Why I think this is important. A few of you are posting things like "so what". "Zeno can't get across the room, big deal." "This is a waste of time." etc. I think there is a very important lesson from this. Infinity is something that we demonstrate with reason. For example, we can imagine that the number 1.9999999... repeating can go on forever. It's a logical possibility. But when infinity is inserted into basic math problems like distance problems, they break down. Problems such as Zeno's or Xenu's paradox show how reason can be used to screw itself. I'm not saying that reason is "bad" or "should be abandoned". Reason is a tool of mankind used to make "understanding" out of an infinite universe. It's a model of the universe. -Xenu
Re: Why I think this is important. Reason doesn't screw itself. As I stated earlier, it's Zeno screwing himself. He knows his action won't get him the wanted result in reality, but he feels it should? What an idiot!!! Please Register or Log in to view the hidden image!
Pure reason is useless and it is idiocy. All reason and theoretical knowledge came from empirical knowledge. Read Kant's Critique of Pure Reason, for heaven's sake.
The solution is simple. Infinity does not exist in reality. It exists only as an abstract concept in math. You cannot keep travelling half the distance, because soon the minimum distance you can travel will be greater than half the previous distance because space and time are quantized. One way to show that you cannot keep dividing in this way is this: Proof x = 0.9999.... 10x = 9.9999.... 10x-x = 9.9999.... - 0.9999.... 9x = 9 x = 1 Therefore 0.9999.... = 1 Infinity is not a number, it is a concept. It is self contradictory and therefore doesn't exist.
Alpha, Ummm, what? You better explain yourself here, because right now I feel you're talking out your ass. If this truly makes sense, please share, then I'll be the idiot. Please Register or Log in to view the hidden image! This is a nice little trick, but that's all it is, a number trick. Firstly, it doesn't prove anything about infinity (as applied to math). Secondly, it doesn't disprove the paradox. Let's say for instance, Zeno's paradox was in 1/4 's instead of 1/2 's. Your new infinite number would be .3333....(repeating). Now let's put this into the formula.... x = 0.3333.... 10x = 3.3333.... 10x - x = 3.3333.... - 0.3333.... 9x = 3 x = 0.3333.... Therefore 0.3333.... = 0.3333.... It all depends on what you define "reality" as.
Is this post directed towards me? If so, you're arguing basically the same thing I am, but I'm showing how reason is "useless and idiocy", at least when it's applied to infinity. I think we're on the same side. Also, what happened to: ??? Please Register or Log in to view the hidden image! And no, I will not read Kant. Please Register or Log in to view the hidden image! -Xenu
Re: Re: Why I think this is important. Yes, he knows his "action" (the paradox) won't get him realistic results. No he doesn't feels it should. He is showing how reason fails in determining reality. Reason is a model. Models have faults. This is one of reason's faults - Infinity. If you are still against Zeno, make a rational case against what he says, rather than criticize him and dish out your subjective opinion. -Xenu
Infinity is a paradox. It is self contradictory. Imagine a point on a flat plane. Now there are an infinite number of directions from that point. (I'm starting with the assumption that infinity exists in order to find a contradiction and therefore prove it doesn't exist.) If you imagine 2 lines radiating from the dot and extending to infinity, you can draw another line in between them, and another between them and so on. You can always fit more, so there's an infinity of directions. Remember the lines have no thickness, so they don't overlap. And you can always go further away from the originating point until the lines diverge enough that you can fit yet more lines in there. More directions. Now imagine a point in 3d space. There's an infinite number of directions from that point. Yet there are clearly more directions than on the plane, because all those directions are included and multiplied by infinity in three dimnesions! So Infinity is more than itself? It doesn't make sense. There's your contradiction. Also, the minimum length is the Plank length, and the minimum time is the Plank time. You can't travel a smaller distance than the Plank length, so eventually one half of the previous distance would be less than the Plank distance, and you wouldn't be able to move forward by such a small amount. So the argument is invalidated because you can't keep travelling half (or a quarter) the distance. No, it's not a "nice little trick." Yours was a nice little trick. How do you get from 9x = 3 to x = 0.3333....? In my equation you divide both sides of the equation by nine so they stay equal. In yours, you divided one side by nine and the other by 3 or something. That doesn't work. It's not allowed in math. Go here for a more detailed explanation. Well, something that exists without paradox for one.
9x = 3 now divide the left side by 9, you get x. now divide the right side by 9 3 divided by 9 = 0.3333....(repeating) Pull out your calculator. It might amaze you. Please Register or Log in to view the hidden image! Like I said, your first problem doesn't disprove anything to me, it's just a mathematical trick that only applies to the 1/2 distance infinity and not the 1/4 distance infinity. This doesn't disprove anything either. Firstly, I'll state this again, the Zeno's paradox that I posted has nothing to do with time. Secondly, why does there need to be a minimum distance, a Plank length? What calls for a minimum length?
