinity as a possibility. If something can be broken down an infinite number of times, that suggests that anything and everything is infinite...including you and I. It would also suggest that it doesnt matter how something is measured in terms of distance, mass, or volume (like I said, those things dont matter)....infinity lies everywhere and in everything.
I think Mr Goodstuffs post was about this... if you break something down an infinite number of times you have an infinite amount of divisions, not an infinite amount of space. if you take all your divisions, all the way to infinity, and sum them, you will get 1 inch, thats why the original measurement is finite Similarly, you can have an infinite series that converges to a real number the thing about infinity is that it isnt real, you can start with 1 inch and break it down to a bunch of pieces that are .0000000000001 inches long but then you can keep going to .00000000000001 inches and furthermore to 0.000000000000000000000000001 inches long. As long as you are dividing you cant gget infinity because division of two real numbers results in a real number. Infinity is not a real number so you will never reach infinity or reach an infinite amount of divisions
Because the word space, as long as it's not describing the universe- refers to dimensions. Infinity has no dimensions. At the same time, infinity contains all possible dimensions, because it has no dimensions. The trick is, when infinity realizes a possible dimension it becomes finite and rational. How it does this, I do not know. I prefer to think of it as the genius of God, could be as much chance as anything but perhaps intellegence played a part somehow? From what I have observed and reasoned, this is true. Just if you want to find it in space- you must realize that space itself is just boundaries drawn on infinity (in theory) From what you were saying, it's not the space that is infinite, it's ability to be divided is the infinite part. Space can only be infinite if it's source is as well- much like the division example is trying to show. Still, we aren't sure if that's infinite or not... It's just a theory that makes some sense. It is a fact we will never be able to comprehend infinity, because what we think about it is in finite terms. When talking about it, you have to adress it as a subject and it isn't one... So it's not possible to define what IS no definition! (aka trippiest shit EVER) try to think of nothing... Just try LOL What we could comprehend would be a shadow it left or something with dimensions it made possible, that's about it. Then again 'it' is not an 'it'... So what is it I'm describing again? Nothing? LOL so mixed up... My understanding on it is only sound when I accept I cannot truly understand it. The moment I try to see it, is the moment it disappears.
An old calc teacher of mine tried explaning it using a hotel (this is probably really common) Bob walks into a hotel that claims to have an infinite number of rooms. He walks in and the person behind the counter says all the rooms are currently full, but i can find you 1. After a short time, the man returns and gives Bob a room key, however nobody left the hotel in that time. Soon Matt walks in and the man gives him the same tak, alks in the back room and then returns with a key. Infinity is real, it isnt really defined, its just bigger than all real numbers. So you may think you are at full capacity (the end of the number line) but there is always another real number to add. So even tho there were, at first, no rooms, the hotel could shift the number line to accomodate Bob and Matt Kinda like i said earlier, you can count the sum of (X+1) and your children can continue and their children, etc. And you will always have a real number even if the number is 3 x 10 ^99999999999999999 Unless you count for an infinite amount of time you will never reach infinity The real number line never ends, you can always add 1 to w/e number yet infinity lies beyond this point thus its imaginary
So that's the twist... Only the infinite can comprehend the infinite! It just keeps going on forever, so only something that went on forever could actually even be on the track to infinity... Infinity can't be achieved then, only set up as possible! It's just a chance it could be infinite, even if it IS! HOLY SHIT THAT'S NUTS!!!
I think I'm pressing on the reason God isn't more tangable! If God is infinite, than God is only something that could be, and never something that is! HOLY SHIT!!! I've reached around this point before but never from this angle... Wow that's incredible, it's like a bright ray of light beaming into this dark room of reality! "What is- is not as important as what can be. Because what can be is ever-changing and what is can never change!" -old quote of mine, based on why God would want an ever-changing universe and not a universe that always stayed the same
I wouldnt say that...maybe it is and maybe it isnt. Its not real in the sense that we can understand it, but if infinity exists then its quite real. Edit: What I do know is this..and this has to be true regarding true infinity: If infinity exists, it exists as a single force and is the only one of its kind. What I mean is that you cant have multiple infinities, does that make any sense? Maybe infinity is a substance, maybe its only an idea....maybe they are one in the same.
My bad, thatt was a typ-o i meant infinty isnt real, as in a real number (like how 1 is real, or -2.4 or pi)
Now you are getting somewhere JesusC! To hear you speak in irrational(subjective) terms, it's almost along the lines of Rasta doing it but it does show that a reason rational thinkers don't accept irrationality at times, is because irrational thinkers couldn't form rational thought about it! Maybe that's the reason Atheists can't get through to Christians- They just don't have the story to interest them and paint a picture easier for them to see; just like a Christian doesn't have the facts to paint a picture easier for them to see... It's all very interesting though... Great thread man!
Yea man I gotta be honest, I never thought that starting a thread about infinity would get the wheels turning in my brain as much as it has. This is pretty much what im all about as a person, spending the majority of my time thinking about things like this. Its hard to be rational when you are trying to understand the idea of infinity, because the idea of it is so irrational when it comes down to it. You have no choice but to think irrationally. I suppose the same can be said about the idea of "god". Dont get me wrong, Im not slipping down the slope to becoming a believer. Im just saying that I can understand why people sound so irrational when attempting to share their ideas of god, if they are thinking along the same lines that I am regarding Infinity. Man, the Universe is an amazing place....I love it here.
Totally feel ya on that one man. I'm always thinking myself, a lot of it is a little too "heavy" for most of my friends in real life but it's who I am It's awesome to see someone completely rational give credit to irrationality; even using subjective reasoning in the process. I hope to see a Bible thumper come to terms with the fact he can't prove God is real next on this forum, that would be great (seen a doubter confirm his suspicion, but never a die-hard start to doubt) The essence of open-mindedness... What a beautiful thing!!! You guys give me a place I can go and feel welcome talking about these things, I really appreciate you guys more than you know. Sometimes I feel like I can't really talk about some things because others won't want to talk about them, prefering some dramatic situation instead of the nature of reality. I've just been really interested in it lately, and this forum helps me understand it all so much better. If it wasn't for the rational thinkers, I don't think I would feel like my philosophy was valid at all. It was rational thinkers like yourself that showed me that both sides are capable of seeing the other.
I understand what you mean. Anytime I try to discuss such things with my friends or even my family, I always seem to get the "this whole thing makes my brain hurt" type of response and the conversation pretty much ends there. This place allows me to free my ideas and express them with people who will actually take them into account and run with them...which is why I post here in the S&P area as much as I do. There isnt any place I can drive to where I can sit with a group of people and discuss the things we discuss here...at least not that im aware of. I really dont come here to talk about weed or certain trips ive had...that stuff really doesnt matter all that much to me. I come here to open my mind and hopefully help others do the same, and when it happens, its a beautiful thing. I guess ive really found a home here, in the sense that I can share my ideas about subjects such as this one with those who will truly listen. I also take great satisfaction in knowning that I will continue to spend my time here on earth thinking about these things.
"This is making my brain hurt" LOL totally feel ya, well this makes my brain feel aware and I enjoy it a lot, so carry on brother! To infinity! The loop to nowhere that's everywhere!