Did you even check the link I posted? I think you should. 0.9999.... = 1 The proof is there. And yes it does apply to 1/4 distance, or any other division for that matter, because you cannot keep travelling a smaller and smaller distance. Read some physics books! I didn't say it had anything to do with time. Honestly, does it matter why right now? There is, just accept it. Do you really need it explained to you?
First he wants to reach point B from point A. Second he tries to apporach point B from point A. Third he starts to complain that he will never reach point B by the method stated above and claims a paradox has occurs. From the list above, all I see is a failed logic. In fact, I don't see any paradox, unless he assumes reaching a goal is same as approaching a goal but never reaches it.
no, no, no, 1) Something (it doesn't have to be a person!) approaches point B from Point A. 2) The manner in which the thing moves is half the distance that it moves before, and then half that, and then half that, (this isn't necessarily in step increments, thinking this way however makes it easier to comprehend) 3) The paradox is, when something moves in this manner, it can move forever and ever and never reach its goal. He isn't trying to prove that trying to reach a goal in this manner is the same as actually reaching a goal (this is what Alpha is trying to say with his .9999... equation) - that's not the paradox. He is showing that reasoning in this way, although logical, doesn't work. The thing moves forever and never reaches its goal. When it comes to infinity, reasoning becomes faulty.
Alpha, Yes I did. That equation may or may not be proof for the 1/2 decreasing distance problem, but it doesn't prove anything about a problem that decreases by 1/4 ths. Otherwise you have to be willing to accept that 0.3333... is equal to 1. Alpha, do you believe that 0.3333... is equal to 1? Are you this irrational? Do I have to show you exactly how I got this again? why not, it's mathematically possible, numbers can be decreased forever That's what the whole 0.9999.... (or 0.3333....) thing is about isn't it? If you are saying that the numbers can't decrease smaller and smaller, then you have just contradicted yourself, because that's exactly what your whole 0.9999... = 1 argument relies on. It matters because you are trying to say that you can rationally dissprove Zeno's paradox, but you can't. You make things up like "you cannot keep travelling a smaller and smaller distance" and try to prove it with the "Plank length". Then when I confront you on what this "minimum Plank length" is you say "Honestly, does it matter why right now? There [it] is, just accept it." Which makes me think you really don't know what the Plank length is and you have no idea what you are talking about.
You're all wrong Please Register or Log in to view the hidden image! It's a shame that these time zones exist. Otherwise I would have replied earlier. First of all: in reality there is no such thing as infinity, in any case not that it affects our lives. However, in mathematics it does exist. Are we not allowed to talk math in the math dept. now?!\ So maybe IRL we have probems at quantum level, but in mathematics, we can ignore them. Secondly: 0,999... <> 1 , even though you think to have proven otherwise. And 3 divided by 9 does not equal 0,333... 3/9 = 1/3. something completely different! 0,333.... and 0,999... are elements of the array of real numbers (R) but not of the array of all quotients (Q). 1 and 1/3 are in both Q and R. The decimal notation is not to be taken lightly.Whenever possible, use the "normal" (pre-Huygens) notation. Thirdly: Alpha, It is NOT your place to lecture others! Your posts show a lack of knowledge (or of understanding, in the more negative scenatio) of several concepts. Infinity cannot be used as an operator in the way numbers can be used. True, there are diffent levels of infinity (called: aleph-0 aleph-1,...) What we're discussing here is all aleph-null stuff. The fun thing of infintity is that the total number of elements of an infinityely large set, equals the total number of elements of two of such sets (or of an infinite amount of infinitely large sets). It's mind-boglint. But don't worry, just accept it. It's just like general relativity: very confusing and contra-intuitive (there is another thread regarding this). Virtus Rationis. ('the power of ratio') Merlijn
Cmon, Kant is not dumb. Everyone has read Kant. You should catch up. Critique of Pure Reason. After that, Phenomenology of Spirit by Hegel is also useful.
Man, it doesn't matter if you say 1/4 the distance! Where the hell are you getting the idea that it makes a difference when you make the fraction smaller? Irrational?! Of course I don't believe that. And I can review your post anytime thank you. Let's review your equation. x = 0.3333... 10x = 3.3333... 10x - x = 3.3333... - 0.3333... 9x = 3 Stop. Here you divide both sides by nine and end up with a repeating decimal. But if you divide both sides by 3 you get: 3x = 1, which is the same as x = 1/3 which converts to the same repeating decimal, but it's inaccurate. It doesn't convert properly. And this is shown when you put 0.9999... into the equation instead. I'm starting to wonder if you're capable of rational thought! The equation doesn't rely on the fact that numbers can't "decrease smaller and smaller", it disproves it!!! Yes, I am saying you can disprove the "paradox" rationally. I'm not "making things up." I said I didn't want to go into it because I didn't have the time, and it could make this whole thing more complicated than it needs to be. The plank length is 1.6160505*10^-35 meters. I did not make it up. Oh, really? Prove otherwise! The proof is there. Ask a math teacher! That's essentially what I was saying. Excuse me?! This is a forum for discussion. This is more of a place for "lectures" than others. And who are you to say who can and cannot "lecture" others. Freedom of speech. I can say what I want. If I think I know the solution to a problem I have a right to say my piece. It is NOT your place to tell others that they can't speak their mind. OK, trying to calm down before I continue... Exactly. Sorry, I can't just accept things. I have an insatiable curiosity. I'm always wondering "Why?" But I'll let it go for now. Especially since everyone who's come close to the solution so far has gone insane. (Godel for example). Alright, let's look at this problem from another perspective. You travel half the distance to your destination. How did you get there? You must have travelled half the distance from your starting point to where you are now, and then half the distance again, and so on. Yet you are clearly there. If Zeno's paradox were true, then you would be unable to move at all, because if you want to move to any point, you must first move half the distance, no matter how close the point is. In this way the paradox is solved through rational thinking.
Alpha, OK I agree with both you and Merlijn, when the problem is worked out you should get 1/3 and not 0.3333... But still does 1/3 = 1? In a 1/4 decreasing Zeno's paradox does the thing that moves get to 1/3 and then stops, Alpha? Does the thing get instantly teleported to the goal once it reaches 1/3 of the distance? Does it sit down and contemplate Kant and Hegel? Please Register or Log in to view the hidden image! Merlijn, Here is the best rationality that 0.9999... = 1, taken from the math site that Alpha posted earlier: .9999... is equal to 1 because no matter how small a difference between .9999... and 1 you ask for, I can write enough 9s to get within that difference. So suppose you want it within .00001 of 1. I can write .99999. This can go on and on. It at first kind of makes sense. But by the same rational, I could describe how similar I am to a toad infinitely (because language is infinite) and no matter how many similarities you require as a minimum, I can keep coming up with more similarities. So I must be a human and a toad right? Alright, my reasoning's a little shakey. Please Register or Log in to view the hidden image! Alpha, since you failed to describe what the Planck length is, I looked it up. Here's a definition that I found: Definition: The length scale at which a classical description of gravity ceases to be valid and quantum mechanics must be taken into account. The value of the Planck length is of the order of 10-35 m (twenty orders of magnitude smaller than the size of a proton, 10-15 m). I found this at: http://physics.about.com/library/dict/bldefplancklength.htm So what I make of it is that below the Planck length, matter is no longer affected by gravity and then follows by quantum mechanics. So what. The definition itself implies that lengths below the Planck length are possible. Different Quantum particles are smaller are they not. So why can't a length be reduced smaller than the Planck length? But like Merlijn said, we're talking about physics with this, Zeno's paradox is strict mathematics. Math is almost pure reason (very little science, or observation). Physics is more science (based on experience. My point all along is that reason alone isn't enough. It's a good model, but it's got holes. You've changed the nature of the problem. The paradox isn't whether or not the thing reaches it's goal. The paradox is that something can move in such a manner forever (1/2's 1/4'th, whatever) and never reach your goal. You might think that it never reaches it's goal because it keeps decreasing speed infinitely. But that doesn't matter, even if the object was in constant acceleration, it would still never reach the goal. Speed is irrelevent. Yes the manner of movement is ridiculous and not in real life, but it is rationally possible. The paradox doesn't exist in real life. It doesn't in physics either. It exists in reason. Reason can be faulty. Plato was wrong! (alright this is a little strong Please Register or Log in to view the hidden image! ) Zero, I've read parts of Kant and Hegel before when I was a philosophy student, and at this stage in my I don't need anymore. Among my philosophy peers, Hegel was a 5 letter dirty word. If I said it, they'd turn around and give me dirty looks. Please Register or Log in to view the hidden image! Merlijn, I want to thank you for your post. You have indirectly solved something for me. I think it is what I needed to solve by posting this thread in the first place. Thanks again.
I am a math teacher! I was merely referring to your own behaviour here. You yourself told us to take physics classes, and the like. Whereas you yourself do not show complete control of the subject yourself. Bu never mind. it's true.... it's an open forum. AGAIN: 0,999...<> 1 because 0,999... is an element of the array of real numbers (R) but not of the array of all quotients (Q). 1 is both in R and Q. There is a small difference. it's infinately small, but it's there. Exactly. Still, I do not know the formal reason why it's wrong... I will look it up, or try to find out myself (when not succesfull). In case you were wondering: the aim for an infinately small distance away from the point you want to go to, was not completetly serious. Please Register or Log in to view the hidden image! I was just curious how you would reply. keep up the good work
I am happy to have helped you Xenu. May I know what it was? Please Register or Log in to view the hidden image!
Err, how is that a paradox? What's wrong with the idea of infinitely close but never equal? A simple graph of y=1/x is all you need to see. If you still think it's a paradox, try limit in math. It's the right tool to solve your paradox, and it sounds pretty logical.
